# A simple mechanochemical model for calcium signalling in embryonic epithelial cells

## TL;DR

This paper introduces a mechanochemical model linking calcium dynamics and mechanical forces in embryonic cells, supported by experimental data, revealing how stretch-sensitive channels influence calcium oscillations during development.

## Contribution

It presents a novel, simplified mechanochemical model incorporating stretch-activated calcium channels and analyzes its bifurcation structure, advancing understanding of calcium-mechanics coupling in embryogenesis.

## Key findings

- Calcium oscillations depend on IP3 levels and stretch activation strength.
- Increasing stretch activation reduces oscillation range and amplitude.
- High stretch activation suppresses calcium oscillations, correlating with embryo abnormalities.

## Abstract

Calcium (Ca2+) signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between Ca2+ signalling and mechanical forces is critical to the healthy development of an embryo but poorly understood. Several types of embryonic cells exhibit calcium-induced contractions and many experiments indicate that Ca2+ signals and contractions are coupled via a two-way mechanochemical coupling. We present a new analysis of experimental data that supports the existence of this coupling during Apical Constriction in Neural Tube Closure. We then propose a mechanochemical model, building on early models that couple Ca2+ dynamics to cell mechanics and replace the bistable Ca2+ release with modern, experimentally validated Ca2+ dynamics. We assume that the cell is a linear viscoelastic material and model the Ca2+-induced contraction stress with a Hill function saturating at high Ca2+ levels. We also express, for the first time, the "stretch-activation" Ca2+ flux in the early mechanochemical models as a bottom-up contribution from stretch-sensitive Ca2+ channels on the cell membrane. We reduce the model to three ordinary differential equations and analyse its bifurcation structure semi-analytically as the $IP_3$ concentration, and the "strength" of stretch activation, $\lambda$ vary. The Ca2+ system ($\lambda=0$, no mechanics) exhibits relaxation oscillations for a certain range of $IP_3$ values. As $\lambda$ is increased the range of $IP_3$ values decreases, the oscillation amplitude decreases and the frequency increases. Oscillations vanish for a sufficiently high value of $\lambda$. These results agree with experiments in embryonic cells that also link the loss of Ca2+ oscillations to embryo abnormalities. The work addresses a very important and understudied question on the coupling of chemical and mechanical signalling in embryogenesis.