Selection pressures on evolution of ribonuclease H explored with rigorous free-energy-based design.

Understanding natural protein evolution and designing novel proteins are motivating interest in development of high-throughput methods to explore large sequence spaces. In this work, we demonstrate the application of multisite λ dynamics (MSλD), a rigorous free energy simulation method, and chemical denaturation experiments to quantify evolutionary selection pressure from sequence-stability relationships and to address questions of design. This study examines a mesophilic phylogenetic clade of ribonuclease H (RNase H), furthering its extensive characterization in earlier studies, focusing on E. coli RNase H (ecRNH) and a more stable consensus sequence (AncCcons) differing at 15 positions. The stabilities of 32,768 chimeras between these two sequences were computed using the MSλD framework. The most stable and least stable chimeras were predicted and tested along with several other sequences, revealing a designed chimera with approximately the same stability increase as AncCcons, but requiring only half the mutations. Comparing the computed stabilities with experiment for 12 sequences reveals a Pearson correlation of 0.86 and root mean squared error of 1.18 kcal/mol, an unprecedented level of accuracy well beyond less rigorous computational design methods. We then quantified selection pressure using a simple evolutionary model in which sequences are selected according to the Boltzmann factor of their stability. Selection temperatures from 110 to 168 K are estimated in three ways by comparing experimental and computational results to evolutionary models. These estimates indicate selection pressure is high, which has implications for evolutionary dynamics and for the accuracy required for design, and suggests accurate high-throughput computational methods like MSλD may enable more effective protein design.

Fast free energy estimates from λ-dynamics with bias-updated Gibbs sampling.

Relative binding free energy calculations have become an integral computational tool for lead optimization in structure-based drug design. Classical alchemical methods, including free energy perturbation or thermodynamic integration, compute relative free energy differences by transforming one molecule into another. However, these methods have high operational costs due to the need to perform many pairwise perturbations independently. To reduce costs and accelerate molecular design workflows, we present a method called λ-dynamics with bias-updated Gibbs sampling. This method uses dynamic biases to continuously sample between multiple ligand analogues collectively within a single simulation. We show that many relative binding free energies can be determined quickly with this approach without compromising accuracy. For five benchmark systems, agreement to experiment is high, with root mean square errors near or below 1.0 kcal mol-1. Free energy results are consistent with other computational approaches and within statistical noise of both methods (0.4 kcal mol-1 or less). Notably, large efficiency gains over thermodynamic integration of 18-66-fold for small perturbations and 100-200-fold for whole aromatic ring substitutions are observed. The rapid determination of relative binding free energies will enable larger chemical spaces to be more readily explored and structure-based drug design to be accelerated.

Addressing Intersite Coupling Unlocks Large Combinatorial Chemical Spaces for Alchemical Free Energy Methods.

Alchemical free energy methods are playing a growing role in molecular design, both for computer-aided drug design of small molecules and for computational protein design. Multisite λ dynamics (MSλD) is a uniquely scalable alchemical free energy method that enables more efficient exploration of combinatorial alchemical spaces encountered in molecular design, but simulations have typically been limited to a few hundred ligands or sequences. Here, we focus on coupling between sites to enable scaling to larger alchemical spaces. We first discuss updates to the biasing potentials that facilitate MSλD sampling to include coupling terms and show that this can provide more thorough sampling of alchemical states. We then harness coupling between sites by developing a new free energy estimator based on the Potts models underlying direct coupling analysis, a method for predicting contacts from sequence coevolution, and find it yields more accurate free energies than previous estimators. The sampling requirements of the Potts model estimator scale with the square of the number of sites, a substantial improvement over the exponential scaling of the standard estimator. This opens up exploration of much larger alchemical spaces with MSλD for molecular design.

Optimizing Multisite λ-Dynamics Throughput with Charge Renormalization.

With the ability to sample combinations of alchemical perturbations at multiple sites off a small molecule core, multisite λ-dynamics (MSλD) has become an attractive alternative to conventional alchemical free energy methods for exploring large combinatorial chemical spaces. However, current software implementations dictate that combinatorial sampling with MSλD must be performed with a multiple topology model (MTM), which is nontrivial to create by hand, especially for a series of ligand analogues which may have diverse functional groups attached. This work introduces an automated workflow, referred to as msld_py_prep, to assist in the creation of a MTM for use with MSλD. One approach for partitioning partial atomic charges between ligands to create a MTM, called charge renormalization, is also presented and rigorously evaluated. We find that msld_py_prep greatly accelerates the preparation of MSλD ready-to-use files and that charge renormalization can provide a successful approach for MTM generation, as long as bookending calculations are applied to correct small differences introduced by charge renormalization. Charge renormalization also facilitates the use of many different force field parameters with MSλD, broadening the applicability of MSλD for computer-aided drug design.

BLaDE: A Basic Lambda Dynamics Engine for GPU-Accelerated Molecular Dynamics Free Energy Calculations.

There is an accelerating interest in practical applications of alchemical free energy methods to problems in protein design, constant pH simulations, and especially computer-aided drug design. In the present paper, we describe a basic lambda dynamics engine (BLaDE) that enables alchemical free energy simulations, including multisite λ dynamics (MSλD) simulations, on graphical processor units (GPUs). We find that BLaDE is 5 to 8 times faster than the current GPU implementation of MSλD-based free energy calculations in CHARMM. We also demonstrate that BLaDE running standard molecular dynamics attains a performance competitive with and sometimes exceeding that of the highly optimized OpenMM GPU code. BLaDE is available as a standalone program and through an API in CHARMM.

Generalizing the Discrete Gibbs Sampler-Based λ-Dynamics Approach for Multisite Sampling of Many Ligands.

In this work, the discrete λ variant of the Gibbs sampler-based λ-dynamics (d-GSλD) method is developed to enable multiple functional group perturbations to be investigated at one or more sites of substitution off a common ligand core. The theoretical framework and special considerations for constructing discrete λ states for multisite d-GSλD are presented. The precision and accuracy of the d-GSλD method is evaluated with three test cases of increasing complexity. Specifically, methyl → methyl symmetric perturbations in water, 1,4-benzene hydration free energies and protein-ligand binding affinities for an example HIV-1 reverse transcriptase inhibitor series are computed with d-GSλD. Complementary MSλD calculations were also performed to compare with d-GSλD's performance. Excellent agreement between d-GSλD and MSλD is observed, with mean unsigned errors of 0.12 and 0.22 kcal/mol for computed hydration and binding free energy test cases, respectively. Good agreement with experiment is also observed, with errors of 0.5-0.7 kcal/mol. These findings support the applicability of the d-GSλD free energy method for a variety of molecular design problems, including structure-based drug design. Finally, a discussion of d-GSλD versus MSλD approaches is presented to compare and contrast features of both methods.

A strategy for proline and glycine mutations to proteins with alchemical free energy calculations.

Computation of the thermodynamic consequences of protein mutations holds great promise in protein biophysics and design. Alchemical free energy methods can give improved estimates of mutational free energies, and are already widely used in calculations of relative and absolute binding free energies in small molecule design problems. In principle, alchemical methods can address any amino acid mutation with an appropriate alchemical pathway, but identifying a strategy that produces such a path for proline and glycine mutations is an ongoing challenge. Most current strategies perturb only side chain atoms, while proline and glycine mutations also alter the backbone parameters and backbone ring topology. Some strategies also perturb backbone parameters and enable glycine mutations. This work presents a strategy that enables both proline and glycine mutations and comprises two key elements: a dual backbone with restraints and scaling of bonded terms, facilitating backbone parameter changes, and a soft bond in the proline ring, enabling ring topology changes in proline mutations. These elements also have utility for core hopping and macrocycle studies in computer-aided drug design. This new strategy shows slight improvements over an alternative side chain perturbation strategy for a set T4 lysozyme mutations lacking proline and glycine, and yields good agreement with experiment for a set of T4 lysozyme proline and glycine mutations not previously studied. To our knowledge this is the first report comparing alchemical predictions of proline mutations with experiment. With this strategy in hand, alchemical methods now have access to the full palette of amino acid mutations.

Automated, Accurate, and Scalable Relative Protein-Ligand Binding Free-Energy Calculations Using Lambda Dynamics.

Accurate predictions of changes to protein-ligand binding affinity in response to chemical modifications are of utility in small-molecule lead optimization. Relative free-energy perturbation (FEP) approaches are one of the most widely utilized for this goal but involve significant computational cost, thus limiting their application to small sets of compounds. Lambda dynamics, also rigorously based on the principles of statistical mechanics, provides a more efficient alternative. In this paper, we describe the development of a workflow to set up, execute, and analyze multisite lambda dynamics (MSLD) calculations run on GPUs with CHARMM implemented in BIOVIA Discovery Studio and Pipeline Pilot. The workflow establishes a framework for setting up simulation systems for exploratory screening of modifications to a lead compound, enabling the calculation of relative binding affinities of combinatorial libraries. To validate the workflow, a diverse data set of congeneric ligands for seven proteins with experimental binding affinity data is examined. A protocol to automatically tailor fit biasing potentials iteratively to flatten the free-energy landscape of any MSLD system is developed, which enhances sampling and allows for efficient estimation of free-energy differences. The protocol is first validated on a large number of ligand subsets that model diverse substituents, which shows accurate and reliable performance. The scalability of the workflow is also tested to screen more than 100 ligands modeled in a single system, which also resulted in accurate predictions. With a cumulative sampling time of 150 ns or less, the method results in average unsigned errors of under 1 kcal/mol in most cases for both small and large combinatorial libraries. For the multisite systems examined, the method is estimated to be more than an order of magnitude more efficient than contemporary FEP applications. The results thus demonstrate the utility of the presented MSLD workflow to efficiently screen combinatorial libraries and explore the chemical space around a lead compound and thus are of utility in lead optimization.

Exploring pH Dependent Host/Guest Binding Affinities.

When the electrostatic environment surrounding binding partners changes between unbound and bound states, the net uptake or release of a proton is possible by either binding partner. This process is pH-dependent in that the free energy required to uptake or release the proton varies with pH. This pH-dependence is typically not considered in conventional free energy methods where the use of fixed protonation states is the norm. In the present paper, we apply a simple two-step approach to calculate the pH-dependent binding free energy of a model cucubit[7]uril host/guest system. By use of λ-dynamics with an enhanced sampling protocol, adaptive landscape flattening, pKa shifts and reference binding free energies upon complexation were determined. This information enables the construction of pH-dependent binding profiles that accurately capture the pKa shifts and reproduce binding free energies at the different pH conditions that were observed experimentally. Our calculations illustrate a general framework for computing pH-dependent binding free energies but also point to some issues in modeling the molecular charge distributions within this series of molecules with CGenFF. However, by introducing some minor charge modifications to the CGenFF force field, we saw significant improvement in accuracy of the calculated pKa shifts.

Overcoming Challenging Substituent Perturbations with Multisite λ-Dynamics: A Case Study Targeting ß-Secretase 1.

Alchemical free energy calculations have made a dramatic impact upon the field of structure-based drug design by allowing functional group modifications to be explored computationally prior to experimental synthesis and assay evaluation, thereby informing and directing synthetic strategies. In furthering the advancement of this area, a series of 21 ß-secretase 1 (BACE1) inhibitors developed by Janssen Pharmaceuticals were examined to evaluate the ability to explore large substituent perturbations, some of which contain scaffold modifications, with multisite λ-dynamics (MSλD), an innovative alchemical free energy framework. Our findings indicate that MSλD is able to efficiently explore all structurally diverse ligand end-states simultaneously within a single MD simulation with a high degree of precision and with reduced computational costs compared to the widely used approach TI/MBAR. Furthermore, computational predictions were shown to be accurate to within 0.5-0.8 kcal/mol when CM1A partial atomic charges were combined with CHARMM or OPLS-AA-based force fields, demonstrating that MSλD is force field independent and a viable alternative to FEP or TI approaches for drug design.

Structure-Based Model of RNA Pseudoknot Captures Magnesium-Dependent Folding Thermodynamics.

We develop a simple, coarse-grained approach for simulating the folding of the Beet Western Yellow Virus (BWYV) pseudoknot toward the goal of creating a transferable model that can be used to study other small RNA molecules. This approach combines a structure-based model (SBM) of RNA with an electrostatic scheme that has previously been shown to correctly reproduce ionic condensation in the native basin. Mg2+ ions are represented explicitly, directly incorporating ion-ion correlations into the system, and K+ is represented implicitly, through the mean-field generalized Manning counterion condensation theory. Combining the electrostatic scheme with a SBM enables the electrostatic scheme to be tested beyond the native basin. We calibrate the SBM to reproduce experimental BWYV unfolding data by eliminating overstabilizing backbone interactions from the molecular contact map and by strengthening base pairing and stacking contacts relative to other native contacts, consistent with the experimental observation that relative helical stabilities are central determinants of the RNA unfolding sequence. We find that this approach quantitatively captures the Mg2+ dependence of the folding temperature and generates intermediate states that better approximate those revealed by experiment. Finally, we examine how our model captures Mg2+ condensation about the BWYV pseudoknot and a U-tail variant, for which the nine 3' end nucleotides are replaced with uracils, and find our results to be consistent with experimental condensation measurements. This approach can be easily transferred to other RNA molecules by eliminating and strengthening the same classes of contacts in the SBM and including generalized Manning counterion condensation.

Ligand Modulates Cross-Coupling between Riboswitch Folding and Transcriptional Pausing.

Numerous classes of riboswitches have been found to regulate bacterial gene expression in response to physiological cues, offering new paths to antibacterial drugs. As common studies of isolated riboswitches lack the functional context of the transcription machinery, we here combine single-molecule, biochemical, and simulation approaches to investigate the coupling between co-transcriptional folding of the pseudoknot-structured preQ1 riboswitch and RNA polymerase (RNAP) pausing. We show that pausing at a site immediately downstream of the riboswitch requires a ligand-free pseudoknot in the nascent RNA, a precisely spaced sequence resembling the pause consensus, and electrostatic and steric interactions with the RNAP exit channel. While interactions with RNAP stabilize the native fold of the riboswitch, binding of the ligand signals RNAP release from the pause. Our results demonstrate that the nascent riboswitch and its ligand actively modulate the function of RNAP and vice versa, a paradigm likely to apply to other cellular RNA transcripts.

Approaching protein design with multisite λ dynamics: Accurate and scalable mutational folding free energies in T4 lysozyme.

The estimation of changes in free energy upon mutation is central to the problem of protein design. Modern protein design methods have had remarkable success over a wide range of design targets, but are reaching their limits in ligand binding and enzyme design due to insufficient accuracy in mutational free energies. Alchemical free energy calculations have the potential to supplement modern design methods through more accurate molecular dynamics based prediction of free energy changes, but suffer from high computational cost. Multisite λ dynamics (MSλD) is a particularly efficient and scalable free energy method with potential to explore combinatorially large sequence spaces inaccessible with other free energy methods. This work aims to quantify the accuracy of MSλD and demonstrate its scalability. We apply MSλD to the classic problem of calculating folding free energies in T4 lysozyme, a system with a wealth of experimental measurements. Single site mutants considering 32 mutations show remarkable agreement with experiment with a Pearson correlation of 0.914 and mean unsigned error of 1.19 kcal/mol. Multisite mutants in systems with up to five concurrent mutations spanning 240 different sequences show comparable agreement with experiment. These results demonstrate the promise of MSλD in exploring large sequence spaces for protein design.

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.

CDOCKER and λ-dynamics for prospective prediction in D3R Grand Challenge 2.

The opportunity to prospectively predict ligand bound poses and free energies of binding to the Farnesoid X Receptor in the D3R Grand Challenge 2 provided a useful exercise to evaluate CHARMM based docking (CDOCKER) and [Formula: see text]-dynamics methodologies for use in "real-world" applications in computer aided drug design. In addition to measuring their current performance, several recent methodological developments have been analyzed retrospectively to highlight best procedural practices in future applications. For pose prediction with CDOCKER, when the protein structure used for rigid receptor docking was close to the crystallographic holo structure, reliable poses were obtained. Benzimidazoles, with a known holo receptor structure, were successfully docked with an average RMSD of 0.97 [Formula: see text]. Other non-benzimidazole ligands displayed less accuracy largely because the receptor structures we chose for docking were too different from the experimental holo structures. However, retrospective analysis has shown that when these ligands were re-docked into their holo structures, the average RMSD dropped to 1.18 [Formula: see text] for all ligands. When sulfonamides and spiros were docked with the apo structure, which agrees more with their holo structure than the structures we chose, five out of six ligands were correctly docked. These docking results emphasize the need for flexible receptor docking approaches. For [Formula: see text]-dynamics techniques, including multisite [Formula: see text]-dynamics (MS[Formula: see text]D), reasonable agreement with experiment was observed for the 33 ligands investigated; root mean square errors of 2.08 and 1.67 kcal/mol were obtained for free energy sets 1 and 2, respectively. Retrospectively, soft-core potentials, adaptive landscape flattening, and biasing potential replica exchange (BP-REX) algorithms were critical to model large substituent perturbations with sufficient precision and within restrictive timeframes, such as was required with participation in Grand Challenge 2. These developments, their associated benefits, and proposed procedures for their use in future applications are discussed.

Gibbs Sampler-Based λ-Dynamics and Rao-Blackwell Estimator for Alchemical Free Energy Calculation.

λ-dynamics is a generalized ensemble method for alchemical free energy calculations. In traditional λ-dynamics, the alchemical switch variable λ is treated as a continuous variable ranging from 0 to 1 and an empirical estimator is utilized to approximate the free energy. In the present article, we describe an alternative formulation of λ-dynamics that utilizes the Gibbs sampler framework, which we call Gibbs sampler-based λ-dynamics (GSLD). GSLD, like traditional λ-dynamics, can be readily extended to calculate free energy differences between multiple ligands in one simulation. We also introduce a new free energy estimator, the Rao-Blackwell estimator (RBE), for use in conjunction with GSLD. Compared with the current empirical estimator, the advantage of RBE is that RBE is an unbiased estimator and its variance is usually smaller than the current empirical estimator. We also show that the multistate Bennett acceptance ratio equation or the unbinned weighted histogram analysis method equation can be derived using the RBE. We illustrate the use and performance of this new free energy computational framework by application to a simple harmonic system as well as relevant calculations of small molecule relative free energies of solvation and binding to a protein receptor. Our findings demonstrate consistent and improved performance compared with conventional alchemical free energy methods.

A magnesium-induced triplex pre-organizes the SAM-II riboswitch.

Our 13C- and 1H-chemical exchange saturation transfer (CEST) experiments previously revealed a dynamic exchange between partially closed and open conformations of the SAM-II riboswitch in the absence of ligand. Here, all-atom structure-based molecular simulations, with the electrostatic effects of Manning counter-ion condensation and explicit magnesium ions are employed to calculate the folding free energy landscape of the SAM-II riboswitch. We use this analysis to predict that magnesium ions remodel the landscape, shifting the equilibrium away from the extended, partially unfolded state towards a compact, pre-organized conformation that resembles the ligand-bound state. Our CEST and SAXS experiments, at different magnesium ion concentrations, quantitatively confirm our simulation results, demonstrating that magnesium ions induce collapse and pre-organization. Agreement between theory and experiment bolsters microscopic interpretation of our simulations, which shows that triplex formation between helix P2b and loop L1 is highly sensitive to magnesium and plays a key role in pre-organization. Pre-organization of the SAM-II riboswitch allows rapid detection of ligand with high selectivity, which is important for biological function.

Adaptive Landscape Flattening Accelerates Sampling of Alchemical Space in Multisite λ Dynamics.

Multisite λ dynamics (MSλD) is a powerful emerging method in free energy calculation that allows prediction of relative free energies for a large set of compounds from very few simulations. Calculating free energy differences between substituents that constitute large volume or flexibility jumps in chemical space is difficult for free energy methods in general, and for MSλD in particular, due to large free energy barriers in alchemical space. This study demonstrates that a simple biasing potential can flatten these barriers and introduces an algorithm that determines system specific biasing potential coefficients. Two sources of error, deep traps at the end points and solvent disruption by hard-core potentials, are identified. Both scale with the size of the perturbed substituent and are removed by sharp biasing potentials and a new soft-core implementation, respectively. MSλD with landscape flattening is demonstrated on two sets of molecules: derivatives of the heat shock protein 90 inhibitor geldanamycin and derivatives of benzoquinone. In the benzoquinone system, landscape flattening leads to 2 orders of magnitude improvement in transition rates between substituents and robust solvation free energies. Landscape flattening opens up new applications for MSλD by enabling larger chemical perturbations to be sampled with improved precision and accuracy.

SMOG 2: A Versatile Software Package for Generating Structure-Based Models.

Molecular dynamics simulations with coarse-grained or simplified Hamiltonians have proven to be an effective means of capturing the functionally important long-time and large-length scale motions of proteins and RNAs. Originally developed in the context of protein folding, structure-based models (SBMs) have since been extended to probe a diverse range of biomolecular processes, spanning from protein and RNA folding to functional transitions in molecular machines. The hallmark feature of a structure-based model is that part, or all, of the potential energy function is defined by a known structure. Within this general class of models, there exist many possible variations in resolution and energetic composition. SMOG 2 is a downloadable software package that reads user-designated structural information and user-defined energy definitions, in order to produce the files necessary to use SBMs with high performance molecular dynamics packages: GROMACS and NAMD. SMOG 2 is bundled with XML-formatted template files that define commonly used SBMs, and it can process template files that are altered according to the needs of each user. This computational infrastructure also allows for experimental or bioinformatics-derived restraints or novel structural features to be included, e.g. novel ligands, prosthetic groups and post-translational/transcriptional modifications. The code and user guide can be downloaded at http://smog-server.org/smog2.

Generalized Manning Condensation Model Captures the RNA Ion Atmosphere.

RNA is highly sensitive to the ionic environment and typically requires Mg(2+) to form compact structures. There is a need for models capable of describing the ion atmosphere surrounding RNA with quantitative accuracy. We present a model of RNA electrostatics and apply it within coarse-grained molecular dynamics simulation. The model treats Mg(2+) ions explicitly to account for ion-ion correlations neglected by mean-field theories. Since mean-field theories capture KCl well, it is treated implicitly by a generalized Manning counterion condensation model. The model extends Manning condensation to deal with arbitrary RNA conformations, nonlimiting KCl concentrations, and the ion inaccessible volume of RNA. The model is tested against experimental measurements of the excess Mg(2+) associated with the RNA, Γ(2+), because Γ(2+) is directly related to the Mg(2+)-RNA interaction free energy. The excellent agreement with experiment demonstrates that the model captures the ionic dependence of the RNA free energy landscape.