Regulators of the actin cytoskeleton such Rho GTPases can modulate forces developed in cells by promoting actomyosin contraction. At the same time, through mechanosensing, tension is known to affect the activity of Rho GTPases. What happens when these effects act in concert? Using a minimal model (1 GTPase coupled to a Kelvin–Voigt element), we show that two-way feedback between signaling (‘RhoA’) and mechanical tension (stretching) leads to a spectrum of cell behaviors, including contracted or relaxed cells, and cells that oscillate between these extremes. When such ‘model cells’ are connected to one another in a row or in a 2D sheet (‘epithelium’), we observe waves of contraction/relaxation and GTPase activity sweeping through the tissue. The minimal model lends itself to full bifurcation analysis, and suggests a mechanism that explains behavior observed in the context of development and collective cell behavior.

Engineered T cells have emerged as highly effective treatments for hematological cancers. Hundreds of clinical programs are underway in efforts to expand the efficacy, safety, and applications of this immuno-therapeutic modality. A primary challenge in developing these “living drugs” is the complexity of their pharmacology, as the drug product proliferates, differentiates, traffics between tissues, and evolves through interactions with patient immune systems. Using publicly available clinical data from Chimeric Antigen Receptor (CAR) T cells, we demonstrate how mathematical models can be used to quantify the relationships between product characteristics, patient physiology, pharmacokinetics and clinical outcomes. As scientists work to develop next-generation cell therapy products, mathematical models will be integral for contextualizing data and facilitating the translation of product designs to clinical strategy.

Collective cell migration plays an important role in development. Here, we study the posterior lateral line primordium (PLLP) a group of about 100 cells, destined to form sensory structures, that migrates from head to tail in the zebrafish embryo. We model mutually inhibitory FGF-Wnt signalling network in the PLLP and link tissue subdivision (Wnt receptor and FGF receptor activity domains) to receptor-ligand parameters. We then use a 3D cell-based simulation with realistic cell-cell adhesion, interaction forces, and chemotaxis. Our model is able to reproduce experimentally observed motility with leading cells migrating up a gradient of CXCL12a, and trailing (FGF receptor active) cells moving actively by chemotaxis towards FGF ligand secreted by the leading cells. The 3D simulation framework, combined with experiments, allows an investigation of the role of cell division, chemotaxis, adhesion, and other parameters on the shape and speed of the PLLP. The 3D model demonstrates reasonable behaviour of control as well as mutant phenotypes. Collective migration of a group of cells plays an important role in the development of an organism. Here we study a specific example in the zebrafish embryo, where a group of about 100 cells (the posterior lateral line primordium, PLLP), destined to form sensory structures, migrates from head to tail. We model the process from the initial polarization to the migration, with a focus on how tissue polarity could arise. Using a 3D deformable-ellipsoid cell-based simulation, we explore the effects of cell-cell, cell-substrate, and cell-chemical interactions. We discuss drag forces experienced by cells and what that implies about the inherent active motion of both leading and trailing cells. The model allows us to test how each of several biological parameters affects the shape, size, effective migration and speed of migration. A subsequent study will be aimed at understanding the formation and deposition of neuromasts.

Male and female moths communicate in complex ways to search for and to select a mate. In a process termed calling, females emit small quantities of pheromones, generating plumes that spread in the environment. Males detect the plume through their antennae and navigate toward the female. The reproductive process is marked by female choice and male–male competition, since multiple males aim to reach the female but only the first can mate with her. This provides an opportunity for female selection on male traits such as chemosensitivity to pheromone molecules and mobility. We develop a mathematical framework to investigate the overall mating likelihood, the mean first arrival time, and the quality of the first male to reach the female for four experimentally observed female calling strategies unfolding over a typical one-week mating period. We present both analytical solutions of a simplified model as well as results from agent-based numerical simulations. Our findings suggest that, by adjusting call times and the amount of released pheromone, females can optimize the mating process. In particular, shorter calling times and lower pheromone titers at onset of the mating period that gradually increase over time allow females to aim for higher-quality males while still ensuring that mating occurs by the end of the mating period.