Entropy and Free Energy of a Mobile Loop Based on the Crystal Structures of the Free and Bound Proteins

Absolute free energy of binding of avidin/biotin, revisited

The binding of biotin to avidin is one of the strongest in nature with absolute free energy of binding, ΔA(0) = -20.4 kcal/mol. Therefore, this complex became a target for a large number of computational studies, which all, however, are based on approximate techniques or simplified models and have led to a wide range of results Therefore, ΔA(0) is calculated here by rigorous statistical mechanical methods and models that consider long-range electrostatics. (1) We apply our method, "hypothetical scanning molecular dynamics with thermodynamic integration" (HSMD-TI) to avidin-biotin modeled by periodic boundary conditions with particle mesh ewald (PME). (2) We apply the double decoupling method (DDM) to this system modeled by the spherical solvent boundary potential (SSBP) and the generalized solvent boundary potential (GSBP). The corresponding results for neutral biotin, ΔA(0) = -29.1 ± 0.8 and -25.2 ± 0.5 kcal/mol are significantly lower than the experimental value; we also provide the result for a charged biotin, ΔA(0) = -33.3 ± 0.8 kcal/mol. It is plausible to suggest that this disagreement with the experiment may stem from ignoring the (positive) contribution of a mobile loop that changes its structure upon ligand binding.

Relative stability of the open and closed conformations of the active site loop of streptavidin

The eight-residue surface loop, 45-52 (Ser, Ala, Val, Gly, Asn, Ala, Glu, Ser), of the homotetrameric protein streptavidin has a "closed" conformation in the streptavidin-biotin complex, where the corresponding binding affinity is one of the strongest found in nature (ΔG ∼ -18 kcal∕mol). However, in most of the crystal structures of apo (unbound) streptavidin, the loop conformation is "open" and typically exhibits partial disorder and high B-factors. Thus, it is plausible to assume that the loop structure is changed from open to closed upon binding of biotin, and the corresponding difference in free energy, ΔF = F(open) - F(closed) in the unbound protein, should therefore be considered in the total absolute free energy of binding. ΔF (which has generally been neglected) is calculated here using our "hypothetical scanning molecular-dynamics" (HSMD) method. We use a protein model in which only the atoms closest to the loop are considered (the "template") and they are fixed in the x-ray coordinates of the free protein; the x-ray conformation of the closed loop is attached to the same (unbound) template and both systems are capped with the same sphere of TIP3P water. Using the force field of the assisted model building with energy refinement (AMBER), we carry out two separate MD simulations (at temperature T = 300 K), starting from the open and closed conformations, where only the atoms of the loop and water are allowed to move (the template-water and template-loop interactions are considered). The absolute F(open) and F(closed) (of loop + water) are calculated from these trajectories, where the loop and water contributions are obtained by HSMD and a thermodynamic integration (TI) process, respectively. The combined HSMD-TI procedure leads to total (loop + water) ΔF = -27.1 ± 2.0 kcal∕mol, where the entropy TΔS constitutes 34% of ΔF, meaning that the effect of S is significant and should not be ignored. Also, ΔS is positive, in accord with the high flexibility of the open loop observed in crystal structures, while the energy ΔE is unexpectedly negative, thus also adding to the stability of the open loop. The loop and the 250 capped water molecules are the largest system studied thus far, which constitutes a test for the efficiency of HSMD-TI; this efficiency and technical issues related to the implementation of the method are also discussed. Finally, the result for ΔF is a prediction that will be considered in the calculation of the absolute free energy of binding of biotin to streptavidin, which constitutes our next project.