Structure-based Coarse Graining Research Articles

Structural Coarse-Graining via Multiobjective Optimization with Differentiable Simulation.

In the realm of multiscale molecular simulations, structure-based coarse-graining is a prominent approach for creating efficient coarse-grained (CG) representations of soft matter systems, such as polymers. This involves optimizing CG interactions by matching static correlation functions of the corresponding degrees of freedom in all-atom (AA) models. Here, we present a versatile method, namely, differentiable coarse-graining (DiffCG), which combines multiobjective optimization and differentiable simulation. The DiffCG approach is capable of constructing robust CG models by iteratively optimizing the effective potentials to simultaneously match multiple target properties. We demonstrate our approach by concurrently optimizing bonded and nonbonded potentials of a CG model of polystyrene (PS) melts. The resulting CG-PS model effectively reproduces both the structural characteristics, such as the equilibrium probability distribution of microscopic degrees of freedom and the thermodynamic pressure of the AA counterpart. More importantly, leveraging the multiobjective optimization capability, we develop a precise and efficient CG model for PS melts that is transferable across a wide range of temperatures, i.e., from 400 to 600 K. It is achieved via optimizing a pairwise potential with nonlinear temperature dependence in the CG model to simultaneously match target data from AA-MD simulations at multiple thermodynamic states. The temperature transferable CG-PS model demonstrates its ability to accurately predict the radial distribution functions and density at different temperatures, including those that are not included in the target thermodynamic states. Our work opens up a promising route for developing accurate and transferable CG models of complex soft-matter systems through multiobjective optimization with differentiable simulation.

Enhancing pressure consistency and transferability of structure-based coarse-graining.

Coarse-graining, which models molecules with coarse-grained (CG) beads, allows molecular dynamics simulations to be applied to systems with large length and time scales while preserving the essential molecular structure. However, CG models generally have insufficient representability and transferability. A commonly used method to resolve this problem is multi-state iterative Boltzmann inversion (MS-IBI) with pressure correction, which matches both the structural properties and pressures at different thermodynamic states between CG and all-atom (AA) simulations. Nevertheless, this method is usually effective only in a narrow pressure range. In this paper, we propose a modified CG scheme to overcome this limitation. We find that the fundamental reason for this limitation is that CG beads at close distances are ellipsoids rather than isotropically compressed spheres, as described in conventional CG models. Hence, we propose a method to compensate for such differences by slightly modifying the radial distribution functions (RDFs) derived from AA simulations and using the modified RDFs as references for pressure-corrected MS-IBI. We also propose a method to determine the initial non-bonded potential using both the target RDF and pressure. Using n-dodecane as a case study, we demonstrate that the CG model developed using our scheme reproduces the RDFs and pressures over a wide range of pressure states, including three reference low-pressure states and two test high-pressure states. The proposed scheme allows for accurate CG simulations of systems in which pressure or density varies with time and/or position.

Broad chemical transferability in structure-based coarse-graining.

Compared to top-down coarse-grained (CG) models, bottom-up approaches are capable of offering higher structural fidelity. This fidelity results from the tight link to a higher resolution reference, making the CG model chemically specific. Unfortunately, chemical specificity can be at odds with compound-screening strategies, which call for transferable parameterizations. Here, we present an approach to reconcile bottom-up, structure-preserving CG models with chemical transferability. We consider the bottom-up CG parameterization of 3441 C7O2 small-molecule isomers. Our approach combines atomic representations, unsupervised learning, and a large-scale extended-ensemble force-matching parameterization. We first identify a subset of 19 representative molecules, which maximally encode the local environment of all gas-phase conformers. Reference interactions between the 19 representative molecules were obtained from both homogeneous bulk liquids and various binary mixtures. An extended-ensemble parameterization over all 703 state points leads to a CG model that is both structure-based and chemically transferable. Remarkably, the resulting force field is on average more structurally accurate than single-state-point equivalents. Averaging over the extended ensemble acts as a mean-force regularizer, smoothing out both force and structural correlations that are overly specific to a single-state point. Our approach aims at transferability through a set of CG bead types that can be used to easily construct new molecules while retaining the benefits of a structure-based parameterization.

Many-Body Neural Network-Based Force Field for Structure-Based Coarse-Graining of Water.

High-fidelity results from atomistic simulations can only be obtained by using accurate force-field (FF) parameters. Although empirical FFs are commonly used in the modeling of atomistic systems due to their simplicity, they have many limitations inherent in the crude approximations associated with their analytical form. Recent advances in neural network-based FFs have led to more accurate FFs by using symmetry functions or full many-body expansions. However, this approach leads to several issues including the arbitrariness of the symmetry functions, and the intangible and uninterpretable interactions which are only known once the positions of all atoms are set. More importantly, training is another bottleneck, as high-quality force and energy information is required, which is usually not accessible from experimental data. To solve these issues within the context of structure-based coarse-graining methods, we switch in this work to a local-search method to target the reference structure instead of using conventional backpropagation algorithms used to target the forces and energies of the reference structure. Our FF is decomposed into two-, three-, and higher-order terms, where each term is modeled with a separate neural network. To show the versatility of our method, we study four different systems, namely, Stillinger-Weber particles as an atomistic case and three water models, namely SPC/E, MB-pol, and ab initio, as coarse-graining cases. We show the successful application of our approach, by reproducing structural properties of different water models, followed by providing insight into the role of two-and three-body interactions. The results of all models indicate that the double-well isotropic pair potential, the signature of water-like behavior in an isotropic system, vanishes upon inclusion of the three-body interaction, showing dominance of the three-body interaction over the two-body interaction in water-like behavior with the single-well isotropic pair potential.

Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures.

Many methodological approaches have been proposed to improve systematic or bottom-up coarse-graining techniques to enhance the representability and transferability of the derived interaction potentials. Transferability describes the ability of a coarse-grained (CG) model to be predictive, i.e., to describe a system at state points different from those chosen for parametrization. Whereas the representability characterizes the accuracy of a CG model to reproduce target properties of the underlying reference or fine-grained model at a given state point. In this article, we shift the focus away from methodological aspects and rather raise the question whether we can overcome the disadvantages of a given method in terms of representability and transferability by systematically selecting the state point at which the CG model gets parametrized. We answer this question by applying the inverse Monte Carlo (IMC) approach-a structure-based coarse-graining method-to derive effective interactions for binary mixtures of simple Lennard-Jones (LJ) particles, which are different in size. For such simple systems we indeed can identify a concentration where the derived potentials show the best performance in terms of structural representability and transferability. This specific concentration is identified by computing the relative entropy which quantifies the information loss between different IMC models and the reference LJ model at varying mixture compositions. Further, we show that an IMC model for mixtures of n-hexane and n-perfluorohexane shows the same trend in transferability as the IMC models for the LJ system. All derived models are more transferable in the direction of increasing concentration of the larger-sized compound.

Accurate Structure-Based Coarse Graining Leads to Consistent Barrier-Crossing Dynamics.

Structure-based coarse graining of molecular systems offers a systematic route to reproduce the many-body potential of mean force. Unfortunately, common strategies are inherently limited by the molecular mechanics force field employed. Here, we extend the concept of multisurface dynamics, initially developed to describe electronic transitions in chemical reactions, to accurately sample the conformational ensemble of a classical system in equilibrium. In analogy to describing different electronic configurations, a surface-hopping scheme couples distinct conformational basins beyond the additivity of the Hamiltonian. The incorporation of more surfaces leads systematically toward improved cross-correlations. The resulting models naturally achieve consistent long-time dynamics for systems governed by barrier-crossing events.

Magic v.3: An integrated software package for systematic structure-based coarse-graining

Molecular simulations of many phenomena related to biomolecular systems, soft matter and nanomaterials require consideration of length scales above 10 nm and time scales longer than 1μs, which necessitates the use of coarse-grained (low resolution) models, where each site of the model represents a group of atoms, and where the solvent is often omitted. Our software package MagiC is designed to perform systematic structure-based coarse-graining of molecular models, in which the effective pairwise potentials between coarse-grained sites of low-resolution molecular models are constructed to reproduce structural distribution functions obtained from modeling of systems in a high resolution (atomistic) description. The software takes as input atomistic trajectories generated by an external molecular dynamics package, and produce as an output interaction potentials for coarse-grained models which can be directly used in a coarse-grained simulations package. Here we present a major update (v.3) of the software with substantially improved functionality, compatibility with several major atomistic and coarse-grained simulations packages (GROMACS, LAMMPS, GALAMOST), analysis suite with graphical possibilities, diagnostics, documentation. We describe briefly the coarse-graining methodology, the structure of the software, describe users actions, and illustrate the whole process with two complex examples: cholesterol containing lipid bilayers and condensation of DNA caused by multivalent ions. Program summaryProgram Title: MagiCProgram Files doi:http://dx.doi.org/10.17632/9gnfxyshj8.1Licensing provisions: GPLv3Programming language: Fortran, PythonNature of problem: Systematic bottom-up multiscale modeling is a complex multi-stage process, in which results of simulations of a high-resolution (atomistic) model are used to construct a low resolution (coarse-grained) model, providing the same structural properties for the coarse-grained system as for the high-resolution system. Within the approach, structural properties of the high-resolution model are computed in terms of radial distribution functions and distributions of intramolecular degrees of freedom. Then the inverse problem is solved, in which the interaction potentials for the low-resolution model are determined which provide distribution functions coinciding with those obtained in the high-resolution simulations. The low-resolution model can be then used for simulations of the same system on larger length and time-scale.Solution method: The presented software package implements all stages of the systematic structure-based coarse-graining. It works as an integrated pipeline, giving the user ability to easily derive a coarse-grained model for a multicomponent complex molecular system and then use it for large-scale simulations. MagiC implements two approaches to solve the inverse problem: (i) the Inverse Monte Carlo method in which the inverse problem is solved using the Newton–Raphson method, with inversion of the Jacobian for the discretized relationship between interaction potentials and structural distribution functions; and (ii) the Iterative Boltzmann approach in which the inverse problem is solved using approximative relationships neglecting correlations between different degrees of freedom. The inverse solver includes also variational Inverse Monte Carlo approach when some of the coarse-grained potentials are fixed while others vary in order to fit the whole set of reference distribution functions.Additional comments: The MagiC main module can be also used for conventional Monte Carlo simulations of molecular systems described by tabulated pairwise potentials in the canonical ensemble.

Structure-based coarse graining of diblock copolymer melts using PRISM theory

We applied our recently proposed systematic and simulation-free strategy for the structure-based coarse graining of multicomponent polymeric systems (Wang, Q., Polymer2017,117, 315) to diblock copolymer melts, where we use the well-developed polymer reference interaction site model (PRISM) theory, instead of the commonly used many-chain molecular simulations, to obtain the structural and thermodynamic properties of both the original and coarse-grained (CG) systems, and to quantitatively examine how the effective non-bonded pair potentials between CG segments and the thermodynamic properties of CG systems vary with the coarse-graining level. We proved that our strategy does not change the spinodal curve, regardless of the original model system, closures, and coarse-graining levels for the two blocks. Using a simple original model system for symmetric diblock copolymer melts, we coarse-grained each block as N/2 segments and examined CG systems with N ranging from 2 to 100. We found that coarse graining (i.e., decreasing N) increases both the peak value and peak location of the partial structure factor characterizing the composition fluctuations in the CG system. Contrary to the common practice in the literature, CG potentials obtained from short-chain systems cannot be directly used for long-chain systems; this is in fact the transferability problem in coarse graining (Louis, A. A., J. Phys.: Condens. Matter2002,14, 9187). We also found that the structure-based coarse graining cannot give thermodynamic consistency at any coarse-graining level, consistent with our previous work on homopolymer melts (Yang, D. L.; Wang, Q., J. Chem. Phys.2015,142, 054905; Wang, Q.; Yang, D. L., Polymer2017,111, 103) and binary polymer blends (Wang, Q., Polymer2017,117, 315).

Addressing the temperature transferability of structure based coarse graining models.

Systematically derived coarse grained (CG) models for molecular liquids do not inherently guarantee transferability to a state point different from its reference, especially when derived on the basis of structure based CG methods like Inverse Monte Carlo (IMC). Several efforts made in the past years to improve the transferability of these models focused on including thermodynamic constraints or on the application of multistate parametrization. Das and Andersen (DA) [Das et al., J. Chem. Phys., 2010, 132, 164106.] proposed a different Ansatz. They derived a correction term added to the system's Hamiltonian to reproduce the virial pressure and the volume fluctuations of the reference system in the CG resolution which does not require further adjustment of the effective pair potential. Herein, we discuss the possibility to achieve temperature transferability with IMC models for selected alkanes following the optimization of the DA approach as proposed by Dunn and Noid (DN) [Dunn et al., J. Chem. Phys., 2015, 143, 243148.]. The work focuses on a novel approach to determine the DN correction term for different state points by linear interpolation.

Systematic and simulation-free coarse graining of multi-component polymeric systems: Structure-based coarse graining of binary polymer blends

We proposed a systematic and simulation-free strategy for the structure-based coarse graining of multi-component polymeric systems using the polymer reference interaction site model theory, and as an example applied it to a simple model system of binary polymer blends. Our structure-based coarse graining ensures that the original and coarse-grained (CG) systems have the same intra- and intermolecular pair correlation functions involving the CG segments (each representing the center-of-mass of a group of consecutive monomers on the same chain in the original system). When applied to binary polymer blends, it does not change the spinodal curve (thus also the critical point), regardless of the original model system and closure used. We also quantitatively examined how the effective non-bonded pair potentials between CG segments and the thermodynamic properties of CG systems vary with the coarse-graining level. As expected, the structure-based coarse graining cannot give thermodynamic consistency (i.e., the same interchain internal energy per chain and virial pressure) between the original and CG systems at any coarse-graining level.

The recent structure-based coarse graining of polymer melts using PRISM theory does not give thermodynamic consistency

The full thermodynamic consistency claimed by Guenza and co-workers in their recent papers (J. McCarty et al., Macromolecules 45 (2012) 8482; A. J. Clark et al., Phys. Rev. Lett. 109 (2012) 168301; and A. J. Clark et al., J. Chem. Phys. 139 (2013) 124906), where they performed structure-based coarse graining of homopolymer melts using the polymer reference interaction site model theory, directly contradicts the well-established and widely cited finding by several research groups. In this Communication, we clearly showed that (1) the full thermodynamic consistency claimed by Guenza and co-workers is simply due to the (incorrect) approximations used in their analytical derivation, (2) none of their criticisms on our work (D. Yang, Q. Wang, J. Chem. Phys. 142 (2015) 054905) given in their Comment (A. J. Clark et al., J. Chem. Phys. 143 (2015) 067101) is valid, and (3) the simulation-free coarse-graining strategy presented in our work is crucially different from the coarse-graining approach in their recent papers.

Systematic and simulation-free coarse graining of homopolymer melts: a structure-based study.

We propose a systematic and simulation-free strategy for coarse graining of homopolymer melts, where each chain of Nm monomers is uniformly divided into N segments, with the spatial position of each segment corresponding to the center-of-mass of its monomers. We use integral-equation theories suitable for the study of equilibrium properties of polymers, instead of many-chain molecular simulations, to obtain the structural and thermodynamic properties of both original and coarse-grained (CG) systems, and quantitatively examine how the effective pair potentials between CG segments and the thermodynamic properties of CG systems vary with N. Our systematic and simulation-free strategy is much faster than those using many-chain simulations, thus effectively solving the transferability problem in coarse graining, and provides the quantitative basis for choosing the appropriate N-values. It also avoids the problems caused by finite-size effects and statistical uncertainties in many-chain simulations. Taking the simple hard-core Gaussian thread model [K. S. Schweizer and J. G. Curro, Chem. Phys. 149, 105 (1990)] as the original system, we demonstrate our strategy applied to structure-based coarse graining, which is quite general and versatile, and compare in detail the various integral-equation theories and closures for coarse graining. Our numerical results show that the effective CG potentials for various N and closures can be collapsed approximately onto the same curve, and that structure-based coarse graining cannot give thermodynamic consistency between original and CG systems at any N < Nm.

Systematic implicit solvent coarse graining of dimyristoylphosphatidylcholine lipids.

We have used systematic structure-based coarse graining to derive effective site-site potentials for a 10-site coarse-grained dimyristoylphosphatidylcholine (DMPC) lipid model and investigated their state point dependence. The potentials provide for the coarse-grained model the same site-site radial distribution functions, bond and angle distributions as those computed in atomistic simulations carried out at four different lipid-water molar ratios. It was shown that there is a non-negligible dependence of the effective potentials on the concentration at which they were generated, which is also manifested in the properties of the lipid bilayers simulated using these potentials. Thus, effective potentials computed at low lipid concentration favor to more condensed and ordered structure of the bilayer with lower average area per lipid, while potentials obtained at higher lipid concentrations provide more fluid-like structure. The best agreement with the reference data and experiment was achieved using the set of potentials derived from atomistic simulations at 1:30 lipid:water molar ratio providing fully saturated hydration of DMPC lipids. Despite theoretical limitations of pairwise coarse-grained potentials expressed in their state point dependence, all the resulting potentials provide a stable bilayer structure with correct partitioning of different lipid groups across the bilayer as well as acceptable values of the average lipid area, compressibility and orientational ordering. In addition to bilayer simulations, the model has proven its robustness in modeling of self-aggregation of lipids from randomly dispersed solution to ordered bilayer structures, bicelles, and vesicles.

MagiC: Software Package for Multiscale Modeling.

We present software package MagiC, which is designed to perform systematic structure-based coarse graining of molecular models. The effective pairwise potentials between coarse-grained sites of low-resolution molecular models are constructed to reproduce structural distribution functions obtained from the modeling of the system in a high resolution (atomistic) description. The software supports coarse-grained tabulated intramolecular bond and angle interactions, as well as tabulated nonbonded interactions between different site types in the coarse-grained system, with the treatment of long-range electrostatic forces by the Ewald summation. Two methods of effective potential refinement are implemented: iterative Boltzmann inversion and inverse Monte Carlo, the latter accounting for cross-correlations between pair interactions. MagiC uses its own Metropolis Monte Carlo sampling engine, allowing parallel simulation of many copies of the system with subsequent averaging of the properties, which provides fast convergence of the method with nearly linear scaling at parallel execution.

Thermodynamic state-dependent structure-based coarse-graining of confined water

We develop thermodynamic state-dependent single-site isotropic coarse-grained potentials to predict the structure of water confined inside graphene slit-like channels by two multiscale simulation approaches: the coarse-grained molecular dynamics (CG-MD) and the empirical potential-based quasi-continuum theory (EQT). The structurally-consistent coarse-grained potentials for the CG-MD and EQT are systematically determined from the reference all-atom SPC/E water MD (AA-MD) results. For optimization of the CG-MD potentials, the relative entropy based coarse-graining method is used, and for determination of the EQT potentials, we develop a potential of mean force matching scheme. The optimized coarse-grained potentials are found to be dependent on the thermodynamic state. They are evaluated for their ability to predict the density profile of confined water, and it is found that the results obtained by the CG-MD and EQT simulations are in good agreement with the reference AA-MD results.

The multiscale coarse-graining method: Assessing its accuracy and introducing density dependent coarse-grain potentials

The ability of particle-based coarse-grain potentials, derived using the recently proposed multiscale coarse-graining (MS-CG) methodology [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] to reconstruct atomistic free-energy surfaces in coarse-grain coordinates is discussed. The MS-CG method is based on force-matching generalized forces associated with the coarse-grain coordinates. In this work, we show that the MS-CG method recovers only part of the atomistic free-energy landscape in the coarse-grain coordinates (termed the potential of mean force contribution). The portion of the atomistic free-energy landscape that is left out in the MS-CG procedure contributes to a pressure difference between atomistic and coarse-grain ensembles. Employing one- and two-site coarse-graining of nitromethane as worked examples, we discuss the virial and compressibility constraints to incorporate a pressure correction interaction into the MS-CG potentials and improve performance at different densities. The nature of the pressure correction interaction is elucidated and compared with those used in structure-based coarse-graining. As pairwise approximations to the atomistic free-energy, the MS-CG potentials naturally depend on the variables describing a thermodynamic state, such as temperature and density. Such dependencies limit state-point transferability. For nitromethane, the one- and two-site MS-CG potentials appear to be transferable across a broad range of temperatures. In particular, the two-site models, which are matched to low and ambient temperature liquid states, perform well in simulations of the ambient crystal structure. In contrast, the transferability of the MS-CG models of nitromethane across different densities is found to be problematic. To achieve better state-point transferability, density dependent MS-CG potentials are introduced and their performance is examined in simulations of nitromethane under various thermodynamic conditions, including shocked states.

Self-assembling dipeptides: including solvent degrees of freedom in a coarse-grained model

In the previous paper [A. Villa, C. Peter, N. F. A. van der Vegt, Phys. Chem. Chem. Phys., 2009, DOI: ], a strategy to develop a solvent-free coarse-grained model for peptides is outlined which is based on an atomistic (force field) description. The coarse-grained model is designed such that it correctly captures the conformational flexibility of the molecules and reproduces the interaction between peptides in aqueous solution. In the present paper, we revisit this model and present a method to devise nonbonded interactions such that also the coarse-grained level maintains explicit solvent degrees of freedom. In this new approach we rely on a structure-based coarse graining methodology which preserves the solvation structure around the peptides in combination with a method to devise nonbonded potentials between peptide beads in a way that the peptide-peptide interaction in water is represented correctly and that results in the correct thermodynamic association behavior. The outlined coarse graining strategy provides us with two (one implicit- and one explicit-solvent) models that are well suited for multiscale-simulation and scale-bridging purposes. We show that this is a powerful tool to efficiently simulate long time-scale and large length-scale biomolecular processes such as peptide self-assembly. In combination with an efficient backmapping methodology we can obtain well-equilibrated atomistic structures of the resulting aggregates.