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Collective motion of cells: from experiments to models
Elod Mehes, Tamas Vicsek
TL;DR
The paper addresses how collective motion differs at the cellular level and how its mechanisms can be understood quantitatively. It reviews experimental observations alongside computational models, concluding that adhesion, interactions, and emergent organization underlie collective migration across developmental, physiological, and pathological contexts.
Problem
Cellular collective motion has distinct interactions from animal swarms, while existing research has emphasized phenomenological observations over quantitative interpretation.
Method
The review synthesizes experimental observations with basic computational models to interpret collective cell motion quantitatively.
Results
The review identifies adhesion, cell interactions, polarity, and emergent organization as recurring features of collective cell migration across in vitro and in vivo systems.
Takeaways & Limitations
Quantitative models can support interpretation of collective cell motion and help design further experiments or potential cancer therapies.
Takeaways & Limitations
The models omit many detailed factors influencing individual-cell motion because they use only a few terms and rely on collective averaging.
Abstract
from arXiv · showhide
Swarming or collective motion of living entities is one of the most common and spectacular manifestations of living systems having been extensively studied in recent years. A number of general principles have been established. The interactions at the level of cells are quite different from those among individual animals therefore the study of collective motion of cells is likely to reveal some specific important features which are overviewed in this paper. In addition to presenting the most appealing results from the quickly growing related literature we also deliver a critical discussion of the emerging picture and summarize our present understanding of collective motion at the cellular level. Collective motion of cells plays an essential role in a number of experimental and real-life situations. In most cases the coordinated motion is a helpful aspect of the given phenomenon and results in making a related process more efficient (e.g., embryogenesis or wound healing), while in the case of tumor cell invasion it appears to speed up the progression of the disease. In these mechanisms cells both have to be motile and adhere to one another, the adherence feature being the most specific to this sort of collective behavior. One of the central aims of this review is both presenting the related experimental observations and treating them in the light of a few basic computational models so as to make an interpretation of the phenomena at a quantitative level as well.
REVIEW
The review is authored by Előd Méhes and Tamás Vicsek.
- Előd Méhes is listed as an author of the review.
- Tamás Vicsek is listed as an author of the review.
- The author listing includes affiliation markers for both authors.
Introduction
The review defines collective cell motion as an emergent behavior shaped by cell–cell interactions and develops quantitative models to interpret it. It emphasizes physical connection, polarity, adhesion, and the distinction between collective migration and loosely coordinated movement.
- Defining collective cell motion: Collective cell motion arises when interactions among cells make their behavior differ from that of isolated cells.
- Defining collective cell motion: The review defines collective migration through sustained physical and functional connections, polarity, and supracellular cytoskeletal organization.
- Main types of collective cell motion: Collective motion is studied across keratocyte sheets, endothelial and epithelial monolayers, and cancer cell groups.
- Main types of collective cell motion: Bacterial collective motion is outside the review’s focus because bacterial motility differs from that of adherent tissue cells.
- Need for quantitative description: The review adds computational models to predominantly phenomenological experimental research for quantitative interpretation and potential experimental or therapeutic design.
- Need for quantitative description: Cell velocity measurements can be obtained through manual tracking, automatic object recognition, or particle image velocimetry.
Collective cell motion in vitro
In vitro studies show that collective migration depends on cell density, leadership, confinement, and intercellular force transmission. These factors produce ordered sheets, streams, fingers, and vortices in epithelial and endothelial systems.
- Sheet migration and streaming: Increasing goldfish keratocyte density produces a continuous transition from individual random migration to ordered collective migration.
- Sheet migration and streaming: Dense endothelial and epithelial monolayers exhibit streaming: globally undirected motion with locally correlated, transient internal flows.
- The role of leadership: Scratch-wound migration involves polarized leader and follower cells, with leader orientation depending on FGF receptor signaling but not an FGF concentration gradient.
- The role of leadership: MDCK traction forces arise not only at the edge but also several rows behind through cryptic lamellipodia.
- The role of geometrical confinement: Confinement below the unconfined motion correlation length induces collective motion in confluent epithelial populations, whereas motion does not emerge below confluence.
- The role of geometrical confinement: Narrow strips increase migration speed, while wider strips support greater coordination and vortices; disrupting intercellular adhesion abolishes coherence.
Collective cell motion in vivo
In vivo, collective cell motion organizes embryonic tissues and organs through adhesion, guidance cues, leader–follower organization, and self-assembly. Examples include vasculogenesis, gastrulation, lateral-line migration, and branching morphogenesis.
- Collective cell motion in vivo: Endothelial precursors self-assemble into polygonal tubular networks during primary vasculogenesis.
- Gastrulation of the zebrafish embryo: Zebrafish mesendoderm migration becomes impaired and less directed when E-cadherin-mediated cell–cell adhesion is weakened.
- Collective migration of the posterior lateral line primordium: The lateral-line primordium migrates cohesively while depositing neuromast clusters that differentiate into sensory epithelial structures.
- Collective migration of the posterior lateral line primordium: Only a few leading primordium cells activate Cxcr4b to direct group polarity, while mutant-receptor cells are excluded from the leading edge.
- Collective migration of the posterior lateral line primordium: Truncating the Sdf1a stripe can reverse primordium migration by 180 degrees while preserving normal neuromast deposition.
- Collective migration in branching morphogenesis: Collective migration contributes to neural crest development and branching morphogenesis during embryonic tissue formation and adult regeneration.
Pattern formation by collective segregation of cells
Cell segregation generates organized tissue patterns through cell-type-specific mechanical properties, active motion, and local interactions, often without external guidance. Experiments link segregation dynamics and final configurations to actomyosin-dependent cortex tension, surface tension, adhesion, and cell motility.
- Pattern formation by collective segregation of cells: Segregation can arise from local cell-cell interactions and differing mechanical or motility properties, rather than external morphogens or chemotactic cues.The review frames segregation as a pattern-forming process relevant to embryonic and non-embryonic systems.
- Pattern formation in vivo: gastrulation and tissue organization: During gastrulation, segregating cell populations form distinct domains that contribute to germ-layer formation and broader tissue organization.Three-dimensional segregation is also described in processes including blastocyst formation and somitogenesis.
- Three-dimensional segregation experiments: Differential actomyosin-dependent cell-cortex tension is required and sufficient to direct cell-type segregation and determine the final configuration of segregated domains.This conclusion comes from experiments using cell types with altered myosin activity.
- Three-dimensional segregation experiments: In zebrafish germ-line progenitors, mesoderm progressively engulfs ectoderm, with algebraic scaling and distinct characteristic exponents for enveloping and engulfed cells.The reported order-parameter scaling depends on system size.
- Three-dimensional segregation experiments: Mixed epithelial cell domains can grow according to an algebraic scaling law and typically complete segregation within 6 hours, without engulfment in one reported in vitro system.The domains remain adjacent, contrasting with the engulfment observed for zebrafish germ-line progenitors.
- Three-dimensional segregation experiments: Cell-cortex tension, rather than adhesion energy, is identified as the main drive of cell contact formation and segregation.Typical adhesion energy per unit area is approximately 1 × 10^-7 N/m, whereas tissue surface tension is on the order of 1 × 10^-3 N/m.
Conceptual interpretations
The review interprets collective cell motion as an emergent phenomenon in which interactions among cells produce system-level patterns that differ from isolated-cell behavior. It uses classification and self-propelled-particle models, including minimal and extended equation-based models, to organize and quantitatively interpret these patterns.
- Emergence and collective behavior: Collective motion is treated as a simple manifestation of collective behavior whose patterns emerge from interactions among many cells.The review notes that a general theoretical framework for coherent cell motion is still lacking.
- Emergence and collective behavior: In collective behavior, neighboring units influence individual actions so strongly that units behave differently from how they would act alone.The resulting systems can display ordered patterns as units change behavior together.
- Classes of collective migration of cells: Collective-motion models use self-propelled particles to represent units moving at approximately constant velocity while interacting with one another.This modeling notion is applied across systems containing interacting moving entities.
- Interpreting collective motion of cells in terms of models/equations: The review distinguishes minimal models with rules sufficient for collective motion from extended models that incorporate additional interactions.Both model types use equations for cell positions and velocities.
- Interpreting collective motion of cells in terms of models/equations: Simple equations omit many factors influencing individual-cell motion because details can average out at the collective level, yielding characteristic behavioral patterns.The review relates these recurring patterns to possible universality classes of collective motion.
Quantitative models
The review presents computational models that quantitatively interpret collective cell migration, wound healing, vascular organization, and segregation. These models reproduce several observed patterns while identifying how motility, adhesion, cohesion, and model assumptions shape collective behavior.
- Quantitative models: Computational models are used to quantitatively interpret collective cell behavior in wound healing, embryonic morphogenesis, immune reactions, and tumor invasion.The review combines general swarming models with models tailored to specific cellular phenomena.
- Quantitative models: Self-propelled-particle models reproduce a continuous transition from disordered to ordered migration as cell density increases.The models extend basic alignment dynamics with adhesive interactions and finite particle size.
- Quantitative models: Streaming models reproduce experimentally observed streaming patterns, shear lines, and vortices in endothelial monolayers.The cell-polarity and memory rules form a positive feedback loop under periodic boundary conditions.
- Quantitative models: Increasing motile force or decreasing cohesion can trigger sheet migration in small populations without specific signaling cues.The model distinguishes non-moving epithelium, sheet migration, and uncoordinated migration regimes as motile force changes.
- Quantitative models: Agent-based and Cellular Potts models reproduce polygonal vascular network formation from preferential adhesion to elongated cell structures.These models address self-organization without an external prepattern.
- Quantitative models: Reduced adhesion or spring force produces less directed and slower collective migration in simulations of mesendoderm cell groups.The simulated results were consistent with experimental observations, while adhesion was hypothesized to reduce individual path variability.
- Modeling of cellular segregation: Cellular Potts simulations using experimentally derived adhesion and cell-cortex tension reproduce observed final configurations of segregating zebrafish germline progenitors.This work combines experimental measurements with computational modeling.
- Modeling of cellular segregation: Moderate local coherent motion considerably accelerates segregation, with self-propelled aligned particles showing growth exponents near 1 versus approximately 1/3 in Potts-model simulations.The faster dynamics resemble earlier two- and three-dimensional observations of cell segregation.
Conclusions
The review argues that combining computational models with experimental data shifts collective-cell research from description toward causal understanding and can guide focused experiments or predictions.
- Computational models can quantitatively interpret collective cell motion and pattern formation in developmental biology.The review presents modeling as a way to move beyond descriptive accounts toward mechanisms.
- Integrating multidisciplinary approaches with experimental data can help design focused tests and predict previously unseen outcomes.