Instabilities and Patterns in Active Systems: Effects of Substrate Friction, Geometry and Shape Fluctuations

<strong>Seminar of the School of Physical Sciences ----------------------------------------------</strong> Title: <strong>Instabilities and Patterns in Active Systems: Effects of Substrate Friction, Geometry and Shape Fluctuations</strong> Speaker: <strong>Pragya Srivastava</strong> (Syracuse University, Syracuse) Date: <strong>August 3, 2015</strong> <strong>Abstract:</strong> I will discuss the effects of substrate friction, geometry and shape changes on the dynamics and pattern formation in active systems with polar and apolar symmetries. I will present three different problems unified by a common theoretical approach based on the continuum modeling of active matter. First, motivated by the experiments on microtubule bundles confined to an oil-water interface, I will discuss the self-sustained dynamics of active nematic films. Upon eliminating the flow in the overdamped limit, one obtains closed equations for the nematic order parameter, with Frank constants renormalized by activity. Large values of activity can drive the renormalized elastic constants negative, Leading to instability of the uniformly ordered state. This minimal model yields emergent patterns of growing complexity with increasing activity. In second part of the talk I will shift the focus to polar active systems and will discuss the effects of substrate geometry in controlling the patterns of acto-myosin filaments in Fission Yeast cells and rod-shaped bacteria such as B. Subtillis. Using continuum models that couple orientation and curvature, I will show that the geometry of the cell is crucial in determining the steady state patterns of acto-myosin filaments. Moreover, the cellular shape not only influences the possible steady state patterns, but also determines their stability. These results are supported by experiments in spherical Fission Yeast cells demonstrating the important role played by cell shape in stabilizing the actor-myosin ring during cytokinesis. Finally, motivated by the observation of coupled fluctuations of acto-myosin density and membrane shape at the leading edges of moving and spreading cells, I will present a continuum model for the coupled dynamics of active cortical actin and the cell membrane.