Low-copy-number molecules are involved in many functions in cells. The intrinsic fluctuations of these numbers can enable stochastic switching between multiple steady states, inducing phenotypic variability. Herein we present a theoretical and computational study based on Master Equations and Fokker-Planck and Langevin descriptions of stochastic switching for a genetic circuit of autoactivation. We show that in this circuit the intrinsic fluctuations arising from low-copy numbers, which are inherently state-dependent, drive asymmetric switching. These theoretical results are consistent with experimental data that have been reported for the bistable system of the gallactose signaling network in yeast. Our study unravels that intrinsic fluctuations, while not required to describe bistability, are fundamental to understand stochastic switching and the dynamical relative stability of multiple states.

We explore the behavior of a wormlike micellar solution under both steady and large amplitude oscillatory shear (LAOS) in a cone-plate geometry through simultaneous bulk rheometry and localized velocimetric measurements. First, particle image velocimetry is used to show that the shear banded profiles observed in steady shear are in qualitative agreement with previous results for flow in the cone-plate geometry. Then under LAOS, we observe the onset of shear-banded flow in the fluid as it is progressively deformed into the non-linear regime -this onset closely coincides with the appearance of higher harmonics in the periodic stress signal measured by the rheometer. These harmonics are quantified using the higher order elastic and viscous Chebyshev coefficients e n and v n , which are shown to grow as the banding behavior becomes more pronounced. The high resolution of the velocimetric imaging system enables spatiotemporal variations in the structure of the banded flow to be observed in great detail. Specifically, we observe that at large strain amplitudes (γ 0 ≥ 1) the fluid exhibits a 3-banded velocity profile with a high shear rate band located in-between two lower shear rate bands adjacent to each wall. This band persists over the full cycle of the oscillation, resulting in no phase lag being observed between the appearance of the band and the driving strain amplitude. In addition to the kinematic measurements of shear banding, the methods used to prevent wall slip and edge irregularities are discussed in detail, and these methods are shown to have a measurable effect on the stability boundaries of the shear banded flow.

We determine both experimentally and numerically the onset of elastic flow instabilities in viscoelastic polymer solutions with different levels of shear thinning.