Multi-Cellular Logistics of Collective Cell Migration

Abstract

During development, the formation of biological networks (such as organs and neuronal networks) is controlled by multicellular transportation phenomena based on cell migration. In multi-cellular systems, cellular locomotion is restricted by physical interactions with other cells in a crowded space, similar to passengers pushing others out of their way on a packed train. The motion of individual cells is intrinsically stochastic and may be viewed as a type of random walk. However, this walk takes place in a noisy environment because the cell interacts with its randomly moving neighbors. Despite this randomness and complexity, development is highly orchestrated and precisely regulated, following genetic (and even epigenetic) blueprints. Although individual cell migration has long been studied, the manner in which stochasticity affects multi-cellular transportation within the precisely controlled process of development remains largely unknown. To explore the general principles underlying multicellular migration, we focus on the migration of neural crest cells, which migrate collectively and form streams. We introduce a mechanical model of multi-cellular migration. Simulations based on the model show that the migration mode depends on the relative strengths of the noise from migratory and non-migratory cells. Strong noise from migratory cells and weak noise from surrounding cells causes “collective migration,” whereas strong noise from non-migratory cells causes “dispersive migration.” Moreover, our theoretical analyses reveal that migratory cells attract each other over long distances, even without direct mechanical contacts. This effective interaction depends on the stochasticity of the migratory and non-migratory cells. On the basis of these findings, we propose that stochastic behavior at the single-cell level works effectively and precisely to achieve collective migration in multi-cellular systems.

Migration of cells in a social context

“…To investigate whether these observed traffic rules on the individual cell level indeed do cause the very varied collective motion we observed, we formulated an agent-based mathematical model using the simplest physically reasonable assumptions for the motion of the individual cell based on three types of input: (i) our own pseudopod observations, (ii) previous experimental studies on chemotaxis of isolated cells, and (iii) Newton's second law of particle motion (SI Appendix, Model Details). This model, which can be considered an extension of the Vicsek model (21,22,42), exploits known cellular biophysics to simulate our experiments with a few hundred cells, a regime that is inaccessible to continuum modeling (43,44). Model cells (Fig.…”

“…This is shown below through a number of statistical tests. Although simpler theoretical models have been presented in the past with the objective of investigating certain traits of the collective migration phenomena (21,22,37,(42)(43)(44)(45), none of these models is able to simultaneously account for a wide variety of the migration data such as ours, and our model thus provides one of the simplest ways of incorporating all of our observations in a physically transparent formulation.…”

Biomechanics of Collective Cell Migration in Cancer Progression: Experimental and Computational Methods

“…Moreover, skewing away from Vicsek's alignment to neighboring cells behavior, this model includes cells that align to the direction of the net force acting upon them. This model was then further improved to investigate the migration behavior of cells [156][157][158][159] . The results revealed that cell packing fraction, moving velocity and noise level controlled whether the cells migrated as collective or dispersive behavior.…”

On the Mechanical Interplay Between Intra- and Inter-Synchronization During Collective Cell Migration: A Numerical Investigation

“…For collective cell migration, we can distinguish between two categories of computational models: (i) the agent-based models (AGMs) and (ii) the continuum models (CMs). AGMs simulate the activity and the interactions of cells within a population and assess their influence on the global system by taking into account the rate of cell division, the cell proliferation, the adhesion between the cells and the substrate, the deformation energy, and the stochastic behavior of the cellular collective (Graner and Glazier 1992;Szabo et al 2006;Vedel et al 2013;Vicsek et al 1995;Yamao et al 2011).…”

“…A few models (McLennan et al 2012;Yamao et al 2011) describe the collective migration focusing on the movement of the neural crest, which occurs in the absence of extracellular signals.…”