Autocrine inhibition of cell motility can drive epithelial branching morphogenesis in the absence of growth

Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix

The mechanical interaction between cells and the extracellular matrix (ECM) is fundamental to coordinate collective cell behavior in tissues. Relating individual cell-level mechanics to tissue-scale collective behavior is a challenge that cell-based models such as the cellular Potts model (CPM) are well-positioned to address. These models generally represent the ECM with mean-field approaches, which assume substrate homogeneity. This assumption breaks down with fibrous ECM, which has nontrivial structure and mechanics. Here, we extend the CPM with a bead-spring model of ECM fiber networks modeled using molecular dynamics. We model a contractile cell pulling with discrete focal adhesion-like sites on the fiber network and demonstrate agreement with experimental spatiotemporal fiber densification and displacement. We show that at high network cross-linking, contractile cell forces propagate over at least eight cell diameters, decaying with distance with power law exponent n= 0.35 - 0.65 typical of viscoelastic ECMs. Further, we use in silico atomic force microscopy to measure local cell-induced network stiffening consistent with experiments. Our model lays the foundation for investigating how local and long-ranged cell-ECM mechanobiology contributes to multicellular morphogenesis.

Multi-scale analysis and modelling of collective migration in biological systems

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.