A neural network potential based on pairwise resolved atomic forces and energies

Molecular simulations have become a key tool in molecular and materials design. Machine learning (ML)-based potential energy functions offer the prospect of simulating complex molecular systems efficiently at quantum chemical accuracy. In previous work, we have introduced the ML-based PairF-Net approach to neural network potentials, that adopts a pairwise interatomic scheme to predicting forces within a molecular system. Here, we further develop the PairF-Net model to intrinsically incorporate energy conservation and couple the model to a molecular mechanical (MM) environment within the OpenMM package. The updated PairF-Net model yields energy and force predictions and dynamical distributions in good agreement with the rMD17 dataset of ten small organic molecules in the gas-phase. We further show that these in vacuo ML models of small molecules can be applied to force predictions in aqueous solution via hybrid ML/MM simulations. We present a new benchmark dataset for these ten molecules in solution, obtained from QM/MM simulations, which we denote as rMD17-aq (https://zenodo.org/records/10048644); and assess the ability of PairF-Net to reproduce the molecular energy, atomic forces and dynamical distributions of these solution conformations via ML/MM simulations.

Molecular dynamics simulations as a guide for modulating small molecule aggregation

Small colloidally aggregating molecules (SCAMs) can be problematic for biological assays in drug discovery campaigns. However, the self-associating properties of SCAMs have potential applications in drug delivery and analytical biochemistry. Consequently, the ability to predict the aggregation propensity of a small organic molecule is of considerable interest. Chemoinformatics-based filters such as ChemAGG and Aggregator Advisor offer rapid assessment but are limited by the assay quality and structural diversity of their training set data. Complementary to these tools, we explore here the ability of molecular dynamics (MD) simulations as a physics-based method capable of predicting the aggregation propensity of diverse chemical structures. For a set of 32 molecules, using simulations of 100 ns in explicit solvent, we find a success rate of 97% (one molecule misclassified) as opposed to 75% by Aggregator Advisor and 72% by ChemAGG. These short timescale MD simulations are representative of longer microsecond trajectories and yield an informative spectrum of aggregation propensities across the set of solutes, capturing the dynamic behaviour of weakly aggregating compounds. Implicit solvent simulations using the generalized Born model were less successful in predicting aggregation propensity. MD simulations were also performed to explore structure-aggregation relationships for selected molecules, identifying chemical modifications that reversed the predicted behaviour of a given aggregator/non-aggregator compound. While lower throughput than rapid cheminformatics-based SCAM filters, MD-based prediction of aggregation has potential to be deployed on the scale of focused subsets of moderate size, and, depending on the target application, provide guidance on removing or optimizing a compound's aggregation propensity.

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.

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.

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.

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.