Assessment of Hydration Thermodynamics at Protein Interfaces with Grid Cell Theory

Sire: An interoperability engine for prototyping algorithms and exchanging information between molecular simulation programs

Sire is a Python/C++ library that is used both to prototype new algorithms and as an interoperability engine for exchanging information between molecular simulation programs. It provides a collection of file parsers and information converters that together make it easier to combine and leverage the functionality of many other programs and libraries. This empowers researchers to use sire to write a single script that can, for example, load a molecule from a PDBx/mmCIF file via Gemmi, perform SMARTS searches via RDKit, parameterize molecules using BioSimSpace, run GPU-accelerated molecular dynamics via OpenMM, and then display the resulting dynamics trajectory in a NGLView Jupyter notebook 3D molecular viewer. This functionality is built on by BioSimSpace, which uses sire's molecular information engine to interconvert with programs such as GROMACS, NAMD, Amber, and AmberTools for automated molecular parameterization and the running of molecular dynamics, metadynamics, and alchemical free energy workflows. Sire comes complete with a powerful molecular information search engine, plus trajectory loading and editing, analysis, and energy evaluation engines. This, when combined with an in-built computer algebra system, gives substantial flexibility to researchers to load, search for, edit, and combine molecular information from multiple sources and use that to drive novel algorithms by combining functionality from other programs. Sire is open source (GPL3) and is available via conda and at a free Jupyter notebook server at https://try.openbiosim.org. Sire is supported by the not-for-profit OpenBioSim community interest company.

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 β 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.

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.

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.

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.

Large-Scale Study of Hydration Environments through Hydration Sites

Hydration sites are locations of interest to water and they can be used to classify the behavior of water around chemical motifs commonly found on the surface of proteins. Inhomogeneous fluid solvation theory (IFST) is a method for calculating hydration free-energy changes from molecular dynamics (MD) trajectories. In this paper, hydration sites are identified from MD simulations of 380 diverse protein structures. The hydration free energies of the hydration sites are calculated using IFST and distributions of these free-energy changes are analyzed. The results show that for some hydration sites near features conventionally regarded as attractive to water, such as hydrogen bond donors, the water molecules are actually relatively weakly bound and are easily displaced. We also construct plots of the spatial density of hydration sites with high, medium, and low hydration free-energy changes which represent weakly and strongly bound hydration sites. It is found that these plots show consistent features around common polar amino acids for all of the proteins studied.

Metabolism and hydrophilicity of the polarised 'Janus face' all-cis tetrafluorocyclohexyl ring, a candidate motif for drug discovery

The metabolism and polarity of the all-cis tetra-fluorocyclohexane motif is explored in the context of its potential as a motif for inclusion in drug discovery programmes. Biotransformations of phenyl all-cis tetra-, tri- and di- fluoro cyclohexanes with the human metabolism model organism Cunninghamella elegans illustrates various hydroxylated products, but limited to benzylic hydroxylation for the phenyl all-cis tetrafluorocyclohexyl ring system. Evaluation of the lipophilicities (log P) indicates a significant and progressive increase in polarity with increasing fluorination on the cyclohexane ring system. Molecular dynamics simulations indicate that water associates much more closely with the hydrogen face of these Janus face cyclohexyl rings than the fluorine face owing to enhanced hydrogen bonding interactions with the polarised hydrogens and water.

Computational Methods Used in Hit-to-Lead and Lead Optimization Stages of Structure-Based Drug Discovery

GPCR modeling approaches are widely used in the hit-to-lead (H2L) and lead optimization (LO) stages of drug discovery. The aims of these modeling approaches are to predict the 3D structures of the receptor-ligand complexes, to explore the key interactions between the receptor and the ligand and to utilize these insights in the design of new molecules with improved binding, selectivity or other pharmacological properties. In this book chapter, we present a brief survey of key computational approaches integrated with hierarchical GPCR modeling protocol (HGMP) used in hit-to-lead (H2L) and in lead optimization (LO) stages of structure-based drug discovery (SBDD). We outline the differences in modeling strategies used in H2L and LO of SBDD and illustrate how these tools have been applied in three drug discovery projects.

GPCRs: What Can We Learn from Molecular Dynamics Simulations?

Advances in the structural biology of G-protein Coupled Receptors have resulted in a significant step forward in our understanding of how this important class of drug targets function at the molecular level. However, it has also become apparent that they are very dynamic molecules, and moreover, that the underlying dynamics is crucial in shaping the response to different ligands. Molecular dynamics simulations can provide unique insight into the dynamic properties of GPCRs in a way that is complementary to many experimental approaches. In this chapter, we describe progress in three distinct areas that are particularly difficult to study with other techniques: atomic level investigation of the conformational changes that occur when moving between the various states that GPCRs can exist in, the pathways that ligands adopt during binding/unbinding events and finally, the influence of lipids on the conformational dynamics of GPCRs.

Dynamics of Hydration Water Plays a Key Role in Determining the Binding Thermodynamics of Protein Complexes

Interfacial waters are considered to play a crucial role in protein–protein interactions, but in what sense and why are they important? Here, using molecular dynamics simulations and statistical thermodynamic analyses, we demonstrate distinctive dynamic characteristics of the interfacial water and investigate their implications for the binding thermodynamics. We identify the presence of extraordinarily slow (~1,000 times slower than in bulk water) hydrogen-bond rearrangements in interfacial water. We rationalize the slow rearrangements by introducing the “trapping” free energies, characterizing how strongly individual hydration waters are captured by the biomolecular surface, whose magnitude is then traced back to the number of water–protein hydrogen bonds and the strong electrostatic field produced at the binding interface. We also discuss the impact of the slow interfacial waters on the binding thermodynamics. We find that, as expected from their slow dynamics, the conventional approach to the water-mediated interaction, which assumes rapid equilibration of the waters’ degrees of freedom, is inadequate. We show instead that an explicit treatment of the extremely slow interfacial waters is critical. Our results shed new light on the role of water in protein–protein interactions, highlighting the need to consider its dynamics to improve our understanding of biomolecular bindings.