Minimal Model of Cellular Symmetry Breaking.

The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry-breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechanochemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities.

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population.

Several independent observations have suggested that the catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent in vitro observations by Gardner et al. [M. K. Gardner et al., Cell 147, 1092 (2011)] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here we investigate, via numerical simulations and mathematical calculations, some of the consequences of the age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically, and purely linear growth. The boundary demarcating the steady-state and non-steady-state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to nonexponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that the age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.

Microtubule catastrophe from protofilament dynamics.

The disappearance of the guanosine triphosphate- (GTP) tubulin cap is widely believed to be the forerunner event for the growth-shrinkage transition ("catastrophe") in microtubule filaments in eukaryotic cells. We study a discrete version of a stochastic model of the GTP cap dynamics, originally proposed by Flyvbjerg, Holy, and Leibler [Phys. Rev. Lett. 73, 2372 (1994)]. Our model includes both spontaneous and vectorial hydrolysis, as well as dissociation of a nonhydrolyzed dimer from the filament after incorporation. In the first part of the paper, we apply this model to a single protofilament of a microtubule. A catastrophe transition is defined for each protofilament, similarly to the earlier one-dimensional models, the frequency of occurrence of which is then calculated under various conditions but without explicit assumption of steady-state conditions. Using a perturbative approach, we show that the leading asymptotic behavior of the protofilament catastrophe in the limit of large growth velocities is remarkably similar across different models. In the second part of the paper, we extend our analysis to the entire filament by making a conjecture that a minimum number of such transitions are required to occur for the onset of microtubule catastrophe. The frequency of microtubule catastrophe is then determined using numerical simulations and compared with analytical and semianalytical estimates made under steady-state and quasi-steady-state assumptions, respectively, for the protofilament dynamics. A few relevant experimental results are analyzed in detail and compared with predictions from the model. Our results indicate that loss of GTP cap in two to three protofilaments is necessary to trigger catastrophe in a microtubule.