Relaxation kinetics of biological dimer adsorption models

We discuss the relaxation kinetics of a one-dimensional dimer adsorption mo del as recently proposed for the binding of biological dimers like kinesin on microtubules. The non-equilibrium dynamics shows several regimes: irreve rsible 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-di ffusion model. We show that there are several possibilities to de ne the au tocorrelation function and that they all asymptotically show exponential de cay, however with different time constants. Our findings remain valid if th ere is an attractive interaction between bound dimers.