Optimal Relabeling of Water Molecules and Single-Molecule Entropy Estimation

Estimation of solvent entropy from equilibrium molecular dynamics simulations is a long-standing problem in statistical mechanics. In recent years, methods that estimate entropy using k-th nearest neighbours (kNN) have been applied to internal degrees of freedom in biomolecular simulations, and for the rigorous computation of positional-orientational entropy of one and two molecules. The mutual information expansion (MIE) and the maximum information spanning tree (MIST) methods were proposed and used to deal with a large number of non-independent degrees of freedom, providing estimates or bounds on the global entropy, thus complementing the kNN method. The application of the combination of such methods to solvent molecules appears problematic because of the indistinguishability of molecules and of their symmetric parts. All indistiguishable molecules span the same global conformational volume, making application of MIE and MIST methods difficult. Here, we address the problem of indistinguishability by relabeling water molecules in such a way that each water molecule spans only a local region throughout the simulation. Then, we work out approximations and show how to compute the single-molecule entropy for the system of relabeled molecules. The results suggest that relabeling water molecules is promising for computation of solvation entropy.

On the coupling between the dynamics of protein and water

The solvation entropy of flexible protein regions is higher than that of rigid regions and contributes differently to the overall thermodynamic stability.

Thermodynamic mechanism for inhibition of lactose permease by the phosphotransferase protein IIAGlc

In a variety of bacteria, the phosphotransferase protein IIAGlcplays a key regulatory role in catabolite repression in addition to its role in the vectorial phosphorylation of glucose catalyzed by the phosphoenolpyruvate:carbohydrate phosphotransferase system (PTS). The lactose permease (LacY) ofEscherichia colicatalyzes stoichiometric symport of a galactoside with an H+, using a mechanism in which sugar- and H+-binding sites become alternatively accessible to either side of the membrane. Both the expression (via regulation of cAMP levels) and the activity of LacY are subject to regulation by IIAGlc(inducer exclusion). Here we report the thermodynamic features of the IIAGlc–LacY interaction as measured by isothermal titration calorimetry (ITC). The studies show that IIAGlcbinds to LacY with aKdof about 5 μM and a stoichiometry of unity and that binding is driven by solvation entropy and opposed by enthalpy. Upon IIAGlcbinding, the conformational entropy of LacY is restrained, which leads to a significant decrease in sugar affinity. By suppressing conformational dynamics, IIAGlcblocks inducer entry into cells and favors constitutive glucose uptake and utilization. Furthermore, the studies support the notion that sugar binding involves an induced-fit mechanism that is inhibited by IIAGlcbinding. The precise mechanism of the inhibition of LacY by IIAGlcelucidated by ITC differs from the inhibition of melibiose permease (MelB), supporting the idea that permeases can differ in their thermodynamic response to binding IIAGlc.