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 one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all

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. If this shock front can reach the size of assembled capsids, then capsid assembly follows either the LMA or a "pseudo" LMA that describes partitioning of capsid proteins between assembled capsids and a metastable, supersaturated solution of free proteins that decays logarithmically slowly. We show that the applicability of the LMA and the pseudo-LMA is governed by two dimensionless parameters: the dimensionless nucleation rate and the dimensionless line energy of incomplete capsids.

that Klenow and Klentaq have minimal sensitivity to pH changes, with proton linkages of ~0.06 and ~0.3 respectively in KCl. Furthermore, osmotic stress data in KCl indicates 500~600 waters are released upon binding by both polymerases. Glutamate is the major intracellular anion accumulated in E.coli in the presence of KCl in the external environment. The 'glutamate effect' is primarily characterized by an increase in DNA binding affinity when chloride is replaced by glutamate. Some proteins also exhibit decreased ionic linkage in glutamate. Klenow exhibits both aspects of the 'glutamate effect'. Substituting glutamate for chloride reduces the ionic linkage for Klenow by >50%. The presence of glutamate also increases the proton linkage of Klenow five fold and decreases water release by ~70% to approximately 150 waters. The dramatic decrease in water release highlights the osmotic nature of the glutamate effect. Glutamate and chloride salts behave as ionic inhibitors of DNA binding but glutamate salts also exhibit an osmotic enhancement effect. While Klentaq's DNA binding affinity is also enhanced by glutamate, its ionic and proton linkages are not altered. The osmotic enhancement is present for Klentaq but it is not as significant in the salt concentration range at which nanomolar Klentaq-DNA binding occurs. E.coli DNA-binding proteins might have evolved to bind tightly at higher salt concentration to utilize the glutamate effect while accumulating intracellular glutamate.

Abstract. Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discretestate stochastic "burnt-bridge" models. The transport of the particles is viewed as an effective diffusion along one-dimensional lattices with periodically distributed weak links. When an unbiased random walker passes the weak link it can be destroyed ("burned") with probability p, providing a bias in the motion of the molecular motor. A new theoretical approach that allows one to calculate exactly all dynamic properties of motor proteins, such as velocity and dispersion, at general conditions is presented. It is found that dispersion is a decreasing function of the concentration of bridges, while the dependence of dispersion on the burning probability is more complex. Our calculations also show a gap in dispersion for very low concentrations of weak links which indicates a dynamic phase transition between unbiased and biased diffusion regimes. Theoretical findings are supported by Monte Carlo computer simulations.

The self-assembly of perfectly ordered closed shells is a challenging process involved in many biological and nanoscale systems. However, most of the aspects that determine their formation are still unknown. Here we investigate the growth of shells by simulating the assembly of spherical structures made of N identical subunits. Remarkably, we show that the formation and energetics of partially assembled shells are dominated by an effective line-tension that can be described in simple thermodynamic terms. In addition, we unveil two mechanisms that can prevent the correct formation of defect-free structures: "hole implosion," which leads to a premature closure of the shell; and "closure catastrophe," which causes a dramatic production of structural disorder during the later stages of the growth of big shells.

Atomic displacements of hydrated proteins are dominated by phonon vibrations at low temperatures and by dissipative large-amplitude motions at high temperatures. A crossover between the two regimes is known as a dynamical transition. Recent experiments indicate a connection between the dynamical transition and the dielectric response of the hydrated protein. We analyze two mechanisms of the coupling between the protein atomic motions and the protein-water interface. The first mechanism considers viscoelastic changes in the global shape of the protein plasticized by its coupling to the hydration shell. The second mechanism involves modulations of the local motions of partial charges inside the protein by electrostatic fluctuations. The model is used to analyze mean-square displacements of iron of metmyoglobin reported by Mössbauer spectroscopy. We show that high displacement of heme iron at physiological temperatures is dominated by electrostatic fluctuations. Two onsets, one arising from the viscoelastic response and the second from electrostatic fluctuations, are seen in the temperature dependence of the mean-square displacements when the corresponding relaxation times enter the instrumental resolution window.

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. Interaction between the backward biased molecular motor and the bridge-burning mechanism yields a complex dynamic behavior. For the reversible dissociation the backward motion of the molecular motor is slowed down. There is a change in the direction of the molecular motor's motion for some range of parameters. The molecular motor also experiences nonmonotonic fluctuations due to the action of two opposing mechanisms: the reduced activity after the burned sites and locking of large fluctuations. Large spatial fluctuations are observed when two mechanisms are comparable. The properties of the molecular motor are different for the irreversible burning of bridges where the velocity and fluctuations are suppressed for some concentration range, and the dynamic transition is also observed. Dynamics of the system is discussed in terms of the effective driving forces and transitions between different diffusional regimes.

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. For viral shells, the AGTI relieves intrinsic elastic stresses by generating corrugation along the perimeter of the assembling shell. The buckling transition of Lidmar, Mirny, and Nelson provides an alternative mechanism for stress release, which in principle would allow for avoidance of AGTIs. For system parameters appropriate for viral shells however, the AGTI appears to be unavoidable. The azimuthal stress condensation produced by the AGTI might actually assist assembly by providing a guiding mechanism for the insertion of pentamers during viral assembly.