2022/04/02 by Doron Grossman, Eytan Katzav, Grossman, Doron +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Micro and Nano Robotics #Microtubule and mitosis dynamics #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2204.00921
openalex publication_date 2022/04/02 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Using a statistical-mechanics approach, we study the effects of geometry and self-avoidance on the ordering of slender filaments inside non-isotropic containers, considering cortical microtubules in plant cells, and packing of genetic material inside viral capsids as concrete examples. Within a mean-field approximation, we show analytically how the shape of the container, together with self-avoidance, affects the ordering of the stiff rods. We find that the strength of the self-avoiding interaction plays a significant role in the preferred packing orientation, leading to a first-order transition for oblate cells, where the preferred orientation changes from azimuthal, along the equator, to a polar one, when self-avoidance is strong enough. While for prolate spheroids the ground state is always a polar-like order, strong self-avoidance results with a deep meta-stable state along the equator. We compute the critical surface describing the transition between azimuthal and polar ordering in the three dimensional parameter space (persistence length, eccentricity, and self-avoidance) and show that the critical behavior of this system is in fact related to the butterfly catastrophe model. We calculate the pressure and shear stress applied by the filament on the surface, and the injection force needed to be applied on the filament in order to insert it into the volume. We compare these results to the pure mechanical study where self-avoidance is ignored, and discuss similarities and differences.