The role of topology and mechanics in uniaxially growing cell networks.

Alexander Erlich,Derek E Moulton,Gareth W Jones,Françoise Tisseur,Alain Goriely

doi:10.1098/rspa.2019.0523

Abstract

In biological systems, the growth of cells, tissues and organs is influenced by mechanical cues. Locally, cell growth leads to a mechanically heterogeneous environment as cells pull and push their neighbours in a cell network. Despite this local heterogeneity, at the tissue level, the cell network is remarkably robust, as it is not easily perturbed by changes in the mechanical environment or the network connectivity. Through a network model, we relate global tissue structure (i.e. the cell network topology) and local growth mechanisms (growth laws) to the overall tissue response. Within this framework, we investigate the two main mechanical growth laws that have been proposed: stress-driven or strain-driven growth. We show that in order to create a robust and stable tissue environment, networks with predominantly series connections are naturally driven by stress-driven growth, whereas networks with predominantly parallel connections are associated with strain-driven growth.

Highlights

Many biological tissues take cues from their mechanical environment to regulate growth and, in turn, generate mechanical stresses on their surrounding [3]
There are three distinct contributions to the linearized dynamics: the diagonal matrices Kω and Kτ depend on the growth law; the positive diagonal matrix D is obtained from the constitutive law; and P encodes the network topology
Our analysis suggests the following mechanism in uniaxial tissue growth dynamics: stress-driven growth laws lead to series connections at the level of the whole network while strain-driven growth leads to parallel connections

Summary

Introduction

Many biological tissues take cues from their mechanical environment to regulate growth and, in turn, generate mechanical stresses on their surrounding [3]. Mechanical growth laws have been studied both for patterning processes in developing tissues [11,12] and regulatory processes in mature tissues [4], both with discrete and continuum models Their forms have been either phenomenologically and micro-structurally inspired [13,14] or based on thermodynamical arguments [15]. While most biological cell networks are two- or three-dimensional, we study here, as a first step, a network deforming along a single axis The advantage of this approach is that the analytical tractability enables concrete connections to be made between topology, the form of growth law, and stability and leads to a broad understanding of the relative role of mechanics and topology in the dynamics of growth, albeit in a simplified geometry. B The topology of the cell network can be encoded by a graph, where nodes correspond to vertical (force-bearing) walls and edges correspond to cells

Growth dynamics of a single cell

Growth dynamics of a network of cells

Mechanical stability of cell assemblies

Length and force balance of an example network system at linear order in ε:

A Strain-driven growth

Discussion