We present a detailed comparison of computational efficiency and precision for several free energy difference (ΔF) methods. The analysis includes both equilibrium and nonequilibrium approaches, and distinguishes between unidirectional and bidirectional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration, and single-ensemble path sampling to more established methodologies. As test cases, we study relative solvation free energies of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation ΔF estimates as compared to other methods used in this report, while also offering rapid estimation of ΔF. The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the unidirectional, “fast-growth” nonequilibrium case. Closer examination of the path sampling approach on a two-dimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.

Determination of protein-protein binding affinity values is key to understanding various underlying biological phenomena, such as how mutations change protein-protein binding. Most existing non-rigorous (fast) and rigorous (slow) methods that rely on all-atom representation of the proteins force the user to choose between speed and accuracy. In an attempt to achieve balance between speed and accuracy, we have combined rigorous umbrella sampling molecular dynamics simulation with a coarse-grained protein model. We predicted the effect of mutations on binding affinity by selecting three protein-protein systems and comparing results to empirical relative binding affinity values, and to non-rigorous modeling approaches. We obtained significant improvement both in our ability to discern stabilizing from destabilizing mutations and in the correlation between predicted and experimental values compared to non-rigorous approaches. Overall our results suggest that using a rigorous affinity calculation method with coarse-grained protein models could offer fast and reliable predictions of protein-protein binding free energies.

The 2014 Ebola virus (EBOV) outbreak in West Africa is the largest in recorded history and resulted in over 11,000 deaths. It is essential that strategies for treatment and containment be developed to avoid future epidemics of this magnitude. With the development of vaccines and antibody-based therapies using the envelope glycoprotein (GP) of the 1976 Mayinga strain, one important strategy is to anticipate how the evolution of EBOV might compromise these efforts. In this study we have initiated a watch list of potential antibody escape mutations of EBOV by modeling interactions between GP and the antibody KZ52. The watch list was generated using molecular modeling to estimate stability changes due to mutation. Every possible mutation of GP was considered and the list was generated from those that are predicted to disrupt GP-KZ52 binding but not to disrupt the ability of GP to fold and to form trimers. The resulting watch list contains 34 mutations (one of which has already been seen in humans) at six sites in the GP2 subunit. Should mutations from the watch list appear and spread during an epidemic, it warrants attention as these mutations may reflect an evolutionary response from the virus that could reduce the effectiveness of interventions such as vaccination. However, this watch list is incomplete and emphasizes the need for more experimental structures of EBOV interacting with antibodies in order to expand the watch list to other epitopes. We hope that this work provokes experimental research on evolutionary escape in both Ebola and other viral pathogens.

We compute the absolute binding affinities for two ligands bound to the FKBP protein using nonequilibrium unbinding simulations. The methodology is straightforward requiring little or no modification to many modern molecular simulation packages. The approach makes use of a physical pathway, eliminating the need for complicated alchemical decoupling schemes. We compare our nonequilibrium results to those obtained via a fully equilibrium approach and to experiment. The results of this study suggest that to obtain accurate results using nonequilibrium approaches one should use the stiff-spring approximation with the second cumulant expansion. From this study we conclude that nonequilibrium simulation could provide a simple means to estimate protein-ligand binding affinities.

Developing a comprehensive description of the equilibrium structural ensembles for intrinsically disordered proteins (IDPs) is essential to understanding their function. The p53 transactivation domain (p53TAD) is an IDP that interacts with multiple protein partners and contains numerous phosphorylation sites. Multiple techniques were used to investigate the equilibrium structural ensemble of p53TAD in its native and chemically unfolded states. The results from these experiments show that the native state of p53TAD has dimensions similar to a classical random coil while the chemically unfolded state is more extended. To investigate the molecular properties responsible for this behavior, a novel algorithm that generates diverse and unbiased structural ensembles of IDPs was developed. This algorithm was used to generate a large pool of plausible p53TAD structures that were reweighted to identify a subset of structures with the best fit to small angle X-ray scattering data. High weight structures in the native state ensemble show features that are localized to protein binding sites and regions with high proline content. The features localized to the protein binding sites are mostly eliminated in the chemically unfolded ensemble; while, the regions with high proline content remain relatively unaffected. Data from NMR experiments support these results, showing that residues from the protein binding sites experience larger environmental changes upon unfolding by urea than regions with high proline content. This behavior is consistent with the urea-induced exposure of nonpolar and aromatic side-chains in the protein binding sites that are partially excluded from solvent in the native state ensemble.