Random-walk model of the sodium-glucose transporter SGLT2 with stochastic steps and inhibition.

Random-walk models are frequently used to model distinct natural phenomena such as diffusion processes, stock-market fluctuations, and biological systems. Here, we present a random-walk model to describe the dynamics of glucose uptake by the sodium-glucose transporter of type 2, SGLT2. Our starting point is the canonical alternating-access model, which suggests the existence of six states for the transport cycle. We propose the inclusion of two new states to this canonical model. The first state is added to implement the recent discovery that the Na+ion can exit before the sugar is released into the proximal tubule epithelial cells. The resulting model is a seven-state mechanism with stochastic steps. Then we determined the transition probabilities between these seven states and used them to write a set of master equations to describe the time evolution of the system. We showed that our model converges to the expected equilibrium configuration and that the binding of Na+and glucose to SGLT2 in the inward-facing conformation must be necessarily unordered. After that, we added another state to implement inhibition in the model. Our results reproduce the experimental dependence of glucose uptake on the inhibitor concentration and they reveal that the inhibitors act by decreasing the number of available SGLT2s, which increases the chances of glucose escaping reabsorption.

Random-walk model of cotransport.

We present a statistical mechanical model to describe the dynamics of an arbitrary cotransport system. Our starting point was the alternating access mechanism, which suggests the existence of six states for the cotransport cycle. Then we determined the 14 transition probabilities between these states, including a leak pathway, and used them to write a set of Master Equations for describing the time evolution of the system. The agreement between the asymptotic behavior of this set of equations and the result obtained from thermodynamics is a confirmation that leakage is compatible with the static head equilibrium condition and that our model has captured the essential physics of cotransport. In addition, the model correctly reproduced the transport dynamics found in the literature.

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)NRMCBP1471-007210.1038/35085077], 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.