CONSTANT-pH MOLECULAR DYNAMICS SIMULATIONS: DEVELOPMENT AND APPLICATIONS

Abstract

Constant-pH molecular dynamics has recently emerged as a useful technique for studying the microscopic details underlying pH dependent properties of proteins. We further develop continuous constant-pH molecular dynamics (CpHMD) in several ways. First, we benchmark the implicit-solvent based CpHMD approach by calculating pKa values for a set of over 100 engineered mutants of hyper-stable variants of staphylococcal nuclease which have titratable residues placed in the hydrophobic interior of the protein and comparing our results to experiment. We present the correlation between the calculated and experimental pKa values and correlations of the calculated pKa error with structural and dynamic quantities of the titratable residues. This analysis allows us to discern the strengths and limitations of implicit-solvent CpHMD.

Secondly, we implement the Langevin algorithm to propagate titration coordinates and develop a pH-based replica exchange protocol to accelerate protonation state sampling in CpHMD. We test the effects these methods have on the convergence of the unprotonated fraction of titratable amino acids. We present statistical tests which allow us to quantify the sampling enhancement. We find that both approaches speed-up protonation-state sampling signicantly.

Next, we develop hybrid-solvent CpHMD to eliminate conformational biases of the generalized Born (GB) implicit-solvent model. In this method, conformational dynamics are governed by the explicit-solvent force field, but protonation state energetics are determined by the GB implicit-solvent model. We calculate pKa values for a series of proteins using both the GB and hybrid-solvent approaches and compare the results to experimental values. We compare the conformational states observed using the GB and the hybrid-solvent approaches and correlate this information with the accuracy of the calculated pKa values. The results indicate that running dynamics in explicit solvent, while using the implicit-solvent model to evaluate protonation-state energetics, yields more realistic conformational sampling which leads to more

accurate pKa calculation.

We then apply hybrid-solvent CpHMD to shed light on the microscopic origins of the pH-dependent assembly of spider dragline silk. We are able to calculate the pH-dependent free energy of N-terminal domain dimerization by calculating pKa values of the N-terminal domain monomer and dimer, and applying linkage thermodynamics. Combining this with pH-dependent conformational changes of the intact dimer allows us to rationalize the experimentally observed pH-dependent dimer formation which is a critical step in silk assembly.

Lastly, we combine the generalized reaction field treament of long-range electrostatics and a charge-neutralization procedure which together allow fully explicit-solvent CpHMD (ECpHMD) to deliver pKa values that are in good agreement with experiment. We test our ECpHMD method on a series of dicarboxylic acids and proteins. We find that the calculated pK a values of dicarboxylic using ECpHMD are more accurate than those from GB-based CpHMD. Overall protein pKa accuracy is on par with the hybrid-solvent approach, but difficulty in sampling conformational states separated by high-energy barriers for residues that participate in strong hydrogen-bond or salt-bridge interactions can reduce pKa accuracy. Initial data suggest this limitation can be overcome by combining the method with more effective sampling techniques. This work paves the way for future application of ECpHMD to study pH-modulated structure and function in chemistry and biology.