On the role of mechanical feedback in synchronous to asynchronous transition during embryogenesis

Experiments have shown that during the initial stage of Zebrafish morphogenesis a synchronous to asynchronous transition (SAT) occurs, as the cells divide extremely rapidly. In the synchronous phase, the cells divide in unison unlike in the asynchronous phase. Despite the widespread observation of SAT in experiments, a theory to calculate the critical number of cell cycles, $n^{*}$, at which asynchronous growth emerges does not exist. Here, using a model for the cell cycle, with the assumption that cell division times are Gaussian distributed with broadening, we predict $n^{*}$ and the time at which the SAT occurs. The theoretical results are in excellent agreement with experiments. The theory, supplemented by agent based simulations, establish that the SAT emerges as a consequence of biomechanical feedback on cell division. The emergence of asynchronous phase is due to linearly increasing fluctuations in the cell cycle times with each round of cell division. We also make several testable predictions, which would further shed light on the role of biomechanical feedback on the growth of multicellular systems.