Theory of mechano-chemical patterning in biphasic biological tissues

Abstract

The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a biologically realistic and unifying approach to emergent pattern formation. Our biphasic model of multicellular tissues incorporates turnover and transport of morphogens controlling cell differentiation and tissue mechanics in a single framework, where one tissue phase consists of a poroelastic network made of cells and the other is the extracellular fluid permeating between cells. While this model encompasses previous theories approximating tissues to inert monophasic media, such as Turing’s reaction-diffusion model, it overcomes some of their key limitations permitting pattern formation via any two-species biochemical kinetics thanks to mechanically induced cross-diffusion flows. Moreover, we unravel a qualitatively different advection-driven instability which allows for the formation of patterns with a single morphogen and which single mode pattern scales with tissue size. We discuss the potential relevance of these findings for tissue morphogenesis.

Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue

“…In the context of the present work, related studies have been performed on particular sub-systems such as decoupled elasticity and diffusion [14]. More recent works tend to integrate further complexity by adding multi-layered coupled systems [15], incorporating domain or mechanical growth [16], the coupling between elasticity-diffusion [17], poroelasticity [18,19], and also porelasticity-diffusion [11], which resembles more the idea we advocate in this work. The key contributions of this paper include a new three-dimensional model for the two-way coupling between poroelasticity and reaction-diffusion, the derivation and discussion of dispersion relations that indicate that the mechano-chemical feedback onsets Turing instabilities (with non-trivial wavenumber) for a range of coupling parameters, the formulation and numerical realisation of a locking-free finite element method, and a sample of numerical results including applications in brain injuries poromechanics.…”

Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media

“…where D 1 , D 2 are positive definite diffusion matrices (however we do not consider here cross-diffusion effects as in e.g. [5,25]). In the well-posedness analysis the reaction kinetics are generic.…”

Mechanochemical models for calcium waves in embryonic epithelia

“…Mechanical properties of different cell types indicate diverse behaviour, including elastic [15,18,45], poroelastic [14,37,50,51], or nonlinear and nonlocal characteristics [36,56] but more predominantly, viscoelastic effects [2,8,10,20,29,47,57]. The specific constitutive rheological model to adopt in a tissue depends on the characteristics of each constituent cell, on the properties inherent to distinct biological states, on the nature and intensity of the stresses and strains that are to be applied, and on the spatio-temporal scales involved.…”