Dissipative Dynamics and the Statistics of Energy States of a Hookean Model for Protein Folding

A generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein-Uhlenbeck process and giving rise to the so called Wigner distribution. A tunably fine- or coarse-grained sampling of the energy landscape yields a family of distributions for the energies and energy spacings.Comment: RevTeX, 24 pages, including 8 figure

Loop formation of microtubules during gliding at high density

The microtubule cytoskeleton, including the associated proteins, forms a complex network essential to multiple cellular processes. Microtubule-associated motor proteins, such as kinesin-1, travel on microtubules to transport membrane bound vesicles across the crowded cell. Other motors, such as cytoplasmic dynein and kinesin-5, are used to organize the cytoskeleton during mitosis. In order to understand the self-organization processes of motors on microtubules, we performed filament-gliding assays with kinesin-1 motors bound to the cover glass with a high density of microtubules on the surface. To observe microtubule organization, 3% of the microtubules were fluorescently labeled to serve as tracers. We find that microtubules in these assays are not confined to two dimensions and can cross one other. This causes microtubules to align locally with a relatively short correlation length. At high density, this local alignment is enough to create ‘intersections’ of perpendicularly oriented groups of microtubules. These intersections create vortices that cause microtubules to form loops. We characterize the radius of curvature and time duration of the loops. These different behaviors give insight into how crowded conditions, such as those in the cell, might affect motor behavior and cytoskeleton organization