Evolution of All-Atom Protein Force Fields to Improve Local and Global Properties

Accurate Calculation of Barnase and SNase Folding Energetics Using Short Molecular Dynamics Simulations and an Atomistic Model of the Unfolded Ensemble: Evaluation of Force Fields and Water Models

As proteins perform most cellular functions, quantitative understanding of protein energetics is required to gain control of biological phenomena. Accurate models of native proteins can be obtained experimentally, but the lack of equally fine models of unfolded ensembles impedes the calculation of protein folding energetics from first principles. Here, we show that an atomistic unfolded ensemble model, consisting of a few dozen conformations built from a protein sequence, can be used in conjunction with an X-ray structure of its native state to calculate accurately by difference the changes in enthalpy and heat capacity of the polypeptide upon folding. The calculation is done using molecular dynamics simulations, popular force fields, and water models, and for the two model proteins studied (barnase and SNase), the results agree within error or are very close to their experimentally determined properties. The enthalpy sampling of the unfolded ensemble is done through short 2 ns simulations that do not significantly modify the representative distribution of R_g of the starting conformations. The impressive accuracy obtained opens the possibility to investigate quantitatively systems or phenomena not amenable to experiment and paves the way for addressing the calculation of protein conformational stability (i.e., the change in Gibbs energy upon folding), a central goal of structural biology. So far, these calculated enthalpy and heat capacity changes, combined with the experimentally determined melting temperatures of the corresponding protein, allow us to reproduce the stability curves of both barnase and SNase.

Bayesian-Maximum-Entropy Reweighting of IDP Ensembles Based on NMR Chemical Shifts

Bayesian and Maximum Entropy approaches allow for a statistically sound and systematic fitting of experimental and computational data. Unfortunately, assessing the relative confidence in these two types of data remains difficult as several steps add unknown error. Here we propose the use of a validation-set method to determine the balance, and thus the amount of fitting. We apply the method to synthetic NMR chemical shift data of an intrinsically disordered protein. We show that the method gives consistent results even when other methods to assess the amount of fitting cannot be applied. Finally, we also describe how the errors in the chemical shift predictor can lead to an incorrect fitting and how using secondary chemical shifts could alleviate this problem.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.