Survival chances of a prey swarm: how the cooperative interaction range affects the outcome

Growth kinetics and power laws indicate distinct mechanisms of cell-cell interactions in the aggregation process

Cellular aggregation is a complex process orchestrated by various kinds of interactions depending on the environment. Different interactions give rise to different pathways of cellular rearrangement and the development of specialized tissues. To distinguish the underlying mechanisms, in this theoretical work, we investigate the spontaneous emergence of tissue patterns from an ensemble of single cells on a substrate following three leading pathways of cell-cell interactions, namely, direct cell adhesion contacts, matrix-mediated mechanical interaction, and chemical signaling. Our analysis shows that the growth kinetics of the aggregation process are distinctly different for each pathway and bear the signature of the specific cell-cell interactions. Interestingly, we find that the average domain size and the mass of the clusters exhibit a power law growth in time under certain interaction mechanisms hitherto unexplored. Further, as observed in experiments, the cluster size distribution can be characterized by stretched exponential functions showing distinct cellular organization processes.

Self-propulsion and self-navigation: Activity is a precursor to jamming

Traffic jams are an everyday hindrance to transport and typically arise when many vehicles have the same or a similar destination. We show, however, that even when uniformly distributed in space and uncorrelated, targets have a crucial effect on transport. At modest densities an instability arises leading to jams with emergent correlations between the targets. By considering limiting cases of the dynamics which map onto active Brownian particles, we argue that motility induced phase separation is the precursor to jams. That is, jams are MIPS seeds that undergo an extra instability due to target accumulation. This provides a quantitative prediction of the onset density for jamming, and suggests how jamming might be delayed or prevented. We study the transition between jammed and flowing phase, and find that transport is most efficient on the cusp of jamming.

Efficient flocking: metric versus topological interactions

Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the local rules of interactions among the individuals, namely, metric versus topological interactions as debated in the current literature. In the case of the metric ruling, the individuals interact with the neighbours within a certain metric distance; by contrast, in the topological ruling, interaction is confined within a number of fixed nearest neighbours. Here, we explore how the range of interaction versus the number of fixed interacting neighbours affects the dynamics of flocking in an unbounded space, as observed in natural scenarios. Our study reveals the existence of a certain threshold value of the interaction radius in the case of metric ruling and a threshold number of interacting neighbours for the topological ruling to reach an ordered state. Interestingly, our analysis shows that topological interaction is more effective in bringing the order in the group, as observed in field studies. We further compare how the nature of the interactions affects the dynamics for various sizes and speeds of the flock.

Survival probability of a lazy prey on lattices and complex networks

We develop a framework to analyse the survival probability of a prey following a minimal effort evasion strategy, that is being chased by N predators on finite lattices or complex networks. The predators independently perform random walks if the prey is not within their sighting radius, whereas, the prey only moves when a predator moves onto a node within its sighting radius. We verify the proposed framework on three different finite lattices with periodic boundaries through numerical simulations and find that the survival probability (P_sur) decays exponentially with a decay rate proportional to P(N, k) (number of permutations), where k is the minimum number of predators required to capture a prey. We then extend the framework onto complex networks and verify its robustness on the networks generated by the Watts-Strogatz (W-S), Barabási-Albert (B-A) models and a few real-world networks. Our analysis predicts that, for the considered lattices, P_sur reduces as the degree of the nodes of the lattice is increased. However, for networks, P_sur initially increases with the average degree of the nodes, reaches a maximum, and then decreases. Furthermore, we analyse the effect of the long-range connections in networks on P_sur in W-S networks. The proposed framework enables one to study the survival probability of such a prey being hunted by multiple predators on any given structure.