CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed.

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Membrane Stabilization of Helical Previtamin D Conformers as Possible Enhancement of Vitamin D Photoproduction.

Photoinduced vitamin D formation occurs 10-15-fold faster in phospholipid bilayers (PLB) than in isotropic solution. It has been hypothesized that amphipatic interactions of the PLB with the rotationally flexible previtamin D (Pre) stabilize its helical conformers, enhancing thermal intramolecular [1,7]-hydrogen transfer, forming vitamin D. To test this hypothesis, we carried out molecular dynamics (MD) simulations of Pre in a PLB composed of dipalmitoylphosphatidylcholine (DPPC). We designed a classical force field capable of accurately describing the equilibrium composition of Pre conformers. Using adaptive biasing force MD simulations, we determined the free energy of Pre conformers in isotropic environments (hexane and gas-phase) and in the anisotropic environment of a DPPC PLB. We find a total increase of 25.5% of the population of both helical conformers (+20.5% g+Zg+ and +5% g-Zg-) in DPPC compared to hexane. In view of ab initio simulations, showing that hydrogen transfer occurs in both helical conformers, our study strongly suggests the validity of the initial hypothesis. Regarding the amphipatic interactions of Pre with the PLB, we find that, similar to cholesterol (Chol) and 7-dehydrocholesterol (7-DHC), Pre entertains hydrogen bonds mainly to the carbonyl groups of DPPC and, to a lesser extent, with phosphate oxygen atoms and rarely to water molecules at the interface. We further report order parameters of the Pre/DPPC system, which are slightly smaller than those for Chol/DPPC and 7-DHC/DPPC, but larger than for pure DPPC. This indicates a loss in membrane viscosity upon photochemical ring-opening of 7-DHC to form Pre.

Modeling Ensembles of Enzyme Reaction Pathways with Hi-MSM Reveals the Importance of Accounting for Pathway Diversity.

Conventional quantum mechanical-molecular mechanics (QM/MM) simulation approaches for modeling enzyme reactions often assume that there is one dominant reaction pathway and that this pathway can be sampled starting from an X-ray structure of the enzyme. These assumptions reduce computational cost; however, their validity has not been extensively tested. This is due in part to the lack of a rigorous formalism for integrating disparate pathway information from dynamical QM/MM calculations. Here, we present a way to model ensembles of reaction pathways efficiently using a divide-and-conquer strategy through Hierarchical Markov State Modeling (Hi-MSM). This approach allows information on multiple, distinct pathways to be incorporated into a chemical kinetic model, and it allows us to test these two assumptions. Applying Hi-MSM to the reaction carried out by dihydrofolate reductase (DHFR) we find (i) there are multiple, distinct pathways significantly contributing to the overall flux of the reaction that the conventional approach does not identify and (ii) that the conventional approach does not identify the dominant reaction pathway. Thus, both assumptions underpinning the conventional approach are violated. Since DHFR is a relatively small enzyme, and configuration space scales exponentially with protein size, accounting for multiple reaction pathways is likely to be necessary for most enzymes.

Obtaining QM/MM binding free energies in the SAMPL8 drugs of abuse challenge: indirect approaches.

Accurately predicting free energy differences is essential in realizing the full potential of rational drug design. Unfortunately, high levels of accuracy often require computationally expensive QM/MM Hamiltonians. Fortuitously, the cost of employing QM/MM approaches in rigorous free energy simulation can be reduced through the use of the so-called "indirect" approach to QM/MM free energies, in which the need for QM/MM simulations is avoided via a QM/MM "correction" at the classical endpoints of interest. Herein, we focus on the computation of QM/MM binding free energies in the context of the SAMPL8 Drugs of Abuse host-guest challenge. Of the 5 QM/MM correction coupled with force-matching submissions, PM6-D3H4/MM ranked submission proved the best overall QM/MM entry, with an RMSE from experimental results of 2.43 kcal/mol (best in ranked submissions), a Pearson's correlation of 0.78 (second-best in ranked submissions), and a Kendall [Formula: see text] correlation of 0.52 (best in ranked submissions).

A replica exchange umbrella sampling (REUS) approach to predict host-guest binding free energies in SAMPL8 challenge.

In this study, we report binding free energy calculations of various drugs-of-abuse to Cucurbit-[8]-uril as part of the SAMPL8 blind challenge. Force-field parameters were obtained from force-matching with different quantum mechanical levels of theory. The Replica Exchange Umbrella Sampling (REUS) approach was used with a cylindrical restraint to enhance the sampling of host-guest binding. Binding free energy was calculated by pulling the guest molecule from one side of the symmetric and cylindrical host, then into and through the host, and out the other side (bidirectional) as compared to pulling only to the bound pose inside the cylindrical host (unidirectional). The initial results with force-matched MP2 parameter set led to RMSE of 4.68 [Formula: see text] from experimental values. However, the follow-up study with CHARMM generalized force field parameters and force-matched PM6-D3H4 parameters resulted in RMSEs from experiment of [Formula: see text] and [Formula: see text], respectively, which demonstrates the potential of REUS for accurate binding free energy calculation given a more suitable description of energetics. Moreover, we compared the free energies for the so called bidirectional and unidirectional free energy approach and found that the binding free energies were highly similar. However, one issue in the bidirectional approach is the asymmetry of profile on the two sides of the host. This is mainly due to the insufficient sampling for these larger systems and can be avoided by longer sampling simulations. Overall REUS shows great promise for binding free energy calculations.

Enantiomerization of Axially Chiral Biphenyls: Polarizable MD Simulations in Water and Butylmethylether.

In this study, we investigate the influence of chiral and achiral cations on the enantiomerization of biphenylic anions in n-butylmethylether and water. In addition to the impact of the cations and solvent molecules on the free energy profile of rotation, we also explore if chirality transfer between a chiral cation and the biphenylic anion is possible, i.e., if pairing with a chiral cation can energetically favour one conformer of the anion via diastereomeric complex formation. The quantum-mechanical calculations are accompanied by polarizable MD simulations using umbrella sampling to study the impact of solvents of different polarity in more detail. We also discuss how accurate polarizable force fields for biphenylic anions can be constructed from quantum-mechanical reference data.

Hierarchical Markov State Model Building to Describe Molecular Processes.

Markov state models can describe ensembles of pathways via kinetic networks but are difficult to create when large free-energy barriers limit unbiased sampling. Chain-of-states simulations allow sampling over large free-energy barriers but are often constructed using a single pathway that is unlikely to thermodynamically average over orthogonal degrees of freedom in complex systems. Here, we combine the advantages of these two approaches in the form of a Markov state model of Markov state models, which we call a Hierarchical Markov state model. In this approach, independent Markov models are constructed in regions of configuration space that are locally well sampled but are separated by large free-energy barriers from other regions. A string method is used to construct an ensemble of pathways connecting the states of these different local Markov models, and the rate through each pathway is then estimated. These rates are then combined with the rate information from the local Markov models in a master equation to predict global rates, fluxes, and populations. By applying this hierarchical approach to tractable systems, a toy potential and dipeptides, we demonstrate that it is more accurate than the conventional single-pathway description. The advantages of this approach are that it (i) is more realistic than the conventional chain-of-states approach, as an ensemble of pathways rather than a single pathway is used to describe processes in high-dimensional systems, and (ii) it resolves the issue of poor sampling in Markov State model building when large free-energy barriers are present. The divide-and-conquer strategy inherent to this approach should make this procedure straightforward to apply to more complex systems.

Multi-phase Boltzmann weighting: accounting for local inhomogeneity in molecular simulations of water-octanol partition coefficients in the SAMPL6 challenge.

Accurately computing partition coefficients is a pivotal part of drug discovery. Specifically, octanol-water partition coefficients can provide information into hydrophobicity of drug-like molecules, as well as a de facto representation of membrane permeability. However, one challenge facing the computation of partition coefficients is the need to encapsulate various microscopic environments. These include areas of largely bulk solvent (i.e., either water or octanol) or regions where octanol is saturated with water or areas of higher salt concentration. Also, tautomeric effects require consideration. Thus, we present a Boltzmann weighting approach that incorporates transfer free energies across varying microscopic media, as well as varying tautomeric state, to compute partition coefficients in the SAMPL6 challenge.

Use of Interaction Energies in QM/MM Free Energy Simulations.

The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.

Force matching as a stepping stone to QM/MM CB[8] host/guest binding free energies: a SAMPL6 cautionary tale.

Use of quantum mechanical/molecular mechanical (QM/MM) methods in binding free energy calculations, particularly in the SAMPL challenge, often fail to achieve improvement over standard additive (MM) force fields. Frequently, the implementation is through use of reference potentials, or the so-called "indirect approach", and inherently relies on sufficient overlap existing between MM and QM/MM configurational spaces. This overlap is generally poor, particularly for the use of free energy perturbation to perform the MM to QM/MM free energy correction at the end states of interest (e.g., bound and unbound states). However, by utilizing MM parameters that best reproduce forces obtained at the desired QM level of theory, it is possible to lessen the configurational disparity between MM and QM/MM. To this end, we sought to use force matching to generate MM parameters for the SAMPL6 CB[8] host-guest binding challenge, classically compute binding free energies, and apply energetic end state corrections to obtain QM/MM binding free energy differences. For the standard set of 11 molecules and the bonus set (including three additional challenge molecules), error statistics, such as the root mean square deviation (RMSE) were moderately poor (5.5 and 5.4 kcal/mol). Correlation statistics, however, were in the top two for both standard and bonus set submissions ([Formula: see text] of 0.42 and 0.26, [Formula: see text] of 0.64 and 0.47 respectively). High RMSE and moderate correlation strongly indicated the presence of systematic error. Identifiable issues were ameliorated for two of the guest molecules, resulting in a reduction of error and pointing to strong prospects for the future use of this methodology.