Efficient implementation of constant pH molecular dynamics on modern graphics processors

The rotamer of the second-sphere histidine in AA9 lytic polysaccharide monooxygenase is pH dependent

Lytic polysaccharide monooxygenases (LPMOs) catalyze a reaction that is crucial for the biological decomposition of various biopolymers and for the industrial conversion of plant biomass. Despite the importance of LPMOs, the exact molecular-level nature of the reaction mechanism is still debated today. Here, we investigated the pH-dependent conformation of a second-sphere histidine (His) that we call the stacking histidine, which is conserved in fungal AA9 LPMOs and is speculated to assist catalysis in several of the LPMO reaction pathways. Using constant-pH and accelerated molecular dynamics simulations, we monitored the dynamics of the stacking His in different protonation states for both the resting Cu(II) and active Cu(I) forms of two fungal LPMOs. Consistent with experimental crystallographic and neutron diffraction data, our calculations suggest that the side chain of the protonated and positively charged form is rotated out of the active site toward the solvent. Importantly, only one of the possible neutral states of histidine (HIE state) is observed in the stacking orientation at neutral pH or when bound to cellulose. Our data predict that, in solution, the stacking His may act as a stabilizer (via hydrogen bonding) of the Cu(II)-superoxo complex after the LPMO-Cu(I) has reacted with O2 in solution, which, in fine, leads to H2O2 formation. Also, our data indicate that the HIE-stacking His is a poor acid/base catalyst when bound to the substrate and, in agreement with the literature, may play an important stabilizing role (via hydrogen bonding) during the peroxygenase catalysis. Our study reveals the pH titration midpoint values of the pH-dependent orientation of the stacking His should be considered when modeling and interpreting LPMO reactions, whether it be for classical LPMO kinetics or in industry-oriented enzymatic cocktails, and for understanding LPMO behavior in slightly acidic natural processes such as fungal wood decay.

Molecular Dynamics as a Tool for Virtual Ligand Screening

Rational drug design is essential for new drugs to emerge, especially when the structure of a target protein or nucleic acid is known. To that purpose, high-throughput virtual ligand screening campaigns aim at discovering computationally new binding molecules or fragments to modulate particular biomolecular interactions or biological activities, related to a disease process. The structure-based virtual ligand screening process primarily relies on docking methods which allow predicting the binding of a molecule to a biological target structure with a correct conformation and the best possible affinity. The docking method itself is not sufficient as it suffers from several and crucial limitations (lack of full protein flexibility information, no solvation and ion effects, poor scoring functions, and unreliable molecular affinity estimation).At the interface of computer techniques and drug discovery, molecular dynamics (MD) allows introducing protein flexibility before or after a docking protocol, refining the structure of protein-drug complexes in the presence of water, ions, and even in membrane-like environments, describing more precisely the temporal evolution of the biological complex and ranking these complexes with more accurate binding energy calculations. In this chapter, we describe the up-to-date MD, which plays the role of supporting tools in the virtual ligand screening (VS) process.Without a doubt, using docking in combination with MD is an attractive approach in structure-based drug discovery protocols nowadays. It has proved its efficiency through many examples in the literature and is a powerful method to significantly reduce the amount of required wet experimentations (Tarcsay et al, J Chem Inf Model 53:2990-2999, 2013; Barakat et al, PLoS One 7:e51329, 2012; De Vivo et al, J Med Chem 59:4035-4061, 2016; Durrant, McCammon, BMC Biol 9:71-79, 2011; Galeazzi, Curr Comput Aided Drug Des 5:225-240, 2009; Hospital et al, Adv Appl Bioinforma Chem 8:37-47, 2015; Jiang et al, Molecules 20:12769-12786, 2015; Kundu et al, J Mol Graph Model 61:160-174, 2015; Mirza et al, J Mol Graph Model 66:99-107, 2016; Moroy et al, Future Med Chem 7:2317-2331, 2015; Naresh et al, J Mol Graph Model 61:272-280, 2015; Nichols et al, J Chem Inf Model 51:1439-1446, 2011; Nichols et al, Methods Mol Biol 819:93-103, 2012; Okimoto et al, PLoS Comput Biol 5:e1000528, 2009; Rodriguez-Bussey et al, Biopolymers 105:35-42, 2016; Sliwoski et al, Pharmacol Rev 66:334-395, 2014).

Reliable and Accurate Prediction of Single-Residue pKa Values through Free Energy Perturbation Calculations

Accurate prediction of the pK_a's of protein residues is crucial to many applications in biological simulation and drug discovery. Here, we present the use of free energy perturbation (FEP) calculations for the prediction of single-protein residue pK_a values. We begin with an initial set of 191 residues with experimentally determined pK_a values. To isolate sampling limitations from force field inaccuracies, we develop an algorithm to classify residues whose environments are significantly affected by crystal packing effects. We then report an approach to identify buried histidines that require significant sampling beyond what is achieved in typical FEP calculations. We therefore define a clean data set not requiring algorithms capable of predicting major conformational changes on which other pK_a prediction methods can be tested. On this data set, we report an RMSE of 0.76 pK_a units for 35 ASP residues, 0.51 pK_a units for 44 GLU residues, and 0.67 pK_a units for 76 HIS residues.

Electrostatics in Computational Biophysics and Its Implications for Disease Effects

This review outlines the role of electrostatics in computational molecular biophysics and its implication in altering wild-type characteristics of biological macromolecules, and thus the contribution of electrostatics to disease mechanisms. The work is not intended to review existing computational approaches or to propose further developments. Instead, it summarizes the outcomes of relevant studies and provides a generalized classification of major mechanisms that involve electrostatic effects in both wild-type and mutant biological macromolecules. It emphasizes the complex role of electrostatics in molecular biophysics, such that the long range of electrostatic interactions causes them to dominate all other forces at distances larger than several Angstroms, while at the same time, the alteration of short-range wild-type electrostatic pairwise interactions can have pronounced effects as well. Because of this dual nature of electrostatic interactions, being dominant at long-range and being very specific at short-range, their implications for wild-type structure and function are quite pronounced. Therefore, any disruption of the complex electrostatic network of interactions may abolish wild-type functionality and could be the dominant factor contributing to pathogenicity. However, we also outline that due to the plasticity of biological macromolecules, the effect of amino acid mutation may be reduced, and thus a charge deletion or insertion may not necessarily be deleterious.

A fine balance of hydrophobic-electrostatic communication pathways in a pH-switching protein

Allostery is the phenomenon of coupling between distal binding sites in a protein. Such coupling is at the crux of protein function and regulation in a myriad of scenarios, yet determining the molecular mechanisms of coupling networks in proteins remains a major challenge. Here, we report mechanisms governing pH-dependent myristoyl switching in monomeric hisactophilin, whereby the myristoyl moves between a sequestered state, i.e., buried within the core of the protein, to an accessible state, in which the myristoyl has increased accessibility for membrane binding. Measurements of the pH and temperature dependence of amide chemical shifts reveal protein local structural stability and conformational heterogeneity that accompany switching. An analysis of these measurements using a thermodynamic cycle framework shows that myristoyl-proton coupling at the single-residue level exists in a fine balance and extends throughout the protein. Strikingly, small changes in the stereochemistry or size of core and surface hydrophobic residues by point mutations readily break, restore, or tune myristoyl switch energetics. Synthesizing the experimental results with those of molecular dynamics simulations illuminates atomistic details of coupling throughout the protein, featuring a large network of hydrophobic interactions that work in concert with key electrostatic interactions. The simulations were critical for discerning which of the many ionizable residues in hisactophilin are important for switching and identifying the contributions of nonnative interactions in switching. The strategy of using temperature-dependent NMR presented here offers a powerful, widely applicable way to elucidate the molecular mechanisms of allostery in proteins at high resolution.

Investigation of the structure and dynamics of gallium binding to high-affinity peptides elucidated by multi-scale simulation, quantum chemistry, NMR and ITC

Gallium (as Ga³⁺) is a Group IIIa metal and its recovery from wastewaters has become increasingly important for its reuse. The use of peptides for recycling offers a low-cost and environmentally-friendly option but the structural characteristics of peptides likely to bind Ga³⁺ are largely unknown. Multiple computational methods, coupled with experimental verification via NMR and Isothermal Calorimetry (ITC), were used to establish that Ga³⁺ binds with high affinity to peptide sequences and to elucidate the structural characteristics that contributed. It was demonstrated that peptide pre-organisation is key to Ga³⁺ binding and that a favourable binding position is necessarily governed by the size and shape of the electrostatic environment as much as individual electrostatic interactions with peptide residues themselves. Given favourable conditions, Ga³⁺ retrieved plausible binding positions involving both charged and uncharged residues that greatly increases the range of bonding possibilities with other peptide sequences and offers insights for binding other metals. The addition of pH buffer substantially improved the affinity of Ga³⁺ and a structural role for a buffer component was demonstrated.

Continuous Constant pH Molecular Dynamics Simulations of Transmembrane Proteins

Many membrane channels, transporters, and receptors utilize a pH gradient or proton coupling to drive functionally relevant conformational transitions. Conventional molecular dynamics simulations employ fixed protonation states, thus neglecting the coupling between protonation and conformational equilibria. Here we describe the membrane-enabled hybrid-solvent continuous constant pH molecular dynamics method for capturing atomic details of proton-coupled conformational dynamics of transmembrane proteins. Example protocols from our recent application studies of proton channels and ion/substrate transporters are discussed.

Large-Scale Assessment of Binding Free Energy Calculations in Active Drug Discovery Projects

Accurate ranking of compounds with regards to their binding affinity to a protein using computational methods is of great interest to pharmaceutical research. Physics-based free energy calculations are regarded as the most rigorous way to estimate binding affinity. In recent years, many retrospective studies carried out both in academia and industry have demonstrated its potential. Here, we present the results of large-scale prospective application of the FEP+ method in active drug discovery projects in an industry setting at Merck KGaA, Darmstadt, Germany. We compare these prospective data to results obtained on a new diverse, public benchmark of eight pharmaceutically relevant targets. Our results offer insights into the challenges faced when using free energy calculations in real-life drug discovery projects and identify limitations that could be tackled by future method development. The new public data set we provide to the community can support further method development and comparative benchmarking of free energy calculations.

GPU-Accelerated Implementation of Continuous Constant pH Molecular Dynamics in Amber: pKa Predictions with Single-pH Simulations

We present a GPU implementation of the continuous constant pH molecular dynamics (CpHMD) based on the most recent generalized Born implicit-solvent model in the pmemd engine of the Amber molecular dynamics package. To test the accuracy of the tool for rapid pK_a predictions, a series of 2 ns single-pH simulations were performed for over 120 titratable residues in 10 benchmark proteins that were previously used to test the various continuous CpHMD methods. The calculated pK_a's showed a root-mean-square deviation of 0.80 and correlation coefficient of 0.83 with respect to experiment. Also, 90% of the pK_a's were converged with estimated errors below 0.1 pH units. Surprisingly, this level of accuracy is similar to our previous replica-exchange simulations with 2 ns per replica and an exchange attempt frequency of 2 ps^-1 (Huang, Harris, and Shen J. Chem. Inf. Model. 2018 , 58 , 1372 - 1383 ). Interestingly, for the linked titration sites in two enzymes, although residue-specific protonation state sampling in the single-pH simulations was not converged within 2 ns, the protonation fraction of the linked residues appeared to be largely converged, and the experimental macroscopic pK_a values were reproduced to within 1 pH unit. Comparison with replica-exchange simulations with different exchange attempt frequencies showed that the splitting between the two macroscopic pK_a's is underestimated with frequent exchange attempts such as 2 ps^-1, while single-pH simulations overestimate the splitting. The same trend is seen for the single-pH vs replica-exchange simulations of a hydrogen-bonded aspartyl dyad in a much larger protein. A 2 ns single-pH simulation of a 400-residue protein takes about 1 h on a single NVIDIA GeForce RTX 2080 graphics card, which is over 1000 times faster than a CpHMD run on a single CPU core of a high-performance computing cluster node. Thus, we envision that GPU-accelerated continuous CpHMD may be used in routine pK_a predictions for a variety of applications, from assisting MD simulations with protonation state assignment to offering pH-dependent corrections of binding free energies and identifying reactive hot spots for covalent drug design.

Relative Contributions of Solubility and Mobility to the Stability of Amorphous Solid Dispersions of Poorly Soluble Drugs: A Molecular Dynamics Simulation Study

Amorphous solid dispersions are considered a promising formulation strategy for the oral delivery of poorly soluble drugs. The limiting factor for the applicability of this approach is the physical (in)stability of the amorphous phase in solid samples. Minimizing the risk of reduced shelf life for a new drug by establishing a suitable excipient/polymer-type from first principles would be desirable to accelerate formulation development. Here, we perform Molecular Dynamics simulations to determine properties of blends of eight different polymer–small molecule drug combinations for which stability data are available from a consistent set of literature data. We calculate thermodynamic factors (mixing energies) as well as mobilities (diffusion rates and roto-vibrational fluctuations). We find that either of the two factors, mobility and energetics, can determine the relative stability of the amorphous form for a given drug. Which factor is rate limiting depends on physico-chemical properties of the drug and the excipients/polymers. The methods outlined here can be readily employed for an in silico pre-screening of different excipients for a given drug to establish a qualitative ranking of the expected relative stabilities, thereby accelerating and streamlining formulation development.

A GPU-Accelerated Parameter Interpolation Thermodynamic Integration Free Energy Method

There has been a resurgence of interest in free energy methods motivated by the performance enhancements offered by molecular dynamics (MD) software written for specialized hardware, such as graphics processing units (GPUs). In this work, we exploit the properties of a parameter-interpolated thermodynamic integration (PI-TI) method to connect states by their molecular mechanical (MM) parameter values. This pathway is shown to be better behaved for Mg2+ → Ca2+ transformations than traditional linear alchemical pathways (with and without soft-core potentials). The PI-TI method has the practical advantage that no modification of the MD code is required to propagate the dynamics, and unlike with linear alchemical mixing, only one electrostatic evaluation is needed (e.g., single call to particle-mesh Ewald) leading to better performance. In the case of AMBER, this enables all the performance benefits of GPU-acceleration to be realized, in addition to unlocking the full spectrum of features available within the MD software, such as Hamiltonian replica exchange (HREM). The TI derivative evaluation can be accomplished efficiently in a post-processing step by reanalyzing the statistically independent trajectory frames in parallel for high throughput. We also show how one can evaluate the particle mesh Ewald contribution to the TI derivative evaluation without needing to perform two reciprocal space calculations. We apply the PI-TI method with HREM on GPUs in AMBER to predict p Ka values in double stranded RNA molecules and make comparison with experiments. Convergence to under 0.25 units for these systems required 100 ns or more of sampling per window and coupling of windows with HREM. We find that MM charges derived from ab initio QM/MM fragment calculations improve the agreement between calculation and experimental results.

Molecular Dynamics as a Tool for Virtual Ligand Screening

Rational drug design is essential for new drugs to emerge, especially when the structure of a target protein or catalytic enzyme is known experimentally. To that purpose, high-throughput virtual ligand screening campaigns aim at discovering computationally new binding molecules or fragments to inhibit a particular protein interaction or biological activity. The virtual ligand screening process often relies on docking methods which allow predicting the binding of a molecule into a biological target structure with a correct conformation and the best possible affinity. The docking method itself is not sufficient as it suffers from several and crucial limitations (lack of protein flexibility information, no solvation effects, poor scoring functions, and unreliable molecular affinity estimation).At the interface of computer techniques and drug discovery, molecular dynamics (MD) allows introducing protein flexibility before or after a docking protocol, refining the structure of protein-drug complexes in the presence of water, ions and even in membrane-like environments, and ranking complexes with more accurate binding energy calculations. In this chapter we describe the up-to-date MD protocols that are mandatory supporting tools in the virtual ligand screening (VS) process. Using docking in combination with MD is one of the best computer-aided drug design protocols nowadays. It has proved its efficiency through many examples, described below.

Toward Fast and Accurate Binding Affinity Prediction with pmemdGTI: An Efficient Implementation of GPU-Accelerated Thermodynamic Integration

We report the implementation of the thermodynamic integration method on the pmemd module of the AMBER 16 package on GPUs (pmemdGTI). The pmemdGTI code typically delivers over 2 orders of magnitude of speed-up relative to a single CPU core for the calculation of ligand-protein binding affinities with no statistically significant numerical differences and thus provides a powerful new tool for drug discovery applications.

Rigidity and flexibility in the tetrasaccharide linker of proteoglycans from atomic-resolution molecular simulation

Proteoglycans (PGs) are covalent conjugates between protein and carbohydrate (glycosaminoglycans). Certain classes of glycosaminoglycans such as chondroitin sulfate/dermatan sulfate and heparan sulfate utilize a specific tetrasaccharide linker for attachment to the protein component: GlcAβ1-3Galβ1-3Galβ1-4Xylβ1-O-Ser. Toward understanding the conformational preferences of this linker, the present work used all-atom explicit-solvent molecular dynamics (MD) simulations combined with Adaptive Biasing Force (ABF) sampling to determine high-resolution, high-precision conformational free energy maps ΔG(φ, ψ) for each glycosidic linkage between constituent disaccharides, including the variant where GlcA is substituted with IdoA. These linkages are characterized by single, predominant (> 97% occupancy), and broad (45° × 60° for ΔG(φ, ψ) < 1 kcal/mol) free-energy minima, while the Xyl-Ser linkage has two such minima similar in free-energy, and additional flexibility from the Ser sidechain dihedral. Conformational analysis of microsecond-scale standard MD on the complete tetrasaccharide-O-Ser conjugate is consistent with ABF data, suggesting (φ, ψ) probabilities are independent of the linker context, and that the tetrasaccharide acts as a relatively rigid unit whereas significant conformational heterogeneity exists with respect to rotation about bonds connecting Xyl to Ser. © 2017 Wiley Periodicals, Inc.