  We consider the dependence of the electron transfer in photosynthetic
complexes on correlation properties of random fluctuations of the protein
environment. The electron subsystem is modeled by a finite network of connected
electron (exciton) sites. The fluctuations of the protein environment are
modeled by random telegraph processes, which act either collectively
(correlated) or independently (uncorrelated) on the electron sites. We derived
an exact closed system of first-order linear differential equations with
constant coefficients, for the average density matrix elements and for their
first moments. Under some conditions, we obtain analytic expressions for the
electron transfer rates. We compare the correlated and uncorrelated regimes,
and demonstrated numerically that the uncorrelated fluctuations of the protein
environment can, under some conditions, either increase or decrease the
electron transfer rates.
