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Calcium (Ca2+) signalling is one of the most important mechanisms ofinformation propagation in the body. In embryogenesis the interplay betweenCa2+ signalling and mechanical forces is critical to the healthy development ofan embryo but poorly understood. Several types of embryonic cells exhibitcalcium-induced contractions and many experiments indicate that Ca2+ signalsand contractions are coupled via a two-way mechanochemical coupling. We presenta new analysis of experimental data that supports the existence of thiscoupling during Apical Constriction in Neural Tube Closure. We then propose amechanochemical model, building on early models that couple Ca2+ dynamics tocell mechanics and replace the bistable Ca2+ release with modern,experimentally validated Ca2+ dynamics. We assume that the cell is a linearviscoelastic material and model the Ca2+-induced contraction stress with a Hillfunction saturating at high Ca2+ levels. We also express, for the first time,the "stretch-activation" Ca2+ flux in the early mechanochemical models as abottom-up contribution from stretch-sensitive Ca2+ channels on the cellmembrane. We reduce the model to three ordinary differential equations andanalyse its bifurcation structure semi-analytically as the $IP_3$concentration, and the "strength" of stretch activation, $\lambda$ vary. TheCa2+ system ($\lambda=0$, no mechanics) exhibits relaxation oscillations for acertain range of $IP_3$ values. As $\lambda$ is increased the range of $IP_3$values decreases, the oscillation amplitude decreases and the frequencyincreases. Oscillations vanish for a sufficiently high value of $\lambda$.These results agree with experiments in embryonic cells that also link the lossof Ca2+ oscillations to embryo abnormalities. The work addresses a veryimportant and understudied question on the coupling of chemical and mechanicalsignalling in embryogenesis.

A simple mechanochemical model for calcium signalling in embryonic epithelial cells