DRhoGEF2 regulates cellular tension and cell pulsations in the Amnioserosa during Drosophila dorsal closure

Coordination of apical constriction in epithelial sheets is a fundamental process during embryogenesis. Here, we show that DRhoGEF2 is a key regulator of apical pulsation and constriction of amnioserosal cells during Drosophila dorsal closure. Amnioserosal cells mutant for DRhoGEF2 exhibit a consistent decrease in amnioserosa pulsations whereas overexpression of DRhoGEF2 in this tissue leads to an increase in the contraction time of pulsations. We probed the physical properties of the amnioserosa to show that the average tension in DRhoGEF2 mutant cells is lower than wild-type and that overexpression of DRhoGEF2 results in a tissue that is more solid-like than wild-type. We also observe that in the DRhoGEF2 overexpressing cells there is a dramatic increase of apical actomyosin coalescence that can contribute to the generation of more contractile forces, leading to amnioserosal cells with smaller apical surface than wild-type. Conversely, in DRhoGEF2 mutants, the apical actomyosin coalescence is impaired. These results identify DRhoGEF2 as an upstream regulator of the actomyosin contractile machinery that drives amnioserosa cells pulsations and apical constriction.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.