Energy-entropy multiscale cell correlation method to predict toluene-water log P in the SAMPL9 challenge.

The energy-entropy multiscale cell correlation (EE-MCC) method is used to calculate toluene-water log P values of 16 drug molecules in the SAMPL9 physical properties challenge. EE-MCC calculates the free energy, energy and entropy from molecular dynamics (MD) simulations of the water and toluene solutions. Specifically, MCC evaluates entropy by partitioning the system into cells of correlated atoms at multiple length scales and further partitioning the local coordinates into energy wells, yielding vibrational and topographical terms from the energy-well sizes and probabilities. The log P values calculated by EE-MCC using three 200 ns MD simulations have a mean average error of 0.82 and standard error of the mean of 0.97 versus experiment, which is comparable with the best methods entered in SAMPL9. The main contribution to log P is from energy. Less polar drugs have more favourable energies of transfer. The entropy of transfer consists of increased solute vibrational and conformational terms in toluene due to weaker interactions, fewer solute positions in the larger-molecule solvent, reduced water vibrational entropy, negligible change in toluene vibrational entropy, and gains in solvent orientational entropy. The solvent entropy contributions here may be slightly underestimated because software limitations and statistical fluctuations meant that only the first shell could be included while averaged over the whole solution. Nonetheless, such issues will be addressed in future software to offer a general method to calculate entropy directly from MD simulation and to provide molecular understanding or guide system design.

Total free energy analysis of fully hydrated proteins.

The total free energy of a hydrated biomolecule and its corresponding decomposition of energy and entropy provides detailed information about regions of thermodynamic stability or instability. The free energies of four hydrated globular proteins with different net charges are calculated from a molecular dynamics simulation, with the energy coming from the system Hamiltonian and entropy using multiscale cell correlation. Water is found to be most stable around anionic residues, intermediate around cationic and polar residues, and least stable near hydrophobic residues, especially when more buried, with stability displaying moderate entropy-enthalpy compensation. Conversely, anionic residues in the proteins are energetically destabilized relative to singly solvated amino acids, while trends for other residues are less clear-cut. Almost all residues lose intraresidue entropy when in the protein, enthalpy changes are negative on average but may be positive or negative, and the resulting overall stability is moderate for some proteins and negligible for others. The free energy of water around single amino acids is found to closely match existing hydrophobicity scales. Regarding the effect of secondary structure, water is slightly more stable around loops, of intermediate stability around ß strands and turns, and least stable around helices. An interesting asymmetry observed is that cationic residues stabilize a residue when bonded to its N-terminal side but destabilize it when on the C-terminal side, with a weaker reversed trend for anionic residues.

Energy-entropy method using multiscale cell correlation to calculate binding free energies in the SAMPL8 host-guest challenge.

Free energy drives a wide range of molecular processes such as solvation, binding, chemical reactions and conformational change. Given the central importance of binding, a wide range of methods exist to calculate it, whether based on scoring functions, machine-learning, classical or electronic structure methods, alchemy, or explicit evaluation of energy and entropy. Here we present a new energy-entropy (EE) method to calculate the host-guest binding free energy directly from molecular dynamics (MD) simulation. Entropy is evaluated using Multiscale Cell Correlation (MCC) which uses force and torque covariance and contacts at two different length scales. The method is tested on a series of seven host-guest complexes in the SAMPL8 (Statistical Assessment of the Modeling of Proteins and Ligands) "Drugs of Abuse" Blind Challenge. The EE-MCC binding free energies are found to agree with experiment with an average error of 0.9 kcal mol-1. MCC makes clear the origin of the entropy changes, showing that the large loss of positional, orientational, and to a lesser extent conformational entropy of each binding guest is compensated for by a gain in orientational entropy of water released to bulk, combined with smaller decreases in vibrational entropy of the host, guest and contacting water.

Energy-entropy prediction of octanol-water logP of SAMPL7 N-acyl sulfonamide bioisosters.

Partition coefficients quantify a molecule's distribution between two immiscible liquid phases. While there are many methods to compute them, there is not yet a method based on the free energy of each system in terms of energy and entropy, where entropy depends on the probability distribution of all quantum states of the system. Here we test a method in this class called Energy Entropy Multiscale Cell Correlation (EE-MCC) for the calculation of octanol-water logP values for 22 N-acyl sulfonamides in the SAMPL7 Physical Properties Challenge (Statistical Assessment of the Modelling of Proteins and Ligands). EE-MCC logP values have a mean error of 1.8 logP units versus experiment and a standard error of the mean of 1.0 logP units for three separate calculations. These errors are primarily due to getting sufficiently converged energies to give accurate differences of large numbers, particularly for the large-molecule solvent octanol. However, this is also an issue for entropy, and approximations in the force field and MCC theory also contribute to the error. Unique to MCC is that it explains the entropy contributions over all the degrees of freedom of all molecules in the system. A gain in orientational entropy of water is the main favourable entropic contribution, supported by small gains in solute vibrational and orientational entropy but offset by unfavourable changes in the orientational entropy of octanol, the vibrational entropy of both solvents, and the positional and conformational entropy of the solute.

Thermodynamic Origin of Differential Excipient-Lysozyme Interactions.

Understanding the intricate interplay of interactions between proteins, excipients, ions and water is important to achieve the effective purification and stable formulation of protein therapeutics. The free energy of lysozyme interacting with two kinds of polyanionic excipients, citrate and tripolyphosphate, together with sodium chloride and TRIS-buffer, are analysed in multiple-walker metadynamics simulations to understand why tripolyphosphate causes lysozyme to precipitate but citrate does not. The resulting multiscale decomposition of energy and entropy components for water, sodium chloride, excipients and lysozyme reveals that lysozyme is more stabilised by the interaction of tripolyphosphate with basic residues. This is accompanied by more sodium ions being released into solution from tripolyphosphate than for citrate, whilst the latter instead has more water molecules released into solution. Even though lysozyme aggregation is not directly probed in this study, these different mechanisms are suspected to drive the cross-linking between lysozyme molecules with vacant basic residues, ultimately leading to precipitation.

How Do Electrostatic Perturbations of the Protein Affect the Bifurcation Pathways of Substrate Hydroxylation versus Desaturation in the Nonheme Iron-Dependent Viomycin Biosynthesis Enzyme?

The viomycin biosynthesis enzyme VioC is a nonheme iron and α-ketoglutarate-dependent dioxygenase involved in the selective hydroxylation of l-arginine at the C3-position for antibiotics biosynthesis. Interestingly, experimental studies showed that using the substrate analogue, namely, l-homo-arginine, a mixture of products was obtained originating from C3-hydroxylation, C4-hydroxylation, and C3-C4-desaturation. To understand how the addition of one CH2 group to a substrate can lead to such a dramatic change in selectivity and activity, we decided to perform a computational study using quantum mechanical (QM) cluster models. We set up a large active-site cluster model of 245 atoms that includes the oxidant with its first- and second-coordination sphere influences as well as the substrate binding pocket. The model was validated against experimental work from the literature on related enzymes and previous computational studies. Thereafter, possible pathways leading to products and byproducts were investigated for a model containing l-Arg and one for l-homo-Arg as substrate. The calculated free energies of activation predict product distributions that match the experimental observation and give a low-energy C3-hydroxylation pathway for l-Arg, while for l-homo-Arg, several barriers are found to be close in energy leading to a mixture of products. We then analyzed the origins of the differences in product distributions using thermochemical, valence bond, and electrostatic models. Our studies show that the C3-H and C4-H bond strengths of l-Arg and l-homo-Arg are similar; however, external perturbations from an induced electric field of the protein affect the relative C-H bond strengths of l-Arg dramatically and make the C3-H bond the weakest and guide the reaction to a selective C3-hydroxylation channel. Therefore, the charge distribution in the protein and the induced electric dipole field of the active site of VioC guides the l-Arg substrate activation to C3-hydroxylation and disfavors the C4-hydroxylation pathway, while this does not occur for l-homo-Arg. Tight substrate positioning and electrostatic perturbations from the second-coordination sphere residues in VioC also result in a slower overall reaction for l-Arg; however, they enable a high substrate selectivity. Our studies highlight the importance of the second-coordination sphere in proteins that position the substrate and oxidant, perturb charge distributions, and enable substrate selectivity.

Convergence behaviour of solvation shells in simulated liquids.

A convenient way to analyse solvent structure around a solute is to use solvation shells, whereby solvent position around the solute is discretised by the size of a solvent molecule, leading to multiple shells around the solute. The two main ways to define multiple shells around a solute are either directly with respect to the solute, called solute-centric, or locally for both solute and solvent molecules alike. It might be assumed that both methods lead to solvation shells with similar properties. However, our analysis suggests otherwise. Solvation shells are analysed in a series of simulations of five pure liquids of differing polarity. Shells are defined locally working outwards from each molecule treated as a reference molecule using two methods: the cutoff at the first minimum in the radial distribution function and the parameter-free Relative Angular Distance method (RAD). The molecular properties studied are potential energy, coordination number and coordination radius. Rather than converging to bulk values, as might be expected for pure solvents, properties are found to deviate as a function of shell index. This behaviour occurs because molecules with larger coordination numbers and radius have more neighbours, which make them more likely to be connected to the reference molecule via fewer shells. The effect is amplified for RAD because of its more variable coordination radii and for water with its more open structure and stronger interactions. These findings indicate that locally defined shells should not be thought of as directly comparable to solute-centric shells or to distance. As well as showing how box size and cutoff affect the non-convergence, to restore convergence we propose a hybrid method by defining a new set of shells with boundaries at the uppermost distance of each locally derived shell.

What Determines the Selectivity of Arginine Dihydroxylation by the Nonheme Iron Enzyme OrfP?

The nonheme iron enzyme OrfP reacts with l-Arg selectively to form the 3R,4R-dihydroxyarginine product, which in mammals can inhibit the nitric oxide synthase enzymes involved in blood pressure control. To understand the mechanisms of dioxygen activation of l-Arg by OrfP and how it enables two sequential oxidation cycles on the same substrate, we performed a density functional theory study on a large active site cluster model. We show that substrate binding and positioning in the active site guides a highly selective reaction through C3 -H hydrogen atom abstraction. This happens despite the fact that the C3 -H and C4 -H bond strengths of l-Arg are very similar. Electronic differences in the two hydrogen atom abstraction pathways drive the reaction with an initial C3 -H activation to a low-energy 5 σ-pathway, while substrate positioning destabilizes the C4 -H abstraction and sends it over the higher-lying 5 π-pathway. We show that substrate and monohydroxylated products are strongly bound in the substrate binding pocket and hence product release is difficult and consequently its lifetime will be long enough to trigger a second oxygenation cycle.

Entropy of Proteins Using Multiscale Cell Correlation.

A new multiscale method is presented to calculate the entropy of proteins from molecular dynamics simulations. Termed Multiscale Cell Correlation (MCC), the method decomposes the protein into sets of rigid-body units based on their covalent-bond connectivity at three levels of hierarchy: molecule, residue, and united atom. It evaluates the vibrational and topographical entropy from forces, torques, and dihedrals at each level, taking into account correlations between sets of constituent units that together make up a larger unit at the coarser length scale. MCC gives entropies in close agreement with normal-mode analysis and smaller than those using quasiharmonic analysis as well as providing much faster convergence. Moreover, MCC provides an insightful decomposition of entropy at each length scale and for each type of amino acid according to their solvent exposure and whether they are terminal residues. While the residue entropy depends weakly on solvent exposure, there is greater variation in entropy components for larger, more polar amino acids, which have increased conformational entropy but reduced vibrational entropy with greater solvent exposure.

Comparison of Free-Energy Methods to Calculate the Barriers for the Nucleophilic Substitution of Alkyl Halides by Hydroxide.

Calculating the free-energy barriers of liquid-phase chemical reactions with explicit solvent is a considerable challenge. Most studies use the energy and entropy of minimized single-point geometries of the reactants and transition state in implicit solvent using normal mode analysis (NMA). Explicit-solvent methods instead make use of the potential of mean force (PMF). Here, we propose a new energy-entropy (EE) method to calculate the Gibbs free energy of reactants and transition states in explicit solvent by combining quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with multiscale cell correlation (MCC). We apply it to six nucleophilic substitution reactions of the hydroxide transfer to methyl and ethyl halides in water, where the halides are F, Cl, and Br. We compare EE-MCC Gibbs free energy barriers using two Hamiltonians, self-consistent charge density functional based tight-binding (SCC-DFTB) and B3LYP/6-31+G* density functional theory (DFT) with respective PMF values, EE-NMA values using B3LYP/6-31+G* and M06/6-31+G* DFT in implicit solvent and experimental values derived via transition state theory. The barriers using SCC-DFTB are found to agree well with the PMF and experiment and previous computational studies, being slightly higher but improving on the lower values obtained for the implicit solvent. Achieving convergence over many degrees of freedom remains a challenge for EE-MCC in explicit-solvent QM/MM systems, particularly for the more expensive B3LYP/6-31+G* and M06/6-31+G* DFT methods, but the insightful decomposition of entropy over all degrees of freedom should make EE-MCC a valuable tool for deepening the understanding of chemical reactions.

Extending the Martini Coarse-Grained Force Field to N-Glycans.

Glycans play a vital role in a large number of cellular processes. Their complex and flexible nature hampers structure-function studies using experimental techniques. Molecular dynamics (MD) simulations can help in understanding dynamic aspects of glycans if the force field parameters used can reproduce key experimentally observed properties. Here, we present optimized coarse-grained (CG) Martini force field parameters for N-glycans, calibrated against experimentally derived binding affinities for lectins. The CG bonded parameters were obtained from atomistic (ATM) simulations for different glycan topologies including high mannose and complex glycans with various branching patterns. In the CG model, additional elastic networks are shown to improve maintenance of the overall conformational distribution. Solvation free energies and octanol-water partition coefficients were also calculated for various N-glycan disaccharide combinations. When using standard Martini nonbonded parameters, we observed that glycans spontaneously aggregated in the solution and required down-scaling of their interactions for reproduction of ATM model radial distribution functions. We also optimized the nonbonded interactions for glycans interacting with seven lectin candidates and show that a relatively modest scaling down of the glycan-protein interactions can reproduce free energies obtained from experimental studies. These parameters should be of use in studying the role of glycans in various glycoproteins and carbohydrate binding proteins as well as their complexes, while benefiting from the efficiency of CG sampling.

Lignin Biodegradation by a Cytochrome P450 Enzyme: A Computational Study into Syringol Activation by GcoA.

A recently characterized cytochrome P450 isozyme GcoA activates lignin components through a selective O-demethylation or alternatively an acetal formation reaction. These are important reactions in biotechnology and, because lignin is readily available; it being the main component in plant cell walls. In this work we present a density functional theory study on a large active site model of GcoA to investigate syringol activation by an iron(IV)-oxo heme cation radical oxidant (Compound I) leading to hemiacetal and acetal products. Several substrate-binding positions were tested and full energy landscapes calculated. The study shows that substrate positioning determines the product distributions. Thus, with the phenol group pointing away from the heme, an O-demethylation is predicted, whereas an initial hydrogen-atom abstraction of the weak phenolic O-H group would trigger a pathway leading to ring-closure to form acetal products. Predictions on how to engineer P450 GcoA to get more selective product distributions are given.

Cross-linking of aromatic phenolate groups by cytochrome P450 enzymes: a model for the biosynthesis of vancomycin by OxyB.

The cytochromes P450 are a versatile class of enzymes involved in many chemical reactions in biosystems and as such they take part in biodegradation as well as biosynthesis pathways in many organisms. These enzymes use molecular oxygen on a heme centre and often react as mono-oxygenases. Lesser known reactions catalyzed by the P450s include desaturation pathways and ring-closure reactions. In this work we study the aromatic cross-linking of glycopeptide units as, for instance, performed by the P450 isozyme OxyB as part of vancomycin biosynthesis. A series of density functional theory studies are reported on a large active site cluster model of 258 atoms containing the heme with its coordinated ligands, a representative substrate and its interacting protein residues. We show that the catalytic cycle intermediates Compound I and Compound II of P450 can rapidly and successively abstract a phenolic hydrogen atom from adjacent peptide groups to give a biradical intermediate with small reaction barriers. The latter can form the ether cross-link between the two aromatic residues, which is the rate-determining step in the reaction mechanism and involves a simultaneous proton transfer from the ipso-position to the ketone. A thermochemical analysis reveals that weak phenolic O-H bonds lead to hydrogen atom abstraction easily by Compound I and Compound II, enabling a selective aromatic cross-linking reaction.

The Attraction of Water for Itself at Hydrophobic Quartz Interfaces.

Structural forces within aqueous water at a solid interface can significantly change surface reactivity and the affinity of solutes toward it. We show using molecular dynamics simulations how hydrophilic and hydrophobic quartz surfaces perturb the orientational structure of aqueous water, ultimately strengthening dipolar forces between molecules in proximity to the interface. When derived as a function of distance from each surface, it was found that both surfaces indirectly enhance the long-range dipolar attraction of water for itself toward the interfacial region. This was found to be longer-ranged for water molecules solvating the hydrophobic surface than those solvating the hydrophilic surface, with a range of up to 2.5 nm from the hydrophobic surface. Our results give direct quantification of surface-induced changes in solvent-solvent attraction, ultimately providing a counterintuitive addition to the balance of hydrophobic forces at aqueous-solid interfaces.

Model for Counterion Binding and Charge Reversal on Protein Surfaces.

The structural stability and solubility of proteins in liquid therapeutic formulations is important, especially since new generations of therapeutics are designed for efficacy before consideration of stability. We introduce an electrostatic binding model to measure the net charge of proteins with bound ions in solution. The electrostatic potential on a protein surface is used to separately group together acidic and basic amino acids into patches, which are then iteratively bound with oppositely charged counterions. This model is aimed toward formulation chemists for initial screening of a range of conditions prior to lab-work. Computed results compare well with experimental zeta potential measurements from the literature covering a range of solution conditions. Importantly, the binding model reproduces the charge reversal phenomenon that is observed with polyvalent ion binding to proteins and its dependence on ion charge and concentration. Intriguingly, protein sequence can be used to give similarly good agreement with experiment as protein structure, interpreted as resulting from the close proximity of charged side chains on a protein surface. Further, application of the model to human proteins suggests that polyanion binding and overcharging, including charge reversal for cationic proteins, is a general feature. These results add to evidence that addition of polyanions to protein formulations could be a general mechanism for modulating solution stability.

Entropy of Simulated Liquids Using Multiscale Cell Correlation.

Accurately calculating the entropy of liquids is an important goal, given that many processes take place in the liquid phase. Of almost equal importance is understanding the values obtained. However, there are few methods that can calculate the entropy of such systems, and fewer still to make sense of the values obtained. We present our multiscale cell correlation (MCC) method to calculate the entropy of liquids from molecular dynamics simulations. The method uses forces and torques at the molecule and united-atom levels and probability distributions of molecular coordinations and conformations. The main differences with previous work are the consistent treatment of the mean-field cell approximation to the approriate degrees of freedom, the separation of the force and torque covariance matrices, and the inclusion of conformation correlation for molecules with multiple dihedrals. MCC is applied to a broader set of 56 important industrial liquids modeled using the Generalized AMBER Force Field (GAFF) and Optimized Potentials for Liquid Simulations (OPLS) force fields with 1.14*CM1A charges. Unsigned errors versus experimental entropies are 8.7 J K - 1 mol - 1 for GAFF and 9.8 J K - 1 mol - 1 for OPLS. This is significantly better than the 2-Phase Thermodynamics method for the subset of molecules in common, which is the only other method that has been applied to such systems. MCC makes clear why the entropy has the value it does by providing a decomposition in terms of translational and rotational vibrational entropy and topographical entropy at the molecular and united-atom levels.

Overcoming the limitations of cutoffs for defining atomic coordination in multicomponent systems.

A common way to understand structure in multimolecular systems is the coordination shell which comprises all the neighbors of an atom. Coordination, however, is nontrivial to determine because there is no obvious way to determine when atoms are neighbors. A common solution is to take all atoms within a cutoff at the first minimum of the radial distribution function, g(r). We show that such an approach cannot be consistently applied to model multicomponent systems, namely mixtures of atoms differing in size or charge. Coordination shells using the total g(r) are found to be too restrictive for atoms of different size while those using pairwise g(r)s are excessive for charged mixtures. The recently introduced relative angular distance algorithm, however, which defines coordination instantaneously from atomic positions, is consistently able to define coordination shells containing the expected neighboring atoms for all these systems. This more robust way to determine coordination should in turn make coordination a more robust way to understand structure. © 2017 Wiley Periodicals, Inc.

Assessment of Hydration Thermodynamics at Protein Interfaces with Grid Cell Theory.

Molecular dynamics simulations have been analyzed with the Grid Cell Theory (GCT) method to spatially resolve the binding enthalpies and entropies of water molecules at the interface of 17 structurally diverse proteins. Correlations between computed energetics and structural descriptors have been sought to facilitate the development of simple models of protein hydration. Little correlation was found between GCT-computed binding enthalpies and continuum electrostatics calculations. A simple count of contacts with functional groups in charged amino acids correlates well with enhanced water stabilization, but the stability of water near hydrophobic and polar residues depends markedly on its coordination environment. The positions of X-ray-resolved water molecules correlate with computed high-density hydration sites, but many unresolved waters are significantly stabilized at the protein surfaces. A defining characteristic of ligand-binding pockets compared to nonbinding pockets was a greater solvent-accessible volume, but average water thermodynamic properties were not distinctive from other interfacial regions. Interfacial water molecules are frequently stabilized by enthalpy and destabilized entropy with respect to bulk, but counter-examples occasionally occur. Overall detailed inspection of the local coordinating environment appears necessary to gauge the thermodynamic stability of water in protein structures.

Locally adaptive method to define coordination shell.

An algorithm is presented to define a particle's coordination shell for any collection of particles. It requires only the particles' positions and no pre-existing knowledge or parameters beyond those already in the force field. A particle's shell is taken to be all particles that are not blocked by any other particle and not further away than a blocked particle. Because blocking is based on two distances and an angle for triplets of particles, it is called the relative angular distance (RAD) algorithm. RAD is applied to Lennard-Jones particles in molecular dynamics simulations of crystalline, liquid, and gaseous phases at various temperatures and densities. RAD coordination shells agree well with those from a cut-off in the radial distribution function for the crystals and liquids and are slightly higher for the gas.

Water's dual nature and its continuously changing hydrogen bonds.

A model is proposed for liquid water that is a continuum between the ordered state with predominantly tetrahedral coordination, linear hydrogen bonds and activated dynamics and a disordered state with a continuous distribution of multiple coordinations, multiple types of hydrogen bond, and diffusive dynamics, similar to that of normal liquids. Central to water's heterogeneous structure is the ability of hydrogen to donate to either one acceptor in a conventional linear hydrogen bond or to multiple acceptors as a furcated hydrogen. Linear hydrogen bonds are marked by slow, activated kinetics for hydrogen-bond switching to more crowded acceptors and sharp first peaks in the hydrogen-oxygen radial distribution function. Furcated hydrogens, equivalent to free, broken, dangling or distorted hydrogens, have barrierless, rapid kinetics and poorly defined first peaks in their hydrogen-oxygen radial distribution function. They involve the weakest donor in a local excess of donors, such that barrierless whole-molecule vibration rapidly swaps them between the linear and furcated forms. Despite the low number of furcated hydrogens and their transient existence, they are readily created in a single hydrogen-bond switch and free up the dynamics of numerous surrounding molecules, bringing about the disordered state. Hydrogens in the ordered state switch with activated dynamics to make the non-tetrahedral coordinations of the disordered state, which can also combine to make the ordered state. Consequently, the ordered and disordered states are both connected by diffusive dynamics and differentiated by activated dynamics, bringing about water's continuous heterogeneity.