Transport cycle of Escherichia coli lactose permease in a nonhomogeneous random walk model

We present Monte Carlo simulations for the transport cycle of Escherichia coli lactose permease (LacY), using as a starting point the model proposed by Kaback et al. [Nat. Rev. Mol. Cell Biol. 2, 610 (2001)], which is based on functional properties of mutants and x-ray structures. Kaback's model suggests the existence of six states for the whole cycle of lactose-H+ symport. However, the free-energy differences between these states have not yet been reported in the literature. Here, we analyzed the biochemical structure of each state and determined a range of possible values for each one of the five free-energy variations. Then, using the Metropolis algorithm in a nonhomogeneous random walk model, we tested all the possible combinations with these values to find the free-energy curve that best reproduces the dynamics of LacY. The agreement between our model predictions and the experimental data suggests that our free-energy curve is appropriate for describing the lactose-H+ symport. We found not only this curve, but also the time of occupancy of the permease at each conformation. In addition, we paved the way in this work to solve an open question related to this transport mechanism, which is the importance of protonation for lactose binding.