Assembly of viruses and the pseudo-law of mass action.

The self-assembly of the protein shell ("capsid") of a virus appears to obey the law of mass action (LMA) despite the fact that viral assembly is a nonequilibrium process. In this paper we examine a model for capsid assembly, the "assembly line model," that can be analyzed analytically. We show that, in this model, efficient viral assembly from a supersaturated solution is characterized by a shock front propagating in the assembly configuration space from small to large aggregate sizes.

Assembly of viral capsids, buckling, and the Asaro-Grinfeld-Tiller instability.

Icosahedral viral shells are characterized by intrinsic elastic stress focused on the 12 structurally required pentamers. We show that, according to thin-shell theory, assembling icosahedral viral shells should be subject to the Asaro-Grinfeld-Tiller instability (AGTI). AGTIs are encountered in growing epitaxial films exposed to extrinsic elastic stress.

Molecular motors interacting with their own tracks.

Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state "burnt-bridge" models. Molecular motors are viewed as diffusing particles that can asymmetrically break or rebuild periodically distributed weak links when passing over them. Our explicit calculations of dynamic properties show that coupling the transport of the unbiased molecular motor with the bridge-burning mechanism leads to a directed motion that lowers fluctuations and produces a dynamic transition in the limit of low concentration of weak links.

Solutions of burnt-bridge models for molecular motor transport.

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called "bridges"), is investigated theoretically by analyzing discrete-state stochastic "burnt-bridge" models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed ("burned") with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties.