Biomedical subjects
Publications and source records attributed to R Zwanzig.
Levinthal's paradox is that finding the native folded state of a protein by a random search among all possible configurations can take an enormously long time. Yet proteins can fold in seconds or less. Mathematical analysis of a simple model shows that a small and physically reasonable energy bias against locally unfavorable configurations, of the order of a few kT, can reduce Levinthal's time to a biologically significant size.
The theory of the kinetics of binding of ligands to a sphere partially covered by receptors is extended to provide the full time dependence of the reactive flux. The ligands diffuse to the receptors; the receptors are either fully or partially absorbing. The total flux into the sphere with many receptors is expressed analytically in terms of the flux into a single isolated receptor on the sphere. At steady state, the Berg-Purcell formula is generalized to the case where the binding to a single receptor is only partially diffusion controlled. At short times, the receptors behave independently and the total flux is the sum of the fluxes to the isolated receptors.
An effective medium treatment is used to extend Berg and Purcell's theory of diffusion-controlled ligand binding to a sphere partially covered by receptors. This treatment takes into account more completely the effects of interference between receptors. The results are in excellent agreement with computer simulations by Northrup.
Diffusion in a spatially rough one-dimensional potential is treated by analysis of the mean first passage time. A general expression is found for the effective diffusion coefficient, which can become very small at low temperatures.
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The growth or decay of population of a single species interacting with a large number of other species (or environment) according to the Volterra-Lotka model is investigated. When the environment is initially very close to its equilibrium level, the growth of a single species follows a generalized Verhulst law, containing hereditary effects. The derivation, modeled on statistical mechanical theories of Brownian motion, leads also to a "noise" source and to its relation to the heredity kernel. A special case, where the hereditary kernel is a damped exponential function of time, is solved numerically. When growth starts at a level much below equilibrium, the population first overshoots equilibrium and then approaches it. When decay starts at a level much higher than equilibrium, the population first decays precipitously to a very low level and then slowly grows toward equilibrium.