Modelling chase-and-run migration in heterogeneous populations

Leadership Through Influence: What Mechanisms Allow Leaders to Steer a Swarm?

Collective migration of cells and animals often relies on a specialised set of “leaders”, whose role is to steer a population of naive followers towards some target. We formulate a continuous model to understand the dynamics and structure of such groups, splitting a population into separate follower and leader types with distinct orientation responses. We incorporate leader influence via three principal mechanisms: a bias in the orientation of leaders towards the destination (orientation-bias), a faster movement of leaders when moving towards the target (speed-bias), and leaders making themselves more clear to followers when moving towards the target (conspicuousness-bias). Analysis and numerical computation are used to assess the extent to which the swarm is successfully shepherded towards the target. We find that successful leadership can occur for each of these three mechanisms across a broad region of parameter space, with conspicuousness-bias emerging as the most robust. However, outside this parameter space we also find various forms of unsuccessful leadership. Forms of excessive influence can result in either swarm-splitting, where the leaders break free and followers are left rudderless, or a loss of swarm cohesion that leads to its eventual dispersal. Forms of low influence, on the other hand, can even generate swarms that move away from the target direction. Leadership must therefore be carefully managed to steer the swarm correctly.

Modelling Cell Invasion: A Review of What JD Murray and the Embryo Can Teach Us

Cell invasion and cell plasticity are critical to human development but are also striking features of cancer metastasis. By distributing a multipotent cell type from a place of birth to distal locations, the vertebrate embryo builds organs. In comparison, metastatic tumor cells often acquire a de-differentiated phenotype and migrate away from a primary site to inhabit new microenvironments, disrupting normal organ function. Countless observations of both embryonic cell migration and tumor metastasis have demonstrated complex cell signaling and interactive behaviors that have long confounded scientist and clinician alike. James D. Murray realized the important role of mathematics in biology and developed a unique strategy to address complex biological questions such as these. His work offers a practical template for constructing clear, logical, direct and verifiable models that help to explain complex cell behaviors and direct new experiments. His pioneering work at the interface of development and cancer made significant contributions to glioblastoma cancer and embryonic pattern formation using often simple models with tremendous predictive potential. Here, we provide a brief overview of advances in cell invasion and cell plasticity using the embryonic neural crest and its ancestral relationship to aggressive cancers that put into current context the timeless aspects of his work.

Stability of a non-local kinetic model for cell migration with density-dependent speed

The aim of this article is to study the stability of a non-local kinetic model proposed by Loy & Preziosi (2020a) in which the cell speed is affected by the cell population density non-locally measured and weighted according to a sensing kernel in the direction of polarization and motion. We perform the analysis in a $d$-dimensional setting. We study the dispersion relation in the one-dimensional case and we show that the stability depends on two dimensionless parameters: the first one represents the stiffness of the system related to the cell turning rate, to the mean speed at equilibrium and to the sensing radius, while the second one relates to the derivative of the mean speed with respect to the density evaluated at the equilibrium. It is proved that for Dirac delta sensing kernels centered at a finite distance, corresponding to sensing limited to a given distance from the cell center, the homogeneous configuration is linearly unstable to short waves. On the other hand, for a uniform sensing kernel, corresponding to uniformly weighting the information collected up to a given distance, the most unstable wavelength is identified and consistently matches the numerical solution of the kinetic equation.

Insights Into the Early Gene Regulatory Network Controlling Neural Crest and Placode Fate Choices at the Neural Border

The neural crest (NC) cells and cranial placodes are two ectoderm-derived innovations in vertebrates that led to the acquisition of a complex head structure required for a predatory lifestyle. They both originate from the neural border (NB), a portion of the ectoderm located between the neural plate (NP), and the lateral non-neural ectoderm. The NC gives rise to a vast array of tissues and cell types such as peripheral neurons and glial cells, melanocytes, secretory cells, and cranial skeletal and connective cells. Together with cells derived from the cranial placodes, which contribute to sensory organs in the head, the NC also forms the cranial sensory ganglia. Multiple in vivo studies in different model systems have uncovered the signaling pathways and genetic factors that govern the positioning, development, and differentiation of these tissues. In this literature review, we give an overview of NC and placode development, focusing on the early gene regulatory network that controls the formation of the NB during early embryonic stages, and later dictates the choice between the NC and placode progenitor fates.