Automated Optimization of Potential Parameters

Drude2019IDPC polarizable force field reveals structure-function relationship of insulin

Intrinsically disordered proteins (IDPs) lack stable tertiary structures under physiological conditions, yet play key roles in biological processes and associated with human complex diseases. Their conformational characteristics and high content of charged residues make the use of polarizable force fields an advantageous for simulating IDPs. The Drude2019IDP polarizable force field, previously introduced, has demonstrated comprehensive enhancements and improvements in dipeptides, short peptides, and IDPs, achieving a balanced sampling between IDPs and structured proteins. However, the performance in simulating 5 dipeptides was found to be underestimate. Therefore, we individually performed reweighting and grid-based energy correction map (CMAP) optimization for these 5 dipeptides, resulting in the enhanced Drude2019IDPC force field. The performance of Drude2019IDPC was evaluated with 5 dipeptides, 5 disordered short peptides, and a representative IDP. The results demonstrated a marked improvement comparing with original Drude2019IDP. To further substantiate the capabilities of Drude2019IDPC, MD simulation and Markov state model (MSM) were applied to wild type and mutant for insulin, to elucidate the difference of conformational characteristics and transition path. The findings reveal that mutation can maintain the monomorphic characteristics, providing insights for engineered insulin development. These results indicate that Drude2019IDPC could be used to reveal the structure-function relationship for other proteins.

Influence of the Lennard-Jones Combination Rules on the Simulated Properties of Organic Liquids at Optimal Force-Field Parametrization

We recently introduced the CombiFF scheme [Oliveira et al., J. Chem. Theory Comput. 2020, 16, 7525], an approach for the automated refinement of force-field parameters against experimental condensed-phase data for large compound families. Using this scheme, once the time-consuming task of target-data selection and curation has been performed, the force-field optimization itself is both straightforward and fast. As a result, CombiFF provides an ideal framework for evaluating the influence of functional-form decisions on the accuracy of a force field at an optimal level of parametrization. We already used this approach to assess the effect of using an all-atom representation compared to united-atom representations in the force field [Oliveira et al., J. Chem. Theory Comput. 2022, 18, 6757]. Here, CombiFF is applied to assess the effect of three Lennard-Jones combination rules, geometric-mean (GM), Lorentz-Berthelot (LB), or Waldman-Hagler (WH), on the simulated properties of organic liquids. The comparison is performed in terms of the experimental liquid density ρ_liq, vaporization enthalpy ΔH_vap, surface-tension coefficient γ, static relative dielectric permittivity ϵ, and self-diffusion coefficient D. The calibrations of the three force-field variants are carried out independently against 2044 experimental values for ρ_liq, and ΔH_vap concerning 1516 compounds. The resulting root-mean-square deviations from experiment are 30.0, 26.9, and 36.7 kg m^-3 for ρ_liq and 2.8, 2.8, and 2.9 kJ mol^-1 for ΔH_vap, when applying the GM, LB, and WH combination rules, respectively. In terms of these (and the other) properties, the three combination rules perform comparatively well, with the GM and LB results being more similar to each other and slightly more accurate compared to experiment. In contrast, the use of distinct combination rules for the parameter calibration and property calculation leads to much larger errors.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Comparison of the United- and All-Atom Representations of (Halo)alkanes Based on Two Condensed-Phase Force Fields Optimized against the Same Experimental Data Set

The level of accuracy that can be achieved by a force field is influenced by choices made in the interaction-function representation and in the relevant simulation parameters. These choices, referred to here as functional-form variants (FFVs), include for example the model resolution, the charge-derivation procedure, the van der Waals combination rules, the cutoff distance, and the treatment of the long-range interactions. Ideally, assessing the effect of a given FFV on the intrinsic accuracy of the force-field representation requires that only the specific FFV is changed and that this change is performed at an optimal level of parametrization, a requirement that may prove extremely challenging to achieve in practice. Here, we present a first attempt at such a comparison for one specific FFV, namely the choice of a united-atom (UA) versus an all-atom (AA) resolution in a force field for saturated acyclic (halo)alkanes. Two force-field versions (UA vs AA) are optimized in an automated way using the CombiFF approach against 961 experimental values for the pure-liquid densities ρ_liq and vaporization enthalpies ΔH_vap of 591 compounds. For the AA force field, the torsional and third-neighbor Lennard-Jones parameters are also refined based on quantum-mechanical rotational-energy profiles. The comparison between the UA and AA resolutions is also extended to properties that have not been included as parameterization targets, namely the surface-tension coefficient γ, the isothermal compressibility κ_T, the isobaric thermal-expansion coefficient α_P, the isobaric heat capacity c_P, the static relative dielectric permittivity ϵ, the self-diffusion coefficient D, the shear viscosity η, the hydration free energy ΔG_wat, and the free energy of solvation ΔG_che in cyclohexane. For the target properties ρ_liq and ΔH_vap, the UA and AA resolutions reach very similar levels of accuracy after optimization. For the nine other properties, the AA representation leads to more accurate results in terms of η; comparably accurate results in terms of γ, κ_T, α_P, ϵ, D, and ΔG_che; and less accurate results in terms of c_P and ΔG_wat. This work also represents a first step toward the calibration of a GROMOS-compatible force field at the AA resolution.

Polarizable Force Field of Intrinsically Disordered Proteins with CMAP and Reweighting Optimization

Intrinsically disordered proteins (IDPs) are highly structurally heterogeneous without a specific tertiary structure under physiology conditions and play key roles in the development of human diseases. Due to the characteristics of diverse conformations, as one of the important methods, molecular dynamics simulation can complement information for experimental methods. Because of the enrichment for charged amino acids for IDPs, polarizable force fields should be a good choice for the simulation of IDPs. However, current polarizable force fields are limited in sampling conformer features of IDPs. Therefore, a polarizable force field was released and named Drude2019IDP based on Drude2019 with reweighting and grid-based potential energy correction map optimization. In order to evaluate the performance of Drude2019IDP, 16 dipeptides, 18 short peptides, 3 representative IDPs, and 5 structural proteins were simulated. The results show that the NMR observables driven by Drude2019IDP are in better agreement with the experiment data than those by Drude2019 on short peptides and IDPs. Drude2019IDP can sample more diverse conformations than Drude2019. Furthermore, the performances of the two force fields are similar to the sample ordered proteins. These results confirm that the developed Drude2019IDP can improve the reproduction of conformers for intrinsically disordered proteins and can be used to gain insight into the paradigm of sequence-disorder for IDPs.

RNA-Specific Force Field Optimization with CMAP and Reweighting

RNA plays a key role in a variety of cell activities. However, it is difficult to capture its structure dynamics by the traditional experimental methods because of the inherent limitations. Molecular dynamics simulation has become a valuable complement to the experimental methods. Previous studies have indicated that the current force fields cannot accurately reproduce the conformations and structural dynamics of RNA. Therefore, an RNA-specific force field was developed to improve the conformation sampling of RNA. The distribution of ζ/α dihedrals of tetranucleotides was optimized by a reweighting method, and the grid-based energy correction map (CMAP) term was first introduced into the Amber RNA force field of ff99bsc0χOL3, named ff99OL3_CMAP1. Extensive validations of tetranucleotides and tetraloops show that ff99OL3_CMAP1 can significantly decrease the population of an incorrect structure, increase the consistency between the simulation results and experimental values for tetranucleotides, and improve the stability of tetraloops. ff99OL3_CMAP1 can also precisely reproduce the conformation of a duplex and riboswitches. These findings confirm that the newly developed force field ff99OL3_CMAP1 can improve the conformer sampling of RNA.

Learning neural network potentials from experimental data via Differentiable Trajectory Reweighting

In molecular dynamics (MD), neural network (NN) potentials trained bottom-up on quantum mechanical data have seen tremendous success recently. Top-down approaches that learn NN potentials directly from experimental data have received less attention, typically facing numerical and computational challenges when backpropagating through MD simulations. We present the Differentiable Trajectory Reweighting (DiffTRe) method, which bypasses differentiation through the MD simulation for time-independent observables. Leveraging thermodynamic perturbation theory, we avoid exploding gradients and achieve around 2 orders of magnitude speed-up in gradient computation for top-down learning. We show effectiveness of DiffTRe in learning NN potentials for an atomistic model of diamond and a coarse-grained model of water based on diverse experimental observables including thermodynamic, structural and mechanical properties. Importantly, DiffTRe also generalizes bottom-up structural coarse-graining methods such as iterative Boltzmann inversion to arbitrary potentials. The presented method constitutes an important milestone towards enriching NN potentials with experimental data, particularly when accurate bottom-up data is unavailable.

A Framework for Stochastic Optimization of Parameters for Integrative Modeling of Macromolecular Assemblies

Integrative modeling of macromolecular assemblies requires stochastic sampling, for example, via MCMC (Markov Chain Monte Carlo), since exhaustively enumerating all structural degrees of freedom is infeasible. MCMC-based methods usually require tuning several parameters, such as the move sizes for coarse-grained beads and rigid bodies, for sampling to be efficient and accurate. Currently, these parameters are tuned manually. To automate this process, we developed a general heuristic for derivative-free, global, stochastic, parallel, multiobjective optimization, termed StOP (Stochastic Optimization of Parameters) and applied it to optimize sampling-related parameters for the Integrative Modeling Platform (IMP). Given an integrative modeling setup, list of parameters to optimize, their domains, metrics that they influence, and the target ranges of these metrics, StOP produces the optimal values of these parameters. StOP is adaptable to the available computing capacity and converges quickly, allowing for the simultaneous optimization of a large number of parameters. However, it is not efficient at high dimensions and not guaranteed to find optima in complex landscapes. We demonstrate its performance on several examples of random functions, as well as on two integrative modeling examples, showing that StOP enhances the efficiency of sampling the posterior distribution, resulting in more good-scoring models and better sampling precision.

Systematic optimization of a fragment-based force field against experimental pure-liquid properties considering large compound families: application to oxygen and nitrogen compounds

The CombiFF approach is a workflow for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. One peculiarity of this approach is that it relies on an electronegativity-equalization scheme to account for induction effects within molecules, with values of the atomic hardness and electronegativity as electrostatic parameters, rather than the partial charges themselves. In a previous article [M. P. Oliveira, M. Andrey, S. R. Rieder, L. Kern, D. F. Hahn, S. Riniker, B. A. C. Horta and P. H. Hünenberger, J. Chem. Theory. Comput. 2020, 16, 7525], CombiFF was introduced and applied to calibrate a GROMOS-compatible united-atom force field for the saturated acyclic (halo-)alkane family. Here, this scheme is employed for the construction of a corresponding force field for saturated acyclic compounds encompassing eight common chemical functional groups involving oxygen and/or nitrogen atoms, namely: ether, aldehyde, ketone, ester, alcohol, carboxylic acid, amine, and amide. Monofunctional as well as homo-polyfunctional compounds are considered. A total of 1712 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 1175 molecules are used for the calibration (339 molecules) and validation (836 molecules) of the 102 non-bonded interaction parameters of the force field. Using initial parameter values based on the GROMOS 2016H66 parameter set, convergence is reached after five iterations. Given access to one processor per simulated system, this operation only requires a few days of wall-clock computing time. After optimization, the root-mean-square deviations from experiment are 29.9 (22.4) kg m-3 for ρliq and 4.1 (5.5) kJ mol-1 for ΔHvap for the calibration (validation) set. Thus, a very good level of agreement with experiment is achieved in terms of these two properties, although the errors are inhomogeneously distributed across the different chemical functional groups.

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

A Data-Driven Hydrophobicity Scale for Predicting Liquid-Liquid Phase Separation of Proteins

An accurate model for macroscale disordered assemblies of biological macromolecules such as those formed in so-called membraneless organelles would greatly assist in studying their structure, function, and dynamics. Recent evidence has suggested that liquid-liquid phase separation (LLPS) underlies the formation of membraneless organelles. While the general mechanism of exchange of macromolecule/water for macromolecule/macromolecule interactions is known to be the driving force for LLPS, the specific interactions involved are not well understood. One way that protein-water and protein-protein interactions have been understood historically is via hydrophobicity scales. However, these scales are typically optimized for describing these relative interactions in certain cases, such as protein folding or insertion of proteins into membranes. To better describe the relative interactions of proteins that undergo LLPS, we have developed a new, data-driven hydrophobicity scale. To determine the new scale, we used coarse-grained molecular dynamics simulations using the hydrophobicity scale coarse-grained model, which relates the interactions between amino acids to their hydrophobicity. Hydrophobicity values were determined via the force-balance method on a library of proteins that includes unfolded, intrinsically disordered, and phase-separating proteins (PSP). The resulting hydrophobicity scale can better predict whether a given protein will undergo LLPS at physiological conditions by using coarse-grained molecular dynamics simulations than existing hydrophobicity scales. This new scale confirms the importance of π-π interactions between amino acids as important drivers of LLPS. This new hydrophobicity scale provides a convenient and compact description of protein-protein interactions for proteins that undergo LLPS and could be used to develop new models to describe interactions between PSP and other components, such as nucleic acids.

Three-site and five-site fixed-charge water models compatible with AMOEBA force field

In a typical biomolecular simulation using Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field, the vast majority molecules in the simulation box consist of water, and these water molecules consume the most CPU power due to the explicit mutual induction effect. To improve the computational efficiency, we here develop two new nonpolarizable water models (with flexible bonds and fixed charges) that are compatible with AMOEBA solute: the 3-site AW3C and 5-site AW5C. To derive the force-field parameters for AW3C and AW5C, we fit to six experimental liquid thermodynamic properties: liquid density, enthalpy of vaporization, dielectric constant, isobaric heat capacity, isothermal compressibility and thermal expansion coefficient, at a broad range of temperatures from 261.15 to 353.15 K under 1.0 atm pressure. We further validate our AW3C and AW5C water models by showing that they can well reproduce the radial distribution function g(r), self-diffusion constant D, and hydration free energy from the AMOEBA03 water model and the experimental observations. Furthermore, we show that our AW3C and AW5C water models can greatly accelerate (>5 times) the bulk water as well as biomolecular simulations when compared to AMOEBA water. Specifically, we demonstrate that the applications of AW3C and AW5C water models to simulate a DNA duplex lead to a threefold acceleration, and in the meanwhile well maintain the structural properties as the fully polarizable AMOEBA water. We expect that our AW3C and AW5C water models hold great promise to be widely applied to simulate complex bio-molecules using the AMOEBA force field.

A Polarization-Consistent Model for Alcohols to Predict Solvation Free Energies

Classical nonpolarizable models, normally based on a combination of Lennard-Jones sites and point charges, are extensively used to model thermodynamic properties of fluids, including solvation. An important shortcoming of these models is that they do not explicitly account for polarization effects, i.e., a description of how the electron density responds to changes in the molecular environment. Instead, polarization is implicitly included, in a mean-field sense, into the parameters of the model, usually by fitting to pure liquid properties (e.g., density). This causes problems when trying to describe thermodynamic properties that involve a change of phase (e.g., enthalpy of vaporization), that directly depend on the electronic response of the medium (e.g., dielectric constant), and that require mixing or solvation in different media (e.g., solvation free energies). Fully polarizable models present a natural route for addressing these limitations but at the price of a much higher computational cost. In this work, we combine the best of those two approaches by running fast simulations using nonpolarizable models and applying post facto corrections to the computed properties in order to account for the effects of polarization. By applying this new paradigm, a new united-atom force field for alcohols is developed that is able to predict both pure liquid properties, including dielectric constant, and solvation free energies in different solvents with a high degree of accuracy. This paves the way for the development of a generic classical nonpolarizable force field that can predict solvation of drug-like molecules in a variety of solvents.

Atomistic Force Fields for Proteins

All-atom, classical force fields for protein molecular dynamics (MD) simulations currently occupy a sweet spot in the universe of computational models, sufficiently detailed to be of predictive value in many cases, yet also simple enough that some biologically relevant time scales (microseconds or more) can now be sampled via specialized hardware or enhanced sampling methods. However, due to their long evolutionary history, there is now a myriad of force field branches in current use, which can make it hard for those entering the simulation field to know which would be the best set of parameters for a given application. In this chapter, I try to give an overview of the historical motivation for the different force fields available, suggestions for how to determine the most appropriate model and what to do if the results are in conflict with experimental evidence.

Bind3P: Optimization of a Water Model Based on Host-Guest Binding Data

We report a water model, Bind3P (Version 0.1), which was obtained by using sensitivity analysis to readjust the Lennard-Jones parameters of the TIP3P model against experimental binding free energies for six host-guest systems, along with pure liquid properties. Tests of Bind3P against >100 experimental binding free energies and enthalpies for host-guest systems distinct from the training set show a consistent drop in the mean signed error, relative to matched calculations with TIP3P. Importantly, Bind3P also yields some improvement in the hydration free energies of small organic molecules and preserves the accuracy of bulk water properties, such as density and the heat of vaporization. The same approach can be applied to more sophisticated water models that can better represent pure water properties. These results lend further support to the concept of integrating host-guest binding data into force field parametrization.

Exploring what prompts ITIC to become a superior acceptor in organic solar cell by combining molecular dynamics simulation with quantum chemistry calculation

A comparison on charge transfer process in OSC between non-fullerene electron acceptor ITIC and PC71BM was taken by microscopic analysis based on the molecular dynamics and quantum chemistry method.

CHARMM36m: an improved force field for folded and intrinsically disordered proteins

The all-atom additive CHARMM36 protein force field is widely used in molecular modeling and simulations. We present its refinement, CHARMM36m (http://mackerell.umaryland.edu/charmm_ff.shtml), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.

Toward Improved Force-Field Accuracy through Sensitivity Analysis of Host-Guest Binding Thermodynamics

Improving the capability of atomistic computer models to predict the thermodynamics of noncovalent binding is critical for successful structure-based drug design, and the accuracy of such calculations remains limited by nonoptimal force field parameters. Ideally, one would incorporate protein-ligand affinity data into force field parametrization, but this would be inefficient and costly. We now demonstrate that sensitivity analysis can be used to efficiently tune Lennard-Jones parameters of aqueous host-guest systems for increasingly accurate calculations of binding enthalpy. These results highlight the promise of a comprehensive use of calorimetric host-guest binding data, along with existing validation data sets, to improve force field parameters for the simulation of noncovalent binding, with the ultimate goal of making protein-ligand modeling more accurate and hence speeding drug discovery.

United polarizable multipole water model for molecular mechanics simulation

We report the development of a united AMOEBA (uAMOEBA) polarizable water model, which is computationally 3-5 times more efficient than the three-site AMOEBA03 model in molecular dynamics simulations while providing comparable accuracy for gas-phase and liquid properties. In this coarse-grained polarizable water model, both electrostatic (permanent and induced) and van der Waals representations have been reduced to a single site located at the oxygen atom. The permanent charge distribution is described via the molecular dipole and quadrupole moments and the many-body polarization via an isotropic molecular polarizability, all located at the oxygen center. Similarly, a single van der Waals interaction site is used for each water molecule. Hydrogen atoms are retained only for the purpose of defining local frames for the molecular multipole moments and intramolecular vibrational modes. The parameters have been derived based on a combination of ab initio quantum mechanical and experimental data set containing gas-phase cluster structures and energies, and liquid thermodynamic properties. For validation, additional properties including dimer interaction energy, liquid structures, self-diffusion coefficient, and shear viscosity have been evaluated. The results demonstrate good transferability from the gas to the liquid phase over a wide range of temperatures, and from nonpolar to polar environments, due to the presence of molecular polarizability. The water coordination, hydrogen-bonding structure, and dynamic properties given by uAMOEBA are similar to those derived from the all-atom AMOEBA03 model and experiments. Thus, the current model is an accurate and efficient alternative for modeling water.

Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model

A set of improved parameters for the AMOEBA polarizable atomic multipole water model is developed. An automated procedure, ForceBalance, is used to adjust model parameters to enforce agreement with ab initio-derived results for water clusters and experimental data for a variety of liquid phase properties across a broad temperature range. The values reported here for the new AMOEBA14 water model represent a substantial improvement over the previous AMOEBA03 model. The AMOEBA14 model accurately predicts the temperature of maximum density and qualitatively matches the experimental density curve across temperatures from 249 to 373 K. Excellent agreement is observed for the AMOEBA14 model in comparison to experimental properties as a function of temperature, including the second virial coefficient, enthalpy of vaporization, isothermal compressibility, thermal expansion coefficient, and dielectric constant. The viscosity, self-diffusion constant, and surface tension are also well reproduced. In comparison to high-level ab initio results for clusters of 2-20 water molecules, the AMOEBA14 model yields results similar to AMOEBA03 and the direct polarization iAMOEBA models. With advances in computing power, calibration data, and optimization techniques, we recommend the use of the AMOEBA14 water model for future studies employing a polarizable water model.

Integrating molecular dynamics simulations with chemical probing experiments using SHAPE-FIT

Integration and calibration of molecular dynamics simulations with experimental data remain a challenging endeavor. We have developed a novel method to integrate chemical probing experiments with molecular simulations of RNA molecules by using a native structure-based model. Selective 2'-hydroxyl acylation by primer extension (SHAPE) characterizes the mobility of each residue in the RNA. Our method, SHAPE-FIT, automatically optimizes the potential parameters of the force field according to measured reactivities from SHAPE. The optimized parameter set allows simulations of dynamics highly consistent with SHAPE probing experiments. Such atomistic simulations, thoroughly grounded in experiment, can open a new window on RNA structure-function relations.

Balanced Protein-Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association

Some frequently encountered deficiencies in all-atom molecular simulations, such as nonspecific protein-protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. To address these issues, we make the simplest possible change, by modifying the short-range protein-water pair interactions, and leaving all the water-water and protein-protein parameters unchanged. We find that a modest strengthening of protein-water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as determined by direct comparison with small-angle X-ray scattering (SAXS) and Förster resonance energy transfer (FRET) data. The modification also results in more realistic protein-protein affinities, and average solvation free energies of model compounds which are more consistent with experiment. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming α-helix and β-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein-protein association, and crowded cellular environments.

Optimizing potentials for a liquid mixture: a new force field for a tert-butanol and water solution

A technology for optimization of potential parameters from condensed-phase simulations (POP) is discussed and illustrated. It is based on direct calculations of the derivatives of macroscopic observables with respect to the potential parameters. The derivatives are used in a local minimization scheme, comparing simulated and experimental data. In particular, we show that the Newton trust region protocol allows for more accurate and robust optimization. We apply the newly developed technology to study the liquid mixture of tert-butanol and water. We are able to obtain, after four iterations, the correct phase behavior and accurately predict the value of the Kirkwood Buff (KB) integrals. We further illustrate that a potential that is determined solely by KB information, or the pair correlation function, is not necessarily unique.

Building Force Fields: An Automatic, Systematic, and Reproducible Approach

The development of accurate molecular mechanics force fields is a significant challenge that must be addressed for the continued success of molecular simulation. We developed the ForceBalance method to automatically derive accurate force field parameters using flexible combinations of experimental and theoretical reference data. The method is demonstrated in the parametrization of two rigid water models, yielding new parameter sets (TIP3P-FB and TIP4P-FB) that accurately describe many physical properties of water.

Non-exponential kinetics and a complete folding pathway of an α-helical heteropeptide: direct observation and comprehensive molecular dynamics

We have performed a combined experimental and computational study of the folding of a 21-residue α-helix-forming heteropeptide (WH21). Temperature jump kinetics with improved dynamic range at several temperatures revealed non-exponential relaxation that could be well described with two time constants of 20 and 300 ns at 298 K. In the computational part, we performed multi-microsecond molecular dynamics simulations of WH21 in explicit water, using the AMBER03 and OPLS/AA potentials. The simulations were in good agreement with available experimental data on helix content and relaxation times. On the basis of 70 individual transitions, we identified the main pathways of helix unfolding. Three paths were found in both force fields, with unfolding progressing through (1) N-terminus, C-terminus, and center; (2) C-terminus, N-terminus, and center; and (3) C-terminus, center, and N-terminus. An additional fourth path starting in the central region and expanding to the termini was detected only with AMBER03. Intermediate structures sampled along the pathway included a central helix with frayed termini, an off-center helix, and a helical hairpin. The simulations suggest that the short relaxation should be assigned to partly cooperative fluctuations of several neighboring hydrogen bonds. Overall, by a combination of ultrafast kinetic measurements and detailed microscopic description through comprehensive molecular dynamics, we have obtained important new insights into the helix folding process.

One Size Does Not Fit All: The Limits of Structure-Based Models in Drug Discovery

A major goal in computational chemistry has been to discover the set of rules that can accurately predict the binding affinity of any protein-drug complex, using only a single snapshot of its three-dimensional structure. Despite the continual development of structure-based models, predictive accuracy remains low, and the fundamental factors that inhibit the inference of all-encompassing rules have yet to be fully explored. Using statistical learning theory and information theory, here we prove that even the very best generalized structure-based model is inherently limited in its accuracy, and protein-specific models are always likely to be better. Our results refute the prevailing assumption that large data sets and advanced machine learning techniques will yield accurate, universally applicable models. We anticipate that the results will aid the development of more robust virtual screening strategies and scoring function error estimations.