Collaborative Assessment of Molecular Geometries and Energies from the Open Force Field.

Force fields form the basis for classical molecular simulations, and their accuracy is crucial for the quality of, for instance, protein-ligand binding simulations in drug discovery. The huge diversity of small-molecule chemistry makes it a challenge to build and parameterize a suitable force field. The Open Force Field Initiative is a combined industry and academic consortium developing a state-of-the-art small-molecule force field. In this report, industry members of the consortium worked together to objectively evaluate the performance of the force fields (referred to here as OpenFF) produced by the initiative on a combined public and proprietary dataset of 19,653 relevant molecules selected from their internal research and compound collections. This evaluation was important because it was completely blind; at most partners, none of the molecules or data were used in force field development or testing prior to this work. We compare the Open Force Field "Sage" version 2.0.0 and "Parsley" version 1.3.0 with GAFF-2.11-AM1BCC, OPLS4, and SMIRNOFF99Frosst. We analyzed force-field-optimized geometries and conformer energies compared to reference quantum mechanical data. We show that OPLS4 performs best, and the latest Open Force Field release shows a clear improvement compared to its predecessors. The performance of established force fields such as GAFF-2.11 was generally worse. While OpenFF researchers were involved in building the benchmarking infrastructure used in this work, benchmarking was done entirely in-house within industrial organizations and the resulting assessment is reported here. This work assesses the force field performance using separate benchmarking steps, external datasets, and involving external research groups. This effort may also be unique in terms of the number of different industrial partners involved, with 10 different companies participating in the benchmark efforts.

A QM/MM Derived Polarizable Water Model for Molecular Simulation.

In this work, we propose an improved QM/MM-based strategy to determine condensed-phase polarizabilities and we use this approach to optimize a new and simple polarizable four-site water model for classical molecular simulation. For the determination of the model value for the polarizability from QM/MM, we show that our proposed consensus-fitting strategy significantly reduces the uncertainty in calculated polarizabilities in cases where the size of the local external electric field is small. By fitting electrostatic, polarization and dispersion properties of our water model based on quantum and/or combined QM/MM calculations, only a single model parameter (describing exchange repulsion) is left for empirical calibration. The resulting model performs well in describing relevant pure-liquid thermodynamic and transport properties, which illustrates the merit of our approach to minimize the number of free variables in our model.

Topological "Shape" in Micellar Dynamics.

For micelles, "shape" is prominent in rheological computations of fluid flow, but this "shape" is often expressed too informally to be useful for rigorous analyses. We formalize topological "shape equivalence" of micelles, both globally and locally, to enable visualization of computational fluid dynamics. Although topological methods in visualization provide significant insights into fluid flows, this opportunity has been limited by the known difficulties in creating representative geometry. We present an agile geometric algorithm to represent the micellar shape for input into fluid flow visualizations. We show that worm-like and cylindrical micelles have formally equivalent shapes, but that visualization accentuates unexplored differences. This global-local paradigm is extensible beyond micelles.

Alchemical prediction of hydration free energies for SAMPL.

Hydration free energy calculations have become important tests of force fields. Alchemical free energy calculations based on molecular dynamics simulations provide a rigorous way to calculate these free energies for a particular force field, given sufficient sampling. Here, we report results of alchemical hydration free energy calculations for the set of small molecules comprising the 2011 Statistical Assessment of Modeling of Proteins and Ligands challenge. Our calculations are largely based on the Generalized Amber Force Field with several different charge models, and we achieved RMS errors in the 1.4-2.2 kcal/mol range depending on charge model, marginally higher than what we typically observed in previous studies (Mobley et al. in J Phys Chem B 111(9):2242-2254, 2007, J Chem Theory Comput 5(2):350-358, 2009, J Phys Chem B 115:1329-1332, 2011; Nicholls et al. in J Med Chem 51:769-779, 2008; Klimovich and Mobley in J Comput Aided Mol Design 24(4):307-316, 2010). The test set consists of ethane, biphenyl, and a dibenzyl dioxin, as well as a series of chlorinated derivatives of each. We found that, for this set, using high-quality partial charges from MP2/cc-PVTZ SCRF RESP fits provided marginally improved agreement with experiment over using AM1-BCC partial charges as we have more typically done, in keeping with our recent findings (Mobley et al. in J Phys Chem B 115:1329-1332, 2011). Switching to OPLS Lennard-Jones parameters with AM1-BCC charges also improves agreement with experiment. We also find a number of chemical trends within each molecular series which we can explain, but there are also some surprises, including some that are captured by the calculations and some that are not.

Dynamical reweighting: improved estimates of dynamical properties from simulations at multiple temperatures.

Dynamical averages based on functionals of dynamical trajectories, such as time-correlation functions, play an important role in determining kinetic or transport properties of matter. At temperatures of interest, the expectations of these quantities are often dominated by contributions from rare events, making the precise calculation of these quantities by molecular dynamics simulation difficult. Here, we present a reweighting method for combining simulations from multiple temperatures (or from simulated or parallel tempering simulations) to compute an optimal estimate of the dynamical properties at the temperature of interest without the need to invoke an approximate kinetic model (such as the Arrhenius law). Continuous and differentiable estimates of these expectations at any temperature in the sampled range can also be computed, along with an assessment of the associated statistical uncertainty. For rare events, aggregating data from multiple temperatures can produce an estimate with the desired precision at greatly reduced computational cost compared with simulations conducted at a single temperature. Here, we describe use of the method for the canonical (NVT) ensemble using four common models of dynamics (canonical distribution of Hamiltonian trajectories, Andersen thermostatting, Langevin, and overdamped Langevin or Brownian dynamics), but it can be applied to any thermodynamic ensemble provided the ratio of path probabilities at different temperatures can be computed. To illustrate the method, we compute a time-correlation function for solvated terminally-blocked alanine peptide across a range of temperatures using trajectories harvested using a modified parallel tempering protocol.

Optimal use of data in parallel tempering simulations for the construction of discrete-state Markov models of biomolecular dynamics.

Parallel tempering (PT) molecular dynamics simulations have been extensively investigated as a means of efficient sampling of the configurations of biomolecular systems. Recent work has demonstrated how the short physical trajectories generated in PT simulations of biomolecules can be used to construct the Markov models describing biomolecular dynamics at each simulated temperature. While this approach describes the temperature-dependent kinetics, it does not make optimal use of all available PT data, instead estimating the rates at a given temperature using only data from that temperature. This can be problematic, as some relevant transitions or states may not be sufficiently sampled at the temperature of interest, but might be readily sampled at nearby temperatures. Further, the comparison of temperature-dependent properties can suffer from the false assumption that data collected from different temperatures are uncorrelated. We propose here a strategy in which, by a simple modification of the PT protocol, the harvested trajectories can be reweighted, permitting data from all temperatures to contribute to the estimated kinetic model. The method reduces the statistical uncertainty in the kinetic model relative to the single temperature approach and provides estimates of transition probabilities even for transitions not observed at the temperature of interest. Further, the method allows the kinetics to be estimated at temperatures other than those at which simulations were run. We illustrate this method by applying it to the generation of a Markov model of the conformational dynamics of the solvated terminally blocked alanine peptide.

Model for the Simulation of the CnEm Nonionic Surfactant Family Derived from Recent Experimental Results.

Using a comprehensive set of recently published experimental results for training and validation, we have developed computational models appropriate for simulations of aqueous solutions of poly(ethylene oxide) alkyl ethers, an important class of micelle-forming nonionic surfactants, usually denoted CnEm. These models are suitable for use in simulations that employ a moderate amount of coarse graining and especially for dissipative particle dynamics (DPD), which we adopt in this work. The experimental data used for training and validation were reported earlier and produced in our laboratory using dynamic light scattering (DLS) measurements performed on 12 members of the CnEm compound family yielding micelle size distribution functions and mass-weighted mean aggregation numbers at each of several surfactant concentrations. The range of compounds and quality of the experimental results were designed to support the development of computational models. An essential feature of this work is that all simulation results were analyzed in a way that is consistent with the experimental data. Proper account is taken of the fact that a broad distribution of micelle sizes exists, so mass-weighted averages (rather than number-weighted averages) over this distribution are required for the proper comparison of simulation and experimental results. The resulting DPD force field reproduces several important trends seen in the experimental critical micelle concentrations and mass-averaged mean aggregation numbers with respect to surfactant characteristics and concentration. We feel it can be used to investigate a number of open questions regarding micelle sizes and shapes and their dependence on surfactant concentration for this important class of nonionic surfactants.

The Role of Chemical Heterogeneity in Surfactant Adsorption at Solid-Liquid Interfaces.

Chemical heterogeneity of solid surfaces disrupts the adsorption of surfactants from the bulk liquid. While its presence can hinder the performance of some formulations, bespoke chemical patterning could potentially facilitate controlled adsorption for nanolithography applications. Although some computational studies have investigated the impact of regularly patterned surfaces on surfactant adsorption, in reality, many interesting surfaces are expected to be stochastically disordered and this is an area unexplored via simulations. In this paper, we describe a new algorithm for the generation of randomly disordered chemically heterogeneous surfaces and use it to explore the adsorption behavior of four model nonionic surfactants. Using novel analysis methods, we interrogate both the global surface coverage (adsorption isotherm) and behavior in localized regions. We observe that trends in adsorption characteristics as surfactant size, head/tail ratio, and surface topology are varied and connect these to underlying physical mechanisms. We believe that our methods and approach will prove useful to researchers seeking to tailor surface patterns to calibrate nonionic surfactant adsorption.

Efficient Algorithm for the Topological Characterization of Worm-like and Branched Micelle Structures from Simulations.

Many surfactant-based formulations are utilized in industry as they produce desirable viscoelastic properties at low concentrations. These properties are due to the presence of worm-like micelles (WLMs), and as a result, understanding the processes that lead to WLM formation is of significant interest. Various experimental techniques have been applied with some success to this problem but can encounter issues probing key microscopic characteristics or the specific regimes of interest. The complementary use of computer simulations could provide an alternate route to accessing their structural and dynamic behavior. However, few computational methods exist for measuring key characteristics of WLMs formed in particle simulations. Further, their mathematical formulations are challenged by WLMs with sharp curvature profiles or density fluctuations along the backbone. Here, we present a new topological algorithm for identifying and characterizing WLMs in particle simulations, which has desirable mathematical properties that address shortcomings in previous techniques. We apply the algorithm to the case of sodium dodecyl sulfate micelles to demonstrate how it can be used to construct a comprehensive topological characterization of the observed structures.

Challenge to Reconcile Experimental Micellar Properties of the CnEm Nonionic Surfactant Family.

We wished to compile a data set of results from the experimental literature to support the development and validation of accurate computational models (force fields) for an important class of micelle-forming nonionic surfactant compounds, the poly(ethylene oxide) alkyl ethers, usually denoted C nE m. However, careful examination of the experimental literature exposed a striking degree of variation in values reported for critical micelle concentrations (cmc) and mean aggregation numbers ( Nagg). This variation was so large that it masked important trends known to exist within this family of molecules, thereby rendering most of the literature data to be of limited utility for force field development. In this work, we describe some reasons for the wide variability in the experimental literature, and we present a set of cmc and aggregation number data for 12 C nE m compounds that we feel is appropriate to use for the construction of and validation of computational models. The cmc values we selected are from the existing experimental literature and represent a carefully chosen and consistent subset that conveys important trends seen by many of the experimental studies. However, for a corresponding and consistent set of weight-averaged aggregation numbers, we needed to perform new dynamic light scattering (DLS) experiments. The results of these experiments were carefully analyzed to obtain not just mean aggregation numbers but also the underlying micelle size distribution functions. Several trends observed in the cmc and Nagg observables are highlighted and serve as challenges for developers of force field and simulation methodology. The analysis of the DLS experiments accounts for the fact that a broad distribution of micelle sizes exists for many of these compounds and that one must be careful to use the appropriate weighted averages (e.g., mass-weighted vs number-weighted averages) in comparing results from different types of experiments and in comparing results from experiments with those from simulations.

Observation of noncooperative folding thermodynamics in simulations of 1BBL.

One of the predictions of the energy landscape theory of protein folding is the possibility of barrierless, "downhill" folding under certain conditions. The protein 1BBL has been proposed to fold by such a downhill mechanism, though this is a matter of some dispute. We carried out extensive replica exchange molecular dynamics simulations on 1BBL in explicit solvent to address this controversy and provide a microscopic picture of its folding thermodynamics. Our simulations show two distinct structural transitions in the folding of 1BBL. A low-temperature transition involves a disordering of the protein's tertiary structure without loss of secondary structure. A distinct, higher temperature transition involves the complete loss of secondary structure and dissolution of the hydrophobic core. In contrast, control simulations of the 1BBL homolog E3BD show a single high temperature unfolding transition. Further simulations of 1BBL at high ionic strength show a significant destabilization of helix II but not helix I, suggesting that the apparent folding cooperativity of 1BBL may be highly dependent on experimental conditions. Although our simulations cannot provide definitive evidence of downhill folding in 1BBL, they clearly show evidence of a complex, non-two-state folding process.

The reaction mechanism for the organocatalytic ring-opening polymerization of l-lactide using a guanidine-based catalyst: hydrogen-bonded or covalently bound?

We have investigated two alternative mechanisms for the ring-opening polymerization of l-lactide using a guanidine-based catalyst, the first involving acetyl transfer to the catalyst, and the second involving only hydrogen bonding to the catalyst. Using computational chemistry methods, we show that the hydrogen bonding pathway is considerably preferred over the acetyl transfer pathway and that this is consistent with experimental information.

Influence of Solvent on the Drug-Loading Process of Amphiphilic Nanogel Star Polymers.

We present an all-atom molecular dynamics study of the effect of a range of organic solvents (dichloromethane, diethyl ether, toluene, methanol, dimethyl sulfoxide, and tetrahydrofuran) on the conformations of a nanogel star polymeric nanoparticle with solvophobic and solvophilic structural elements. These nanoparticles are of particular interest for drug delivery applications. As drug loading generally takes place in an organic solvent, this work serves to provide insight into the factors controlling the early steps of that process. Our work suggests that nanoparticle conformational structure is highly sensitive to the choice of solvent, providing avenues for further study as well as predictions for both computational and experimental explorations of the drug-loading process. Our findings suggest that when used in the drug-loading process, dichloromethane, tetrahydrofuran, and toluene allow for a more extensive and increased drug-loading into the interior of nanogel star polymers of the composition studied here. In contrast, methanol is more likely to support shallow or surface loading and, consequently, faster drug release rates. Finally, diethyl ether should not work in a formulation process since none of the regions of the nanogel star polymer appear to be sufficiently solvated by it.

Kinetic computational alanine scanning: application to p53 oligomerization.

We have developed a novel computational alanine scanning approach that involves analysis of ensemble unfolding kinetics at high temperature to identify residues that are critical for the stability of a given protein. This approach has been applied to dimerization of the oligomerization domain (residues 326-355) of tumor suppressor p53. As validated by experimental results, our approach has reasonable success in identifying deleterious mutations, including mutations that have been linked to cancer. We discuss a method for determining the effect of mutations on the location of the dimerization transition state.

Interfacial fluctuations of block copolymers: a coarse-grain molecular dynamics simulation study.

The lamellar and cylindrical phases of block copolymers have a number of technological applications, particularly when they occur in supported thin films. One such application is block copolymer lithography, the use of these materials to subdivide or enhance submicrometer patterns defined by optical or electron beam methods. A key parameter of all lithographic methods is the line edge roughness (LER), because the electronic or optical activities of interest are sensitive to small pattern variations. While mean-field models provide a partial picture of the LER and interfacial width expected for the block interface in a diblock copolymer, these models lack chemical detail. To complement mean-field approaches, we have carried out coarse-grain molecular dynamics simulations on model poly(ethyleneoxide)-poly(ethylethylene) (PEO-PEE) lamellae, exploring the influence of chain length and hypothetical chemical modifications on the observed line edge roughness. As expected, our simulations show that increasing chi (the Flory-Huggins parameter) is the most direct route to decreased roughness, although the addition of strong specific interactions at the block interface can also produce smoother patterns.

Spatial Distribution of Hydrophobic Drugs in Model Nanogel-Core Star Polymers.

Star polymers with a cross-linked nanogel core are promising carriers of cargo for therapeutic applications due to the synthetic control of amphiphilicity of arms and stability at infinite dilution. Three nanogel-core star polymers were investigated to understand how the arm-block chemical structure controls loading efficiency of a model drug, ibuprofen, and its spatial distribution. The spatial distribution profiles of hydrophobic core, hydrophilic corona, and encapsulated drug were determined by small-angle neutron scattering (SANS). SANS provides the nanometer-scale sensitivity to determine how the arm-block chemistry enhances the sequestering of ibuprofen. Validated molecular dynamics simulations capture the trends in drug profile and polymer segment distribution with further details on drug orientation distribution. This work provides a basis to study structure-function relationships in macromolecular-based carriers of cargo and represents a path toward validated and predictive simulation.

Effect of Hydrophobic Core Topology and Composition on the Structure and Kinetics of Star Polymers: A Molecular Dynamics Study.

We present a molecular dynamics study of the effect of core chemistry on star polymer structural and kinetic properties. This work serves to validate the choice of a model adamantane core used in previous simulations to represent larger star polymeric systems in an aqueous environment, as well as to explore how the choice of size and core chemistry using a dendrimer or nanogel core may affect these polymeric nanoparticle systems, particularly with respect to thermosensitivity and solvation properties that are relevant for applications in drug loading and delivery.

Building a More Predictive Protein Force Field: A Systematic and Reproducible Route to AMBER-FB15.

The increasing availability of high-quality experimental data and first-principles calculations creates opportunities for developing more accurate empirical force fields for simulation of proteins. We developed the AMBER-FB15 protein force field by building a high-quality quantum chemical data set consisting of comprehensive potential energy scans and employing the ForceBalance software package for parameter optimization. The optimized potential surface allows for more significant thermodynamic fluctuations away from local minima. In validation studies where simulation results are compared to experimental measurements, AMBER-FB15 in combination with the updated TIP3P-FB water model predicts equilibrium properties with equivalent accuracy, and temperature dependent properties with significantly improved accuracy, in comparison with published models. We also discuss the effect of changing the protein force field and water model on the simulation results.

Simulation and Experiments To Identify Factors Allowing Synthetic Control of Structural Features of Polymeric Nanoparticles.

To develop a detailed picture of the microscopic structure of gelcore star polymers and to elucidate parameters of the synthetic process that might be exploited to control this structure, simulations of their synthesis were performed that were based on a particular synthetic approach. A range of results was observed from gelation at high reactant concentrations to the formation of various sizes and compositions of star polymers. Contrary to the prevailing experimental viewpoint, the simulations always suggest the production of a broad distribution of star polymer sizes. However, the GPC traces computed from simulation results are in good qualitative agreement with experiment. Topologically, the gelcore star polymers produced by simulation are not compact but, rather, sparse blobs loosely connected by filaments of linker when modeled in a good solvent. This is reflected in scaling relationships that relate polymer size (e.g., radius of gyration) and degree of polymerization. The arm-core composition is observed to be stoichiometric, strongly reflecting relative reactant concentrations during the synthesis. Reactions within star polymers that result in greater intramolecular cross-linking compete with those between star polymers that result in the production of larger star polymers from the joining of smaller ones. The balance in this competition can be controlled through the overall reactant concentration to limit and control resulting star polymer size. Therefore, the mean size, as well as the mean number of arms, can be controlled during synthesis by careful tuning of the overall ratio of the arm and linker reactant concentrations and the total reactant concentration.

Toward a Standard Protocol for Micelle Simulation.

In this paper, we present protocols for simulating micelles using dissipative particle dynamics (and in principle molecular dynamics) that we expect to be appropriate for computing micelle properties for a wide range of surfactant molecules. The protocols address challenges in equilibrating and sampling, specifically when kinetics can be very different with changes in surfactant concentration, and with minor changes in molecular size and structure, even using the same force field parameters. We demonstrate that detection of equilibrium can be automated and is robust, for the molecules in this study and others we have considered. In order to quantify the degree of sampling obtained during simulations, metrics to assess the degree of molecular exchange among micellar material are presented, and the use of correlation times are prescribed to assess sampling and for statistical uncertainty estimates on the relevant simulation observables. We show that the computational challenges facing the measurement of the critical micelle concentration (CMC) are somewhat different for high and low CMC materials. While a specific choice is not recommended here, we demonstrate that various methods give values that are consistent in terms of trends, even if not numerically equivalent.