Predicting Binding Free Energies in a Large Combinatorial Chemical Space Using Multisite λ Dynamics.

In this study, we demonstrate the extensive scalability of the biasing potential replica exchange multisite λ dynamics (BP-REX MSλD) free energy method by calculating binding affinities for 512 inhibitors to HIV Reverse Transcriptase (HIV-RT). This is the largest exploration of chemical space using free energy methods known to date, requires only a few simulations, and identifies 55 new inhibitor designs against HIV-RT predicted to be at least as potent as a tight binding reference compound (i.e., as potent as 56 nM). We highlight that BP-REX MSλD requires an order of magnitude less computational resources than conventional free energy methods while maintaining a similar level of precision, overcomes the inherent poor scalability of conventional free energy methods, and enables the exploration of combinatorially large chemical spaces in the context of in silico drug discovery.

Deep learning for computational chemistry.

The rise and fall of artificial neural networks is well documented in the scientific literature of both computer science and computational chemistry. Yet almost two decades later, we are now seeing a resurgence of interest in deep learning, a machine learning algorithm based on multilayer neural networks. Within the last few years, we have seen the transformative impact of deep learning in many domains, particularly in speech recognition and computer vision, to the extent that the majority of expert practitioners in those field are now regularly eschewing prior established models in favor of deep learning models. In this review, we provide an introductory overview into the theory of deep neural networks and their unique properties that distinguish them from traditional machine learning algorithms used in cheminformatics. By providing an overview of the variety of emerging applications of deep neural networks, we highlight its ubiquity and broad applicability to a wide range of challenges in the field, including quantitative structure activity relationship, virtual screening, protein structure prediction, quantum chemistry, materials design, and property prediction. In reviewing the performance of deep neural networks, we observed a consistent outperformance against non-neural networks state-of-the-art models across disparate research topics, and deep neural network-based models often exceeded the "glass ceiling" expectations of their respective tasks. Coupled with the maturity of GPU-accelerated computing for training deep neural networks and the exponential growth of chemical data on which to train these networks on, we anticipate that deep learning algorithms will be a valuable tool for computational chemistry. © 2017 Wiley Periodicals, Inc.

Biasing Potential Replica Exchange Multisite λ-Dynamics for Efficient Free Energy Calculations.

Traditional free energy calculation methods are well-known for their drawbacks in scalability and speed in converging results particularly for calculations with large perturbations. In the present work, we report on the development of biasing potential replica exchange multisite λ-dynamics (BP-REX MSλD), which is a free energy method that is capable of performing simultaneous alchemical free energy transformations, including perturbations between flexible moieties. BP-REX MSλD and the original MSλD are applied to a series of symmetrical 2,5-benzoquinone derivatives covering a diverse chemical space and range of conformational flexibility. Improved λ-space sampling is observed for the BP-REX MSλD simulations, yielding a 2-5-fold increase in the number of transitions between substituents compared to traditional MSλD. We also demonstrate the efficacy of varying the value of c, the parameter that controls the ruggedness of the landscape mediating the sampling of λ-states, based on the flexibility of the fragment. Finally, we developed a protocol for maximizing the transition frequency between fragments. This protocol reduces the "kinetic barrier" for alchemically transforming fragments by grouping and ordering based on volume. These findings are applied to a challenging test set involving a series of geldanamycin-based inhibitors of heat shock protein 90 (Hsp90). Even though the perturbations span volume changes by as large as 60 Å(3), the values for the free energy change achieve an average unsigned error (AUE) of 1.5 kcal/mol relative to experimental Kd measurements with a reasonable correlation (R = 0.56). Our results suggest that the BP-REX MSλD algorithm is a highly efficient and scalable free energy method, which when utilized will enable routine calculations on the order of hundreds of compounds using only a few simulations.

Accurate modeling of ionic surfactants at high concentration.

Molecular dynamics (MD) simulation is a useful tool for simulating formulations of surfactant mixtures from first-principles, which can be used to predict surfactant morphology and other industrially relevant thermodynamic properties. However, the surfactant structure is sensitive to the parameters used in MD simulations, and in the absence of extensive validation against experimental data, it is often not obvious a priori which range of parameter sets to choose. In this work, we compare the performance of ion parameters implemented in nonpolarizable classical MD simulations, and its effect on simulations of an idealized solution of sodium dodecyl sulfate (SDS). We find that previous artifacts reported in simulations of larger SDS constructs are a direct consequence of using parameters that poorly model ionic interactions at high concentration. Using osmotic pressure and/or other thermodynamic properties measured at finite concentration, such as Kirkwood-Buff integrals, is shown to be the most cost-effective means to validate and parametrize existing force fields. Our findings highlight the importance of optimizing intermolecular parameters for simulations of systems with a high local concentration, which may be applicable in other contexts, such as in molecular crowding, hotspot mapping, protein folding, and modeling pH effects.

pH-dependent transient conformational states control optical properties in cyan fluorescent protein.

A recently engineered mutant of cyan fluorescent protein (WasCFP) that exhibits pH-dependent absorption suggests that its tryptophan-based chromophore switches between neutral (protonated) and charged (deprotonated) states depending on external pH. At pH 8.1, the latter gives rise to green fluorescence as opposed to the cyan color of emission that is characteristic for the neutral form at low pH. Given the high energy cost of deprotonating the tryptophan at the indole nitrogen, this behavior is puzzling, even if the stabilizing effect of the V61K mutation in proximity to the protonation/deprotonation site is considered. Because of its potential to open new avenues for the development of optical sensors and photoconvertible fluorescent proteins, a mechanistic understanding of how the charged state in WasCFP can possibly be stabilized is thus important. Attributed to the dynamic nature of proteins, such understanding often requires knowledge of the various conformations adopted, including transiently populated conformational states. Transient conformational states triggered by pH are of emerging interest and have been shown to be important whenever ionizable groups interact with hydrophobic environments. Using a combination of the weighted-ensemble sampling method and explicit-solvent constant pH molecular dynamics (CPHMD(MSλD)) simulations, we have identified a solvated transient state, characterized by a partially open ß-barrel where the chromophore pKa of 6.8 is shifted by over 20 units from that of the closed form (6.8 and 31.7, respectively). This state contributes a small population at low pH (12% at pH 6.1) but becomes dominant at mildly basic conditions, contributing as much as 53% at pH 8.1. This pH-dependent population shift between neutral (at pH 6.1) and charged (at pH 8.1) forms is thus responsible for the observed absorption behavior of WasCFP. Our findings demonstrate the conditions necessary to stabilize the charged state of the WasCFP chromophore (namely, local solvation at the deprotonation site and a partial flexibility of the protein ß-barrel structure) and provide the first evidence that transient conformational states can control optical properties of fluorescent proteins.

Parameter choice matters: validating probe parameters for use in mixed-solvent simulations.

Probe mapping is a common approach for identifying potential binding sites in structure-based drug design; however, it typically relies on energy minimizations of probes in the gas phase and a static protein structure. The mixed-solvent molecular dynamics (MixMD) approach was recently developed to account for full protein flexibility and solvation effects in hot-spot mapping. Our first study used only acetonitrile as a probe, and here, we have augmented the set of functional group probes through careful testing and parameter validation. A diverse range of probes are needed in order to map complex binding interactions. A small variation in probe parameters can adversely effect mixed-solvent behavior, which we highlight with isopropanol. We tested 11 solvents to identify six with appropriate behavior in TIP3P water to use as organic probes in the MixMD method. In addition to acetonitrile and isopropanol, we have identified acetone, N-methylacetamide, imidazole, and pyrimidine. These probe solvents will enable MixMD studies to recover hydrogen-bonding sites, hydrophobic pockets, protein-protein interactions, and aromatic hotspots. Also, we show that ternary-solvent systems can be incorporated within a single simulation. Importantly, these binary and ternary solvents do not require artificial repulsion terms like other methods. Within merely 5 ns, layered solvent boxes become evenly mixed for soluble probes. We used radial distribution functions to evaluate solvent behavior, determine adequate mixing, and confirm the absence of phase separation. We recommend that radial distribution functions should be used to assess adequate sampling in all mixed-solvent techniques rather than the current practice of examining the solvent ratios at the edges of the solvent box.

Uncovering pH-dependent transient states of proteins with buried ionizable residues.

The role of pH in regulating biological activity is ubiquitous, and understanding pH-mediated activity has traditionally relied on analyzing static biomolecular structures of highly populated ground states solved near physiological pH. However, recent advances have shown the increasing importance of transiently populated states, the characterization of which is extremely challenging but made plausible with the development of techniques such as relaxation dispersion NMR spectroscopy. To unlock the pH dependence of these transient states with atomistic-level details, we applied the recently developed explicit solvent constant pH molecular dynamics (CPHMD(MSλD)) framework to a series of staphylococcal nuclease (SNase) mutants with buried ionizable residues and probed their dynamics in different pH environments. Among our key findings is the existence of open states in all SNase mutants containing "buried" residues with highly shifted pKa's, where local solvation around the protonation site was observed. The calculated pKa demonstrated good agreement with experimental pKa's, with a low average unsigned error of 1.3 pKa units and correlation coefficient R(2) = 0.78. Sampling both open and closed states in their respective pH range, where they are expected to be dominant, was necessary to reproduce experimental pKa's, and in the most extreme examples of pKa shifts measured, it can be interpreted that the open-state structures are transient at physiological pH, contributing a small population of 1-2%. This suggests that buried ionizable residues can trigger conformational fluctuations that may be observed as transient-state structures at physiological pH. Furthermore, the coupled relationship of both open and closed states and their role in recapitulating macroscopic experimental observables suggest that structural analysis of buried residues may benefit from looking at structural pairs, as opposed to the conventional approach of looking at a single static ground-state conformation.

Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism.

pH is a ubiquitous regulator of biological activity, including protein-folding, protein-protein interactions, and enzymatic activity. Existing constant pH molecular dynamics (CPHMD) models that were developed to address questions related to the pH-dependent properties of proteins are largely based on implicit solvent models. However, implicit solvent models are known to underestimate the desolvation energy of buried charged residues, increasing the error associated with predictions that involve internal ionizable residue that are important in processes like hydrogen transport and electron transfer. Furthermore, discrete water and ions cannot be modeled in implicit solvent, which are important in systems like membrane proteins and ion channels. We report on an explicit solvent constant pH molecular dynamics framework based on multi-site λ-dynamics (CPHMD(MSλD)). In the CPHMD(MSλD) framework, we performed seamless alchemical transitions between protonation and tautomeric states using multi-site λ-dynamics, and designed novel biasing potentials to ensure that the physical end-states are predominantly sampled. We show that explicit solvent CPHMD(MSλD) simulations model realistic pH-dependent properties of proteins such as the Hen-Egg White Lysozyme (HEWL), binding domain of 2-oxoglutarate dehydrogenase (BBL) and N-terminal domain of ribosomal protein L9 (NTL9), and the pKa predictions are in excellent agreement with experimental values, with a RMSE ranging from 0.72 to 0.84 pKa units. With the recent development of the explicit solvent CPHMD(MSλD) framework for nucleic acids, accurate modeling of pH-dependent properties of both major class of biomolecules-proteins and nucleic acids is now possible.

pH-dependent dynamics of complex RNA macromolecules.

The role of pH-dependent protonation equilibrium in modulating RNA dynamics and function is one of the key unanswered questions in RNA biology. Molecular dynamics (MD) simulations can provide insight into the mechanistic roles of protonated nucleotides, but it is only capable of modeling fixed protonation states and requires prior knowledge of the key residue's protonation state. Recently, we developed a framework for constant pH molecular dynamics simulations (CPHMDMSλD) of nucleic acids, where the nucleotides' protonation states are modeled as dynamic variables that are coupled to the structural dynamics of the RNA. In the present study, we demonstrate the application of CPHMDMSλD to the lead-dependent ribozyme; establishing the validity of this approach for modeling complex RNA structures. We show that CPHMDMSλD accurately predicts the direction of the pKa shifts and reproduces experimentally-measured microscopic pKa values with an average unsigned error of 1.3 pKa units. The effects of coupled titration states in RNA structures are modeled, and the importance of conformation sampling is highlighted. The general accuracy of CPHMDMSλD simulations in reproducing pH-dependent observables reported in this work demonstrates that constant pH simulations provides a powerful tool to investigate pH-dependent processes in nucleic acids.

Towards Accurate Prediction of Protonation Equilibrium of Nucleic Acids.

The role of protonated nucleotides in modulating the pH-dependent properties of nucleic acids is one of the emerging frontiers in the field of nucleic acid biology. The recent development of a constant pH molecular dynamics simulation (CPHMDMSλD) framework for simulating nucleic acids has provided a tool for realistic simulations of pH-dependent dynamics. We enhanced the CPHMDMSλD framework with pH-based replica exchange (pH-REX), which significantly improves the sampling of both titration and spatial coordinates. The results from our pKa calculations for the GAAA tetraloop, which was predicted with lower accuracy previously due to sampling challenges, demonstrates that pH-REX reduces the average unsigned error (AUE) to 0.7 pKa units, and the error of the most poorly predicted residue A17 was drastically reduced from 2.9 to 1.2 pKa unit. Lastly, we show that pH-REX CPHMDMSλD simulations can be used to identify the dominant conformation of nucleic acid structures in alternate pH environments. This work suggests that pH-REX CPHMDMSλD simulations provide a practical tool for predicting nucleic acid protonation equilibrium from first-principles, and offering structural and mechanistic insight into the study of pH-dependent properties of nucleic acids.

Characterizing the protonation state of cytosine in transient G·C Hoogsteen base pairs in duplex DNA.

G·C Hoogsteen base pairs can form transiently in duplex DNA and play important roles in DNA recognition, replication, and repair. G·C Hoogsteen base pairs are thought to be stabilized by protonation of cytosine N3, which affords a second key hydrogen bond, but experimental evidence for this is sparse because the proton cannot be directly visualized by X-ray crystallography and nuclear magnetic resonance spectroscopy. Here, we combine NMR and constant pH molecular dynamics simulations to directly investigate the pKa of cytosine N3 in a chemically trapped N1-methyl-G·C Hoogsteen base pair within duplex DNA. Analysis of NMR chemical shift perturbations and NOESY data as a function of pH revealed that cytosine deprotonation is coupled to a syn-to-anti transition in N1-methyl-G, which results in a distorted Watson-Crick geometry at pH >9. A four-state analysis of the pH titration profiles yields a lower bound pKa estimate of 7.2 ± 0.1 for the G·C Hoogsteen base pair, which is in good agreement with the pKa value (7.1 ± 0.1) calculated independently using constant pH MD simulations. Based on these results and pH-dependent NMR relaxation dispersion measurements, we estimate that under physiological pH (pH 7-8), G·C Hoogsteen base pairs in naked DNA have a population of 0.02-0.002%, as compared to 0.4% for A·T Hoogsteen base pairs, and likely exist primarily as protonated species.

Constant pH Molecular Dynamics Simulations of Nucleic Acids in Explicit Solvent.

The nucleosides of adenine and cytosine have pKa values of 3.50 and 4.08, respectively, and are assumed to be unprotonated under physiological conditions. However, evidence from recent NMR and X-Ray crystallography studies has revealed the prevalence of protonated adenine and cytosine in RNA macromolecules. Such nucleotides with elevated pKa values may play a role in stabilizing RNA structure and participate in the mechanism of ribozyme catalysis. With the work presented here, we establish the framework and demonstrate the first constant pH MD simulations (CPHMD) for nucleic acids in explicit solvent in which the protonation state is coupled to the dynamical evolution of the RNA system via λ-dynamics. We adopt the new functional form λ(Nexp) for λ that was recently developed for Multi-Site λ-Dynamics (MSλD) and demonstrate good sampling characteristics in which rapid and frequent transitions between the protonated and unprotonated states at pH = pKa are achieved. Our calculated pKa values of simple nucleotides are in a good agreement with experimentally measured values, with a mean absolute error of 0.24 pKa units. This work demonstrates that CPHMD can be used as a powerful tool to investigate pH-dependent biological properties of RNA macromolecules.

The high dielectric constant of staphylococcal nuclease is encoded in its structural architecture.

The pK(a) values of Lys-66, Glu-66, and Asp-66 buried in the interior of the staphylococcal nuclease Δ+PHS variant were reported to be shifted by as much as 5 pK(a) units from their normal values. Reproducing the pK(a) of these buried ionizable residues using continuum electrostatic calculations required the use of a high protein dielectric constant of 10 or higher. The apparent high dielectric constant has been rationalized as a consequence of a local structural reorganization or increased fluctuations in the microenvironment of the mutation site (Chimenti, M. S., et al. J. Mol. Biol. 2011, 405, 361-377). We have calculated the dielectric constant of Δ+PHS and the Lys-66, Asp-66, and Glu-66 mutants from first principles using the Kirkwood-Fröhlich equation and discovered that staphylococcal nuclease has a naturally high dielectric constant ranging from 20 to 30. This high dielectric constant does not change significantly with the mutation of residue 66 or with the ionization of the mutated residues. Calculation of the spatial dependence of the dielectric constant for the microenvironment of residue-66 produces a value of about 10, which matches well with the apparent dielectric constant needed to reproduce pK(a) values from continuum electrostatic calculations. Our results suggest an alternative explanation that the high dielectric constant of staphylococcal nuclease is a property resulting from the intrinsic backbone fluctuations originating from its structural architecture.