10 research outputs found
Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
We investigate the motion of a run-and-tumble particle (RTP) in one
dimension. We find the exact probability distribution of the particle with and
without diffusion on the infinite line, as well as in a finite interval. In the
infinite domain, this probability distribution approaches a Gaussian form in
the long-time limit, as in the case of a regular Brownian particle. At
intermediate times, this distribution exhibits unexpected multi-modal forms. In
a finite domain, the probability distribution reaches a steady state form with
peaks at the boundaries, in contrast to a Brownian particle. We also study the
relaxation to the steady state analytically. Finally we compute the survival
probability of the RTP in a semi-infinite domain. In the finite interval, we
compute the exit probability and the associated exit times. We provide
numerical verifications of our analytical results
The Role of Multifilament Structures and Lateral Interactions in Dynamics of Cytoskeleton Proteins and Assemblies
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