Relaxation kinetics of biological dimer adsorption models

¹ Institut für Theoretische Physik, Technische Universität München D-85747 Garching, Germany
² Physics Department, Harvard University - Cambridge, MA 02138, USA

Received: 15 May 2000
Accepted: 10 August 2001

Abstract

We discuss the relaxation kinetics of a one-dimensional dimer adsorption model as recently proposed for the binding of biological dimers like kinesin on microtubules. The non-equilibrium dynamics shows several regimes: irreversible adsorption on short time scales, an intermediate plateau followed by a power law regime and finally exponential relaxation towards equilibrium. In all four regimes we give analytical solutions. The algebraic decay and the scaling behaviour can be explained by mapping onto a simple reaction-diffusion model. We show that there are several possibilities to define the autocorrelation function and that they all asymptotically show exponential decay, however with different time constants. Our findings remain valid if there is an attractive interaction between bound dimers.