Representability and Transferability of Kirkwood-Buff Iterative Boltzmann Inversion Models for Multicomponent Aqueous Systems

Reverse Mapping of Coarse Grained Polyglutamine Conformations from PRIME20 Sampling

An inverse coarse-graining protocol is presented for generating and validating atomistic structures of large (bio-) molecules from conformations obtained via a coarse-grained sampling method. Specifically, the protocol is implemented and tested based on the (coarse-grained) PRIME20 protein model (P20/SAMC), and the resulting all-atom conformations are simulated using conventional biomolecular force fields. The phase space sampling at the coarse-grained level is performed with a stochastical approximation Monte Carlo approach. The method is applied to a series of polypeptides, specifically dimers of polyglutamine with varying chain length in aqueous solution. The majority (>70 %) of the conformations obtained from the coarse-grained peptide model can successfully be mapped back to atomistic structures that remain conformationally stable during 10 ns of molecular dynamics simulations. This work can be seen as the first step towards the overarching goal of improving our understanding of protein aggregation phenomena through simulation methods.

Insight into the Density-Dependence of Pair Potentials for Predictive Coarse-Grained Models

We investigate the temperature- and density-dependence of effective pair potentials for 1-site coarse-grained (CG) models of two industrial solvents, 1,4-dioxane and tetrahydrofuran. We observe that the calculated pair potentials are much more sensitive to density than to temperature. The generalized-Yvon-Born-Green framework reveals that this striking density-dependence reflects corresponding variations in the many-body correlations that determine the environment-mediated indirect contribution to the pair mean force. Moreover, we demonstrate, perhaps surprisingly, that this density-dependence is not important for accurately modeling the intermolecular structure. Accordingly, we adopt a density-independent interaction potential and transfer the density-dependence of the calculated pair potentials into a configuration-independent volume potential. Furthermore, we develop a single global potential that accurately models the intermolecular structure and pressure-volume equation of state across a very wide range of liquid state points. Consequently, this work provides fundamental insight into the density-dependence of effective pair potentials and also provides a significant step toward developing predictive CG models for efficiently modeling industrial solvents.

Stability, Speed, and Constraints for Structural Coarse-Graining in VOTCA

Structural coarse-graining involves the inverse problem of deriving pair potentials that reproduce target radial distribution functions. Despite its clear mathematical formulation, there are open questions about the existing methods concerning speed, stability, and physical representability of the resulting potentials. In this work, we make progress on several aspects of iterative methods used to solve the inverse problem. Based on integral equation theory, we derive fast Gauss-Newton schemes applicable to very general systems, including molecules with bonds and mixtures. Our methods are similar to inverse Monte Carlo in terms of convergence speed and have a similar cost per iteration as iterative Boltzmann inversion. We investigate stability problems in our schemes and in the inverse Monte Carlo method and propose modifications to fix them. Furthermore, we establish how the pair potential can be constrained at each iteration to reproduce the pressure, Kirkwood-Buff integral, or the enthalpy of vaporization. We demonstrate the potential of our approach in deriving coarse-grained force fields for nine different solvents and their mixtures. All methods described are implemented in the free and open VOTCA software framework for systematic coarse-graining.

Cosolvent Exclusion Drives Protein Stability in Trimethylamine N-Oxide and Betaine Solutions

Using a combination of molecular dynamics simulation, dialysis experiments, and electronic circular dichroism measurements, we studied the solvation thermodynamics of proteins in two osmolyte solutions, trimethylamine N-oxide (TMAO) and betaine. We showed that existing force fields are unable to capture the solvation properties of the proteins lysozyme and ribonuclease T1 and that the inaccurate parametrization of protein-osmolyte interactions in these force fields promoted an unphysical strong thermal denaturation of the trpcage protein. We developed a novel force field for betaine (the KBB force field) which reproduces the experimental solution Kirkwood-Buff integrals and density. We further introduced appropriate scaling to protein-osmolyte interactions in both the betaine and TMAO force fields which led to successful reproduction of experimental protein-osmolyte preferential binding coefficients for lysozyme and ribonuclease T1 and prevention of the unphysical denaturation of trpcage in osmolyte solutions. Correct parametrization of protein-TMAO interactions also led to the stabilization of the collapsed conformations of a disordered elastin-like peptide, while the uncorrected parameters destabilized the collapsed structures. Our results establish that the thermodynamic stability of proteins in both betaine and TMAO solutions is governed by osmolyte exclusion from proteins.

Automatic multi-objective optimization of coarse-grained lipid force fields using SwarmCG

The development of coarse-grained (CG) molecular models typically requires a time-consuming iterative tuning of parameters in order to have the approximated CG models behave correctly and consistently with, e.g., available higher-resolution simulation data and/or experimental observables. Automatic data-driven approaches are increasingly used to develop accurate models for molecular dynamics simulations. However, the parameters obtained via such automatic methods often make use of specifically designed interaction potentials and are typically poorly transferable to molecular systems or conditions other than those used for training them. Using a multi-objective approach in combination with an automatic optimization engine (SwarmCG), here, we show that it is possible to optimize CG models that are also transferable, obtaining optimized CG force fields (FFs). As a proof of concept, here, we use lipids for which we can avail reference experimental data (area per lipid and bilayer thickness) and reliable atomistic simulations to guide the optimization. Once the resolution of the CG models (mapping) is set as an input, SwarmCG optimizes the parameters of the CG lipid models iteratively and simultaneously against higher-resolution simulations (bottom-up) and experimental data (top-down references). Including different types of lipid bilayers in the training set in a parallel optimization guarantees the transferability of the optimized lipid FF parameters. We demonstrate that SwarmCG can reach satisfactory agreement with experimental data for different resolution CG FFs. We also obtain stimulating insights into the precision-resolution balance of the FFs. The approach is general and can be effectively used to develop new FFs and to improve the existing ones.

A microcanonical approach to temperature-transferable coarse-grained models using the relative entropy

Bottom-up coarse-graining methods provide systematic tools for creating simplified models of molecular systems. However, coarse-grained (CG) models produced with such methods frequently fail to accurately reproduce all thermodynamic properties of the reference atomistic systems they seek to model and, moreover, can fail in even more significant ways when used at thermodynamic state points different from the reference conditions. These related problems of representability and transferability limit the usefulness of CG models, especially those of strongly state-dependent systems. In this work, we present a new strategy for creating temperature-transferable CG models using a single reference system and temperature. The approach is based on two complementary concepts. First, we switch to a microcanonical basis for formulating CG models, focusing on effective entropy functions rather than energy functions. This allows CG models to naturally represent information about underlying atomistic energy fluctuations, which would otherwise be lost. Such information not only reproduces energy distributions of the reference model but also successfully predicts the correct temperature dependence of the CG interactions, enabling temperature transferability. Second, we show that relative entropy minimization provides a direct and systematic approach to parameterize such classes of temperature-transferable CG models. We calibrate the approach initially using idealized model systems and then demonstrate its ability to create temperature-transferable CG models for several complex molecular liquids.

Cross-correlation corrected friction in (generalized) Langevin models

We propose a route for parameterizing isotropic (generalized) Langevin [(G)LE] thermostats with the aim to correct the dynamics of coarse-grained (CG) models with pairwise conservative interactions. The approach is based on the Mori-Zwanzig formalism and derives the memory kernels from Q-projected time correlation functions. Bottom-up informed (GLE and LE) thermostats for a CG star-polymer melt are investigated, and it is demonstrated that the inclusion of memory in the CG simulation leads to predictions of polymer diffusion in quantitative agreement with fine-grained simulations. Interestingly, memory effects are observed in the diffusive regime. We demonstrate that previously neglected cross-correlations between the "irrelevant" and the CG degree of freedom are important and lie at the origin of shortcomings in previous CG simulations.

Coarse-grained model of a nanoscale-segregated ionic liquid for simulations of low-temperature structure and dynamics

We perform molecular dynamics simulations to study the structure and dynamics of the ionic liquid [Omim][TFSI] in a broad temperature range. A particular focus is the progressing nanoscale segregation into polar and nonpolar regions upon cooling. As this analysis requires simulations of large systems for long times, we use the iterative Boltzmann inversion method to develop a new coarse-grained (CG) model from a successful all-atom (AA) model. We show that the properties are similar for both levels of description at room temperature, while the CG model shows stronger nanoscale segregation and faster diffusion dynamics than its AA counterpart at low temperatures. Exploiting these features of the CG model, we find that the characteristic length scale of the structural inhomogeneity nearly doubles to ∼3 nm when the temperature is decreased to about 200 K. Moreover, we observe that the nanoscale segregation is characterized by a bicontinuous morphology. In worm-like nonpolar regions, the ends of the octyl rests of the cations preferentially aggregate in the centers, while the other parts of the alkyl chains tend to be aligned parallel on a next-neighbor level and point outward, allowing for an integration of the imidazolium head groups of the cations into polar regions together with the anions, resembling to some degree the molecular arrangement in cylindrical micelles.

Swarm-CG: Automatic Parametrization of Bonded Terms in MARTINI-Based Coarse-Grained Models of Simple to Complex Molecules via Fuzzy Self-Tuning Particle Swarm Optimization

We present Swarm-CG, a versatile software for the automatic iterative parametrization of bonded parameters in coarse-grained (CG) models, ideal in combination with popular CG force fields such as MARTINI. By coupling fuzzy self-tuning particle swarm optimization to Boltzmann inversion, Swarm-CG performs accurate bottom-up parametrization of bonded terms in CG models composed of up to 200 pseudo atoms within 4-24 h on standard desktop machines, using default settings. The software benefits from a user-friendly interface and two different usage modes (default and advanced). We particularly expect Swarm-CG to support and facilitate the development of new CG models for the study of complex molecular systems interesting for bio- and nanotechnology. Excellent performances are demonstrated using a benchmark of 9 molecules of diverse nature, structural complexity, and size. Swarm-CG is available with all its dependencies via the Python Package Index (PIP package: swarm-cg). Demonstration data are available at: www.github.com/GMPavanLab/SwarmCG.

Experimentally determined strengths of favorable and unfavorable interactions of amide atoms involved in protein self-assembly in water

Folding and other protein self-assembly processes are driven by favorable interactions between O, N, and C unified atoms of the polypeptide backbone and side chains. These processes are perturbed by solutes that interact with these atoms differently than water does. Amide NH···O=C hydrogen bonding and various π-system interactions have been better characterized structurally or by simulations than experimentally in water, and unfavorable interactions are relatively uncharacterized. To address this situation, we previously quantified interactions of alkyl ureas with amide and aromatic compounds, relative to interactions with water. Analysis yielded strengths of interaction of each alkylurea with unit areas of different hybridization states of unified O, N, and C atoms of amide and aromatic compounds. Here, by osmometry, we quantify interactions of 10 pairs of amides selected to complete this dataset. An analysis yields intrinsic strengths of six favorable and four unfavorable atom-atom interactions, expressed per unit area of each atom and relative to interactions with water. The most favorable interactions are sp2O-sp2C (lone pair-π, presumably n-π*), sp2C-sp2C (π-π and/or hydrophobic), sp2O-sp2N (hydrogen bonding) and sp3C-sp2C (CH-π and/or hydrophobic). Interactions of sp3C with itself (hydrophobic) and with sp2N are modestly favorable, while sp2N interactions with sp2N and with amide/aromatic sp2C are modestly unfavorable. Amide sp2O-sp2O interactions and sp2O-sp3C interactions are more unfavorable, indicating the preference of amide sp2O to interact with water. These intrinsic interaction strengths are used to predict interactions of amides with proteins and chemical effects of amides (including urea, N-ethylpyrrolidone [NEP], and polyvinylpyrrolidone [PVP]) on protein stability.

Evidence of information limitations in coarse-grained models

Developing accurate coarse-grained (CG) models is critical for addressing long time and length scale phenomena with molecular simulations. Here, we distinguish and quantify two sources of error that are relevant to CG models in order to guide further methods development: "representability" errors, which result from the finite basis associated with the chosen functional form of the CG model and mapping operator, and "information" errors, which result from the limited kind and quantity of data supplied to the CG parameterization algorithm. We have performed a systematic investigation of these errors by generating all possible CG models of three liquids (butane, 1-butanol, and 1,3-propanediol) that conserve a set of chemically motivated locality and topology relationships. In turn, standard algorithms (iterative Boltzmann inversion, IBI, and multiscale coarse-graining, MSCG) were used to parameterize the models and the CG predictions were compared with atomistic results. For off-target properties, we observe a strong correlation between the accuracy and the resolution of the CG model, which suggests that the approximations represented by MSCG and IBI deteriorate with decreasing resolution. Conversely, on-target properties exhibit an extremely weak resolution dependence that suggests a limited role of representability errors in model accuracy. Taken together, these results suggest that simple CG models are capable of utilizing more information than is provided by standard parameterization algorithms, and that model accuracy can be improved by algorithm development rather than resorting to more complicated CG models.

Quantifying Interactions of Nucleobase Atoms with Model Compounds for the Peptide Backbone and Glutamine and Asparagine Side Chains in Water

Alkylureas display hydrocarbon and amide groups, the primary functional groups of proteins. To obtain the thermodynamic information that is needed to analyze interactions of amides and proteins with nucleobases and nucleic acids, we quantify preferential interactions of alkylureas with nucleobases differing in the amount and composition of water-accessible surface area (ASA) by solubility assays. Using an established additive ASA-based analysis, we interpret these thermodynamic results to determine interactions of each alkylurea with five types of nucleobase unified atoms (carbonyl sp²O, amino sp³N, ring sp²N, methyl sp³C, and ring sp²C). All alkylureas interact favorably with nucleobase sp²C and sp³C atoms; these interactions become more favorable with an increasing level of alkylation of urea. Interactions with nucleobase sp²O are most favorable for urea, less favorable for methylurea and ethylurea, and unfavorable for dialkylated ureas. Contributions to overall alkylurea-nucleobase interactions from interactions with each nucleobase atom type are proportional to the ASA of that atom type with proportionality constant (interaction strength) α, as observed previously for urea. Trends in α-values for interactions of alkylureas with nucleobase atom types parallel those for corresponding amide compound atom types, offset because nucleobase α-values are more favorable. Comparisons between ethylated and methylated ureas show interactions of amide compound sp³C with nucleobase sp²C, sp³C, sp²N, and sp³N atoms are favorable while amide sp³C-nucleobase sp²O interactions are unfavorable. Strongly favorable interactions of urea with nucleobase sp²O but weakly favorable interactions with nucleobase sp³N indicate that amide sp²N-nucleobase sp²O and nucleobase sp³N-amide sp²O hydrogen bonding (NH···O═C) interactions are favorable while amide sp²N-nucleobase sp³N interactions are unfavorable. These favorable amide-nucleobase hydrogen bonding interactions are prevalent in specific protein-nucleotide complexes.

Transferable Coarse-Grained Models of Liquid-Liquid Equilibrium Using Local Density Potentials Optimized with the Relative Entropy

Bottom-up coarse-grained (CG) models are now regularly pursued to enable large length and time scale molecular simulations of complex, often macromolecular systems. However, predicting fluid phase equilibria using such models remains fundamentally challenging. A major problem stems from the typically low transferability of CG models beyond the densities and/or compositions at which they are parametrized, which is necessary if they are to describe distinct structural and thermodynamic properties unique to each phase. CG model transferability is compounded by the representation of the inherently multibody coarse interactions using pair potentials that neglect higher order effects. Here, we propose to construct transferable single site CG models of liquid mixtures by supplementing traditional CG pair interactions with local density potentials, which constitute a computationally inexpensive mean-field approach to describe many-body effects, in that site energies are modulated by the local solution environment. To illustrate the approach, we use intra- and interspecies local density potentials to develop CG models of benzene-water solutions that show impressive transferability in structural metrics (pair correlation functions, density profiles) throughout composition space, in contrast to pair-only CG representations. While further refinement may be necessary to represent more complex thermodynamic properties, like the liquid-liquid interfacial tension, the generality and improvement offered by the local density approach are highly encouraging for enabling complex phase equilibrium modeling using CG models.

Addressing the temperature transferability of structure based coarse graining models

We present a novel idea to improve the temperature transferability of structure based coarse graining models.

Experimental Atom-by-Atom Dissection of Amide-Amide and Amide-Hydrocarbon Interactions in H2O

Quantitative information about amide interactions in water is needed to understand their contributions to protein folding and amide effects on aqueous processes and to compare with computer simulations. Here we quantify interactions of urea, alkylated ureas, and other amides by osmometry and amide-aromatic hydrocarbon interactions by solubility. Analysis of these data yields strengths of interaction of ureas and naphthalene with amide sp2O, amide sp2N, aliphatic sp3C, and amide and aromatic sp2C unified atoms in water. Interactions of amide sp2O with urea and naphthalene are favorable, while amide sp2O-alkylurea interactions are unfavorable, becoming more unfavorable with increasing alkylation. Hence, amide sp2O-amide sp2N interactions (proposed n-σ* hydrogen bond) and amide sp2O-aromatic sp2C (proposed n-π*) interactions are favorable in water, while amide sp2O-sp3C interactions are unfavorable. Interactions of all ureas with sp3C and amide sp2N are favorable and increase in strength with increasing alkylation, indicating favorable sp3C-amide sp2N and sp3C-sp3C interactions. Naphthalene results show that aromatic sp2C-amide sp2N interactions in water are unfavorable while sp2C-sp3C interactions are favorable. These results allow interactions of amide and hydrocarbon moieties and effects of urea and alkylureas on aqueous processes to be predicted or interpreted in terms of structural information. We predict strengths of favorable urea-benzene and N-methylacetamide interactions from experimental information to compare with simulations and indicate how amounts of hydrocarbon and amide surfaces buried in protein folding and other biopolymer processes and transition states can be determined from analysis of urea and diethylurea effects on equilibrium and rate constants.

Bayesian calibration of coarse-grained forces: Efficiently addressing transferability

Generating and calibrating forces that are transferable across a range of state-points remains a challenging task in coarse-grained (CG) molecular dynamics. In this work, we present a coarse-graining workflow, inspired by ideas from uncertainty quantification and numerical analysis, to address this problem. The key idea behind our approach is to introduce a Bayesian correction algorithm that uses functional derivatives of CG simulations to rapidly and inexpensively recalibrate initial estimates f0 of forces anchored by standard methods such as force-matching. Taking density-temperature relationships as a running example, we demonstrate that this algorithm, in concert with various interpolation schemes, can be used to efficiently compute physically reasonable force curves on a fine grid of state-points. Importantly, we show that our workflow is robust to several choices available to the modeler, including the interpolation schemes and tools used to construct f0. In a related vein, we also demonstrate that our approach can speed up coarse-graining by reducing the number of atomistic simulations needed as inputs to standard methods for generating CG forces.

Directly Modifying the Nonbonded Potential Based on the Standard Iterative Boltzmann Inversion Method for Coarse-Grained Force Fields

Effective potentials are of great importance for coarse-grained (CG) simulations, which can be obtained by the structure-based iterative Boltzmann inversion (IBI) method. However, the standard IBI method is incapable of maintaining the mechanical and thermodynamic properties of the CG model in agreement with those of the all-atom model. Unlike the existing techniques, such as introducing friction force as the dissipative force to reduce the superatom motion while keeping the conservative force arising from the CG potential intact, we directly modified the standard IBI nonbonded potential by adding an empirical function. According to an analysis of the dissipative particle dynamics, the additional function did compensate for the friction reduction of the standard IBI CG model. In this work, the thermal fluctuation information from the nonbonded radial distribution function was incorporated into the additional empirical function. As an illustration of the new CG force fields, we presented simulations of the stress-strain relation and thermodynamic properties in terms of cis-polyisoprene and compared the statistical structure information of the superatoms with those of the IBI CG model and the all-atom model. It should be emphasized that the additional empirical function contributed to compensating for the friction reduction, irrespective of the functional form it took. In this sense, the proposed method was easily operable.

Transferability of a coarse-grained atactic polystyrene model: the non-bonded potential effect

In this paper, we construct an efficient and simple coarse grained (CG) model for atactic polystyrene (PS) by using a 1 : 1 mapping scheme at 463 K and 1 atm pressure and derive the corresponding bonded and non-bonded potentials in the CG force field (FF) via a direct Boltzmann inversion approach and a combined structure-based and thermodynamic quantities-based CG method, respectively.

Transferability of the coarse-grained potentials for trans-1,4-polybutadiene

The CG torsion potential has a dual effect on the reproduction of crystallization of trans-1,4-polybutadiene in CG simulation.

Derivation of coarse-grained potentials via multistate iterative Boltzmann inversion

In this work, an extension is proposed to the standard iterative Boltzmann inversion (IBI) method used to derive coarse-grained potentials. It is shown that the inclusion of target data from multiple states yields a less state-dependent potential, and is thus better suited to simulate systems over a range of thermodynamic states than the standard IBI method. The inclusion of target data from multiple states forces the algorithm to sample regions of potential phase space that match the radial distribution function at multiple state points, thus producing a derived potential that is more representative of the underlying interactions. It is shown that the algorithm is able to converge to the true potential for a system where the underlying potential is known. It is also shown that potentials derived via the proposed method better predict the behavior of n-alkane chains than those derived via the standard IBI method. Additionally, through the examination of alkane monolayers, it is shown that the relative weight given to each state in the fitting procedure can impact bulk system properties, allowing the potentials to be further tuned in order to match the properties of reference atomistic and/or experimental systems.