Modelling cell movement, cell differentiation, cell sorting and proportion regulation in Dictyostelium discoideum aggregations

Chemotaxis in heterogeneous environments: A multi-agent model of decentralized gathering past obstacles

Chemotaxis, cell migration in response to chemical gradients, is known to promote self-organization of microbiological populations. However, the modeling of chemotaxis in heterogeneous environments is still limited. This study analyzes a decentralized gathering process in environments with physical as well as chemical barriers, using a multi-agent model for Disctyostelium discoideum colonies. Employing a topology-independent metric to quantify the system evolution, we study dynamical features emerging from complex social interactions. The results show that obstacles may hamper the gathering process by altering the flux of chemical signals among amoebas, acting as local topological perturbations. We also find that a minimal set of agent's rules for robust gathering does not require explicit mechanisms for obstacle sensing and avoidance; moreover, random cell movements concur in preventing multiple stable clusters and improve the gathering efficacy. Hence, we speculate that chemotactic cells can avoid obstacles without needing specialized mechanisms: tradeoffs of social interactions and individual fluctuations are sufficient to guarantee the aggregation of the whole colony past numerous obstacles.

Differential cell motion: A mathematical model of anterior posterior sorting

Here, we investigate how a subpopulation of cells can move through an aggregate of cells. Using a stochastic force-based model of Dictyostelium discoideum when the population is forming a slug, we simulate different strategies for prestalk cells to reliably move to the front of the slug while omitting interaction with the substrate thus ignoring the overall motion of the slug. Of the mechanisms that we simulated, prestalk cells being more directed is the best strategy followed by increased asymmetric motive forces for prestalk cells. The lifetime of the cell adhesion molecules, while not enough to produce differential motion, did modulate the results of the strategies employed. Finally, understanding and simulating the appropriate boundary conditions are essential to correctly predict the motion.

The Use of Diffusion Calculations and Monte Carlo Simulations to Understand the Behavior of Cells in Dictyostelium Communities

Microbial communities are the simplest possible model of multicellular tissues, allowing studies of cell-cell interactions to be done with as few extraneous factors as possible. For instance, the eukaryotic microbe Dictyostelium discoideum proliferates as single cells, and when starved, the cells aggregate together and form structures of ~20,000 cells. The cells use a variety of signals to direct their movement, inform each other of their local cell density and whether they are starving, and organize themselves into groups of ~20,000 cells. Mathematical models and computational approaches have been a key check on, and guide of, the experimental work. In this minireview, I will discuss diffusion calculations and Monte Carlo simulations that were used for Dictyostelium studies that offer general paradigms for several aspects of cell-cell communication. For instance, computational work showed that diffusible secreted cell-density sensing (quorum) factors can diffuse away so quickly from a single cell that the local concentration will not build up to incorrectly cause the cell to sense that it is in the presence of a high density of other cells secreting that signal. In another example, computation correctly predicted a mechanism that allows a group of cells to break up into subgroups. These are thus some examples of the power and necessity of computational work in biology.

Traveling pulse emerges from coupled intermittent walks: A case study in sheep

Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronising when they decide to switch between the two modes. We propose a model for the individual decision making process, based on switching rates between stopped / walking states that depend on behind / ahead locations and states of the others. We parametrize this model from data. Next, we translate this (microscopic) individual-based model into its density-flow (macroscopic) equations counterpart. Numerical solving these equations display a traveling pulse propagating at constant speed even though each individual is at any moment either stopped or walking. Considering the minimal model embedded in these equations, we derive analytically the steady shape of the pulse (sech square). The parameters of the pulse (shape and speed) are expressed as functions of individual parameters. This pulse emerges from the non linear coupling of start/stop individual decisions which compensate exactly for diffusion and promotes a steady ratio of walking / stopped individuals, which in turn determines the traveling speed of the pulse. The system seems to converge to this pulse from any initial condition, and to recover the pulse after perturbation. This gives a high robustness to this coordination mechanism.

Progress and perspectives in signal transduction, actin dynamics, and movement at the cell and tissue level: lessons from Dictyostelium

Movement of cells and tissues is a basic biological process that is used in development, wound repair, the immune response to bacterial invasion, tumour formation and metastasis, and the search for food and mates. While some cell movement is random, directed movement stimulated by extracellular signals is our focus here. This involves a sequence of steps in which cells first detect extracellular chemical and/or mechanical signals via membrane receptors that activate signal transduction cascades and produce intracellular signals. These intracellular signals control the motile machinery of the cell and thereby determine the spatial localization of the sites of force generation needed to produce directed motion. Understanding how force generation within cells and mechanical interactions with their surroundings, including other cells, are controlled in space and time to produce cell-level movement is a major challenge, and involves many issues that are amenable to mathematical modelling.