Conventional molecular dynamics simulations are incapable of sampling many important interactions in biomolecular systems due to their high dimensionality and rough energy landscapes. To observe rare events and calculate transition rates in these systems, enhanced sampling is a necessity. In particular, the study of ligand-protein interactions necessitates a diverse ensemble of protein conformations and transition states, and for many systems, this occurs on prohibitively long time scales. Previous strategies such as WExplore that can be used to determine these types of ensembles are hindered by problems related to the regioning of conformational space. Here, we propose a novel, regionless, enhanced sampling method that is based on the weighted ensemble framework. In this method, a value referred to as “trajectory variation” is optimized after each cycle through cloning and merging operations. This method allows for a more consistent measurement of observables and broader sampling resulting in the efficient exploration of previously unexplored conformations. We demonstrate the performance of this algorithm with the N-dimensional random walk and the unbinding of the trypsin-benzamidine system. The system is analyzed using conformation space networks, the residence time of benzamidine is confirmed, and a new unbinding pathway for the trypsin-benzamidine system is found. We expect that resampling of ensembles by variation optimization will be a useful general tool to broadly explore free energy landscapes.
more »
« less
Quality over quantity: Sampling high probability rare events with the weighted ensemble algorithm
Abstract The prediction of (un)binding rates and free energies is of great significance to the drug design process. Although many enhanced sampling algorithms and approaches have been developed, there is not yet a reliable workflow to predict these quantities. Previously we have shown that free energies and transition rates can be calculated by directly simulating the binding and unbinding processes with our variant of the WE algorithm “Resampling of Ensembles by Variation Optimization”, or “REVO”. Here, we calculate binding free energies retrospectively for three SAMPL6 host‐guest systems and prospectively for a SAMPL9 system to test a modification of REVO that restricts its cloning behavior in quasi‐unbound states. Specifically, trajectories cannot clone if they meet a physical requirement that represents a high likelihood of unbinding, which in the case of this work is a center‐of‐mass to center‐of‐mass distance. The overall effect of this change was difficult to predict, as it results in fewer unbinding events each of which with a much higher statistical weight. For all four systems tested, this new strategy produced either more accurate unbinding free energies or more consistent results between simulations than the standard REVO algorithm. This approach is highly flexible, and any feature of interest for a system can be used to determine cloning eligibility. These findings thus constitute an important improvement in the calculation of transition rates and binding free energies with the weighted ensemble method.
more »
« less
- Award ID(s):
- 1761320
- PAR ID:
- 10385193
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Computational Chemistry
- Volume:
- 44
- Issue:
- 8
- ISSN:
- 0192-8651
- Page Range / eLocation ID:
- p. 935-947
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Improper reaction coordinates can pose significant problems for path-based binding free energy calculations. Particularly, omission of long timescale motions can lead to over-estimation of the energetic barriers between the bound and unbound states. Many methods exist to construct the optimal reaction coordinate using a pre-defined basis set of features. Although simulations are typically conducted in explicit solvent, the solvent atoms are often excluded by these feature sets—resulting in little being known about their role in reaction coordinates, and ultimately, their role in determining (un)binding rates and free energies. In this work, analysis is done on an extensive set of host-guest unbinding trajectories, working to characterize differences between high and low probability unbinding trajectories with a focus on solvent-based features, including host-ion interactions, guest-ion interactions and location-dependent ion densities. We find that differences in ion densities as well as guest-ion interactions strongly correlate with differences in the probabilities of reactive paths that are used to determine free energies of (un)binding and play a significant role in the unbinding process.more » « less
-
We propose a free energy calculation method for receptor–ligand binding, which have multiple binding poses that avoids exhaustive enumeration of the poses. For systems with multiple binding poses, the standard procedure is to enumerate orientations of the binding poses, restrain the ligand to each orientation, and then, calculate the binding free energies for each binding pose. In this study, we modify a part of the thermodynamic cycle in order to sample a broader conformational space of the ligand in the binding site. This modification leads to more accurate free energy calculation without performing separate free energy simulations for each binding pose. We applied our modification to simple model host–guest systems as a test, which have only two binding poses, by using a single decoupling method (SDM) in implicit solvent. The results showed that the binding free energies obtained from our method without knowing the two binding poses were in good agreement with the benchmark results obtained by explicit enumeration of the binding poses. Our method is applicable to other alchemical binding free energy calculation methods such as the double decoupling method (DDM) in explicit solvent. We performed a calculation for a protein–ligand system with explicit solvent using our modified thermodynamic path. The results of the free energy simulation along our modified path were in good agreement with the results of conventional DDM, which requires a separate binding free energy calculation for each of the binding poses of the example of phenol binding to T4 lysozyme in explicit solvent. © 2019 Wiley Periodicals, Inc.more » « less
-
null (Ed.)One of the long-standing holy grails of molecular evolution has been the ability to predict an organism’s fitness directly from its genotype. With such predictive abilities in hand, researchers would be able to more accurately forecast how organisms will evolve and how proteins with novel functions could be engineered, leading to revolutionary advances in medicine and biotechnology. In this work, we assemble the largest reported set of experimental TEM-1 β-lactamase folding free energies and use this data in conjunction with previously acquired fitness data and computational free energy predictions to determine how much of the fitness of β-lactamase can be directly predicted by thermodynamic folding and binding free energies. We focus upon β-lactamase because of its long history as a model enzyme and its central role in antibiotic resistance. Based upon a set of 21 β-lactamase single and double mutants expressly designed to influence protein folding, we first demonstrate that modeling software designed to compute folding free energies such as FoldX and PyRosetta can meaningfully, although not perfectly, predict the experimental folding free energies of single mutants. Interestingly, while these techniques also yield sensible double mutant free energies, we show that they do so for the wrong physical reasons. We then go on to assess how well both experimental and computational folding free energies explain single mutant fitness. We find that folding free energies account for, at most, 24% of the variance in β-lactamase fitness values according to linear models and, somewhat surprisingly, complementing folding free energies with computationally-predicted binding free energies of residues near the active site only increases the folding-only figure by a few percent. This strongly suggests that the majority of β-lactamase’s fitness is controlled by factors other than free energies. Overall, our results shed a bright light on to what extent the community is justified in using thermodynamic measures to infer protein fitness as well as how applicable modern computational techniques for predicting free energies will be to the large data sets of multiply-mutated proteins forthcomingmore » « less
-
Protein adsorption to solid carbohydrate interfaces is critical to many biological processes, particularly in biomass deconstruction. To engineer more-efficient enzymes for biomass deconstruction into sugars, it is necessary to characterize the complex protein–carbohydrate interfacial interactions. A carbohydrate-binding module (CBM) is often associated with microbial surface-tethered cellulosomes or secreted cellulase enzymes to enhance substrate accessibility. However, it is not well known how CBMs recognize, bind, and dissociate from polysaccharides to facilitate efficient cellulolytic activity, due to the lack of mechanistic understanding and a suitable toolkit to study CBM–substrate interactions. Our work outlines a general approach to study the unbinding behavior of CBMs from polysaccharide surfaces using a highly multiplexed single-molecule force spectroscopy assay. Here, we apply acoustic force spectroscopy (AFS) to probe a Clostridium thermocellum cellulosomal scaffoldin protein (CBM3a) and measure its dissociation from nanocellulose surfaces at physiologically relevant, low force loading rates. An automated microfluidic setup and method for uniform deposition of insoluble polysaccharides on the AFS chip surfaces are demonstrated. The rupture forces of wild-type CBM3a, and its Y67A mutant, unbinding from nanocellulose surfaces suggests distinct multimodal CBM binding conformations, with structural mechanisms further explored using molecular dynamics simulations. Applying classical dynamic force spectroscopy theory, the single-molecule unbinding rate at zero force is extrapolated and found to agree with bulk equilibrium unbinding rates estimated independently using quartz crystal microbalance with dissipation monitoring. However, our results also highlight critical limitations of applying classical theory to explain the highly multivalent binding interactions for cellulose–CBM bond rupture forces exceeding 15 pN.more » « less
An official website of the United States government
