Anomalous relaxation kinetics of biological lattice-ligand binding models

We discuss theoretical models for the cooperative binding dynamics of ligands to substrates, such as dimeric motor proteins to microtubules or more extended macromolecules like tropomyosin to actin filaments. We study the effects of steric constraints, size of ligands, binding rates and interaction between neighboring proteins on the binding dynamics and binding stoichiometry. Starting from an empty lattice the binding dynamics goes, quite generally, through several stages. The first stage represents fast initial binding closely resembling the physics of random sequential adsorption processes. Typically this initial process leaves the system in a metastable locked state with many small gaps between blocks of bound molecules. In a second stage the gaps annihilate slowly as the ligands detach and reattach. This results in an algebraic decay of the gap concentration and interesting scaling behavior. Upon identifying the gaps with particles we show that the dynamics in this regime can be explained by mapping it onto various reaction-diffusion models. The final approach to equilibrium shows some interesting dynamic scaling properties. We also discuss the effect of cooperativity on the equilibrium stoichiometry, and their consequences for the interpretation of biochemical and image reconstruction results.Comment: REVTeX, 20 pages, 17 figures; review, to appear in Chemical Physics; v2: minor correction

Reduced-Order Modeling of Reacting Supersonic Flows in Scramjet Nozzles

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83629/1/AIAA-2010-6958-311.pd

ELECTIONS AND THE THEORY OF CAMPAIGN CONTRIBUTIONS: A SURVEY AND CRITICAL ANALYSIS

The formal theory of campaign contributions in elections has expanded in the past decade. The basic assumptions and results of these models are examined and analyzed. The assumptions of the models are often inappropriate for the political actors considered and the results are sometimes not empirically supported. We suggest ways in which these models may be altered to alleviate some of these problems. Copyright 1992 Blackwell Publishers Ltd..