A simple mechanochemical model for calcium signalling in embryonic epithelial cells

Abstract

Calcium signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between calcium 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 calcium signals and contractions are coupled via a two-way mechanochemical feedback mechanism. We present a new analysis of experimental data that supports the existence of this coupling during apical constriction. We then propose a simple mechanochemical model, building on early models that couple calcium dynamics to the cell mechanics and we replace the hypothetical bistable calcium release with modern, experimentally validated calcium dynamics. We assume that the cell is a linear, viscoelastic material and we model the calcium-induced contraction stress with a Hill function, i.e. saturating at high calcium levels. We also express, for the first time, the “stretch-activation” calcium flux in the early mechanochemical models as a bottom-up contribution from stretch-sensitive calcium channels on the cell membrane. We reduce the model to three ordinary differential equations and analyse its bifurcation structure semi-analytically as two bifurcation parameters vary—the concentration, and the “strength” of stretch activation, . The calcium system ( , no mechanics) exhibits relaxation oscillations for a certain range of values. As is increased the range of values decreases and oscillations eventually vanish at a sufficiently high value of . This result agrees with experimental evidence in embryonic cells which also links the loss of calcium oscillations to embryo abnormalities. Furthermore, as is increased the oscillation amplitude decreases but the frequency increases. Finally, we also identify the parameter range for oscillations as the mechanical responsiveness factor of the cytosol increases. This work addresses a very important and not well studied question regarding the coupling between chemical and mechanical signalling in embryogenesis.

Mapping calcium dynamics in a developing tubular structure

“…During embryonic development, cells and tissues generate mechanical forces. The effects of these forces on morphogenetic processes have been linked to Ca 2+ signalling 100, 101 . In addition, the developing notochord of Ciona is known to express ion channels that may transduce mechanical forces into Ca 2+ signals 62 .…”

From spikes to intercellular waves: tuning intercellular Ca2+signaling dynamics modulates organ size control

“…signaling is connected to the regulation of cell mechanics is not currently understood and warrants further investigation. One possibility is that tension impacts the level of gap junction communication between cell and may also influence the activity of mechanosensitive ion channels (Kaouri et al, 2019). Feedback between calcium signaling and cell mechanics may play important roles in ensuring tissue growth and morphogenesis.…”

Effects of time delays and viscoelastic parameters in oscillatory response of cell monolayers

“…These oscillations have been associated with the coupling between the chemical and mechanical signalling [19,11], or the relation between cell polarity and force transmission [18,21], with a potential dependence on the confinement [20]. More recently, it has been observed that the relocation of actomyosin components from medial to junctional areas of the cell may trigger these pulsatile response, suggesting that this biochemical delay between motor molecules is responsible of the observed oscillations [26].…”

“…More recently, it has been observed that the relocation of actomyosin components from medial to junctional areas of the cell may trigger these pulsatile response, suggesting that this biochemical delay between motor molecules is responsible of the observed oscillations [26]. Some recent works have analysed the dynamics of the chemo-mechanical coupling through diffusion reaction equations, with applications in apical constriction in epithelia [11], monolayers on substrates [18,21] or wound healing [22]. In order to analyse the stability of such systems, we here focus on the delay and model it explicitly by resorting to a delayed cell rheology and the resulting delay differential equations, in similar manner to the stress analysis in yeast [13], neural axons conduction [3], transport in respiratory systems [5], or in cell maturation [10].…”