The Heisenberg Chain as a Dynamical Model for Protein Synthesis - Some Theoretical and Experimental Results

Abstract

The integrable Heisenberg quantum chain with certain non-diagonal boundary fields is the generator of a Markov process known as asymmetric exclusion process with open boundary conditions. This is a driven lattice gas where particles hop randomly along a one-dimensional chain and are injected and absorbed at the boundaries. This model has been suggested in 1968 by MacDonald, Gibbs and Pipkin as a model for the kinetics of protein synthesis on nucleic acid templates. The exact solution of the steady state of the system (corresponding to the exact ground state of the Heisenberg chain) which was obtained recently is shown to be in qualitative agreement with experimental data. The exact solution supports some of the original conclusions drawn from a mean field treatment by MacDonald et al. but gives deeper insight into one important aspect.