Note: network random walk model of two-state protein folding: test of the theory.

We study two-state protein folding in the framework of a toy model of protein dynamics. This model has an important advantage: it allows for an analytical solution for the sum of folding and unfolding rate constants [A. M. Berezhkovskii, F. Tofoleanu, and N.-V. Buchete, J. Chem. Theory Comput. 7, 2370 (2011)10.1021/ct200281d] and hence for the reactive flux at equilibrium. We use the model to test the Kramers-type formula for the reactive flux, which was derived assuming that the protein dynamics is described by a Markov random walk on a network of complex connectivity [A. Berezhkovskii, G. Hummer, and A. Szabo, J. Chem. Phys. 130, 205102 (2009)10.1063/1.3139063]. It is shown that the Kramers-type formula leads to the same result for the reactive flux as the sum of the rate constants.