Comparing individual-based models of collective cell motion in a benchmark flow geometry.

Collectively coordinated cell migration plays a role in tissue embryogenesis, cancer, homeostasis and healing. To study these processes, different cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended detailed cell shape contours. In the spirit of what Osborne et al. [PLOS Comput. Biol., 2017, 13, 1-34] did for cellular tissue structure simulation models, we here compare five simulation models of collective cell migration, chosen to be representatives in increasing order of included detail. They are Vicsek-Grégoire particles, Szabó-like particles, self-propelled Voronoi model, cellular Potts model, and multiparticle cells, where each model includes cell motility. We examine how these models compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. For this purpose, we use a benchmark that discriminates between complex material flow models, and that can be experimentally approached using cell cultures: the flow within a channel around a circular obstacle, that is, the geometry Stokes used in his historical 1851 experiment. For each model we explain how to best implement it; vary cell density, attraction force and alignment interaction; draw the resulting maps of velocity, density and deformation fields; and eventually discuss its respective advantages and limitations. We thus provide a recommendation on how to select a model to answer a given question, and we examine whether models of motile particles and motile cells display similar collective effects.

A single active ring model with velocity self-alignment.

Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to explore countless possibilities and test hypotheses. Here, we introduce a two-dimensional, extended active matter model for biological cells. A ring of interconnected self-propelled particles represents the cell. Neighboring particles are subject to harmonic and bending potentials. Within a characteristic time, each particle's self-velocity tends to align with its scattering velocity after an interaction. Translational modes, rotational modes, and mixtures of these appear as collective states. Using analytical results derived from active Brownian particles, we identify effective characteristic time scales for ballistic and diffusive movements. Finite-size scale investigation shows that the ring diffusion increases linearly with its size when in collective movement. A study on the ring shape reveals that all collective states are present even when bending forces are weak. In that case, when in a translational mode, the collective velocity aligns with the largest ring's direction in a spontaneous polarization emergence.

Mean-cluster approach indicates cell sorting time scales are determined by collective dynamics.

Cell migration is essential to cell segregation, playing a central role in tissue formation, wound healing, and tumor evolution. Considering random mixtures of two cell types, it is still not clear which cell characteristics define clustering time scales. The mass of diffusing clusters merging with one another is expected to grow as t^{d/d+2} when the diffusion constant scales with the inverse of the cluster mass. Cell segregation experiments deviate from that behavior. Explanations for that could arise from specific microscopic mechanisms or from collective effects, typical of active matter. Here we consider a power law connecting diffusion constant and cluster mass to propose an analytic approach to model cell segregation where we explicitly take into account finite-size corrections. The results are compared with active matter model simulations and experiments available in the literature. To investigate the role played by different mechanisms we considered different hypotheses describing cell-cell interaction: differential adhesion hypothesis and different velocities hypothesis. We find that the simulations yield normal diffusion for long time intervals. Analytic and simulation results show that (i) cluster evolution clearly tends to a scaling regime, disrupted only at finite-size limits; (ii) cluster diffusion is greatly enhanced by cell collective behavior, such that for high enough tendency to follow the neighbors, cluster diffusion may become independent of cluster size; (iii) the scaling exponent for cluster growth depends only on the mass-diffusion relation, not on the detailed local segregation mechanism. These results apply for active matter systems in general and, in particular, the mechanisms found underlying the increase in cell sorting speed certainly have deep implications in biological evolution as a selection mechanism.

Differential adhesion between moving particles as a mechanism for the evolution of social groups.

The evolutionary stability of cooperative traits, that are beneficial to other individuals but costly to their carrier, is considered possible only through the establishment of a sufficient degree of assortment between cooperators. Chimeric microbial populations, characterized by simple interactions between unrelated individuals, restrain the applicability of standard mechanisms generating such assortment, in particular when cells disperse between successive reproductive events such as happens in Dicyostelids and Myxobacteria. In this paper, we address the evolutionary dynamics of a costly trait that enhances attachment to others as well as group cohesion. By modeling cells as self-propelled particles moving on a plane according to local interaction forces and undergoing cycles of aggregation, reproduction and dispersal, we show that blind differential adhesion provides a basis for assortment in the process of group formation. When reproductive performance depends on the social context of players, evolution by natural selection can lead to the success of the social trait, and to the concomitant emergence of sizeable groups. We point out the conditions on the microscopic properties of motion and interaction that make such evolutionary outcome possible, stressing that the advent of sociality by differential adhesion is restricted to specific ecological contexts. Moreover, we show that the aggregation process naturally implies the existence of non-aggregated particles, and highlight their crucial evolutionary role despite being largely neglected in theoretical models for the evolution of sociality.

Preferential duplication of intermodular hub genes: an evolutionary signature in eukaryotes genome networks.

Whole genome protein-protein association networks are not random and their topological properties stem from genome evolution mechanisms. In fact, more connected, but less clustered proteins are related to genes that, in general, present more paralogs as compared to other genes, indicating frequent previous gene duplication episodes. On the other hand, genes related to conserved biological functions present few or no paralogs and yield proteins that are highly connected and clustered. These general network characteristics must have an evolutionary explanation. Considering data from STRING database, we present here experimental evidence that, more than not being scale free, protein degree distributions of organisms present an increased probability for high degree nodes. Furthermore, based on this experimental evidence, we propose a simulation model for genome evolution, where genes in a network are either acquired de novo using a preferential attachment rule, or duplicated with a probability that linearly grows with gene degree and decreases with its clustering coefficient. For the first time a model yields results that simultaneously describe different topological distributions. Also, this model correctly predicts that, to produce protein-protein association networks with number of links and number of nodes in the observed range for Eukaryotes, it is necessary 90% of gene duplication and 10% of de novo gene acquisition. This scenario implies a universal mechanism for genome evolution.

Cell sorting based on motility differences.

Self-propelled particles are used to simulate cell aggregates in a model considering homogeneous adhesion forces between cells and using only motility differences as segregation drivers. The tendency of cells to follow their neighbors is also included in the formulation. Three model variants are explored, and the conditions on which motility differences may produce segregation are mapped in parameter diagrams. The evolution of the order parameter measuring cell segregation is similar to those found by models based on differential adhesion. It is also found that, considering only velocity differences, the faster cells envelope the slower ones, which is opposite to the ordering observed in early experiments by Jones and co-workers [Jones, Evans, and Lee, Exp. Cell. Res. 180, 287 (1989)].

Towards a genome-wide transcriptogram: the Saccharomyces cerevisiae case.

Analysis of genome-wide expression data poses a challenge to extract relevant information. The usual approaches compare cellular expression levels relative to a pre-established control and genes are clustered based on the correlation of their expression levels. This implies that cluster definitions are dependent on the cellular metabolic state, eventually varying from one experiment to another. We present here a computational method that order genes on a line and clusters genes by the probability that their products interact. Protein-protein association information can be obtained from large data bases as STRING. The genome organization obtained this way is independent from specific experiments, and defines functional modules that are associated with gene ontology terms. The starting point is a gene list and a matrix specifying interactions. Considering the Saccharomyces cerevisiae genome, we projected on the ordering gene expression data, producing plots of transcription levels for two different experiments, whose data are available at Gene Expression Omnibus database. These plots discriminate metabolic cellular states, point to additional conclusions, and may be regarded as the first versions of 'transcriptograms'. This method is useful for extracting information from cell stimuli/responses experiments, and may be applied with diagnostic purposes to different organisms.

cAMP diffusion in Dictyostelium discoideum: a Green's function method.

A Green's function method is developed to approach the spatiotemporal equations describing the cAMP production in Dictyostelium discoideum, markedly reducing numerical calculations times: cAMP concentrations and gradients are calculated just at the amoeba locations. A single set of parameters is capable of reproducing the different observed behaviors, from cAMP synchronization, spiral waves and reaction-diffusion patterns to streaming and mound formation. After aggregation, the emergence of a circular motion of amoebas, breaking the radial cAMP field symmetry, is observed.

Self-propelled particle model for cell-sorting phenomena.

A self-propelled particle model is introduced to study cell sorting occurring in some living organisms. This allows us to evaluate the influence of intrinsic cell motility separately from differential adhesion with fluctuations, a mechanism previously shown to be sufficient to explain a variety of cell rearrangement processes. We find that the tendency of cells to actively follow their neighbors greatly reduces segregation time scales. A finite-size analysis of the sorting process reveals clear algebraic growth laws as in physical phase-ordering processes, albeit with unusual scaling exponents.

Cellular automata on high-dimensional hypercubes.

The emergence of nontrivial collective behavior is studied in large families of cellular automata rules implemented on high-dimensional hypercubes. Evidence is found that the region of rule space where such macroscopic dynamics exists is well-defined in the infinite-dimension limit.