  Many biological systems can be described by finite Markov models. A general
method for simplifying master equations is presented that is based on merging
adjacent states. The approach preserves the steady-state probability
distribution and all steady-state fluxes except the one between the merged
states. Different levels of coarse graining of the underlying microscopic
dynamics can be obtained by iteration, with the result being independent of the
order in which states are merged. A criterion for the optimal level of coarse
graining or resolution of the process is proposed via a tradeoff between the
simplicity of the coarse-grained model and the information loss relative to the
original model. As a case study, the method is applied to the cycle kinetics of
the molecular motor kinesin.
