research paper on information flow

Information flows, organizational structure, and corporate governance

European Corporate Governance Institute – Finance Working Paper No. 841/2022

Olin Business School Center for Finance & Accounting Research Paper No. 2022/05

Handbook of Corporate Finance (ed. by David Denis), Chapter 14, pp. 511-547

51 Pages Posted: 11 Aug 2022 Last revised: 14 Jun 2024

Nadya Malenko

Boston College, Carroll School of Management; National Bureau of Economic Research (NBER); Finance Theory Group (FTG); Centre for Economic Policy Research (CEPR); European Corporate Governance Institute (ECGI)

Information Flows, Organizational Structure, and Corporate Governance

Date Written: April 28, 2023

This survey provides an overview of theoretical and empirical research on information flows in corporations. It highlights key frictions preventing effective information flows and discusses how organizational structure and corporate governance can alleviate these frictions, focusing on three broad topics: 1) organizational design, such as the choice between centralized and decentralized decision-making; 2) composition and decision-making process of the board of directors; and 3) communication among shareholders and between shareholders and management in the context of shareholder activism. The goal of the survey is to draw connections between theoretical and empirical work and point out directions for future research.

Keywords: communication, organizational structure, delegation, board of directors, shareholder activism, information flows, committee decision-making

JEL Classification: D23, D82, D83, G34, L22

Suggested Citation: Suggested Citation

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Boston college, carroll school of management ( email ).

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• Published: 17 February 2021

Inference and analysis of cell-cell communication using CellChat

• Suoqin Jin   ORCID: orcid.org/0000-0002-5131-0215 1 , 2 ,
• Christian F. Guerrero-Juarez   ORCID: orcid.org/0000-0002-6245-6412 1 , 2 , 3 , 4 ,
• Lihua Zhang 1 , 2 ,
• Ivan Chang 5 , 6 ,
• Raul Ramos 2 , 3 , 4 ,
• Chen-Hsiang Kuan 3 , 4 , 7 , 8 ,
• Peggy Myung   ORCID: orcid.org/0000-0002-2970-4170 9 , 10 ,
• Maksim V. Plikus   ORCID: orcid.org/0000-0002-8845-2559 2 , 3 , 4 &
• Qing Nie   ORCID: orcid.org/0000-0002-8804-3368 1 , 2 , 3  

Nature Communications volume  12 , Article number:  1088 ( 2021 ) Cite this article

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• Cell signalling
• Cellular signalling networks
• Regulatory networks

Understanding global communications among cells requires accurate representation of cell-cell signaling links and effective systems-level analyses of those links. We construct a database of interactions among ligands, receptors and their cofactors that accurately represent known heteromeric molecular complexes. We then develop CellChat, a tool that is able to quantitatively infer and analyze intercellular communication networks from single-cell RNA-sequencing (scRNA-seq) data. CellChat predicts major signaling inputs and outputs for cells and how those cells and signals coordinate for functions using network analysis and pattern recognition approaches. Through manifold learning and quantitative contrasts, CellChat classifies signaling pathways and delineates conserved and context-specific pathways across different datasets. Applying CellChat to mouse and human skin datasets shows its ability to extract complex signaling patterns. Our versatile and easy-to-use toolkit CellChat and a web-based Explorer ( http://www.cellchat.org/ ) will help discover novel intercellular communications and build cell-cell communication atlases in diverse tissues.

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Introduction.

Signaling crosstalk via soluble and membrane-bound factors is critical for informing diverse cellular decisions, including decisions to activate cell cycle or programmed cell death, undergo migration or differentiate along the lineage 1 , 2 , 3 . Single-cell RNA-sequencing (scRNA-seq) technologies have led to discovery of cellular heterogeneity and differentiation trajectories at unprecedented resolution level 4 , 5 . While most current scRNA-seq data analysis approaches allow detailed cataloging of cell types and prediction of cellular differentiation trajectories, they have limited capability in probing underlying intercellular communications that often drive heterogeneity and cell state transitions. Yet, scRNA-seq data inherently contains gene expression information that could be used to infer such intercellular communications 6 , 7 .

Several methods have been recently developed to infer cell–cell communication from scRNA-seq data 8 , 9 , 10 , 11 , 12 , 13 , 14 , such as SingleCellSignalR 9 , iTALK 10 , and NicheNet 13 . However, these and other similar methods usually use only one ligand/one receptor gene pairs, often neglecting that many receptors function as multi-subunit complexes. For example, soluble ligands from the TGFβ pathway signal via heteromeric complexes of type I and type II receptors 15 . More recently, to address this limitation, CellPhoneDB v2.0 has been developed, which predicts enriched signaling interactions between two cell populations by considering the minimum average expression of the members of the heteromeric complex 16 . However, it does so without considering other important signaling cofactors, including soluble agonists, antagonist, as well as stimulatory and inhibitory membrane-bound co-receptors. Other limitations of current databases or tools include the lack of: (a) systematically curated classification of ligand-receptor pairs into functionally related signaling pathways; (b) intuitive visualization of both autocrine and paracrine signaling interactions; (c) systems approaches for analyzing complex cell–cell communication; and (d) capability of accessing signaling crosstalk for continuous cell state trajectories given the fact that biological variability between cells can be discrete or continuous.

Here we develop CellChat, an open source R package ( https://github.com/sqjin/CellChat ) to infer, visualize and analyze intercellular communications from scRNA-seq data. First, we manually curate a comprehensive signaling molecule interaction database that takes into account the known structural composition of ligand-receptor interactions, such as multimeric ligand-receptor complexes, soluble agonists and antagonists, as well as stimulatory and inhibitory membrane-bound co-receptors. Next, CellChat infers cell-state specific signaling communications within a given scRNA-seq data using mass action models, along with differential expression analysis and statistical tests on cell groups, which can be both discrete states or continuous states along the pseudotime cell trajectory. CellChat also provides several visualization outputs to facilitate intuitive user-guided data interpretation. CellChat can quantitatively characterize and compare the inferred intercellular communications through social network analysis tool 17 , pattern recognition methods 18 , 19 and manifold learning approaches 20 . Such analyses enable identification of the specific signaling roles played by each cell population, as well as generalizable rules of intercellular communications within complex tissues. We showcase CellChat’s overall capabilities by applying it to both our own and publicly deposited mouse skin scRNA-seq datasets from embryonic development and adult wound healing stages, as well as human skin scRNA-seq dataset from a diseased state. A systematic comparison with several existing tools for cell–cell communication is also presented.

Overview of CellChat

CellChat requires gene expression data from cells as the user input and models the probability of cell–cell communication by integrating gene expression with prior knowledge of the interactions between signaling ligands, receptors and their cofactors (Fig.  1a ). To establish intercellular communications, CellChat can operate in label-based and label-free modes (Fig.  1b ). In its label-based mode, CellChat requires user-assigned cell labels as the input. In its label-free mode, CellChat requires user input in form of a low-dimensional representation of the data, such as principal component analysis or diffusion map. For the latter, CellChat automatically groups cells by building a shared neighbor graph based on the cell–cell distance in the low-dimensional space or the pseudotemporal trajectory space (see “Methods” section). Upon receiving input data, CellChat models intercellular communications via the following three modules:

a Overview of the ligand-receptor interaction database. CellChatDB takes into account known composition of the ligand-receptor complexes, including complexes with multimeric ligands and receptors, as well as several cofactor types: soluble agonists, antagonists, co-stimulatory and co-inhibitory membrane-bound receptors. CellChatDB contains 2021 validated interactions, including 60% of secreting interactions. In addition, 48% of the interactions involve heteromeric molecular complexes. b CellChat either requires user assigned cell labels as input or automatically groups cells based on the low-dimensional data representation supplied as input. c CellChat models the communication probability and identifies significant communications. d CellChat offers several visualization outputs for different analytical tasks. Different colors in the hierarchy plot and circle plot represent different cell groups. Colors in the bubble plot are proportional to the communication probability, where dark and yellow colors correspond to the smallest and largest values. e CellChat quantitatively measures networks through approaches from graph theory, pattern recognition and manifold learning, to better facilitate the interpretation of intercellular communication networks and the identification of design principles. In addition to analyzing individual dataset, CellChat also delineates signaling changes across different contexts, such as different developmental stages and biological conditions.

Cross-referencing ligand-receptor interaction database. The accuracy of the assigned roles for the signaling molecules and their interactions is crucial for predicting biologically meaningful intercellular communications. We manually curated a literature-supported signaling molecule interaction database, called CellChatDB, which takes into account the known composition of ligand-receptor complexes, including complexes with multimeric ligands and receptors, as well as several cofactors: soluble agonists, antagonists, co-stimulatory and co-inhibitory membrane-bound receptors (Fig.  1a , Supplementary Fig.  1a , Supplementary Note  1 ). CellChatDB incorporates signaling molecule interaction information from the KEGG Pathway database 21 , a collection of manually drawn signaling pathway maps assembled by expert curators based on existing literature. It also includes information from recent experimental studies. CellChatDB contains 2,021 validated molecular interactions, including 60% of paracrine/autocrine signaling interactions, 21% of extracellular matrix (ECM)-receptor interactions and 19% of cell–cell contact interactions. 48% of the interactions involve heteromeric molecular complexes and 25% of the interactions are curated by us from recent literature (Fig.  1a ). Furthermore, each interaction is manually classified into one of the 229 functionally related signaling pathways based on the literature.

Inference and visualization of intercellular communications. To predict significant communications, CellChat identifies differentially over-expressed ligands and receptors for each cell group (Fig.  1b ; also see “Methods” section). To quantify communications between two cell groups mediated by these signaling genes, CellChat associates each interaction with a probability value. The latter is modeled by the law of mass action based on the average expression values of a ligand by one cell group and that of a receptor by another cell group, as well as their cofactors (see “Methods” scetion). Significant interactions are identified on the basis of a statistical test that randomly permutes the group labels of cells and then recalculates the interaction probability (Fig.  1c , see “Methods” section). An intercellular communication network is a weighted directed graph composed of significant connections between interacting cell groups. CellChat also provides an informative and intuitive visualization method, called hierarchical plot, to highlight autocrine and paracrine signaling communications between cell groups of interest. This hierarchical plot provides an overview of inferred intercellular communication network for each signaling pathway or ligand-receptor pair, consisting of two components: the left portion shows autocrine and paracrine signaling to certain cell groups of interest, and the right portion shows autocrine and paracrine signaling to the remaining cell groups in the dataset. In addition, CellChat implements several other visualization ways, including circle plot and bubble plot (Fig.  1d , see “Methods” section).

Quantitative analysis of intercellular communications. To facilitate the interpretation of the complex intercellular communication networks, CellChat quantitatively measures networks through methods abstracted from graph theory, pattern recognition and manifold learning (see “Methods” section). CellChat performs a variety of analyses in an unsupervised manner (Fig.  1e ). First, it can determine major signaling sources and targets, as well as mediators and influencers within a given signaling network using centrality measures from network analysis, such as out-degree, in-degree, betweenness, and information metrics (see “Methods” section). Second, it can predict key incoming and outgoing signals for specific cell types, as well as coordinated responses among different cell types by leveraging pattern recognition approaches. Outgoing patterns reveal how the sender cells (i.e., cells as signal source) coordinate with each other, as well as how they coordinate with certain signaling pathways to drive communication. Incoming patterns show how the target cells (i.e., cells as signal receivers) coordinate with each other, as well as how they coordinate with certain signaling pathways to respond to incoming signals. Third, it can group signaling pathways by defining similarity measures and performing manifold learning from both functional and topological perspectives. Fourth, it can delineate conserved and context-specific signaling pathways by joint manifold learning of multiple networks across datasets. Overall, these functionalities allow CellChat to deconvolute complex intercellular communications in an easily interpretable way and predict biologically meaningful discoveries from scRNA-seq data.

CellChat identifies communication patterns and predicts functions for poorly studied pathways

We showcase CellChat functionalities by applying it to several recently published mouse skin scRNA-seq datasets from embryonic development 22 and adult wound healing stages 23 . Choice of skin was determined by our prior expertise on the aspects of skin morphogenesis and regeneration, its complex cellular make-up and the fact that the role of many signaling pathways in skin is well-established, which enables meaningful literature-based interpretation of a portion of CellChat predictions. First, we ran CellChat analysis on scRNA-seq dataset for day 12 mouse skin wound tissue 23 . This dataset contains 21,898 cells, which cluster into 25 cell groups, including nine fibroblast (FIB), five myeloid (MYL) and six endothelial (ENDO) groups, as well as several other cell types such as T cells (TC), B cells (BC), dendritic cells (DC), and lymphatic endothelial cells (LYME) (Supplementary Fig.  2a–h ; see “Methods” section).

CellChat detected 60 significant ligand-receptor pairs among the 25 cell groups, which were further categorized into 25 signaling pathways, including TGFβ, non-canonical WNT (ncWNT), TNF, SPP1, PTN, PDGF, CXCL, CCL, and MIF pathways. Network centrality analysis of the inferred TGFβ signaling network identified that several myeloid cell populations are the most prominent sources for TGFβ ligands acting onto fibroblasts (Fig.  2a, b ). Of note one myeloid population MYL-A is also the dominant mediator, suggesting its role as a gatekeeper of cell–cell communication. These findings are consistent with the known critical role played by myeloid cells in initiating inflammation during skin wound healing and driving activation of skin-resident fibroblasts via TGFβ signaling 24 , 25 , 26 , 27 , 28 , 29 . Importantly, CellChat also predicted that certain endothelial cell populations, as well as several fibroblast populations, both known sources of TGFβ ligands, significantly contribute to myeloid-dominated TGFβ signal production in the wound. This reveals that TGFβ signaling network in skin wounds is complex and highly redundant with multiple ligand sources targeting large portion of wound fibroblasts. Interestingly, CellChat shows that the majority of TGFβ interactions among wound cells are paracrine, with only one fibroblast and one myeloid population demonstrating significant autocrine signaling (Fig.  2b ). Notably, among all known ligand-receptor pairs, wound TGFβ signaling is dominated by Tgfb1 ligand and its multimeric Tgfbr1/Tgfbr2 receptor (Fig.  2c ). In contrast with TGFβ, CellChat analysis of inferred ncWNT signaling network revealed its very distinct, non-redundant structure with only one ligand (Wnt5a) and only one population of fibroblasts (FIB-D) driving largely fibroblast-to-fibroblast, fibroblast-to-endothelial and to a lesser extent fibroblast-to-myeloid signaling (Fig.  2d–f ). FIB-D cells highly expressed Crabp1 and were enriched for cell cycle genes (Supplementary Fig.  2d ), which likely represent an actively cycling subset of Crabp1 -positive cells in upper wound dermis 23 , 30 . Network centrality analysis confirmed that FIB-D is a prominent influencer controlling the communications (Fig.  2e ). Importantly, elevated expression of WNT5A in fibroblasts and its role in scarring has recently been reported 31 , 32 , 33 , 34 .

a Hierarchical plot shows the inferred intercellular communication network for TGFβ signaling. This plot consists of two parts: Left and right portions highlight the autocrine and paracrine signaling to fibroblast states and to other non-fibroblast skin cell states, respectively. Solid and open circles represent source and target, respectively. Circle sizes are proportional to the number of cells in each cell group and edge width represents the communication probability. Edge colors are consistent with the signaling source. FIB-A – I: nine fibroblast cell groups; MYL-A – E: five myeloid cell groups; ENDO-A – F: six endothelial cell groups; TC: T cell; BC: B cell; SCH: Schwan cell; DC: Dendritic cell, LYME: Lymphatic endothelial cell; (b) Heatmap shows the relative importance of each cell group based on the computed four network centrality measures of TGFβ signaling network. c Relative contribution of each ligand-receptor pair to the overall communication network of TGFβ signaling pathway, which is the ratio of the total communication probability of the inferred network of each ligand-receptor pair to that of TGFβ signaling pathway. d The inferred ncWNT signaling network. e Relative contribution of each ncWNT ligand-receptor pair. f The computed network centrality measures of ncWNT signaling. g The inferred outgoing communication patterns of secreting cells, which shows the correspondence between the inferred latent patterns and cell groups, as well as signaling pathways. The thickness of the flow indicates the contribution of the cell group or signaling pathway to each latent pattern. h The inferred incoming communication patterns of target cells. i Projecting signaling pathways onto a two-dimensional manifold according to their functional similarity. Each dot represents the communication network of one signaling pathway. Dot size is proportional to the overall communication probability. Different colors represent different groups of signaling pathways. j Two different similarity measures are used to quantify the similarity among the inferred networks. Examples showing the functional similarity with similar major sources/targets, and structural similarity with similar network topology. k Projecting signaling pathways onto a two-dimensional manifold according to their structural similarity.

In addition to exploring detailed communications for individual pathways, an important question is how multiple cell groups and signaling pathways coordinate to function. To address this question, CellChat employs a pattern recognition method based on non-negative matrix factorization to identify the global communication patterns, as well as the key signals in different cell groups (see “Methods” section). The output of this analysis is a set of the so-called communication patterns that connect cell groups with signaling pathways either in the context of outgoing signaling (i.e., treating cells as senders) or incoming signaling (i.e., treating cells as receivers). Application of this analysis uncovered five patterns for outgoing signaling (Fig.  2g ) and five patterns for incoming signaling (Fig.  2h ). This output, for example, reveals that a large portion of outgoing fibroblast signaling is characterized by pattern #4, which represents multiple pathways, including but not limited to ncWNT, SPP1, MK, and PROS (Fig.  2g ). All of the outgoing myeloid cell signaling is characterized by pattern #2, representing such pathways as TGFβ, TNF, CSF, IL1, and RANKL. On the other hand, the communication patterns of target cells (Fig.  2h ) shows that incoming fibroblast signaling is dominated by two patterns #1 and #3, which include signaling pathways such as TGFβ and ncWNT, as well as PDGF, TNF, MK, and PTN among others. Majority of incoming myeloid cell signaling is characterized by the pattern #4, driven by CSF and CXCL pathways. Notably, both incoming and outgoing signaling by Schwann cells share the same pattern #1 with wound fibroblasts (Fig.  2g-h ). These results show that: (1) two distinct cell types in the same tissue can rely on largely overlapping signaling networks; and that (2) certain cell types, such as fibroblasts, simultaneously activate multiple signaling patterns and pathways, while other cell types, such as myeloid cells or B cells, rely on fewer and more homogeneous communication patterns. Moreover, cross-referencing outgoing and incoming signaling patterns also provides a quick insight into the autocrine-acting vs. paracrine-acting pathways for a given cell type. For example, major autocrine-acting pathways between wound fibroblasts are MK, SEMA3, PROS, and ncWNT, and major paracrine-acting myeloid-to-fibroblasts pathways are TGFβ and TNF (Fig.  2g-h ).

Further, CellChat is able to quantify the similarity between all significant signaling pathways and then group them based on their cellular communication network similarity. Grouping can be done either based on functional or structural similarity (see “Methods” section). Application of functional similarity grouping identified four groups of pathways (Fig.  2i ). Group #1 is dominated by inflammatory pathways (e.g., TGFβ, TNF, IL, CCL) and largely represents paracrine signaling from myeloid and endothelial cells to fibroblasts. Group #2, which includes ncWNT, EGF, GAS, and PROS pathways, largely represents autocrine signaling between wound fibroblasts. Group #3, which includes CXCL and APELIN pathways, represents signaling from endothelial cells, while group #4, which includes MK, PTN, and SPP1 pathways, represents promiscuous signaling (i.e., signaling with high connectivity) and is dominated by signals from certain fibroblast populations and myeloid cells. By identifying poorly studied pathways that group together with other pathways, whose role is well known, this CellChat analysis can predict putative functions of the former. Different from grouping on the basis of functional similarity, which heavily weighs in similarity between sender and receiver cell groups, grouping based on structural similarity is primarily driven by the similarity of signaling network topology (Fig.  2j ; see “Methods” section). Structural similarity grouping also identified four groups of signaling pathways (Fig.  2k ). Group #1 represents pathways that have very few senders and numerous receivers, such as ncWNT; group #2 represents pathways with numerous senders and receivers, such as TGFβ and PTN; group #3 represents pathways with numerous senders and few receivers, such as CCL and IL1; and group #4 represents pathways with few senders and few receivers, such as PROS, IL2, and CXCL. Thus, grouping based on structural similarity reveals general mode of how sender and receiver cells utilize a given signaling pathway. Collectively, CellChat can identify key features of intercellular communications within a given scRNA-seq dataset and predict putative functions for poorly understood signaling pathways.

CellChat reveals continuous cell lineage-associated signaling events

In addition to discrete cell states, our framework can be applied to continuous cell states along the pseudotemporal trajectory (see “Methods” section). We demonstrate this utility using scRNA-seq data on embryonic day E14.5 mouse skin 22 , when both dermal and epidermal cell lineages undergo rapid specification and give rise to new cell types within the developing hair follicles 22 , 35 , 36 . First, we inferred pseudotemporal trajectories for dermal and epidermal embryonic skin cells using the diffusion map approach (Fig.  3a-b ; Supplementary Fig.  3a–d ; see “Methods” section). Dermal cell trajectory, which on one end contains Sox2 -high hair follicle dermal condensate (DC) cells, was divided into seven groups, that include five fibroblast states (FIB-A, FIB-B, FIB-C, FIB-D, FIB-E) and two DC states (DC-A and DC-B). A linear sequence of these trajectory groups recapitulates sequential stages of embryonic skin fibroblast lineage specification process (Fig.  3a ). Embryonic epidermal cell trajectory starts from basal epidermal cells and progresses either toward Edar -high epithelial placode cells or toward Krt1 -high and Lor -high suprabasal epidermal cells. Collectively, epidermal lineage specification events are represented by two basal, one placode and three suprabasal trajectory groups (Fig.  3b ).

a Left: Diffusion map projecting dermal skin cells onto the low-dimensional space and showing the dermal differentiation from fibroblasts to DC (dermal condensate) cells. Cells are grouped based on their location in this space. Right: Density plot showing the distribution of expression for selected marker genes in each cell group/population. b Diffusion map showing the epidermal trajectory and associated density plot for selected marker genes. c Hierarchical plot showing dermal and epidermal interactions via canonical WNT signaling. Left and right portions show the autocrine and paracrine signaling to dermal trajectory and epidermal trajectory, respectively. Circle sizes are proportional to the number of cells in each cell group and edge width represents the communication probability. d Violin plot showing the expression distribution of signaling genes involved in the inferred WNT signaling network. e The dermal and epidermal interactions via ncWNT signaling. f The expression distribution of signaling genes involved in the inferred ncWNT signaling network. g The outgoing signaling patterns of secreting cells visualized by alluvial plot, which shows the correspondence between the inferred latent patterns and cell groups, as well as signaling pathways. The thickness of the flow indicates the contribution of the cell group or signaling pathway to each latent pattern. The height of each pattern is proportional to the number of its associated cell groups or signaling pathways. Outgoing patterns reveal how the sender cells coordinate with each other, as well as how they coordinate with certain signaling pathways to drive communication. h Incoming signaling patterns of target cells. Incoming patterns show how the target cells coordinate with each other, as well as how they coordinate with certain signaling pathways to respond to incoming signaling.

We applied CellChat to study dermal-epidermal communication along these sequential cell lineage states. 88 significant ligand-receptor interactions within 22 signaling pathways were predicted, including WNT, ncWNT, TGFβ, PDGF, NGF, FGF, and SEMA3. Previous studies showed that activation of canonical WNT signaling is required for DC cell specification in the embryonic skin 22 , 36 , 37 , 38 , 39 , 40 . Indeed, CellChat-inferred canonical WNT signaling network indicates that epidermal cells are the primary ligand source, which acts both in autocrine manner between epidermal cell populations, as well as in paracrine way from epidermal to dermal cells (Fig.  3c ). Notably, two WNT ligand-receptor pairs, namely Wnt6–Fzd10/Lrp6 and Wnt6–Fzd2/Lrp6 were the dominant contributors to this communication network (Fig.  3d and Supplementary Fig.  4a ), which is consistent with the previous report that Wnt6 is the highest expressed canonical WNT ligand in embryonic mouse skin 41 . Signaling communication network for ncWNT pathway differs substantially from that of canonical WNT pathway. Late stage fibroblast state FIB-E was the primary ncWNT source, signaling both in autocrine and paracrine manner (Fig.  3e ) with Wnt5a–Fzd2 and Wnt5–Fzd10 ligand-receptor pairs driving the signaling (Fig.  3f and Supplementary Fig.  4b–c ). These results suggest distinct roles for canonical WNT and ncWNT pathways in skin morphogenesis. In another example, we analyzed the FGF signaling network (Supplementary Fig.  4d–h ) and found it to be similar to the ncWNT signaling network, with the additional epithelial placode-derived Fgf20 signaling (Supplementary Fig.  4e and h ). This is consistent with the known role of placode-derived FGF20 signaling in hair follicle morphogenesis 22 , 42 , 43 . In another distinct example of TGFβ pathway, epithelial placode cells and to a lesser extent early DC-A cells were the driving sources of TGFβ ligands to dermal cells (Supplementary Fig.  4i–k ). These findings are consistent with the known role for TGFβ signaling in early hair follicle morphogenesis 44 , 45 .

We then ran CellChat pattern recognition module to uncover the key sequential signaling events along the process of skin morphogenesis. To predict the sequential signaling events, we combined the communication pattern analysis with the inferred pseudotemporal cell events. The dermal and epidermal trajectory analysis potentially revealed the pseudotemporal order of different cell types, and the communication pattern analysis identified strong signals that were sent or received by certain cell types. At the outgoing end of signaling, we predicted that FGF and GALECTIN signals are first secreted by FIB-A cells (Fig.  3g ). FIB-B and FIB-C cells then coordinate production of GAS signaling. Next, FIB-D, and FIB-E fibroblasts along with suprabasal epidermal cells coordinate secretion of numerous ligands for pathways such as ncWNT, EGF, IGF, CXCL, and SEMA3; while DC-A and epithelial placode cells jointly secrete ligands for TGFβ pathway. At the same time, basal epidermal cells dominantly drive WNT, PDGF, NGF, and VISFATIN signaling pathways. On the other hand, at the incoming end of signaling, fibroblasts are driven by patterns #1 and #2 involving pathways such as FGF, PDGF, SEMA3, TGFβ, IGF, and GALECTIN (Fig.  3h ). DC and epithelial placode cells are driven by the pattern #4, which includes HH and CXCL signaling; basal epidermal cells are dominated by pattern #3 pathways—WNT, ncWNT, and EGF; while suprabasal epidermal cells are the primary target for GRN (granulin) signaling within pattern #5. Together, CellChat analysis faithfully recovers many signaling events with well-established roles in embryonic skin and hair follicle morphogenesis and systematically predicts a number of additional signaling patterns along dermal and epidermal cell lineage trajectories.

CellChat predicts key signaling events between spatially colocalized cell populations

To further demonstrate the predictive nature of CellChat, we studied signaling communication between E14.5 dermal condensate (DC) and epithelial placode cells, since these cells spatially colocalize and actively signal to each other during the initial stages of embryonic hair follicle formation (Fig.  4a ). Three DC states—pre-DC, DC1, and DC2, and one placode state were identified (Supplementary Fig.  3e–f ; see “Methods” section). CellChat analysis on these four cell states identified placode cells as the dominant communication “hub”, which secretes and receives signals via 44 and 19 ligand-receptor pairs, respectively (Fig.  4b ). Prominent bidirectional forward and reverse signals were identified for DC states, suggesting that the cell state transition along pre-DC-DC1-DC2 cell lineage trajectory is highly regulated. Specifically, FGF pathway exhibited abundant signaling interactions among all four states with FGF ligands being dominantly secreted by pre-DC and DC2 states (Fig.  4c ). Fgf10 was the major ligand contributing to dermal FGF signaling (Supplementary Fig.  5a ), which is the known DC signature gene 36 . Epithelial placode cells distinctly secreted Fgf20 both in autocrine and in paracrine manner to all three DC states (Supplementary Fig.  5a ), which is consistent with the known role of placode-derived FGF20 signaling in hair follicle morphogenesis 22 , 42 , 43 . For another major signaling pathway in early hair follicle morphogenesis—canonical WNT, epithelial placode cells were the major source of ligands (Fig.  4c ), prominently expressing primarily autocrine Wnt3 and Wnt6 . CellChat also predicted that this dominant epithelial autocrine WNT signaling was supplemented by a minor DC-derived Wnt9a paracrine signaling (Supplementary Fig.  5b-d ). In contrast with canonical WNT, the inferred ncWNT signaling network revealed that DC cells express only one ligand, Wnt5a , that drives paracrine DC-to-placode and autocrine DC-to-DC signaling (Supplementary Fig.  5e ). This result implies distinct roles for canonical WNT and ncWNT pathways in hair follicle morphogenesis.

a Spatial diagram of placode, pre-DC, DC1 and DC2 cells during hair follicle (HF) development at E14.5. DC: dermal condensate. b Number of significant ligand-receptor pairs between any pair of two cell populations. The edge width is proportional to the indicated number of ligand-receptor pairs. c The inferred FGF and WNT signaling networks. Circle sizes are proportional to the number of cells in each cell group and edge width represents the communication probability. d All the significant ligand-receptor pairs that contribute to the signaling sending from placode to three DC states. The dot color and size represent the calculated communication probability and p -values. p -values are computed from one-sided permutation test. e The outgoing communication patterns of secreting cells, which shows the correspondence between the inferred latent patterns and cell groups, as well as signaling pathways. f Incoming communication patterns of target cells. g The inferred Pros1-Axl signaling network, as well as the scRNA-seq expression distribution of the Pros1 ligand, the Axl receptor and cell migration marker Thy1 . The edge width represents the communication probability. h RNAscope data ( n   =4 independent experiments) showing spatial distribution of Edn3 (red) , Axl (green), and Thy1 (white) transcripts in early-stage developing hair follicle from E14.5 embryonic mouse skin. Epithelial placode and dermal condensate (DC) are annotated and outlined with dashed lines. Solid white curved arrows in the bottom-right panel mark CellChat-predicted Pros1-Axl signaling within skin space. DAPI (teal) stains nuclei. Scale bar: 50 μm. i The inferred Edn3-Ednrb signaling network, as well as the scRNA-seq expression distribution of the melanocyte marker Dct , Edn3 ligand and its receptor Ednrb . DC: dermal condensate; MELA: melanocytes; ( j ) RNAscope data ( n  = 4 independent experiments) showing spatial distribution of Dct (green), Edn3 (red), and Ednrb (white) transcripts in early-stage developing hair follicle from E14.5 embryonic mouse skin. Arrowheads mark possible melanocyte populations. Solid white curved arrows in the top-right panel mark CellChat-predicted Edn3-Ednrb signaling within skin space. DAPI (teal) stains nuclei. Scale bar: 50 μm.

By systematically investigating the predicted placode-to-DC signals, we found 21 ligand-receptor pairs implicating WNT, TGFβ, SEMA3, PTN, PDGF, MK, and FGF signaling pathways in the process of DC specification (Fig.  4d ). Pattern recognition analysis further revealed that pre-DC and DC2 states jointly coordinate outgoing signals for ncWNT, FGF, IGF, EDN, and SEMA3 pathways (pattern #1 in Fig.  4e ). DC1 dominantly drives PROS signaling (pattern #3), while epithelial placode cells drive outgoing WNT, TGFβ, PDGF, MK, PTN, and PTH signaling (pattern #2, Supplementary Fig.  5f ). At the incoming end of signaling, pre-DC cells respond to SEMA3 and PTH signaling (pattern #3 in Fig.  4f ); DC1 and DC2 cells respond to TGFβ, PDGF, EDN, and PROS signaling (pattern #1) and epithelial placode cells respond to WNT, ncWNT, IGF, MK, and PTN signaling (pattern #2, Supplementary Fig.  5f ).

CellChat revealed that at E14.5, DC cells respond to autocrine PROS signaling (Fig.  4g ). Pros1 is the ligand for the pathway, which signals via the receptor tyrosine kinase Axl . Signaling via Axl has been implicated in conferring cells with migratory properties in different biological context, including EMT-mediated cancer invasion 46 , 47 , 48 , and directional migration has been recently shown to be crucial for normal dermal condensate formation upon hair follicle morphogenesis 42 . We examined CellChat’s prediction of active PROS signaling in DC cells by RNAscope technique for Edn3 as DC marker, Axl and Thy1 (Cd90) as a marker of cell migration 49 , 50 and EMT process 51 . As expected from scRNA-seq, Axl expression was co-localized with Edn3 and Thy1 expression, which was concentrated in DC with significantly lower levels elsewhere (Fig.  4h ). This RNAscope result is consistent with the possibility of autocrine PROS signaling in DC, likely driven via Pros1 - Axl signaling.

During early hair follicle formation at E14.5, melanoblasts (melanocyte precursor cells) migrate into the hair placode from the dermis and then become differentiated toward melanocytes. However, the mechanisms of melanocyte migration into placode remain incompletely understood 52 . Therefore, we further studied the cell–cell communication among placodes, DC cells and melanocyte cells (including three melanocyte subpopulations: MELA-A, MELA-B, and MELA-C; see “Methods” section and Supplementary Fig.  3g ). CellChat revealed that melanocytes strongly respond to DC cells via previously unrecognized EDN signaling (Fig.  4i ). Edn3 is a ligand of the EDN pathway, which regulates melanocyte migration 53 . Therefore, CellChat prediction suggests DC cells induce early directed migration of melanocytes. To experimentally examine this prediction, we used the RNAscope technique to spatially map expression of Dct , which marks late-stage melanocyte precursors, Edn3 ligand and its receptor Ednrb in E14.5 embryonic mouse skin. As expected, Dct + melanocytes (i.e., MELA-C subpopulation) localize in and around epithelial placode. They also express Ednrb . In turn, Edn3 is specifically enriched in DC cells (preDC, DC1, and DC2 subpopulations), while Ednrb is also enriched in a portion of DC cells (likely DC2 subpopulation). Scattered Ednrb + /Edn3 neg /Dct neg cells inside dermal condensate are likely undifferentiated melanoblasts (i.e., MELA-A/B subpopulations) (Fig.  4j ). This spatial Edn3, Ednrb, Dct co-expression pattern is highly consistent with the scRNA-seq data (Fig.  4i ). Thus, our RNAscope result confirms the CellChat prediction of Edn3 - Ednrb signaling from DC cells to melanocytes, implying the roles for DC cells in inducing early-stage directed migration of melanocytes into placodes. It also shows potential autocrine Edn3 - Ednrb signaling within the dermal condensate.

Joint learning of time-course scRNA-seq data to uncover dynamic communication patterns

Next, we demonstrate how CellChat can be applied to studying temporal changes of intercellular communications in the same tissue (Fig.  5a ). For this purpose, we performed combined analysis on two embryonic mouse skin scRNA-seq datasets from days E13.5 and E14.5 22 . Unsupervised clustering of E13.5 and E14.5 datasets identified 11 skin cell populations at E13.5 and E14.5 and additional two populations (i.e., dermal DC and pericytes) specific to E14.5 (Supplementary Fig.  3a–d ; see “Methods” section).

a Schematic illustration of cellular composition of embryonic skin at E13.5 and E14.5. Different cell populations are color-coded to match colors in panel e and h . FIB-A: fibroblast type A; FIB-B: fibroblast type B; FIB-P: proliferative fibroblasts. MYL: myeloid cell; ENDO: endothelial cell; MELA: melanocytes; b Jointly projecting and clustering signaling pathways from E13.5 and E14.5 into a shared two-dimensional manifold according to their functional similarity. Circle and square symbols represent the signaling networks from E13.5 and E14.5 respectively. Each dot or square represents the communication network of one signaling pathway. Dot or square size is proportional to the total communication probability. Different colors represent different groups of signaling pathways. c Magnified view of each pathway group. d The overlapping signaling pathways between E13.5 and E14.5 were ranked based on their pairwise Euclidean distance in the shared two-dimensional manifold. e The inferred WNT signaling network at E13.5. Left and right portions show the autocrine and paracrine signaling to dermis and epidermis, respectively. Circle sizes are proportional to the number of cells in each cell group and edge width represents the communication probability. f Relative contribution of each ligand-receptor pair to the overall WNT signaling network at E13.5. g Expression distribution of WNT signaling genes at E13.5. h The inferred WNT signaling network at E14.5. i Relative contribution of each ligand-receptor pair at E14.5. j The expression distribution of WNT signaling genes at E14.5. k All significant signaling pathways were ranked based on their differences of overall information flow within the inferred networks between E13.5 and E14.5. The top signaling pathways colored red are more enriched in E13.5, the middle ones colored black are equally enriched in E13.5 and E14.5, and the bottom ones colored green are more enriched in E14.5. l The dot plot showing the comparison of outgoing signaling patterns of secreting cells between E13.5 and E14.5. The dot size is proportional to the contribution score computed from pattern recognition analysis. Higher contribution score implies the signaling pathway is more enriched in the corresponding cell group.

We inferred intercellular communications for the above two datasets separately, and then analyzed them together via joint manifold learning and classification of the inferred communication networks based on their functional similarity. The functional similarity analysis requires the same cell population composition between two datasets. Thus, for such analysis we used only 11 common cell populations between E13.5 and E14.5 datasets. As the result, the signaling pathways associated with inferred networks from both datasets were mapped onto a shared two-dimensional manifold and clustered into groups. We identified four pathway groups (Fig.  5b-c ). Groups #1 and #3 were dominated by growth factor pathways such as PDGF, NGF, FGF, EGF, and ANGPTL, while groups #2 and #5 dominantly contained inflammation-related pathways such as CCL, IL2, IL4, OSM, LIFR, and VISFATIN. As expected, the majority of the same signaling pathways from E13.5 and E14.5 were grouped together such as CCL, CSF, ANGPTL, PDGF, VEGF, ncWNT, and MK, suggesting that these pathways are essential for skin morphogenesis at both time points and likely do not critically regulate new developmental events at E14.5, such as hair follicle morphogenesis or dermal maturation. However, WNT and KIT signaling were classified into different groups, consistent with profound and multi-faceted role of WNT signaling in skin morphogenesis 22 , 54 . By computing the Euclidean distance between any pair of the shared signaling pathways in the shared two-dimensional manifold, we observed a large distance for WNT and KIT and to a lesser extent for RANKL, IL2, FGF, GALECTIN, EGF, TGFβ, and NGF pathways (Fig.  5d , Supplementary Fig.  6a-d ). We specifically examined how WNT communications change over one day of skin development (Fig.  5e-j , Supplementary Data 2 ). At both embryonic time points, basal epidermal cells were the dominant source of WNT ligands, with further minor contribution from fibroblasts. Yet, compared to E13.5, when only basal epidermal cells were the WNT targets, at E14.5 fibroblasts gained WNT responsiveness. Further, melanocytes emerged as the new minor source of WNT signaling, helping to drive an overall increase in WNT communication network complexity. Collectively, the joint manifold learning enables the identification of signaling pathways that undergo embryonic stage-dependent change.

Next, we compared the information flow for each signaling pathway between E13.5 and E14.5 time points. The information flow for a given signaling pathway is defined by the sum of communication probability among all pairs of cell groups in the inferred network. We found that some pathways, including ANGPTL, APELIN, CSF, FGF, RANKL, and TGFβ maintain similar flow between the time points (black in Fig.  5k ). We interpret that these pathways are equally important in the developing skin at both time points. In contrast, other pathways prominently change their information flow at E14.5 as compared to E13.5: (i) turn off (NT, TWEAK), (ii) decrease (such as PTN, MK), (iii) turn on (TNF), or (iv) increase (such as WNT, GALECTIN, KIT, IGF, VEGF).

Moreover, we studied the detailed changes in the outgoing signaling across all significant pathways using pattern recognition analysis (Fig.  5l ; see “Methods” section). We found that skin fibroblasts change their major and minor outgoing communication patterns between E13.5 and E14.5. At E13.5, early fibroblast state FIB-A dominates the outgoing signaling. Over one day period, the minor signaling of late fibroblast states FIB-B and FIB-P become major and includes ANGPTL, IGF, VEGF, KIT, SEMA3 pathways (Supplementary Fig.  6a-h ). This suggests the balancing changes in the levels and patterns of ligand expression. On the other hand, endothelial cells (ENDO), melanocytes (MELA) and skin-resident myeloid cells (MYL) maintain their outgoing signaling patterns. Complex outgoing signaling dynamics were observed in the epidermis. Basal epidermal cells at E14.5 maintain secreted signaling patterns for NGF, PDGF, VISFATIN, and WNT, yet turn off signaling including for KIT and Neurotrophin (NT), and turn on signaling including for VEGF, PTN and LIFR. On the other hand, spinous epidermal cells prominently redesign their outgoing signaling. They turn off or decrease four pathways, such as PDGF (Supplementary Fig.  6e and 6g ), turn on SEMA3 pathway, and maintain three pathways—IGF, MK, and PTN (Supplementary Fig.  6 f and 6h ). Prominent change in spinous cell signaling is consistent with known epidermal stratification event that occurs in mice at the transition between E13.5 and E14.5 55 , 56 . Taken together, CellChat analysis on joint scRNA-seq datasets enables multifaceted assessment of intercellular communication patterns across biological times, such as embryonic developmental time scale.

Joint learning of conserved and context-specific communication patterns between distinct scRNA-seq datasets

We also used CellChat to compare cell–cell communication patterns between two scRNA-seq datasets, one from embryonic day E13.5 skin 22 and another from adult day 12 wound skin 23 (Fig.  6a ). While representing the same tissue (skin) from the same species (mouse) and containing some of the same principal cell types, such as fibroblasts, these two datasets are from vastly distinct biological contexts— embryonic morphogenesis vs. wound-induced repair. As such, this case study presents an opportunity to discover signaling logic and signal conservation principles. First, we performed joint manifold learning and classification of the inferred communication networks based on their topological similarity (functional similarity cannot be performed because of the vastly different cell type composition). We identified four signaling pathway groups (Fig.  6b–c ). Intriguingly, none of the groups are unique to a given dataset, suggesting that the entire spectrum of communications is represented in both skin states. There are, however, dataset-specific enrichments, especially in groups #1 and # 4, which are dominated by signaling networks of the embryonic skin (8 out of 14 and 6 out of 9, respectively). The other two groups #2 and #3 are nearly equally contributed by the communication networks and contain several overlapping pathways from both skin states. By computing the Euclidean distance between any pair of the shared signaling pathways in the shared two-dimensions space, we observed a large distance for signaling pathways like IGF, PDGF, CSF, PROS, and CCL (Supplementary Fig.  7a-b ), suggesting that these pathways exhibit significantly different communication network architectures. However, other signaling pathways show relatively small distances, including ANGPTL, RANKL, TGFb, SEMA3, IL2, PTN, ncWNT, MK, EGF, APELN, and EDN (Supplementary Fig.  7c ), which are also grouped together (Fig.  6c–d ). This suggests similar communication network architectures for these overlapping pathways in both skin states. Closer look at the MK (Midkine) pathway (Fig.  6e–f ) shows its high signaling redundancy (i.e., multiple signaling sources) and high target promiscuity (i. e. all cell groups can function as MK targets). The latter finding suggests that certain pathways have highly conserved signaling architecture (i.e., high degree of redundancy) which is largely independent of the specific cellular composition of the tissue.

a Schematic illustration of cellular composition of skin during embryonic morphogenesis at E13.5 and during adult wound-induced repair at day 12. Different cell populations are color-coded to match colors in panel e and f , respectively. b Jointly projecting and clustering signaling pathways from E13.5 and wound onto shared two-dimensional manifold according to their structural similarity of the inferred networks. Circle and square symbols represent the signaling networks from E13.5 and wound respectively. Each circle or square represents the communication network of one signaling pathway. Circle or square size is proportional to the total communication probability of that signaling network. Different colors represent different groups of signaling pathways. c Magnified view of each pathway group. d The overlapping signaling pathways between E13.5 and wound were ranked based on their pairwise Euclidean distance in the shared two-dimensional manifold. Larger distance implies larger difference. e–f Hierarchical plot showing the inferred intercellular communication network of MK signaling pathway at E13.5 and wound, respectively. Circle sizes are proportional to the number of cells in each cell group and edge width represents the communication probability. g All the significant signaling pathways were ranked based on their differences of overall information flow within the inferred networks between E13.5 and wound. The overall information flow of a signaling network is calculated by summarizing all the communication probabilities in that network. The top signaling pathways colored by red are more enriched in E13.5, and the bottom ones colored by green were more enriched in the wound.

We also compared the information flow (i.e., the overall communication probability) across the two skin datasets. Intriguingly, 19 out of 34 pathways are highly active, albeit at different levels, both in embryonic skin and in adult skin wounds (Fig.  6g ). These likely represent core signaling pathways necessary for skin function independent of the specific point in the biological time scale (i.e., embryonic vs. adult). Nine pathways are active only in embryonic skin. These include such important pathways for skin morphogenesis as FGF 37 , 43 , 57 , 58 , 59 , 60 and WNT 22 , 36 , 37 , 38 , 39 , 40 . Four pathways are specifically active in wounded skin, including known regulators of wound-induced skin repair SPP1 (osteopontin) 61 , 62 , 63 , MIF (macrophage migration inhibitory factor) 64 , 65 , 66 and IL1 67 , 68 , 69 . Taken together, this CellChat approach allows system-level classification and discovery of signaling communication network architecture principles.

Joint learning of normal and diseased human skin to discover major signaling changes in response to disease

As CellChatDB also includes curated ligand-receptor interactions of human, we next employed CellChat to detect the signaling changes between so-called lesional (diseased) and nonlesional (normal) skin from patients with atopic dermatitis (AD) using recently published human skin scRNA-seq dataset 70 (Fig.  7a ). The original study revealed that lesional skin was enriched for chemokine signals (including CCL19 ) from inflammatory fibroblasts to inflammatory immune cells, including dendritic cells (DC) and T cells (TC). This was validated using immunofluorescence staining 70 . Therefore, we used CellChat to study the intercellular communication among fibroblasts (four subpopulations: APOE  + FIB, FBN1  + FIB, COL11A  + FIB, and Inflam.FIB), DCs (four subpopulations: cDC1, cDC2, LC, and Inflam.DC), and TCs (four subpopulations: TC, Inflam.TC, CD40LG  + TC and NKT) (Supplementary Fig.  8a–e , see “Methods” section).

a Schematic illustration of scRNA-seq on cells from nonlesional (NL, normal) and lesional (LS, diseased) human skin from patients with atopic dermatitis. b Jointly projecting and clustering signaling pathways from NL and LS skin onto shared two-dimensional manifold according to functional similarity of the inferred networks. Circle and square symbols represent the signaling networks from NL and LS respectively. Each dot or square represents the communication network of one signaling pathway. Dot or square size is proportional to the communication probability. Different colors represent different groups of signaling pathways. c Significant signaling pathways were ranked based on differences in the overall information flow within the inferred networks between NL and LS skin. The overall information flow of a signaling network is calculated by summarizing all communication probabilities in that network. The top signaling pathways colored red are enriched in NL skin, and these colored green were enriched in the LS skin. d Comparison of the significant ligand-receptor pairs between NL and LS skin, which contribute to the signaling from Inflam.FIB (i.e., inflammatory fibroblasts) to dendritic cells (DC) and T cells (TC) including cDC1, cDC2, LS, Inflam.DC, TC, Inflam.TC, CD40LG  + TC, and NKT subpopulations. The highlighted CCL19-CCR7 signaling was previously validated using immunofluorescence staining. Dot color reflects communication probabilities and dot size represents computed p-values. Empty space means the communication probability is zero. p -values are computed from one-sided permutation test. e Expression distribution of ligand CCL19 and its receptor CCR7 in NL (red) and LS (green) skin. f Hierarchical plot showing inferred intercellular communication network of CCL19-CCR7 signaling in LS skin. Left and right portions show autocrine and paracrine signaling to fibroblast and immune cells, respectively. Circle sizes are proportional to the number of cells in each cell group and edge width represents the communication probability. Note that CellChat predicted no significant CCL19-CCR7 signaling in NL skin. FIB: fibroblasts; Inflam.FIB: inflammatory fibroblasts; cDC: conventional dendritic cell; Inflam.DC: inflammatory dendritic cell; LC: Langerhans cell; TC: T cell; Inflam.TC: inflammatory T cell; NKT: natural killer T cell.

We inferred intercellular communication networks for the nonlesional (NL) and lesional (LS) skin separately, and then jointly mapped them onto a shared two-dimensional manifold and clustered them into groups based on their functional similarity. We identified four pathway groups (Fig.  7b ). Almost all the same signaling pathways from NL and LS were grouped together such as VEGF, GAS, LIGHT, CD40, and MIF, suggesting that these pathways are essential for both nonlesional and lesional skin and likely do not critically contribute to disease pathogenesis. By comparing the overall communication probability between nonlesional and lesional skin, we found that 11 out of 16 signaling pathways were highly active in lesional skin, including 9 pathways involved in inflammatory and immune response, such as CXCL, LIGHT, GLAECTIN, COMPLEMENT, MIF, CSF, IL4, CCL, and TNF (Fig.  7c ). Four pathways were specifically active in lesional skin, including known inflammatory signals CSF, IL4, CCL, and TNF, suggesting that these pathways might critically contribute to disease progression. Specific to CCL signaling, CellChat identified ligand-receptor pair CCL19 - CCR7 as the most significant signaling, contributing to the communication from Inflam.FIB to Inflam.DC (Fig.  7d–f ). This is in agreement with a reported experimental finding 70 . Ligand MIF and its multi-subunit receptor CD74/CD44 were found to act as major signaling from Inflam.FIB to Inflam.TC in lesional skin compared to nonlesional skin (Fig.  7d and Supplementary Fig.  9a–c ). Ligand CXCL12 and its receptor CXCR4 were also found to be highly active in lesional skin, in particular, for the signaling from Inflam.FIB to cDC2 and Inflam.DC (Fig.  7d and Supplementary Fig.  9a–c ). Together, CellChat’s joint analysis using an example of human lesional and nonlesional skin enables the discovery of major signaling changes that might drive disease pathogenesis.

Comparison with other cell–cell communication inference tools

We compared CellChat with three other tools for inferring intercellular communications—SingleCellSignalR 9 , iTALK 10 , and CellPhoneDB 16 using the same four mouse skin datasets analyzed by CellChat (see “Methods” section). Currently existing tools, such as SingleCellSignalR and iTALK, typically use only one ligand/one receptor gene pairs, largely neglecting the effect of multiple receptors. We computed the percentage of false positive interactions caused by the above fact. False positive interactions are defined as the interactions with multi-subunits that are partially identified by these tools (see “Methods” section). We found that the average rate of false positive interactions identified by SingleCellSignalR and iTALK was 10.6% and 14.3%, respectively (Supplementary Fig.  10 ), suggesting the importance of accurate representation of known ligand-receptor interactions. Of note, failed detection of interactions with multi-subunits might be also caused by low expression of multi-subunits of the receptors that are not captured using scRNA-seq.

We also compared the performance of CellChat with CellPhoneDB, which considers multi-subunit ligand–receptor complexes. We reasoned that any given method can be regarded as more accurate if its predictions more significantly overlap with the predictions of more than one other method. We found that CellChat predictions had more overlapping interactions with both SingleCellSignalR and iTALK predictions across all four scRNA-seq datasets (Supplementary Fig.  11a ). CellChat and CellPhoneDB shared ~50% predicted interactions (Supplementary Fig.  11a ). To assess the sensitivity of inferred communications to the input data, we used subsampling of 90, 80, or 70% of the total number of cells in each dataset, and then computed the true positive rate (TPR), false positive rate (FPR), and accuracy (ACC) by comparing subsampled datasets with the original dataset. CellChat produced a slightly higher TPR, lower FPR and higher ACC in comparison with CellPhoneDB (Supplementary Fig.  11b ). Both CellChat and CellPhoneDB were relatively robust to subsampling, which is likely because both methods infer cell–cell communication based on cell clusters. Such robustness in terms of subsampling is very useful when analyzing the rapidly growing volume of scRNA-seq data.

Next, we compared cell–cell communication networks inferred by CellChat, CellPhoneDB, iTALK, and SingleCellSignalR using an example of four spatially colocalized cell populations in E14.5 embryonic mouse skin (Fig.  4 ). We compared the inferred significant ligand-receptor (L-R) pairs for any two cell subpopulations between CellChat and other methods. Here we only retained the top 10% of L-R pairs (the most significant) inferred by iTALK and SingleCellSignalR to ensure the comparable number of L-R pairs with that by CellChat. The average numbers of L-R pairs between two cell subpopulations inferred by the above four methods were 12, 37, 14, and 12, respectively (Supplementary Table  1 ). We found that CellChat shared more L-R pairs with CellPhoneDB than with iTALK, likely due to the fact that both CellChat and CellPhoneDB consider multi-subunit complexes and determine the significant L-R pairs using a statistical approach. SingleCellSignalR shared very few L-R pairs with the other three methods, suggesting a potentially different logic for quantifying and ranking L-R interactions. Moreover, the majority of shared L-R pairs between CellChat and CellPhoneDB were independently ranked as top pairs by CellPhoneDB (Supplementary Data  1 ). This result suggests that although CellChat infers fewer L-R pairs than CellPhoneDB, it captures the strongest (and likely the most significant) L-R interactions.

We also systematically evaluated different methods based on the assumption that spatially adjacent cell types should have stronger cell–cell communication than spatially distant cells. We have studied cell–cell communication for four spatially colocalized cell populations in E14.5 embryonic mouse skin, including Placodes, pre-DC, DC1, and DC2 (Fig.  4 ). We now added seven cell types that are likely not spatially adjacent to the above four cell populations–FIB (fibroblasts), MELA (melanocytes), Spinous (spinous epithelial cells), MYL (myeloid cells), Immune (other immune cells), ENDO (endothelial cells) and Muscle. We then computed the number of inferred interactions, as well as the sum of interaction probabilities or scores between each cell type and the four spatially colocalized cell populations. We found that CellChat consistently captures stronger interactions in spatially adjacent cells than distant cells both in terms of the number of interactions and the interaction probabilities (Supplementary Fig.  12a-b ). CellPhoneDB also performed well at discriminating spatially-adjacent from distant cells. iTALK failed to capture stronger interactions in spatially adjacent cells as compared to spatially distant cells for FIB, MELA, MYL, and ENDO. SingleCellSignalR also failed for FIB and ENDO. By considering all seven cell types together, we found that both CellChat and CellPhoneDB can significantly distinguish spatially adjacent from distant cells, whereas iTALK and SingleCellSignalR predicted stronger interactions in spatially adjacent cells than distant cells with no statistically significant differences (Supplementary Fig.  12c ). Since CellPhoneDB infers more interactions than CellChat, we tested whether the top interactions predicted by CellPhoneDB can also distinguish spatially adjacent from distant cells. For the top 10%, top 20% and top 30% interactions predicted by CellPhoneDB, the difference between spatially adjacent and distant cells was not as significant as with CellChat (Supplementary Fig.  13a-b ), suggesting that CellChat performed better at capturing stronger interactions. Together, our analyses show that although CellChat produces fewer interactions, it performs well at predicting stronger interactions.

The unique characteristics and capabilities of CellChat and its comparison with other relevant tools are summarized in Supplementary Table  2 . First, CellChatDB database incorporates not only multi-subunit structure of ligand-receptor complexes but also soluble and membrane-bound stimulatory and inhibitory cofactors, leading to a more comprehensive database than those used by other tools. We also quantitatively showed the differences and the strengths of CellChatDB in comparison to other existing analogous databases, including CellTalkDB 71 , CellPhoneDB 16 , iTALK 10 , SingleCellSignalR 9 , Ramilowski2015 72 , NicheNet 13 , and ICELLNET 73 . Compared to the above databases, CellChatDB provides an important resource for the community to study biologically meaningful cell–cell communication (Supplementary Fig.  1b and Supplementary Note  1 ). Second, CellChat allows users to input a low-dimensional representation of the data, a particularly useful function when analyzing continuous states along pseudotime trajectories. Third, CellChat can extract higher order information from the inferred communications for identification of major signaling sources, targets and essential mediators, as well as the prediction of coordinated responses among different cell types. Fourth, CellChat can group signaling pathways based on similarity of their communication patterns to identify signaling pathways with similar architectures, and possibly functions. Finally, CellChat can uncover conserved vs. context-specific communication patterns through manifold learning of multiple communication networks simultaneously.

In this work we report a database of signaling ligand-receptor interactions that considers the multimeric structure of ligand-receptor complexes and additional effects on the core interaction by soluble and membrane-bound stimulatory and inhibitory cofactors. The ligand-receptor pairs are also classified into functionally related signaling pathways via systematic manual curation based on peer-reviewed literature. Comprehensive recapitulation of known molecular interactions is essential for developing biologically meaningful understanding of intercellular communications from scRNA-seq data. For example, signaling via BMP, IL, Interferon, TGFβ pathways requires the presence of more than one membrane-bound receptor subunits. Further, many pathways, such as BMP and WNT, are prominently modulated by their cofactors, both positively and negatively. To our knowledge, CellChatDB is the first manually curated signaling interaction database in mouse that considers multimeric structure. Although users can map human genes to their mouse orthologues using available tools such as biomaRt 74 , some molecular interactions are found in mouse but not in human and vice-versa and these are typically lost during such mapping. CellChatDB additionally provides the signaling interactions in human by first automatically mapping to human orthologues and then manually adding the interactions specific to human.

Integration of all known molecular interactions when studying intercellular communication requires new modeling frameworks. To this end, we derived a mass action-based model for quantifying the communication probability between a given ligand and its cognate receptor. We modeled the signaling communication probability between two cell groups by considering the proportion of cells in each group across all sequenced cells. This is important because abundant cell populations tend to send collectively stronger signals than the rare cell populations. With the increasing number of datasets on unsorted single-cell transcriptomes in the Human Cell Atlas, tools with such consideration will be potentially in high demand. For the users who are interested in analyzing sorting-enriched single cells, we provide an option of removing the potential artifact of population size when inferring cell–cell communication. In addition, CellChat estimates the level of ligands by the geometric mean of the subunits. Due to the low amounts of mRNA in individual cells, dropout events often occur in scRNA-seq data 75 , leading to possible zero expression of subunits. However, dropouts are unlikely to affect strong signals predicted by CellChat because dropouts commonly happen for genes with low expression 75 , 76 .

CellChat R package is a versatile and easy-to-use toolkit for inferring, analyzing and visualizing cell–cell communication from any given scRNA-seq data. It provides several graphical outputs to facilitate different post-analysis tasks. Of particular note is our customized hierarchical plot that provides an intuitive way to visualize oftentimes complex details of signaling by a given pathway, including: (i) clear view of source and target cell populations, (ii) easy-to-identified directionality and probability of signaling, and (iii) paracrine vs. autocrine signaling links. We demonstrated CellChat’s diverse functionalities by applying it to finding continuous cell lineage-associated signaling events, communications between spatially colocalized cell populations, temporal changes in time-course scRNA-seq data, and conserved and context-specific communications between datasets from distinct biological contexts.

A user-friendly web-based CellChat Explorer ( http://www.cellchat.org/ ) was also built, which contains two major components: (a) Ligand-Receptor Interaction Explorer, which allows easy exploration of our ligand-receptor interaction database CellChatDB, and (b) Cell–Cell Communication Atlas Explorer, which allows easy exploration of the cell–cell communication. For any given scRNA-seq dataset that has been processed by our CellChat R-package, we can host the predicted results on our server, allowing easy exploration and comparison of cell–cell communication. While at present the Cell–Cell Communication Atlas only hosts the skin scRNA-seq datasets analyzed in this study, we envision its rapid growth to become a community-driven web portal for cell–cell communication in a broad range of tissues at single-cell resolution.

The successful performance of CellChat lies in utilizing a mass action-based model to integrate all known molecular interactions, including the core interaction between ligands and receptors with multi-subunit structure, and additional modulation by cofactors. While ligand-receptor interactions and law-of-mass-action happen at the protein level, mRNA levels are commonly used to approximate the protein level. A higher level of molecular details (e.g., protein levels in individual cells) could further improve the modeling accuracy of CellChat and related tools. Due to the technical difficulties of capturing single-cell proteomic information at present time, a comprehensive modeling of ligand-receptor interactions remains challenging. Determining a set of biologically meaningful parameters in the mass action model remains challenging, particularly when considering that different pairs of ligands and receptors often have different dissociation constants (i.e., the parameter Kh in Hill function) and different degree of cooperativity (i.e., the parameter n in Hill function). Although these parameters lack explicit biological connections in our current model, the Hill function can be considered as a nonlinear approximation of the ligand-receptor interactions. By computing the Jaccard similarity between the interactions inferred using different choices of the parameters Kh and n , we noticed that the inferred ligand-receptor interactions by CellChat are relatively robust to those parameters within certain ranges for all four tested datasets (Supplementary Fig.  14 ).

CellChat communication pattern analysis can uncover coordinated responses among different cell types. Different cell types may simultaneously activate the same cell type-independent signaling patterns or different cell type-specific signaling patterns. Different numbers of patterns provide different resolutions when recovering coordinated responses (Supplementary Note  2 ; Supplementary Fig.  15 ). This analysis can potentially help to derive general cell–cell communication principles.

Cell clustering is a pre-requisite for cell–cell communication analysis with CellChat and other tools, such as CellPhoneDB, iTALK and SingleCellSignalR. While different number of cell clusters may naturally affect the inferred ligand-receptor interactions, with a fixed cluster number the clustering results using different methods or parameters will unlikely have major impact on the inferred ligand-receptor interactions. This is because our cell–cell communication is inferred at the cluster level, only depending on estimation of the average gene expression in each cell cluster. We demonstrated these two points using an example of E14.5 mouse embryonic skin dataset with four spatially colocalized cell subpopulations (Supplementary Note  2 ; Supplementary Fig.  16 ). In general, cell clustering needs to be carried out carefully in order to capture biologically meaningful cell populations before cell–cell communication analysis.

The number of inferred ligand-receptor pairs clearly depends on the method for calculating the average gene expression per cell group. Here we systematically explored the inferred ligand-receptor pairs using different methods by calculating the average gene expression per cell group, including mean (i.e., simply calculating the average gene expression), 5% truncated mean (i.e., calculating the average gene expression by discarding 5% from each end of the data), 10% truncated mean, trimean (i.e., the method used in CellChat) and median. For the four studied datasets, there are about 15% more dropped ligand-receptor pairs when calculating the average gene expression using trimean compared to the 10% truncated mean (Supplementary Fig.  17 ). Compared to other cell–cell communication tools, such as CellPhoneDB, which uses a 10% truncated mean, CellChat produces fewer ligand-receptor interactions. However, as seen in our comparison study on spatially adjacent subpopulations (Supplementary Fig.  13a, b ), CellChat performs well at predicting stronger interactions.

Although we found CellChat’s predictions can recapitulate known biology to a substantial degree, systematic evaluation of predicted cell–cell communication networks is challenging due to the lack of ground truth 7 . Here we employed three strategies to compare the performance of different computational methods. First, we reason that a more accurate method will have a larger proportion of overlapped predictions with other methods. However, such assumption has the following two limitations: (1) Similar methods tend to generate similar results regardless of accuracy; and (2) Different ligand-receptor databases used in each method could contribute to the variety of predicted interactions. Second, we comprehensively compared the inferred interactions for any two cell subpopulations on a specific dataset. We found that the shared interactions between CellChat and other methods were independently ranked as top pairs by other methods including CellPhoneDB. Third, we reason that spatially adjacent cell types should have stronger cell–cell communication than spatially distant cells. CellChat performs better in distinguishing spatially adjacent from distant cells both in terms of the number of interactions and the interaction strengths. Together, our analyses show that although CellChat produces fewer interactions than other methods, it performs well at predicting stronger interactions, which is helpful for narrowing down on interactions for further experimental validations. Other types of single-cell data such as proteomics 77 and spatial transcriptomics 78 when available are also helpful and important to benchmark and optimize these cell–cell communication methods in future studies.

Recent advances in spatially resolved transcriptomic techniques offer an opportunity to explore spatial organization of cells in tissues 78 . The integration of spatial information with scRNA-seq data will likely offer new insights into cellular crosstalk 79 , 80 . The present version of CellChat provides an easy-to-use tool for intercellular communication analysis on conventional, non-spatially resolved scRNA-seq data. While it remains to be tested, we believe it can be relatively easily adjusted, such as via introduction of spatial constrains on cell–cell signaling, to build intercellular communication networks on spatially resolved transcriptomic datasets. As single-cell multi-omics data is becoming more common 81 , 82 , we anticipate that methods like CellChat, which are able to perform system-level analyses, will serve as useful hypothesis-generating tools whose predictive power will extend beyond the ability to classify cell populations and establish their lineage relationships, which currently dominate single-cell genomics studies.

Database construction for ligand-receptor interactions

To construct a database of ligand-receptor interactions that comprehensively represents the current state of knowledge, we manually reviewed other publicly available signaling pathway databases, as well as peer-reviewed literature and developed CellChatDB. CellChatDB is a database of literature-supported ligand-receptor interactions in both mouse and human. The majority of ligand–receptor interactions in CellChatDB were manually curated on the basis of KEGG (Kyoto Encyclopedia of Genes and Genomes) signaling pathway database ( https://www.genome.jp/kegg/pathway.html ). Additional signaling molecular interactions were gathered from recent peer-reviewed experimental studies. We took into account not only the structural composition of ligand-receptor interactions, that often involve multimeric receptors, but also cofactor molecules, including soluble agonists and antagonists, as well as co-stimulatory and co-inhibitory membrane-bound receptors that can prominently modulate ligand-receptor mediated signaling events. The detailed steps for how CellChatDB was built and how to update CellChatDB by adding user-defined ligand-receptor pairs were provided in Supplementary Note  1 . To further analyze cell–cell communication in a more biologically meaningful way, we grouped all of the interactions into 229 signaling pathway families, such as WNT, ncWNT, TGFβ, BMP, Nodal, Activin, EGF, NRG, TGFα, FGF, PDGF, VEGF, IGF, chemokine and cytokine signaling pathways (CCL, CXCL, CX3C, XC, IL, IFN), Notch and TNF. The supportive evidences for each signaling interaction is included within the database.

Inference of intercellular communications

a) Identification of differentially expressed signaling genes. To infer the cell state-specific communications, we first identified differentially expressed signaling genes across all cell groups within a given scRNA-seq dataset, using the Wilcoxon rank sum test with the significance level of 0.05.

b) Calculation of ensemble average expression. To account for the noise effects, we calculated the ensemble average expression of signaling genes in a given cell group using a statistically robust mean method:

where Q 1 , Q 2 , and Q 3 is the first, second and third quartile of the expression levels of a signaling gene in a cell group.

c) Calculation of intercellular communication probability. We modeled ligand-receptor mediated signaling interactions using the law of mass action. Since the physical process of ligand-receptor binding involves protein-protein interactions, we used a random walk based network propagation technique 83 , 84 to project the gene expression profiles onto a high-confidence experimentally validated protein-protein network from STRINGdb 83 , 85 . Based on the projected ligand and receptor profiles, the communication probability P i,j from cell groups i to j for a particular ligand-receptor pair k was modeled by:

Here L i and R j represent the expression level of ligand L and receptor R in cell group i and cell group j , respectively. The expression level of ligand L with m1 subunits (i.e., \(L_{i,1}, \cdots ,L_{i,m1}\) ) was approximated by their geometric mean, implying that the zero expression of any subunit leads to an inactive ligand. Similarly, we computed the expression level of receptor R with m2 subunits. In addition, co-stimulatory and co-inhibitory membrane-bound receptors are capable of modulating signaling via the control of receptor activation 86 . For the ligand-receptor pair with multiple co-stimulatory receptors, we computed the average expression of these co-stimulatory receptors (denoted by RA) and then used a linear function to model the positive modulation of the receptor expression. For each ligand-receptor pair with multiple co-inhibitory receptors, we modeled them using the same approach. A Hill function was used to model the interactions between L and R with a parameter K h whose default value was set to be 0.5 as the input data has a normalized range from 0 to 1. The extracellular agonists and antagonists from both sender and receiver cells are able to directly or indirectly modulate the ligand-receptor interaction 86 . For the ligand-receptor pair with multiple soluble agonists, we computed the average expression of these agonists (denoted by AG) and then used a Hill function to model the positive modulation of the ligand-receptor interaction. For the ligand-receptor pair with multiple soluble antagonists, we modeled them using the same approach. The effect of cell proportion in each cell group was also included in the probability calculation when analyzing unsorted single-cell transcriptomes, where n i a n d n j are the numbers of cells in cell groups i and j , respectively, a n d n is the total number of cells in a given dataset. Together, the communication probabilities among all pairs of cell groups across all pairs of ligand-receptor were represented by a three-dimensional array P ( K  ×  K  ×  N ), where K is the number of cell groups and N is the number of ligand-receptor pairs or signaling pathways. The communication probability of a signaling pathway was computed by summarizing the probabilities of its associated ligand-receptor pairs. It should be noted that we did not perform normalization along the second dimension of P such that \(\mathop {\sum }\limits_j P_{i,j}^k = 1\)  because the normalized data are not suitable for comparing the communication probability between different cell groups across multiple signaling pathways. The communication probability here only represents the interaction strength and is not exactly a probability.

d) Identification of statistically significant intercellular communications. The significant interactions between two cell groups are identified using a permutation test by randomly permuting the group labels of cells, and then recalculating the communication probability P i,j between cell group i and cell group j through a pair of ligand L and receptor R . The p -value of each P i,j is computed by:

where the probability P i,j (m) is the communication probability for the m -th permutation. M  is the total number of permutations ( M  = 100 by default). The interactions with p -value <0.05 are considered significant.

Discovery of dominant senders, receivers, mediators, and influencers in the intercellular communication networks

To allow ready identification of major signaling sources, targets, essential mediators and key influencers, as well as other high-order information in intercellular communications, the centrality metrics from graph theory, previously used for social network analysis, were adopted 17 . Specifically, we used measures in weighted-directed networks, including out-degree, in-degree, flow betweenesss and information centrality, to respectively identify dominant senders, receivers, mediators and influencers for the intercellular communications. In a weighted-directed network with the weights as the computed communication probabilities, the out-degree, computed as the sum of communication probabilities of the outgoing signaling from a cell group, and the in-degree, computed as the sum of the communication probabilities of the incoming signaling to a cell group, can be used to identify the dominant cell senders and receivers of signaling networks, respectively. Flow betweenness score 87 measures a group of cells’ capability as gatekeeper to control communication flow between any two cell groups. Information centrality score provides a hybrid measure, for example by combining closeness and eigenvector, for information flow within a signaling network, and a higher value indicates greater control on the information flow 87 . Other popular centrality metrics, such as hub, authority, EigenCentrality and PageRank 88 , can be also used to identify highly influential cell groups in the intercellular communications. The flow betweenness and information centrality are calculated by the package sna 87 . Other measures are computed by the package igraph ( https://igraph.org/ ).

Identification of major signals for specific cell groups and global communication patterns

To identify key signals and latent communication patterns among all signaling pathways, CellChat uses an unsupervised learning method non-negative matrix factorization that has been successfully applied in pattern recognition 18 , 19 , 82 , 89 . First, the latent patterns were found for sending cells by summarizing the communication probability array P (three-dimensional) along the second dimension to obtain a two-dimensional matrix P j . A non-negative matrix factorization was then carried out via:

where the two low-dimensional matrices W and H are the cell loading and signaling loading matrices with sizes K  ×  R and R  ×  N , respectively. Each of the R columns in W and the corresponding rows in H is considered as a communication pattern. W ir is the loading values of cell group i in pattern r , representing the contributions of cell group i in pattern r . H rk represents the contributions of ligand-receptor pair or signaling pathway k in pattern r . As the number of patterns increases, there might be redundant patterns, making it difficult to interpret the communication patterns. We chose five patterns as the initial default because the number of cell groups and significant signaling pathways are relatively small. In addition, we inferred the number of patterns based on two metrics that have been implemented in the NMF R package, including Cophenetic and Silhouette 90 . Both metrics measure the stability for a particular number of patterns based on a hierarchical clustering of the consensus matrix. For a range of the number of patterns, a suitable number of patterns is the one at which Cophenetic and Silhouette values begin to drop suddenly.

In sum, the matrix W represents the R latent patterns of cell groups, indicating how these cell groups coordinate to send signals; the matrix H represents the R latent patterns of ligand-receptor pairs or signaling pathways, indicating how these ligand-receptor pairs or signaling pathways work together to send signals; the connection of W with H predicts the key signals sent from certain cell groups. Similarly, we summarized the communication probability array P along the first dimension to infer the key signals received by certain cell groups, as well as their latent patterns. Together, outgoing patterns reveal how the sender cells (i.e., cells as signal sources) coordinate with each other, as well as how they coordinate with certain signaling pathways to drive communication. Incoming patterns show how the target cells (i.e., cells as signal receivers) coordinate with each other, as well as how they coordinate with certain signaling pathways to respond to incoming signals.

To intuitively show the associations of latent patterns with cell groups and ligand-receptor pairs or signaling pathways, we used alluvial plots implemented in the ggalluvial package ( https://cran.r-project.org/web/packages/ggalluvial/index.html ). We first normalized each row of W and each column of H to be [0,1], and then set the elements in W and H to be zero if they are less than 0.5. Such thresholding allows to uncover the most enriched cell groups and signaling pathways associated with each inferred pattern, that is, each cell group or signaling pathway is associated with only one inferred pattern. These thresholded matrices W and H are used as inputs for creating alluvial plots. To directly relate cell groups with their enriched signaling pathways, we set the elements in W and H to be zero if they are less than 1/ R where R is the number of latent patterns. By using a less strict threshold, more enriched signaling pathways associated each cell group might be obtained. Using a contribution score of each cell group to each signaling pathway computed by multiplying W by H , we constructed a dot plot in which the dot size is proportion to the contribution score to show association between cell group and their enriched signaling pathways.

Quantification of similarity among intercellular communication networks

Two different similarity measures were used to quantify the similarity among intercellular communication networks. A functional similarity S was calculated based on the overlap of communications via the Jaccard similarity defined by:

where G and G’ are two signaling networks and E ( G ) is the set of communications in signaling network G . High degree of functional similarity indicates major senders and receivers are similar, and it can be interpreted as the two signaling pathways or two ligand-receptor pairs exhibit similar and/or redundant roles.

A structural similarity was used to compare their signaling network structure, without considering the similarity of senders and receivers, using a previously developed measure for structural topological differences 91 . The dissimilarity measure between signaling networks G and G’ with the number of cell groups being N and M , respectively, is calculated by:

where G c indicates the complement of G , and JSD is the Jensen–Shannon divergence and NND is defined as:

with \({\mathrm{JSD}}\left( {P_1, \ldots ,P_N} \right) = \frac{1}{N}\mathop {\sum }\limits_{i,j}^N p_i(j){\mathrm{log}}( {\frac{{p_i(j)}}{{u_j}}} )\) and \(u_j = ( {\mathop {\sum }\limits_{i = 1}^N p_i( j )} )/N\) being the Jensen–Shannon divergence and the average of the N distributions, respectively. \(P_i = \left\{ {p_i\left( j \right)} \right\}\) is the distance distribution in each cell group i , where p i ( j ) is the fraction of cell groups connected to cell group i at distance j . d is the signaling network’s diameter. \({\mathrm{JSD}}(u_G,u_{G{\prime}})\) measures the difference between the signaling networks’ averaged cell group-distance distributions, u G and \(u_{G{\prime}}\) , and \({\mathrm{JSD}}(P_{\alpha G},\,P_{\alpha G{\prime}})\) measures the difference between the α -centrality values of the signaling networks. w 1 , w 2 , and w 3 are the weights of each term with w 1  +  w 2  +  w 3  = 1. Similar to a previous study 91 , we selected w 1  = 0.45, w 2  = 0.45, and w 3  = 0.1. The structural similarity S was computed by one minus dissimilarity measure D .

Manifold and classification learning of intercellular communication networks

The manifold learning of the inferred intercellular communication networks consists of three steps. First, we built a shared nearest neighbor (SNN) similarity network Gs of all signaling pathways, which was constructed by calculating the k -nearest signaling pathways of each signaling pathway using the calculated functional or structural similarity matrix S of intercellular communication networks. The fraction of shared nearest signaling pathways between a given signaling pathway and its neighbors was used as weights of the SNN network. The number of nearest neighbors k was chosen as the square root of the total number of signaling pathways. Second, we smoothed the similarity matrix S using Gs  ×  S . This smooth process provides a better representation of the similarity between signaling pathways to allow filtering of the weak similarity (potentially noise-induced) and enhancing the strong similarity 82 . Finally, we performed uniform manifold approximation and projection (UMAP) 92 on the smoothed similarity matrix. To better visualize the similarity of intercellular communication networks, we used the first two dimensions of the learned manifold, where each dot in this two-dimensional space represents an individual signaling pathway or ligand-receptor pair.

Moreover, to group the signaling pathways based on their similarity of intercellular communication networks in an unsupervised manner, we performed k -means clustering of the first two components of the learned manifold. The number of signaling groups was determined according to the eigenvalue spectrum by analyzing the Laplacian matrix derived from a consensus matrix 5 , 12 . First, we performed k -means clustering multiple times for different values of k (e.g., 2–10). Second, we constructed a consensus matrix representing the probability of two signaling pathways being in the same group across multiple values of k . We then pruned the consensus matrix by setting the elements to be zero if they are less than 0.3 to ensure better robustness to noise. Third, we estimated the number of signaling groups by computing the eigenvalues of the associated Laplacian matrix of the constructed consensus matrix. More generally, the number of signaling groups is usually determined by the first or second largest eigenvalue gap (i.e., the difference between consecutive eigenvalues) based on the spectral graph theory 93 .

Classification of cells into groups

CellChat provides built-in functions to classify cells into groups. Briefly, a SNN graph of all cells is first constructed via the calculation of the k -nearest neighbors (20 by default) for each cell based on the low-dimensional representation space (e.g., via principle component analysis and diffusion map analysis) of the scRNA-seq data. The low-dimensional representation space can be either provided by user or computed by CellChat. Next, cells are clustered into groups by applying the Louvain community detection algorithm 94 to the constructed SNN graph. The number of cell groups is determined either by user-input resolution parameter in the Louvain algorithm or by an eigenvalue spectrum by analyzing the Laplacian matrix derived from multiple runs of Louvain algorithm with different resolution parameters.

Single-cell RNA-seq datasets, data preprocessing, and analysis

Mouse skin wound dataset. We used our recently published scRNA-seq dataset from mouse skin wounds 23 . This dataset included 21,819 cells and was generated via 10X Genomics platform (GEO accession code: GSE113854). Briefly, scRNA-seq was performed on unsorted cells isolated from mouse skin wound dermis from day 12 post-wounding. Unsupervised clustering identified fibroblasts (FIB, ~65%), immune cell populations, including myeloid cells (MYL, 15%), T lymphocytes (TCELL, 4%), B lymphocytes (BCELL, 3%), dendritic cells (DC, 1%), endothelial cells (ENDO, 9%), lymphatic endothelial cells (LYME, 1%), Schwann cells (SCH, 1%) and red blood cells (RBC, 1%). For the intercellular communication analysis, we excluded red blood cells and used the remaining 21,557 cells. The digital data matrices were normalized by a global method, in which the expression value of each gene was divided by the total expression in each cell and multiplied by a scale factor (10,000 by default). These values were then log-transformed with a pseudocount of 1. Normalized data were used for all the analyses. To investigate the heterogeneity of intercellular communications among different cell subpopulations, we performed subclustering analysis on the cell types, whose abundance in the dataset was greater than 5% using the Louvain community detection method. The number of cell groups was determined by the eigengap approach.

Embryonic mouse skin dataset. Recently published embryonic mouse skin datasets 22 were downloaded from GEO (accession codes: GSM3453535, GSM3453536, GSM3453537, and GSM3453538) and included two Embryonic day E13.5 biological replicates and two Embryonic day E14.5 biological replicates. These samples contain unsorted whole-skin cells captured via 10X Genomics platform. For both E13.5 and E14.5 scRNA-seq datasets, we removed the cells with the amount of UMI count less than 2500 and greater than 50000, as well as the cells with the number of genes less than 1000 and the fraction of mitochondrial counts greater than 20%. 12,951 cells at E13.5 and 12,197 cells at E14.5 were used for downstream analyses. First, we performed clustering analysis of cells from E13.5 and E14.5 using the Louvain community detection method, respectively. The values of the resolution parameter in the Louvain community detection method were explored to produce the major cell populations in embryonic skin 22 , 95 . Thus, 11 and 13 cell populations were identified at E13.5 and E14.5, respectively (Supplementary Fig.  3a–d ). The cell populations were annotated based on the known markers 22 , 95 . Compared to E13.5, there were two specific populations at E14.5, including dermal condensate (DC) cells and pericytes. Second, we performed subclustering analysis of DC cells, basal cells and melanocytes at E14.5, respectively. This analysis identified three DC states including pre-DC, DC1, and DC2, three basal state including basal, proliferative basal and placode cells, and three melanocyte subpopulations including MELA-A, MELA-B, and MELA-C (Supplementary Fig.  3e-g ). Third, we performed pseudotime analysis on epidermal and dermal cells at E14.5 using diffusion map, respectively.

Human disease skin dataset. The processed transcriptomic data of 17,349 cells from four lesional and four non-lesional human skin samples (patient ID: S1, S2, S3, S5, S7, S11, S14, and S15) from patients with atopic dermatitis was downloaded from GEO database under accession code GSE147424 70 . We performed the integration analysis of these eight samples using Seurat V3 package based on the tutorial from https://satijalab.org/seurat/v3.2/immune_alignment.html . Unsupervised clustering analysis segregated these combined cells into 10 broad cell types (Supplementary Fig.  8a-b ), including fibroblasts (FIB), dendritic cells (DC), and T cells (TC). The original study highlighted the cell–cell communication among fibroblasts, dendritic cells and T cells 70 . Therefore, following the analysis from the original study 70 , we performed the second-level clustering analysis of FIB, DC, and TC. FIB was clustered into five subgroups with distinct markers, including APOE high FIB ( APOE  + FIB), FBN1  + FIB, COL11A  + FIB, Inflam.FIB (inflammatory FIB expressing chemokines such as CCL19 ) and a small T cell group expressing CD3D (Supplementary Fig.  8c ). This contaminated TC population was removed for further analysis. DC was also separated into five subgroups, including cDC1 (type A DC), cDC2 (type B DC), LC (Langerhans cells), Inflam.DC (inflammatory DC) and other immune cells that does not express DC markers such as CD1A and CD1C (Supplementary Fig.  8d ). This contaminated immune cell group was also removed for further analysis. TC was clustered into four subgroups, including TC, Inflam.TC (inflammatory TC), CD40LG  + TC and NKT (NK T cells) (Supplementary Fig.  8e ). Together, CellChat was applied to 7563 cells from lesional and nonlesional skin involved in twelve cell groups, including APOE  + FIB, FBN1  + FIB, COL11A  + FIB, Inflam.FIB, cDC1, cDC2, LC, Inflam.DC, TC, Inflam.TC, CD40LG  + TC, and NKT.

Method comparisons

We compare the performance of CellChat with three other tools, including SingleCellSignalR 9 , iTALK 10 , and CellPhoneDB 16 . We compare our database CellChatDB with other existing analogous databases, including CellTalkDB 71 , CellPhoneDB 16 , iTALK 10 , SingleCellSignalR 9 , Ramilowski2015 72 , NicheNet 13  and ICELLNET 73 . SingleCellSignalR scores a given ligand-receptor interaction between two cell populations using a regularized product score approach based on average expression levels of a ligand and its receptor and an ad hoc approach for estimating an appropriate score threshold. iTALK identifies differentially expressed ligands and receptors among different cell populations and accounts for the matched ligand-receptor pairs as significant interactions. CellPhoneDB v2.0 predicts enriched signaling interactions between two cell populations by considering the minimum average expression of the members of the heteromeric complex and performing empirical shuffling to calculate which ligand–receptor pairs display significant cell-state specificity. The detailed description of how these methods were performed is available in Supplementary Note  3 .

Both CellChat and CellPhoneDB, but not SingleCellSignalR, and iTALK, consider multi-subunit structure of ligands and receptors to represent heteromeric complexes accurately. To evaluate the effect of neglecting multi-subunit structure of ligands and receptors, we compute false positive rates for the tools that use only one ligand and one receptor gene pairs. The false positive interactions are defined by the interactions with multi-subunits that are partially identified by iTALK and SingleCellSignalR. The ground truth of the interactions with multi-subunits is based on our curated CellChatDB database. For example, for Tgfb1 ligand and its heteromeric receptor Tgfbr1/Tgfbr2 curated in CellChatDB, if the method only identifies one of the two pairs (Tgfb1–Tgfbr1 and Tgfb1–Tgfbr2), then we consider this prediction as one false positive interaction.

We performed subsampling of scRNA-seq datasets using a ‘geometric sketching’ approach, which maintains the transcriptomic heterogeneity within a dataset with a smaller subset of cells 96 . We evaluated the robustness of inferred interactions from subsampled datasets using three measures, including TPR, FPR, and ACC, which were defined in Supplementary Note  3 . Note that such subsampling analysis was used to evaluate the consistency rather than accuracy.

RNAscope in situ assay

Frozen E14.5 mouse skin tissue sections were used for RNA in situ hybridization using RNAscope® kit v2 (323100, Advanced Cell Diagnostics). The following mouse probes from Advanced Cell Diagnostics were used: Dct probe (460461-C2), Edn3 (505841), Ednrb (473801-C3), Axl (450931-C2), Thy1 (430661-C3). We have complied with all relevant ethical regulations for animal testing and research. All animal experiments have been approved by the International Animal Care and Use Committee (IACUC) of the University of California, Irvine.

Reporting summary

Further information on research design is available in the  Nature Research Reporting Summary linked to this article.

Data availability

CellChatDB is included in the CellChat repository ( https://github.com/sqjin/CellChat ). KEGG pathway database is available at https://www.genome.jp/kegg/pathway.html . The datasets analyzed in this study are available from the Gene Expression Omnibus (GEO) repository under the following accession numbers: GSE113854 , GSE122043 (including four samples GSM3453535, GSM3453536, GSM3453537, GSM3453538;) and GSE147424 .

Code availability

CellChat is publicly available as an R package. Source codes, as well as tutorials have been deposited at the GitHub repository ( https://github.com/sqjin/CellChat ). The web-based CellChat Explorer, including Ligand-Receptor Interaction Explorer for exploring the ligand-receptor interaction database and Cell–Cell Communication Atlas Explorer for exploring the intercellular communications in tissues, is available at http://www.cellchat.org/ .

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Acknowledgements

This work was supported by the NSF grant DMS1763272, grant from the Simons Foundation (594598, QN), NIH grants U01AR073159, R01GM123731, and P30AR07504, Pew Charitable Trust (MVP), LEO Foundation grants LF-OC-20-000611 and LF-AW_RAM-19-400008 (MVP). C.F.G.-J. is supported by UC Irvine Chancellor’s ADVANCE Postdoctoral Fellowship and a gift from the Howard Hughes Medical Institute Hanna H. Gray Postdoctoral Fellowship Program.

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Suoqin Jin, Christian F. Guerrero-Juarez, Lihua Zhang & Qing Nie

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Suoqin Jin, Christian F. Guerrero-Juarez, Lihua Zhang, Raul Ramos, Maksim V. Plikus & Qing Nie

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S.J., M.V.P. and Q.N. conceived the project. M.V.P. and Q.N. supervised the research. S.J., M.V.P. and C.F.G.-J. curated the database. S.J. and L.Z. developed and implemented the computational approach. S.J., C.F.G.-J., L. Z, M.V.P. and Q.N. performed data analysis. R.R. and C.-H.K. performed and analyzed RNAscope experiments. I.C., M.V.P. and S.J. developed the web interface. S.J. and C.F.G.-J. prepared the figures. S.J., M.V.P. and Q.N. wrote the manuscript. P.M. edited the manuscript. All authors read and approved the final manuscript.

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Jin, S., Guerrero-Juarez, C.F., Zhang, L. et al. Inference and analysis of cell-cell communication using CellChat. Nat Commun 12 , 1088 (2021). https://doi.org/10.1038/s41467-021-21246-9

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JON BARWISE, DOV GABBAY, CHRYSAFIS HARTONAS, On the Logic of Information Flow, Logic Journal of the IGPL , Volume 3, Issue 1, March 1995, Pages 7–49, https://doi.org/10.1093/jigpal/3.1.7

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Table of contents

Research paper outline example, how to write a research paper outline, formatting your research paper outline, language in research paper outlines.

• Definition of measles
• Rise in cases in recent years in places the disease was previously eliminated or had very low rates of infection
• Figures: Number of cases per year on average, number in recent years. Relate to immunization
• Symptoms and timeframes of disease
• Risk of fatality, including statistics
• How measles is spread
• Immunization procedures in different regions
• Different regions, focusing on the arguments from those against immunization
• Immunization figures in affected regions
• High number of cases in non-immunizing regions
• Illnesses that can result from measles virus
• Fatal cases of other illnesses after patient contracted measles
• Summary of arguments of different groups
• Summary of figures and relationship with recent immunization debate
• Which side of the argument appears to be correct?

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Follow these steps to start your research paper outline:

• Decide on the subject of the paper
• Write down all the ideas you want to include or discuss
• Organize related ideas into sub-groups
• Arrange your ideas into a hierarchy: What should the reader learn first? What is most important? Which idea will help end your paper most effectively?
• Create headings and subheadings that are effective
• Format the outline in either alphanumeric, full-sentence or decimal format

There are three different kinds of research paper outline: alphanumeric, full-sentence and decimal outlines. The differences relate to formatting and style of writing.

• Alphanumeric
• Full-sentence

An alphanumeric outline is most commonly used. It uses Roman numerals, capitalized letters, arabic numerals, lowercase letters to organize the flow of information. Text is written with short notes rather than full sentences.

• Sub-point of sub-point 1

Essentially the same as the alphanumeric outline, but with the text written in full sentences rather than short points.

• Additional sub-point to conclude discussion of point of evidence introduced in point A

A decimal outline is similar in format to the alphanumeric outline, but with a different numbering system: 1, 1.1, 1.2, etc. Text is written as short notes rather than full sentences.

• 1.1.1 Sub-point of first point
• 1.1.2 Sub-point of first point
• 1.2 Second point

To write an effective research paper outline, it is important to pay attention to language. This is especially important if it is one you will show to your teacher or be assessed on.

There are four main considerations: parallelism, coordination, subordination and division.

Parallelism: Be consistent with grammatical form

Parallel structure or parallelism is the repetition of a particular grammatical form within a sentence, or in this case, between points and sub-points. This simply means that if the first point is a verb , the sub-point should also be a verb.

Example of parallelism:

• Include different regions, focusing on the different arguments from those against immunization

Coordination: Be aware of each point’s weight

Your chosen subheadings should hold the same significance as each other, as should all first sub-points, secondary sub-points, and so on.

Example of coordination:

• Include immunization figures in affected regions
• Illnesses that can result from the measles virus

Subordination: Work from general to specific

Subordination refers to the separation of general points from specific. Your main headings should be quite general, and each level of sub-point should become more specific.

Example of subordination:

Division: break information into sub-points.

Your headings should be divided into two or more subsections. There is no limit to how many subsections you can include under each heading, but keep in mind that the information will be structured into a paragraph during the writing stage, so you should not go overboard with the number of sub-points.

Ready to start writing or looking for guidance on a different step in the process? Read our step-by-step guide on how to write a research paper .

Cite this Scribbr article

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Gahan, C. (2023, August 15). How to Create a Structured Research Paper Outline | Example. Scribbr. Retrieved September 23, 2024, from https://www.scribbr.com/research-paper/outline/

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A Review on the Role of the Neuroscience of Flow States in the Modern World

Joshua gold.

1 Centre for Mental Health, Swinburne Neuroimaging (SNI), Swinburne University of Technology, P.O. Box 218, Hawthorn, Melbourne, VIC 3122, Australia; ua.ude.niws@iraicroicj

Joseph Ciorciari

2 Department of Psychological Sciences, Swinburne University of Technology, P.O. Box 218, Hawthorn, Melbourne, VIC 3122, Australia

Flow states have been shown to help people reach peak performance, yet this elusive state is not easily attained. The review describes the current state of literature on flow by addressing the environmental influences as well as the cognitive and neurocognitive elements that underlie the experience. In particular, the research focusses on the transition of cognitive control from an explicit to an implicit process. This is further expanded upon to look at the current, yet related neurocognitive research of high performance associated with the implicit process of automaticity. Finally, the review focusses on transcranial direct current stimulation (tDCS) as a novel method to facilitates an induction of flow states. Implications are aimed at a general technique to improve on skill acquisition and overall performance.

1. Introduction to Flow

The scientific community has as of late begun to explore the field of expertise and its components. One element however that has begun to gain a growing amount of attention is the peak performance found in flow states, whether it be in sport, business or other professional endeavors. Flow is described as a state of optimal performance denoted by smooth and accurate performance with an acute absorption in the task to the point of time dissociation and dissociative tendencies [ 1 , 2 , 3 ]. In the modern workplace there are so many distractions, from messages to meetings, that result in a reduction of productivity. Yet a 10-year longitudinal study Cranston and Keller [ 4 ] showed people in flow states were 500% more productive. Whilst much research has been performed on the personality components of flow there is still much to explore when it comes to the neurocognitive underpinnings of flow to better understand the workings and catalysts for this elusive state. This review focusses on describing the current state of flow research on neurocognitive understandings and provides an insight into the key theories and experimental implications being presented in the research surrounding flow states.

Transcendent, spiritual experiences similar to flow states have long shared reports with countless of religious references dating back centuries by spiritual authors. Flow then found its entrance into the mainstream with Maslow [ 5 ] ‘peak experiences’ and has since been appropriated into popular culture with many names including “in the zone” and “in the moment”. Although a long history exists of this high functioning state, much of its inner workings and route of initiation is shrouded in mystery. Csikszentmihalyi [ 6 ] first described the flow state and noticed the conditions for entering this experiential state include a balance of challenges or action opportunities with an individual’s skill as well as clear and well-defined goals with immediate feedback.

According to Csikszentmihalyi [ 7 ] flow theory, the flow experience relates to the skill set perceived to be possessed by the individual relative to the perceived challenges of the activity. Challenges can be considered as “opportunities for action” thus flow is produced by any situation that requires skill [ 3 ]. The phenomenology of flow further suggests that the enjoyment of a task is due to a discovery found within the interaction of the task. For instance, at first the task might appear boring or anxiety provoking but if the action opportunities become clearer or the skill level improves the task becomes more engaging and finally enjoyable. The discovery of more complex behaviors results in an emergent motivation that transforms a previously unengaging task into that which is intrinsically motivating [ 8 ]. Therefore, complexity of the skill must increase to meet the increasing complexity of the task’s challenge in order for the person to remain in flow. Csikszentmihalyi [ 7 ] developed the flow state model to help illustrate this state change as seen in Figure 1 . For instance, when the challenges and skills are low, a person will likely experience apathy, considered an experience of the lowest quality and the lowest intensity on the flow state model. Whereas, when the skills are greater than those needed for the challenges, the person is more likely to experience boredom/ relaxation, considered an experience of higher quality than apathy. As the level of challenge increases, the experience moves toward control. In contrast to this, when challenges are greater than the skills required by the person, the experience of worry/ anxiety is more likely. Then as the skill level increases, the experience moves toward arousal. Therefore, based on this model, flow states are believed to be accessed when skills and challenges are both high and in equilibrium, resulting in an experience of the highest quality [ 9 ].

Csikszentmihalyi’s flow model [ 7 ] describes psychological states in terms of challenge level and skill level.

Nonetheless, flow rarely occurs in everyday life because challenges and skills are rarely balanced, but even these two parameters do not guarantee flow. Therefore, flow requires activities to have a further set of particular criteria [ 9 ]. Firstly, the activity typically requires learning of skills, and have clear goals with quick and unambiguous feedback. This affords a sense of control over reality by understanding what needs to be done and how they are performing. This activity design also works best when concentration and involvement is facilitated by separating a person from their everyday existence by focusing on the particular reality of the activity, such as particular uniforms and special rules of the activity that are not necessarily relevant to everyday living [ 9 ].

People in flow mention that they become so absorbed in the activity that they do not have any attention to spare to become distracted by anything else. People have also mentioned a collection of other psychological phenomena associated with states. These include: (a) a feeling of control over the activity; (b) an experience of time distortion, in which a person loses awareness of how time is passing (c) the removal of self-consciousness in which a person loses the awareness of themselves as well as thoughts of everyday problems; (d) a feeling of transcendence where the person feels a sense of unity with the activity. See Table 1 for a list of full 9 components.

Nine components associated with the flow state experience [ 9 ] (Csikszentmihalyi, 1990).

Therefore, when a person has a perceived adequacy of skills matched with above average challenges, as part of a goal-directed, rule bound system that provides clear feedback, the person can find complete absorption that removes the possibility of any distractions from thoughts irrelevant to the task at hand. In this focused space a person has an opportunity to find such a level of immersion in the activity that they will feel an inspired sense of control, a complete removal of self-consciousness, a distortion of time and a feeling of transcendence.

Furthermore, it has also been found that flow states can be reached by any person performing any sort of task as long as they can ascertain an adequate level of skill. These levels of skill require an expertise that can afford the smooth performance state associated with flow and consequently with higher expertise is believed higher flow values [ 10 ]. Many people were studied in many different situations and all were able to achieve the optimal experience from the activity. Flow states have become such common place in all areas of society that people use many ways of describing the state such as “wired in”, “in the groove”, “in the moment” and “the zone” to name a few. This experience has typically been described throughout the ages as forms of religious fervor but now has moved into the current day through many other forms of engaging activities. Flow has been recorded in everything from business transactions, sports, video gaming, music, art and yoga. These flow states all share in a series of similar characteristics that were attributed to flow by Csikszentmihalyi. It is the subjective challenges and skills, not the objective ones, that impact on the quality of a someone’s experience [ 8 ]. Numerous studies have further highlighted the similar subjective experience of flow states in various activities, such as sport [ 11 ], gambling [ 12 ], skateboarding [ 13 ], education [ 14 ] to name a few. No matter what the activity, the elicitation of this flow state is considered by many to be the “Holy Grail” of performance [ 15 ].

1.1. Environmental Influences on Flow

Even when one has satisfied the conditions stipulated as necessary to reach the flow state, this however still does not conclusively answer how certain people are able to reach this state nor why and whether all people are able to attain such a state [ 16 ]. One element noted by Csikszentmihalyi that influences entrance into flow states is the level demanded by the critical implications of the activity [ 9 ]. This has been shown to ascribe to a normative continuum to the flow experience based on the task’s personal importance. For example, surgery and mountain climbing are highly critical tasks, which are more often reported to result in intense, ecstatic flow experiences whereas absorbing yet less critical tasks such as reading, and video games have less intense flow experiences.

Additionally, flow states have been shown to be moderated by the level of perceived importance a person places on a task. A study by Engeser and Rheinberg [ 17 ] showed that importance impacts the skill/ challenge requirements. During activities considered important such as exams, flow was high when the challenge was low while activities considered less important such as playing Pac-Man, flow was highest when there was a skills/ challenge balance but low when the challenge was too low or high. Additionally, this study showed the importance of achievement motives, based on the risk taking models of Atkinson [ 18 ], who showed how the explicit motive of fear of failure and the implicit motive of hope for success influenced the preference towards a balance of challenge and skill. In particular, people with the hope for success are more likely to experience flow during balanced skills/ challenge task compared to individuals high in fear of failure who experience less flow when balanced.

In considering these additional implications of criticality, importance and achievement motives, these lead to the introduction of environmental aspects such as the role of the task. For instance, how do these elements apply to work compared to recreational task? A study by Csikszentmihalyi and LeFevre [ 19 ] showed surprisingly that flow was three times more likely to occur during work than recreation. However, even within work it depends on the role. For instance, managers reported the highest levels of flow in work while general workers reported the highest level in recreational flow. Furthermore, a recent study by Viljoen [ 20 ] of part time and professional musicians on the experience of flow looked at these elements to show the differences in their approach to the task. Occupational musicians showed a significant connection between mindfulness and frequency of playing which is associated to accessing flow. Yet, part time musicians found that a professional musician’s occupation became routine and likely inhibited flow. To clarify, mindfulness has described as a connecting bridge between our mind and the present moment, allowing the person to stay aware of what is happening in that very moment [ 21 ]. Therefore, mindfulness appears to share similar attributes that may support flow state facilitation. Additionally, the struggle of financial security for occupational musicians placed stress on many musicians which also was distracting from achieving flow states. Therefore, it is worth considering the difference of recreational and occupational roles and the related levels of task frequency regarding perceived expertise when measuring flow states.

When delving further into what flow is and how far reaching and common flow states are in modern society, it is also important to understand why flow is so relevant to modern day society. In the modern workplace, there are so many opportunities to be distracted from work with messages, meetings and social media, it is difficult to not become distracted or overwhelmed. When in a flow state, the individual is considered to perform at their full capacity [ 22 , 23 ]. Flow has commonly been associated with intense concentration [ 9 ], a higher behavioral efficiency and creativity [ 24 ], and heightened sense of playfulness [ 25 ]. Furthermore, the intrinsic rewards associated with autotelic experience is likely to increase learning efficiencies [ 24 ], as well as better remembering of the experience and also more likely to seek such experiences more often [ 9 ]. This helps drives the person to ever-higher levels of complexity in the challenge of the activity, ultimately improving their skill level. Such increases have also been shown to impact positively on the associated group with many successful scientists, sports stars and artists mentioning flow as relevant to their work and improving their performance whether it be in sports, arts or workplace productivity [ 9 ]. Flow is also characterized by an elevated sense of self-control [ 26 ] and higher positive subjective experiences [ 7 ].

1.2. Flow Measurement

The primary method of studying flow has been through questionnaires as well as interviews for more qualitative explorations. For example, Larson and Csikszentmihalyi [ 27 ] developed the experience sample method (ESM) which would ask participants to mark in real time at certain times throughout their day of their flow experience. The problem with this and other methods is, as was already stated, flow states require acute concentration to the point where little to no attentional resources is misallocated. Also, the individual experiences a loss of self-consciousness where self-reflective thoughts and fear of social evaluation are not present. Therefore, the introspection necessary for these measuring techniques has the danger of inhibiting the flow experience as it requires resources to be allocated to a different cognitive set as these are retrospective by nature [ 28 ].

Since ESM, the Flow State Scale (FSS) was introduced, which operationalizes flow by transforming it’s nine elements into dimensions that load equally on a composite flow score [ 29 ]. The FSS considers flow as a ‘degree’ of flow on a continuum instead of a discrete ‘peak’ experience, which can be used to portray the experiential quality as a level of intensity of flow within the activity [ 3 ]. The intensity of the flow experience is considered to elevate as more of the nine elements increase in score. The FSS is typically given at the end of a task in order not to force the participant out of the state during the task, however, people will experience a range of affective states across trial periods [ 30 ]. Self-reported flow experience scales at the end of a task measure the experience across the whole task rather than for a particular time period. This may further be influenced by the recency effect in memory which may color the memory of the entire trial by the most recent experience toward the end of the trial [ 31 ]. Such pitfalls of studying the dynamics underpinning flow states limit how far researchers explore this elusive state to optimal performance and our understanding of consciousness. Researchers have since begun to address this limitation through the use of psychophysiological methodologies, which focus on the expression of psychological phenomena in bodily processes, to explore the dynamic nature of flow experience throughout the entire task.

Psychophysiological measures—such as hypnosis, meditation and sleep—have been employed to explore the more complex physiological aspects of human consciousness. These measures include electrocardiography (ECG), electromyography (EMG) and skin conductance and have begun to be utilized in the study of flow states. More recently electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) are shedding new light on the neurocognitive elements of flow states. However, these studies have not accumulated enough evidence to define a common acceptance of the neurocognitive functioning and thus researchers continue to address flow states from different methodological backgrounds and these different motivations result in differing perspectives. Select studies have now begun to measure flow states and demonstrate the psychological effects of flow with physiological results utilizing various physiological variations to justify experimental design decisions, yet this results in conflicting results from multiple research queries. Therefore, during this exploratory phase, precise research questions are still ill-defined due to the disparate results.

1.3. Flow Neurocognitive Mechanisms

As flow research has continued to delve deeper into its neural functioning, theorists have naturally moved to explain the neurocognitive mechanisms underpinning the state. Dietrich [ 32 ] proposed a flexibility/ efficiency trade off, which addresses the balance between implicit and explicit processing systems used to acquire, memorize and represent knowledge [ 33 ]. Theories of implicit/ explicit processing has been guided by the modern understanding on neuroscience which assumes a more hierarchical development of cognitive functions where an increase of integrated neural structures continues to increase the level of complex processing. Therefore, Dietrich [ 32 ] introduced the first neurocognitive model for flow states as the transient hypofrontality hypothesis (THH) which considered flow a state of transient downregulation of the highest cognitive hierarchical component, the prefrontal cortices, defining flow processes in the form of transition from explicit to implicit information-processing systems.

The majority of research [ 34 ] have found a consensus about the nature of the explicit system, different to the implicit system, as a rule based system linked to language function and conscious awareness across many tasks, e.g., the serial reaction time task [ 35 ], the dynamic control task [ 36 ] and many others. However, there is still contradictory evidence found in the explicit reasoning ability of Köhler’s apes [ 37 ] despite their presence of language. Nonetheless, whilst verbalizability appears to be the general standard, a better theoretical principle is still needed for conscious awareness. Conscious awareness has been described along similar lines as the implicit and explicit system with both on and offline systems that work to establish consciousness. Systems offline to consciousness are reflexive, rigid and fast responding, such as a frog snapping at a fly. However, as it is organizationally inefficient to house the ever-increasing number of complex reflexes, a more effective system proposed would be to include a temporary buffer that enables the organism to examine multiple representation of the plan of action before making a decision [ 38 ].

Conscious online elements appear to share a close relationship with working memory and executive control. Executive control directs our attention and the working memory. It also links the past, present and future by providing a moment-to-moment permanence. Findings on the association between the prefrontal cortex with this prevailing model was developed by Crick and Koch [ 38 ] which states that conscious awareness can only exist if the brain activity projects to the prefrontal cortex. Crick and Koch’s theory however is not a complete theory of conscious awareness and therefore we are relegated to using the operational definition that explicit processes are able to be explained verbally [ 38 ].

Studies have started identifying the prefrontal regions involvement in the explicit system due to evidence of the dorsolateral prefrontal cortex (DLPFC) acting both as a working memory buffer for the content of consciousness, as well as selecting content through the executive attentional network [ 39 , 40 ]. The medial temporal lobe structures have also been identified as relevant underlying circuitry [ 41 ]. An argument has been presented that the explicit system is a more recent evolutionary occurrence and present in animals with more highly developed prefrontal areas [ 42 ]. Support is found for this in the late phylogeny and ontogeny development of the prefrontal cortex [ 43 ]. Furthermore, the structure of information processing is known to be hierarchical and due to the sophistication of the explicit knowledge representation, such higher order structures are believed to be localized in the prefrontal areas [ 42 ].

Two distinct parallel processing tracts have been identified that traverse the brain and process the incoming information differently. The emotional tract processes more typically in a non-algorithmic skill-based manner that attaches values to help evaluate the biological significance of the information. The second tract performs detailed featured analysis in a computational mode free from any interpretations of salient information. Whilst both pathways begin to converge at the thalamus, the cognitive pathway feeds through the hippocampal formation and temporal, occipital and parietal cortices (TOP), helping provide a degree of selective attention required to process incoming information [ 44 ].

As connections continue to take place along the hierarchical pathways, full convergence appears to occur at the Dorsolateral Prefrontal Cortex (DLPFC) [ 45 ]. The DLPFC is primarily involved in executive functioning by enabling higher functionality such as self-reflective consciousness, abstract thinking, and theory of mind [ 46 ]. Furthermore, it plans, formulating appropriate strategies and subsequently directs the motor cortices to initiate the process. It is at these prefrontal functioning in which the control over the cortices are the most sophisticated. The DLPFC is also responsible for temporal integration [ 47 ], directed and sustained attention [ 48 ], and working memory [ 45 ], which facilitate an intricate cognitive framework that actively attends to information, thus affording a buffer to hold such information in mind, whilst organizing it in space-time [ 40 ].

This cognitive tract is broken up into two attentional tracts of its own: Top down and bottom-up processing. As explained by Corbetta and Shulman [ 49 ], voluntary shifts of attention are thought to be mediated by the dorsal frontoparietal system resulting in goal-directed, “top-down” signals arising from knowledge about the current activity such as finding your way home. On the other hand, the ventral frontoparietal system mediates the automatic “bottom-up” capture of attention guided by salient properties inherent in the stimuli, such as your unique and alarming ringtone. The DLPFC has been shown to exhibit a top-down functionality which inhibits maladaptive and inappropriate cognitive and emotional behavior [ 50 ]. The frontal lobes appear to be based on more universal principles which inhibit people from compulsively acting on immediate cues [ 51 ]. Therefore, the frontal lobes help free us from slavery to direct environmental triggers. It is the inhibitory abilities of the top-down processes that allow a person to remain task focused and not be guided by more salient bottom up processes [ 52 ].

1.4. Neurocognitive Models of Flow

The two predominant neurocognitive theories of flow states have helped guide flow research to better understand its function in order to be able to further support access and entry into flow. The first, transient hypofrontality hypothesis (THH) by Dietrich [ 32 ] proposes that during flow states, these explicit executive functions of the frontal cortices are inhibited. This reduction of frontal activity is expected to reduce interference from explicit processing such as self-referential thought and thereby freeing up more resources to be dedicated to the faster implicit processing system such as actioning of automatized processes. Recently studies have begun using psychophysiological measures to test the THH of flow experiences with a variety of testing for Electroencephalography (EEG) with shooting [ 53 ], arithmetic [ 54 ], video games [ 55 ] and memory tasks [ 56 ], as well as Functional Magnetic Resonance Imaging (fMRI) for arithmetic tasks [ 57 , 58 ]. For instance, Hirao [ 59 ] conducted a near-infrared spectroscopy (fNIRS) on occupational therapy students who completed a verbal fluency test. Whilst there were only 2 channels in the study (FP1/2), the results supported the THH in which a negative correlation was associated between higher flow states resulting in a suppression of prefrontal activity.

However, the synchronization theory of flow (STF) proposed by Weber and Tamborini [ 60 ] disputes the THH due to many flow-like activities such as hypnosis and meditation showing strong frontal activity in neuroimaging studies occurring when in these altered states of consciousness as well as in flow studies [ 61 ]. Therefore, STF instead focusses on the neuronal efficient, feature binding processes of synchronizing neurons and networks to more effectively communicate and create “holistic, higher-order experiences” that resemble flow states.

STF’s foundation is based on Posner et al., [ 62 ] tripartite theory of attention that focuses on the neurocognitive structures of attention including the frontal and parietal cortices relating to “alerting” (the process of becoming aware of a stimulus), the top-down componentry of the dorsal attention network including the superior and inferior parietal lobes, the frontal eye fields, and the superior colliculus for “orienting” (allocating attentional resources to a stimulus), and the prefrontal “executive” regions for goal-directed processing. A few studies to date have provided support for STF [ 63 , 64 , 65 ], with one of the first fMRI studies by Klasen et al. [ 66 ], who broke down a video game into five operationalized elements of flow that can be observed as characteristics of the activity to find activation in relevant attention and reward structures that support the STF.

Whilst there are fundamental differences in both THH and STF, they do share a similar belief in the role of the emotional tract in managing automatization of implicit processes as well as intrinsic reward. Implicit categorization has found less agreement with these theories than what has been found for the explicit system. While the role of explicit knowledge in consciousness is thought to create a more behaviorally flexible global workspace to test hypotheses [ 67 ], the role of implicit knowledge is believed to be more task-specific and thus less flexible due to the difficulty to access from other parts of the system [ 68 ].

One thing agreed on is that the implicit system is not accessible to the conscious awareness [ 54 , 69 ]. However, unlike memory theorists [ 70 ] (e.g., Schacter) who hold that ‘implicit’ implies no conscious awareness of the details or even that a memory was stored, a weaker criterion is used for category learning, which only requires that the nature of learning has no conscious access [ 34 ]. However, there may be an awareness of some learning occurring because trial-by-trial feedback is typically present. For instance, when a participant receives feedback that their action was correct, they will understand and be conscious of a learning having taken place. Implicit categorization theory is relevant to flow experiences as the literature has stated such states require clear and timely feedback. When feedback has been removed people are then restricted to verbalized rules [ 34 ].

There has been a lot of research also supporting the implicit system as experience or skill based and conveyed through performance rather than verbally [ 39 ]. Implicit categorization learning was shown in a study by Spiering and Ashby [ 71 ] to provide optimal training results when the challenge level of the task begins with difficult examples and then move to easier examples after it is understood that no simple verbal rule is sufficient. Rather than getting locked into a verbalized single rule, implicit learning allows decision making to take a more integrative approach from different perceptual dimensions. This information integration approach is maximized only at the pre-decisional stage as two or more stimulus components are integrated [ 72 ].

While it has typically been assumed that an exemplar-similarity-based system should dominate information-integration tasks [ 73 , 74 ], COVIS instead assumes a procedural-learning system. COVIS, an acronym for “competition between verbal and implicit systems”, which describes the process of the verbal system dominating initially due to the strength of its connections but with task repetition the implicit system supersedes the explicit verbal system bias. Yet both systems remain active retaining a significant proportion of categorization judgments after learning is complete [ 72 ].

Although the neural substrates are less clear for the implicit system, the basal ganglia (BG) have most often been critically associated with implicit system [ 41 ]. The BG are interconnected masses of gray matter positioned in the interior regions of the limbic cortices and in the upper part of the brainstem. This key region of the BG receives all extrastriate visual cortex projections, with about 10,000 visual glutaminergic connections to each caudate cell in the striatum [ 75 ]. Projections are then sent to various cortical premotor and prefrontal regions via two synaptic pathway convergences. The first synaptic connection is via the globus palladus and substantia nigra pars reticula which has dopaminergic connections while the second synapse of the ventral anterior nucleus of the thalamus projects off to premotor areas, specifically Brodmann’s Area 8 [ 76 ].

COVIS places an emphasis on this synaptic convergence as a critical site of procedural learning [ 77 ]. In particular, it appears there are three factors which contribute to cortical-striatal strengthening via long term potentiation (LTP): strong presynaptic; and postsynaptic activation; as well as dopamine release [ 78 , 79 ]. While presynaptic and postsynaptic activations are considered to play an important role for LTP via stimulus driven high threshold sensory cortical cells [ 80 ], dopamine is considered more as a reward-mediated training signal [ 79 ]. These synapses however weaken through long term depression if either postsynaptic activation or dopamine release is not present [ 78 ]. This could occur for example if an incorrect response is given resulting in an absence of dopamine release or if only a weak response is recorder by the visual cortical cell. Maddox et al., [ 81 ] showed support for an interesting prediction by this three-factor model that if feedback was delayed by more than 2.5 s then information integration learning would be severely inhibited. This appears to lend support to the notion that flow states may require timely and accurate feedback whereas explicit learning in rule-based tasks of equal difficulty could sustain delays.

Implicit systems are believed to process parallel tasks due to the limitations of bandwidth that exist in the working memory of the explicit systems [ 82 ]. Cowan presented evidence of the working memory capacity with a 4 ± 1 limit, after rehearsal and chunking were catered for [ 83 ]. Therefore, the explicit system appears to be capacity limited, where information demands are too great parallel tasks are collapsed into fewer chunks deeming some information inaccessible [ 82 ]. Implicit systems on the other hand seem to not share the same limitations. When learning a new task such as driving a car, this is a multidimensional task with many elements working in parallel. While the cortex is considered to be utilized for managing the input of novel information due to the requirement of goal directed attention and flexibility, working memory typically would be overwhelmed as instructions typically involve more than four independent bits of information. Therefore, instructions could be broken down into smaller components that could then be combined into larger chunks once the skill is sufficiently acquired. The explicit instructions would form a mental representation of the task that requires the premotor, primary motor and parietal cortex, as well as the cerebellum, to execute it [ 84 ]. Because of the limited ability to combine items into chunks, learning slows down due to capacity restrictions. The BG are believed to be a passive observer during this time building its own representation of the action [ 85 ]. After sufficient practice, neural control is gradually shifted to the BG [ 86 ] and also the supplementary motor cortex, motor cortex, thalamus, and hippocampus [ 84 ]. Ultimately, this internalizes the pattern of this activity into “muscle memory” and thereby affords the BG primary control without much reliance placed on the prefrontal explicit regions [ 87 ]. This internalization frees up computational space of the executive function for other activities such as observing the surrounding environment, due to a lessening of demand from working memory. This may be useful for flow as it frees the person from needing to focus on the skill of the task and gives more buffering room for anticipating the potential challenges of the task.

Furthermore, a basic level of skill acquisition is needed to have a flow experience, as the implicit system requires a series of learnt specialized and independent response patterns to output [ 3 ]. These automated stimulus response procedures are believed to require many hours of highly dedicated practice. Learning of automated responses takes time because of the limited ability of the explicit working memory to transfer specialized and reflexive response patterns to the implicit system due to capacity restrictions [ 32 , 86 ]. Automaticity, in which thoughts and behaviours occur without the need for conscious guidance, can be both conscious and unconscious [ 88 ]. Unconscious automaticity are defined as automatic processes that do not require any willful initiation and operate independent of conscious control [ 89 ]. This is exemplified with a priming that biases further processing of an event without the person necessarily even consciously aware of the connection. Such as seeing a beer advertisement along with a hot day and suddenly realizing you are thirsty and want a beer.

Conscious automaticity are automatic thoughts and behaviours that provide efficient implementation of an action by providing faster processing through the removal of conscious monitoring as well as the use of minimal attention capacity [ 89 ]. The modern standard for determining automaticity is if the behaviour can be produced in parallel and without attention [ 88 ]. Skill acquisition is generally conscious labored and slow but becomes automatic with consistent and frequent practice. These mentally disparate processes are then repackaged into a fluid arrangement of actions that can be set off by a single thought [ 90 ]. Furthermore, automaticity enables assumptions to be made based on experience which creates greater outcome predictability. The more a person monitors their intentions throughout their actions, the more their experience will be consciously willed and nonautomatic.

A key component of the BG, the dorsal striatum, has been associated with the role of automatized implicit learning, in particular, both STF and THH models have shown strong support not only for automatization of implicit functions but also dopaminergic influence in which fMRI flow studies have exhibited BG and striatal activation [ 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 ], along with increased striatal dopamine during flow states in support of the role of implicit control of BG [ 91 , 92 ]. The striatum’s volume increased after a skill acquisition period of a video game task [ 93 ]. It is also assumed that the striatum is an early development in human evolution because of its central location and action as an input nucleus for the BG. The caudate nucleus of the striatum has also been shown as the primary input structure of the procedural learning system using the COVIS model [ 77 ]. It is long known that to effectively multitask two things simultaneously requires one task to be implicit [ 94 ]. Thereby, implicit systems are ultimately more efficient than their explicit counterpart. People that have entered flow states often refer to an automatic processing in which they report task focused behaviour without conscious thinking which suggests a form of frontal inhibition required for successful entry into the state.

Furthermore, a key site of pleasurable experience of rewards is associated with the dopamine rich striatum, due to dopamine’s role in rewarding behavior by predicting rewarding outcomes that would result in reward-seeking experiences [ 95 ], which lends support to the autotelic nature of flow states. Because of the autotelic nature and high criticality of flow, we are moved to consider the role of novelty as relevant to the induction of flow states. In the novelty hypothesis, during a period of high criticality, when a person is exposed to a new situation that results in a challenge that is equal to the skill level, the person may be pushed up into a level in which their skill is just below the level of challenge being presented. This additional stimulation may be enough to absorb the final amount of explicit buffering systems in order to fully immerse the performer in the task.

2. Exploration of Flow Functions

As flow states are considered a complex combination of multiple cognitive features it has been difficult to delineate specific neurocognitive markers. Studies for the most part still rely on a mix between psychophysiological measures and probing post-task self-report questionnaires. The conflict still remains that as soon as the participant is asked about their experience, they are forced to self-reflect which will move them out of the flow state. We can therefore begin to break down some of the key neurological elements to test whether they can be defined as key elements of flow states in order to further identify key elements that may be relevant to the neurocognitive functionality of flow states. Particular elements of flow to be defined are that it occurs within an activity which is balanced with an individual’s abilities, whilst fully immersed in the task and self-referential thoughts are completely inhibited. However, we can look at previous studies looking at similar cognitive functions such as expert performance, creativity, focused attention and mental workload to help delineate neurocognitive landmarks that will help us identify the elements of flow activity.

The EEG is a well validated measure for examining psychological states during skilled motor performance [ 96 , 97 ]. In particular, results have highlighted the left frontal and temporal regions as playing key roles in expert performance with increased alpha power in EEG occurring in expert marksmen compared to novice shooters [ 96 , 97 , 98 ]. EEG has also been used across a range of activities including weightlifting [ 99 ], golf [ 100 ] and archery [ 101 ] all revealing a reduction in left hemispheric activity. In a recent study, a comparison of neuro-anatomical characteristics also showed that expert divers have significantly increased cortical thickness in the left superior temporal sulcus compared to the non-athlete group [ 102 ]. The superior temporal gyrus houses several important cortical structures, including Wernicke’s area known to be involved in the comprehension of language. To follow on, this pattern of increased alpha activity in the left temporal region has been most commonly interpreted as representing a reduction in cortical activations, reducing verbalizations associated with the left brain and enabling more resources to be allocated to the visual-spatial processes of the right brain [ 103 ]. This has been further supported by lower coherence estimates of left temporal regions with motor regions by expert marksmen [ 104 ]. This pattern suggests less cortico-cortical communication and a suppression of analytic processing influence thus simplifying a complex process and alleviating the need for a division of cognitive resources.

Additionally, a key antecedent of flow utilizes the challenge/skills-balance which indicates a state of high mental workload from deep involvement in the task [ 9 ]. This has been shown in psychophysiological studies on flow, in which decreased heart rate variability was shown during challenge/ skills-balance in a knowledge task [ 105 ]. EEG has also been used to evaluate mental workload in which a reduction of alpha activity and an increase of theta is present due to the tasks increased difficulty levels [ 106 , 107 ]. Alpha frequencies are categorized into three frequency bands (8–13 Hz, 8–10 Hz, and 11–13 Hz). Alpha activity in general (8–13 Hz) represents lower levels of consciousness and awareness, while an alpha reduction results in increased mental activity [ 108 ]. The low alpha band (8–10 Hz) is associated with the mechanisms of arousal, attention and effort as well as general cognitive processing while high alpha (11–13 Hz) selectively acts according to the encoding of the stimulus [ 109 ].

Sports performance has also been shown to improve when implementing hypnotic techniques using flow state suggestions [ 110 , 111 , 112 ]. It is not yet understood how hypnosis increases performance or the experience of flow. One suggestion by Crawford and Gruzelier [ 113 ] is a shift is made from an analytical think style to become more holistic after hypnosis, allowing access to processes that are important for athletic performance. Shifts from the left (analytical verbal and conscious side of the brain) to the right hemisphere (holistic, nonverbal, imaginative side of the brain) have been shown during hypnosis [ 114 ]. It has been further shown that there are strong correlations between hypnosis with absorption [ 115 ]. A correlation has also been shown between absorption and dissociation, in which the ability to become absorbed in a task is another way to induce dissociative control [ 116 ]. Task absorption and dissociation are considered key component to the higher levels of the flow phenomenology.

Additionally, theta activity has been shown as relevant for evaluating cognitive processing during flow like tasks such as meditation. Lutz et al. [ 117 ] experienced meditators and novices were tested at the beginning and end of a three-month meditation retreat, using an attentional blink test. In experienced meditators, results significantly improved whilst presenting increased theta phase-locking, i.e., a reduced variability of theta phases across trials. These results are considered to show a more stable execution of neural processing [ 118 ]. Furthermore, multiple fMRI studies have highlighted attentional networks providing support for increased activity in prefrontal networks during focused [ 119 ], meditation-like attention [ 120 ].

Positive affect and motivational orientation, two elements associated with flow phenomenology, have also found links to changes in frontal EEG asymmetry [ 121 ]. In particular, increased left alpha frontal activation was correlated with approach-related motivation [ 122 ]. This is also shown by higher activity of the frontal left associated with trait measures of behavioral activation [ 123 ]. Specifically, positive emotions were correlated with high left frontal activity, while negative emotions were correlated with increased relative right frontal activity [ 124 ]. Ultimately a pattern of the relationship between frontal EEG asymmetry, motivational direction, and affective valence has been shown for performance settings.

3. Flow Facilitation

To further test the neurocognitive mechanisms of different states and in particular flow states, technologies such as transcranial direct current stimulation (tDCS) have been utilized to provide a clearer understanding on the underlying processes. TDCS is a non-invasive form of brain stimulation that alters cortical excitability based on the direction of current flow at subthreshold levels of the neuronal membrane potential. Anodal stimulation has been shown to increase cortical excitability over the region of electrode placement, while cathodal stimulation inhibits the region’s neuronal excitability. The level of neuronal activity modulation depends on the current density, which is governed by elements such as current strength and electrode variability. Furthermore, the length of after-effects is dependent on stimulation duration. i.e., excitability effects have been shown to last up to 60 min [ 125 ], yet results have also shown effects fading after 30 min of stimulation [ 126 ].

While tDCS has been used for clinical settings such as depression, Parkinson’s disease and pain management, it has also shown to improve performance in normal participants including working memory [ 127 ], visuo-motor learning [ 128 ], and categorical learning [ 129 ]. Many experimental paradigms have been implemented on motor learning including the more frequently used: skill acquisition and adaptation [ 130 ]. New motor skill acquisition involves the ability to execute new motor abilities that improve performance beyond previous levels. Skill acquisition can take weeks or months while skill can decrease due to a lack of ongoing practice. Strategies that improve skill acquisition and retention can be of great scientific and practical interest. For instance, Clark & Coffman [ 131 ] showed a unique use of anodal tDCS over parietal and frontal regions for improving skill acquisition speeds by enhancing performance in threat detection within natural scenes that are typically relevant for the effective management of many skills throughout our everyday and specialized work tasks.

Adaptation for sensorimotor tasks, unlike skill acquisition, addresses a new framework of well learned movements and spatial goals instead of requiring new capabilities of muscle activations to be updated. While adaptation can be assisted with explicit control processes, it can also update entirely implicitly [ 132 ]. Functionally, adaptation focusses on an error decrease by changing challenge levels to facilitate a return to the previous level of performance, while participants movements are updated due to changes in motor outputs or sensory inputs. TDCS has been shown specifically to enhance adaptation of real world cognitive multi-tasks by specifically targeting the goal-directed dorsal attention network by right parietal anodal stimulation and thereby resulting in improved task performance [ 133 ]. It is important to acknowledge that tDCS has been shown to result in ceiling effects for experts compared to novice performers in which at a certain level of expertise, tDCS has been shown to not have a significant impact on performance [ 134 , 135 , 136 , 137 ].

More recently tDCS has begun to be implemented to explore its potential role in facilitating flow. In a recent study, Ulrich et al., [ 138 ] facilitated higher flow scores for people experiencing low flow after stimulating them during an arithmetic task with a prefrontal (fpZ) anodal tDCS to target the medial prefrontal cortex (MPFC). This is an interesting result as Ulrich et al., [ 57 ] showed support for the THH with a deactivation of MPFC during an fMRI study on flow, interpreted as a reduction of explicit functionality of self-referential activity, yet only the excitatory anodal tDCS over the prefrontal regions resulted in an enhancement toward flow states. This was uniquely for people specifically experiencing low flow in which more research is needed for the general population. A tDCS study by Gold & Ciorciari [ 139 ] explored flow for novice gamers who typically didn’t find during videogames and expert video gamers who did. The tDCS set up focused on an anodal right parietal and cathodal left frontal stimulation that also showed support for flow state induction, this time in alignment with a deactivation of MPFC associated with high flow states. Therefore, we see here an introduction into the facilitative role of tDCS experience enhancement that can potentially improve people’s skill level in order that the participant could reach the skill-challenge balance [ 133 ] that allows for a greater movement into flow states [ 140 ]. Other transcranial stimulation technologies may be worth considering for future research on flow that may also show a facilitative effect such as transcranial alternating current stimulation (tACS) which stimulate at a specific frequency and has shown to result in entrainment of neural networks to improve cognitive performance such as spatial reasoning [ 141 ] and working memory [ 142 ].

4. Conclusions

This collection of results from the literature begins to show what type of elements in a person’s professional environment need to be taken into consideration to help facilitate flow along with an understanding of the importance of supporting a transference of skills from explicit knowledge systems to implicit procedural systems. The literature appeared to highlight the role of the BG and its related components as a key research direction in which to further explore to enable a greater facilitation of skill automaticity that appears highly related to flow state.

Furthermore, there appears to be support in the literature for a particular neurocognitive activity pattern for flow induction in which expertise and flow studies appear to show a hemispheric shift away from the frontal left evidenced by a resulting reduction of left frontal activity and an increase in frontal alpha while facilitating a greater allocation of neuronal resources to the visual-spatial processes of the right brain, thus resulting in higher levels of performance. Recent interventions such as tDCS have been shown to have a positive effect on the facilitation of flow states that have followed this pattern and with more research may prove to be an effective intervention for real life applications as they are low cost, safe and non-invasive. Due to their simple application, it may be possible to conceive a work environment in which people are working at high levels of productivity with low levels of distractibility from low voltage of electricity.

This research received no external funding.

Conflicts of Interest

The authors declare no conflict of interest.

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Research Paper – Structure, Examples and Writing Guide

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Research Paper

Definition:

Research Paper is a written document that presents the author’s original research, analysis, and interpretation of a specific topic or issue.

It is typically based on Empirical Evidence, and may involve qualitative or quantitative research methods, or a combination of both. The purpose of a research paper is to contribute new knowledge or insights to a particular field of study, and to demonstrate the author’s understanding of the existing literature and theories related to the topic.

Structure of Research Paper

The structure of a research paper typically follows a standard format, consisting of several sections that convey specific information about the research study. The following is a detailed explanation of the structure of a research paper:

The title page contains the title of the paper, the name(s) of the author(s), and the affiliation(s) of the author(s). It also includes the date of submission and possibly, the name of the journal or conference where the paper is to be published.

The abstract is a brief summary of the research paper, typically ranging from 100 to 250 words. It should include the research question, the methods used, the key findings, and the implications of the results. The abstract should be written in a concise and clear manner to allow readers to quickly grasp the essence of the research.

Introduction

The introduction section of a research paper provides background information about the research problem, the research question, and the research objectives. It also outlines the significance of the research, the research gap that it aims to fill, and the approach taken to address the research question. Finally, the introduction section ends with a clear statement of the research hypothesis or research question.

Literature Review

The literature review section of a research paper provides an overview of the existing literature on the topic of study. It includes a critical analysis and synthesis of the literature, highlighting the key concepts, themes, and debates. The literature review should also demonstrate the research gap and how the current study seeks to address it.

The methods section of a research paper describes the research design, the sample selection, the data collection and analysis procedures, and the statistical methods used to analyze the data. This section should provide sufficient detail for other researchers to replicate the study.

The results section presents the findings of the research, using tables, graphs, and figures to illustrate the data. The findings should be presented in a clear and concise manner, with reference to the research question and hypothesis.

The discussion section of a research paper interprets the findings and discusses their implications for the research question, the literature review, and the field of study. It should also address the limitations of the study and suggest future research directions.

The conclusion section summarizes the main findings of the study, restates the research question and hypothesis, and provides a final reflection on the significance of the research.

The references section provides a list of all the sources cited in the paper, following a specific citation style such as APA, MLA or Chicago.

How to Write Research Paper

You can write Research Paper by the following guide:

• Choose a Topic: The first step is to select a topic that interests you and is relevant to your field of study. Brainstorm ideas and narrow down to a research question that is specific and researchable.
• Conduct a Literature Review: The literature review helps you identify the gap in the existing research and provides a basis for your research question. It also helps you to develop a theoretical framework and research hypothesis.
• Develop a Thesis Statement : The thesis statement is the main argument of your research paper. It should be clear, concise and specific to your research question.
• Plan your Research: Develop a research plan that outlines the methods, data sources, and data analysis procedures. This will help you to collect and analyze data effectively.
• Collect and Analyze Data: Collect data using various methods such as surveys, interviews, observations, or experiments. Analyze data using statistical tools or other qualitative methods.
• Organize your Paper : Organize your paper into sections such as Introduction, Literature Review, Methods, Results, Discussion, and Conclusion. Ensure that each section is coherent and follows a logical flow.
• Write your Paper : Start by writing the introduction, followed by the literature review, methods, results, discussion, and conclusion. Ensure that your writing is clear, concise, and follows the required formatting and citation styles.
• Edit and Proofread your Paper: Review your paper for grammar and spelling errors, and ensure that it is well-structured and easy to read. Ask someone else to review your paper to get feedback and suggestions for improvement.
• Cite your Sources: Ensure that you properly cite all sources used in your research paper. This is essential for giving credit to the original authors and avoiding plagiarism.

Research Paper Example

Note : The below example research paper is for illustrative purposes only and is not an actual research paper. Actual research papers may have different structures, contents, and formats depending on the field of study, research question, data collection and analysis methods, and other factors. Students should always consult with their professors or supervisors for specific guidelines and expectations for their research papers.

Research Paper Example sample for Students:

Title: The Impact of Social Media on Mental Health among Young Adults

Abstract: This study aims to investigate the impact of social media use on the mental health of young adults. A literature review was conducted to examine the existing research on the topic. A survey was then administered to 200 university students to collect data on their social media use, mental health status, and perceived impact of social media on their mental health. The results showed that social media use is positively associated with depression, anxiety, and stress. The study also found that social comparison, cyberbullying, and FOMO (Fear of Missing Out) are significant predictors of mental health problems among young adults.

Introduction: Social media has become an integral part of modern life, particularly among young adults. While social media has many benefits, including increased communication and social connectivity, it has also been associated with negative outcomes, such as addiction, cyberbullying, and mental health problems. This study aims to investigate the impact of social media use on the mental health of young adults.

Literature Review: The literature review highlights the existing research on the impact of social media use on mental health. The review shows that social media use is associated with depression, anxiety, stress, and other mental health problems. The review also identifies the factors that contribute to the negative impact of social media, including social comparison, cyberbullying, and FOMO.

Methods : A survey was administered to 200 university students to collect data on their social media use, mental health status, and perceived impact of social media on their mental health. The survey included questions on social media use, mental health status (measured using the DASS-21), and perceived impact of social media on their mental health. Data were analyzed using descriptive statistics and regression analysis.

Results : The results showed that social media use is positively associated with depression, anxiety, and stress. The study also found that social comparison, cyberbullying, and FOMO are significant predictors of mental health problems among young adults.

Discussion : The study’s findings suggest that social media use has a negative impact on the mental health of young adults. The study highlights the need for interventions that address the factors contributing to the negative impact of social media, such as social comparison, cyberbullying, and FOMO.

Conclusion : In conclusion, social media use has a significant impact on the mental health of young adults. The study’s findings underscore the need for interventions that promote healthy social media use and address the negative outcomes associated with social media use. Future research can explore the effectiveness of interventions aimed at reducing the negative impact of social media on mental health. Additionally, longitudinal studies can investigate the long-term effects of social media use on mental health.

Limitations : The study has some limitations, including the use of self-report measures and a cross-sectional design. The use of self-report measures may result in biased responses, and a cross-sectional design limits the ability to establish causality.

Implications: The study’s findings have implications for mental health professionals, educators, and policymakers. Mental health professionals can use the findings to develop interventions that address the negative impact of social media use on mental health. Educators can incorporate social media literacy into their curriculum to promote healthy social media use among young adults. Policymakers can use the findings to develop policies that protect young adults from the negative outcomes associated with social media use.

References :

• Twenge, J. M., & Campbell, W. K. (2019). Associations between screen time and lower psychological well-being among children and adolescents: Evidence from a population-based study. Preventive medicine reports, 15, 100918.
• Primack, B. A., Shensa, A., Escobar-Viera, C. G., Barrett, E. L., Sidani, J. E., Colditz, J. B., … & James, A. E. (2017). Use of multiple social media platforms and symptoms of depression and anxiety: A nationally-representative study among US young adults. Computers in Human Behavior, 69, 1-9.
• Van der Meer, T. G., & Verhoeven, J. W. (2017). Social media and its impact on academic performance of students. Journal of Information Technology Education: Research, 16, 383-398.

Appendix : The survey used in this study is provided below.

Social Media and Mental Health Survey

• How often do you use social media per day?
• Less than 30 minutes
• 30 minutes to 1 hour
• 1 to 2 hours
• 2 to 4 hours
• More than 4 hours
• Which social media platforms do you use?
• Others (Please specify)
• How often do you experience the following on social media?
• Social comparison (comparing yourself to others)
• Cyberbullying
• Fear of Missing Out (FOMO)
• Have you ever experienced any of the following mental health problems in the past month?
• Do you think social media use has a positive or negative impact on your mental health?
• Very positive
• Somewhat positive
• Somewhat negative
• Very negative
• In your opinion, which factors contribute to the negative impact of social media on mental health?
• Social comparison
• In your opinion, what interventions could be effective in reducing the negative impact of social media on mental health?
• Education on healthy social media use
• Counseling for mental health problems caused by social media
• Social media detox programs
• Regulation of social media use

Thank you for your participation!

Applications of Research Paper

Research papers have several applications in various fields, including:

• Advancing knowledge: Research papers contribute to the advancement of knowledge by generating new insights, theories, and findings that can inform future research and practice. They help to answer important questions, clarify existing knowledge, and identify areas that require further investigation.
• Informing policy: Research papers can inform policy decisions by providing evidence-based recommendations for policymakers. They can help to identify gaps in current policies, evaluate the effectiveness of interventions, and inform the development of new policies and regulations.
• Improving practice: Research papers can improve practice by providing evidence-based guidance for professionals in various fields, including medicine, education, business, and psychology. They can inform the development of best practices, guidelines, and standards of care that can improve outcomes for individuals and organizations.
• Educating students : Research papers are often used as teaching tools in universities and colleges to educate students about research methods, data analysis, and academic writing. They help students to develop critical thinking skills, research skills, and communication skills that are essential for success in many careers.
• Fostering collaboration: Research papers can foster collaboration among researchers, practitioners, and policymakers by providing a platform for sharing knowledge and ideas. They can facilitate interdisciplinary collaborations and partnerships that can lead to innovative solutions to complex problems.

When to Write Research Paper

Research papers are typically written when a person has completed a research project or when they have conducted a study and have obtained data or findings that they want to share with the academic or professional community. Research papers are usually written in academic settings, such as universities, but they can also be written in professional settings, such as research organizations, government agencies, or private companies.

Here are some common situations where a person might need to write a research paper:

• For academic purposes: Students in universities and colleges are often required to write research papers as part of their coursework, particularly in the social sciences, natural sciences, and humanities. Writing research papers helps students to develop research skills, critical thinking skills, and academic writing skills.
• For publication: Researchers often write research papers to publish their findings in academic journals or to present their work at academic conferences. Publishing research papers is an important way to disseminate research findings to the academic community and to establish oneself as an expert in a particular field.
• To inform policy or practice : Researchers may write research papers to inform policy decisions or to improve practice in various fields. Research findings can be used to inform the development of policies, guidelines, and best practices that can improve outcomes for individuals and organizations.
• To share new insights or ideas: Researchers may write research papers to share new insights or ideas with the academic or professional community. They may present new theories, propose new research methods, or challenge existing paradigms in their field.

Purpose of Research Paper

The purpose of a research paper is to present the results of a study or investigation in a clear, concise, and structured manner. Research papers are written to communicate new knowledge, ideas, or findings to a specific audience, such as researchers, scholars, practitioners, or policymakers. The primary purposes of a research paper are:

• To contribute to the body of knowledge : Research papers aim to add new knowledge or insights to a particular field or discipline. They do this by reporting the results of empirical studies, reviewing and synthesizing existing literature, proposing new theories, or providing new perspectives on a topic.
• To inform or persuade: Research papers are written to inform or persuade the reader about a particular issue, topic, or phenomenon. They present evidence and arguments to support their claims and seek to persuade the reader of the validity of their findings or recommendations.
• To advance the field: Research papers seek to advance the field or discipline by identifying gaps in knowledge, proposing new research questions or approaches, or challenging existing assumptions or paradigms. They aim to contribute to ongoing debates and discussions within a field and to stimulate further research and inquiry.
• To demonstrate research skills: Research papers demonstrate the author’s research skills, including their ability to design and conduct a study, collect and analyze data, and interpret and communicate findings. They also demonstrate the author’s ability to critically evaluate existing literature, synthesize information from multiple sources, and write in a clear and structured manner.

Characteristics of Research Paper

Research papers have several characteristics that distinguish them from other forms of academic or professional writing. Here are some common characteristics of research papers:

• Evidence-based: Research papers are based on empirical evidence, which is collected through rigorous research methods such as experiments, surveys, observations, or interviews. They rely on objective data and facts to support their claims and conclusions.
• Structured and organized: Research papers have a clear and logical structure, with sections such as introduction, literature review, methods, results, discussion, and conclusion. They are organized in a way that helps the reader to follow the argument and understand the findings.
• Formal and objective: Research papers are written in a formal and objective tone, with an emphasis on clarity, precision, and accuracy. They avoid subjective language or personal opinions and instead rely on objective data and analysis to support their arguments.
• Citations and references: Research papers include citations and references to acknowledge the sources of information and ideas used in the paper. They use a specific citation style, such as APA, MLA, or Chicago, to ensure consistency and accuracy.
• Peer-reviewed: Research papers are often peer-reviewed, which means they are evaluated by other experts in the field before they are published. Peer-review ensures that the research is of high quality, meets ethical standards, and contributes to the advancement of knowledge in the field.
• Objective and unbiased: Research papers strive to be objective and unbiased in their presentation of the findings. They avoid personal biases or preconceptions and instead rely on the data and analysis to draw conclusions.

Advantages of Research Paper

Research papers have many advantages, both for the individual researcher and for the broader academic and professional community. Here are some advantages of research papers:

• Contribution to knowledge: Research papers contribute to the body of knowledge in a particular field or discipline. They add new information, insights, and perspectives to existing literature and help advance the understanding of a particular phenomenon or issue.
• Opportunity for intellectual growth: Research papers provide an opportunity for intellectual growth for the researcher. They require critical thinking, problem-solving, and creativity, which can help develop the researcher’s skills and knowledge.
• Career advancement: Research papers can help advance the researcher’s career by demonstrating their expertise and contributions to the field. They can also lead to new research opportunities, collaborations, and funding.
• Academic recognition: Research papers can lead to academic recognition in the form of awards, grants, or invitations to speak at conferences or events. They can also contribute to the researcher’s reputation and standing in the field.
• Impact on policy and practice: Research papers can have a significant impact on policy and practice. They can inform policy decisions, guide practice, and lead to changes in laws, regulations, or procedures.
• Advancement of society: Research papers can contribute to the advancement of society by addressing important issues, identifying solutions to problems, and promoting social justice and equality.

Limitations of Research Paper

Research papers also have some limitations that should be considered when interpreting their findings or implications. Here are some common limitations of research papers:

• Limited generalizability: Research findings may not be generalizable to other populations, settings, or contexts. Studies often use specific samples or conditions that may not reflect the broader population or real-world situations.
• Potential for bias : Research papers may be biased due to factors such as sample selection, measurement errors, or researcher biases. It is important to evaluate the quality of the research design and methods used to ensure that the findings are valid and reliable.
• Ethical concerns: Research papers may raise ethical concerns, such as the use of vulnerable populations or invasive procedures. Researchers must adhere to ethical guidelines and obtain informed consent from participants to ensure that the research is conducted in a responsible and respectful manner.
• Limitations of methodology: Research papers may be limited by the methodology used to collect and analyze data. For example, certain research methods may not capture the complexity or nuance of a particular phenomenon, or may not be appropriate for certain research questions.
• Publication bias: Research papers may be subject to publication bias, where positive or significant findings are more likely to be published than negative or non-significant findings. This can skew the overall findings of a particular area of research.
• Time and resource constraints: Research papers may be limited by time and resource constraints, which can affect the quality and scope of the research. Researchers may not have access to certain data or resources, or may be unable to conduct long-term studies due to practical limitations.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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• Manoj Kumar Pulligilla 1 &
• C. Vanmathi 1  

For smart cities, predicting traffic flow is crucial to lower traffic jams and enhancing transportation efficiency. The smart city needs effective models, highly dependable networks, and data privacy for traffic flow prediction (Traff-FP). The majority of current research uses a central training mode and ignores privacy issue conveyed by distributed traffic data. In this paper, an effective traffic flow prediction (ETraff-FP) is proposed to forecast traffic flow using actual historical traffic data. Initially, pre-processing is carried out using data normalization and handling missing value. The three major components of Traff-FP framework for each local Traff-FP model are recurrent long short-term capture network (RLSCN), federated gated graph attentive network (FGAN) and semantic connection relationship capture network (SCRCN). The long-term spatio and temporal information in each location has been captured by RLSCN, which encompasses constituents like fully connected (FC) layers, convolution, and bidirectional long short term memory (BiLSTM) to collect short-term information. FGAN, which incorporates bi-directional gated recurrent unit (Bi-GRU), exchanges short-term spatio-temporal hidden information while it trains local Traff-FP model using elliptic curve diffie-hellman (ECDiff-H) algorithm. Accordingly, the hyper parameters of ETraff-FP are tuned using extended remora optimization algorithm (EReOA). The ETraff-FP framework is trained and tested with TaxiNYC and TaxiBJ datasets. For simulation, python platform is utilized and various evaluation metrics are analysed. Accordingly, the ETraff-FP framework has reached better improvements with MSE of 8.98% and 10.57%, RMSE of 8.62% and 18.65%, MAE of 2.11% and 10.57%, R2-score of 0.959% and 0.913%, and MAPE of 21.12% and 24.89% against the existing methods using TaxiNYC and TaxiBJ datasets. Overall, the proposed work not only advances the state-of-the-art in traffic flow prediction but also proves the value of enabling effective and efficient traffic management systems in urban and smart city environments.

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Pulligilla, M.K., Vanmathi, C. A traffic flow prediction framework based on integrated federated learning and Recurrent Long short-term networks. Peer-to-Peer Netw. Appl. (2024). https://doi.org/10.1007/s12083-024-01792-x

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Heat transfer enhancement in a 3d-printed compact heat exchanger.

1. Introduction

1.1. additive manufacturing, 1.2. heat exchange in complex structures, 2. the experimental facility, 3. experimental data, 4. conclusions.

• The test results confirmed that the HTC value has a slight dependence on the heat flux density during refrigerant condensation. The heat exchange coefficient gradually increases with the heat flux density. However, a four-fold increase in q causes only a 10% increase in the value of the α on the cooled surface.
• The thermal power strongly depends on the type of coolant. The highest values were observed during cooling with a 10% mPCM slurry. The lowest heat flux values were noted for water cooling. It was also found that the heat flux increases during the PCM phase transition. The influence of mass share on the value of heat flux was also observed. The higher the mass fraction of mPCM in the mixture, the greater the heat flux.
• The OHTC also depends on the type of coolant. The lowest values were observed during water cooling. The highest overall heat exchange coefficient values were noted during the 10% mPCM slurry cooling. It was also found that the overall heat exchange coefficient increased during the PCM phase transition. For the 10% mPCM, there was an over 11% increase in the overall heat exchange coefficient. The influence of mass share on the value of heat flux was also observed. The higher the mass fraction of mPCM in the mixture, the greater the heat flux.
• The refrigerant’s HTC values depend on the thickness of the condensate film. The HTC values decrease significantly between 0.00003 and 0.001 m of the thickness of the condensate film.
• The value of the HTC is proportional to the increase in the velocity of the condensate, which results from the laminar nature of the condensate flow. An increase in the condensate velocity reduces the thickness of the condensate layer, which reduces the value of thermal resistance and increases the value of the HTC.
• The authors demonstrated the possibility of using Equation (9) to determine the value of the HTC during condensation of the refrigerant on the surface of a smooth pipe bundle inside a compact heat exchanger made by 3D printing. This equation can be used in compact heat exchanger projects.
• The research results indicate the need to conduct further experimental research on the heat exchange enhancement regarding the impact of process parameters such as Δt log , or the mass fraction of the mPCM in the cooling liquid, and the internal geometry of 3D-printed mini heat exchangers.
• The future direction of the experimental research is to determine the effect of the state of matter of the phase change material mixture on the flow resistance in compact heat exchangers, and the impact of deposits of cooling mixtures on the operating parameters of heat exchangers.

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Data availability statement, conflicts of interest, nomenclature.

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Kruzel, M.; Bohdal, T.; Dutkowski, K. Heat Transfer Enhancement in a 3D-Printed Compact Heat Exchanger. Energies 2024 , 17 , 4754. https://doi.org/10.3390/en17184754

Kruzel M, Bohdal T, Dutkowski K. Heat Transfer Enhancement in a 3D-Printed Compact Heat Exchanger. Energies . 2024; 17(18):4754. https://doi.org/10.3390/en17184754

Kruzel, Marcin, Tadeusz Bohdal, and Krzysztof Dutkowski. 2024. "Heat Transfer Enhancement in a 3D-Printed Compact Heat Exchanger" Energies 17, no. 18: 4754. https://doi.org/10.3390/en17184754

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