A Gauss-Newton method for iterative optimization of memory kernels for generalized Langevin thermostats in coarse-grained molecular dynamics simulations

In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations of such thermostats allow for an accurate representation of diffusivities/long-time dynamics, a correct description of the dynamics on all time scales generally requires non-Markovian, i.e., non-time-local, thermostats. These thermostats typically take the form of a Generalized Langevin Equation (GLE) determined by a memory kernel. In this work, we use a Markovian embedded formulation of a position-independent GLE thermostat acting independently on each CG degree of freedom. Extracting the memory kernel of this CG model from atomistic reference data requires several approximations. Therefore, this task is best understood as an inverse problem. While our recently proposed approximate Newton scheme allows for the iterative optimization of memory kernels (IOMK), Markovian embedding remained potentially error-prone and computationally expensive. In this work, we present an IOMK-Gauss-Newton scheme (IOMK-GN) based on IOMK that allows for the direct parameterization of a Markovian embedded model.

Resolving the dynamic properties of entangled linear polymers in non-equilibrium coarse grain simulation with a priori scaling factors

The molecular weight of polymers can influence the material properties, but the molecular weight at the experiment level sometimes can be a huge burden for property prediction with full-atomic simulations. The traditional bottom-up coarse grain (CG) simulation can reduce the computation cost. However, the dynamic properties predicted by the CG simulation can deviate from the full-atomic simulation result. Usually, in CG simulations, the diffusion is faster and the viscosity and modulus are much lower. The fast dynamics in CG are usually solved by a posteriori scaling on time, temperature, or potential modifications, which usually have poor transferability to other non-fitted physical properties because of a lack of fundamental physics. In this work, a priori scaling factors were calculated by the loss of degrees of freedom and implemented in the iterative Boltzmann inversion. According to the simulation results on 3 different CG levels at different temperatures and loading rates, such a priori scaling factors can help in reproducing some dynamic properties of polycaprolactone in CG simulation more accurately, such as heat capacity, Young's modulus, and viscosity, while maintaining the accuracy in the structural distribution prediction. The transferability of entropy-enthalpy compensation and a dissipative particle dynamics thermostat is also presented for comparison. The proposed method reveals the huge potential for developing customized CG thermostats and offers a simple way to rebuild multiphysics CG models for polymers with good transferability.

Multiscale, Multiresolution Coarse-Grained Model via a Hybrid Approach: Solvation, Structure, and Self-Assembly of Aromatic Tripeptides

Short aromatic peptides have been observed to assemble into diverse nanostructures, including fibers, tubes, and vesicles, using computational techniques. However, the computational studies have employed top-down coarse-grained (CG) models, which are unable to capture the assembly along with the conformation, packing, and organization of the peptides within the aggregates in a manner that is consistent with the all atom (AA) representation of the molecules. In this study, a hybrid structure- and force-based approach is adapted to develop a bottom-up CG force field of triphenylalanine using reference data from AA trajectories. This approach follows a flexible methodology to approximate the chemical complexity of the underlying AA representation with the chosen CG representation. Two CG models are developed with distinct representations of the aromatic side chains. The first uses a simple single-bead representation, while the second uses a three-bead representation to more accurately represent the planarity of the ring. The one-bead model yields nanorods, while the three-bead model results in nanospheres. The role of different chemical groups in the assembly of nanostructures is identified, along with the importance of steric effects on the packing of the peptides within assemblies.

DiAMoNDBack: Diffusion-Denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces

Coarse-grained molecular models of proteins permit access to length and time scales unattainable by all-atom models and the simulation of processes that occur on long time scales, such as aggregation and folding. The reduced resolution realizes computational accelerations, but an atomistic representation can be vital for a complete understanding of mechanistic details. Backmapping is the process of restoring all-atom resolution to coarse-grained molecular models. In this work, we report DiAMoNDBack (Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping) as an autoregressive denoising diffusion probability model to restore all-atom details to coarse-grained protein representations retaining only Cα coordinates. The autoregressive generation process proceeds from the protein N-terminus to C-terminus in a residue-by-residue fashion conditioned on the Cα trace and previously backmapped backbone and side-chain atoms within the local neighborhood. The local and autoregressive nature of our model makes it transferable between proteins. The stochastic nature of the denoising diffusion process means that the model generates a realistic ensemble of backbone and side-chain all-atom configurations consistent with the coarse-grained Cα trace. We train DiAMoNDBack over 65k+ structures from the Protein Data Bank (PDB) and validate it in applications to a hold-out PDB test set, intrinsically disordered protein structures from the Protein Ensemble Database (PED), molecular dynamics simulations of fast-folding mini-proteins from DE Shaw Research, and coarse-grained simulation data. We achieve state-of-the-art reconstruction performance in terms of correct bond formation, avoidance of side-chain clashes, and the diversity of the generated side-chain configurational states. We make the DiAMoNDBack model publicly available as a free and open-source Python package.

Understanding the thermomechanical behavior of graphene-reinforced conjugated polymer nanocomposites via coarse-grained modeling

Graphene-reinforced conjugated polymer (CP) nanocomposites are attractive for flexible and electronic devices, but their mechanical properties have been less explored at a fundamental level. Here, we present a predictive multiscale modeling framework for graphene-reinforced poly(3-alkylthiophene) (P3AT) nanocomposites via atomistically informed coarse-grained molecular dynamics simulations to investigate temperature-dependent thermomechanical properties at a molecular level. Our results reveal reduced graphene dispersion with increasing graphene loading. Nanocomposites with shorter P3AT side chains, lower temperatures, and higher graphene content exhibit stronger mechanical responses, which correlates with polymer dynamics. The elastic modulus increases linearly with the graphene content, which slightly deviates from the "Halpin-Tsai" micromechanical model prediction. Local stiffness analysis shows that graphene possesses the highest stiffness, followed by the P3AT backbone and side chains. Deformation-induced stronger chain alignment of the P3AT backbone compared to graphene may further promote conductive behavior. Our findings provide insights into the dynamical heterogeneity of nanocomposites, paving the way for understanding and predicting their thermomechanical properties.

Comparison of Friction Parametrization from Dynamics and Material Properties for a Coarse-Grained Polymer Melt

In this work, we extend an approach to coarse-grained (CG) modeling for polymer melts in which the conservative potential is parametrized using the iterative Boltzmann inversion (IBI) method and the accelerated dynamics inherent to IBI are corrected using the dissipative Langevin thermostat with a single tunable friction parameter (J. Chem. Phys. 2021, 154, 084114). Diffusive measures from picoseconds to nanoseconds are used to determine the Langevin friction factor to apply to the CG model to recover all-atom (AA) dynamics; the resulting friction factors are then compared for consistency. Here, we additionally parametrize the CG dynamics using a material property, the zero-shear viscosity, which we measure using the Green-Kubo (GK) method. Two materials are studied, squalane as a function of temperature and the same polystyrene oligomers previously studied as a function of chain length. For squalane, the friction derived from the long-time diffusive measures and the viscosity all strongly increase with decreasing temperature, showing an Arrhenius-like dependence, and remain consistent with each other over the entire temperature range. In contrast, the friction required for the picosecond diffusive measurement, the Debye-Waller factor, is somewhat lower than the friction from long-time measures and relatively insensitive to temperature. A time-dependent friction would be required to exactly reproduce the AA measurements during the caging transition connecting these two extremes over the entire timespan at this level of coarse-graining. For the polystyrene oligomers for which we previously characterized the diffusive friction, the viscosity-parametrized frictions are consistent with the diffusive measures for the smallest chain length. However, for the longer chains, we find different trends based on measurement method with friction derived from rotational diffusion remaining nearly constant, friction derived from translational diffusion showing a modestly increasing trend, and viscosity-derived friction showing a modest decreasing trend. This seems to indicate that there is some sensitivity of the friction measurement method for systems with increased relaxation times and that in particular, the unsteady dynamics of the individual parametrization schemes plays a role in this. Increased difficulty in applying the GK method with increasing relaxation time of the longer chain systems is also discussed. Overall, we find that when the material is in a high-temperature melt state and the viscosity measurement is reliable, the friction parametrization from the diffusive friction measures is consistent and the lower cost diffusive parametrization is a reliable means for modeling viscosity. Our data give insight into the time-dependent friction one might compute using a non-Markovian approach to enable the recovery of AA dynamics over a wider range of time scales than can be computed using a single friction.

Assessing the Validity of NMR Relaxation Rates Obtained from Coarse-Grained Simulations of PEG-Water Mixtures

NMR relaxometry is a powerful and well-established experimental approach for characterizing dynamic processes in soft matter systems. All-atom (AA) resolved simulations are typically employed to gain further microscopic insights while reproducing the relaxation rates R₁. However, such approaches are limited to time and length scales that prevent to model systems such as long polymer chains or hydrogels. Coarse graining (CG) can overcome this barrier at the cost of losing atomistic details that impede the calculation of NMR relaxation rates. Here, we address this issue by performing a systematic characterization of dipolar relaxation rates R₁ on a PEG-H₂O mixture at two different levels of details: AA and CG. Remarkably, we show that NMR relaxation rates R₁ obtained at the CG level obey the same trends when compared to AA calculations but with a systematic offset. This offset is due to, on the one hand, the lack of an intramonomer component and, on the other hand, the inexact positioning of the spin carriers. We show that the offset can be corrected for quantitatively by reconstructing a posteriori the atomistic details for the CG trajectories.

A hybrid approach for coarse-graining helical peptoids: Solvation, secondary structure, and assembly

Protein mimics such as peptoids form self-assembled nanostructures whose shape and function are governed by the side chain chemistry and secondary structure. Experiments have shown that a peptoid sequence with a helical secondary structure assembles into microspheres that are stable under various conditions. The conformation and organization of the peptoids within the assemblies remains unknown and is elucidated in this study via a hybrid, bottom-up coarse-graining approach. The resultant coarse-grained (CG) model preserves the chemical and structural details that are critical for capturing the secondary structure of the peptoid. The CG model accurately captures the overall conformation and solvation of the peptoids in an aqueous solution. Furthermore, the model resolves the assembly of multiple peptoids into a hemispherical aggregate that is in qualitative agreement with the corresponding results from experiments. The mildly hydrophilic peptoid residues are placed along the curved interface of the aggregate. The composition of the residues on the exterior of the aggregate is determined by two conformations adopted by the peptoid chains. Hence, the CG model simultaneously captures sequence-specific features and the assembly of a large number of peptoids. This multiscale, multiresolution coarse-graining approach could help in predicting the organization and packing of other tunable oligomeric sequences of relevance to biomedicine and electronics.

Multiscale equilibration of highly entangled isotropic model polymer melts

We present a computationally efficient multiscale method for preparing equilibrated, isotropic long-chain model polymer melts. As an application, we generate Kremer-Grest melts of 1000 chains with 200 entanglements and 25 000-2000 beads/chain, which cover the experimentally relevant bending rigidities up to and beyond the limit of the isotropic-nematic transition. In the first step, we employ Monte Carlo simulations of a lattice model to equilibrate the large-scale chain structure above the tube scale while ensuring a spatially homogeneous density distribution. We then use theoretical insight from a constrained mode tube model to introduce the bead degrees of freedom together with random walk conformational statistics all the way down to the Kuhn scale of the chains. This is followed by a sequence of simulations with carefully parameterized force-capped bead-spring models, which slowly introduce the local bead packing while reproducing the larger-scale chain statistics of the target Kremer-Grest system at all levels of force-capping. Finally, we can switch to the full Kremer-Grest model without perturbing the structure. The resulting chain statistics is in excellent agreement with literature results on all length scales accessible in brute-force simulations of shorter chains.

Bottom-Up Informed and Iteratively Optimized Coarse-Grained Non-Markovian Water Models with Accurate Dynamics

Molecular dynamics (MD) simulations based on coarse-grained (CG) particle models of molecular liquids generally predict accelerated dynamics and misrepresent the time scales for molecular vibrations and diffusive motions. The parametrization of Generalized Langevin Equation (GLE) thermostats based on the microscopic dynamics of the fine-grained model provides a promising route to address this issue, in conjunction with the conservative interactions of the CG model obtained with standard coarse graining methods, such as iterative Boltzmann inversion, force matching, or relative entropy minimization. We report the application of a recently introduced bottom-up dynamic coarse graining method, based on the Mori-Zwanzig formalism, which provides accurate estimates of isotropic GLE memory kernels for several CG models of liquid water. We demonstrate that, with an additional iterative optimization of the memory kernels (IOMK) for the CG water models based on a practical iterative optimization technique, the velocity autocorrelation function of liquid water can be represented very accurately within a few iterations. By considering the distinct Van Hove function, we demonstrate that, with the presented methods, an accurate representation of structural relaxation can be achieved. We consider several distinct CG potentials to study how the choice of the CG potential affects the performance of bottom-up informed and iteratively optimized models.

Understanding dynamics in coarse-grained models. II. Coarse-grained diffusion modeled using hard sphere theory

The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

Temporally Coherent Backmapping of Molecular Trajectories From Coarse-Grained to Atomistic Resolution

Coarse-graining offers a means to extend the achievable time and length scales of molecular dynamics simulations beyond what is practically possible in the atomistic regime. Sampling molecular configurations of interest can be done efficiently using coarse-grained simulations, from which meaningful physicochemical information can be inferred if the corresponding all-atom configurations are reconstructed. However, this procedure of backmapping to reintroduce the lost atomistic detail into coarse-grain structures has proven a challenging task due to the many feasible atomistic configurations that can be associated with one coarse-grain structure. Existing backmapping methods are strictly frame-based, relying on either heuristics to replace coarse-grain particles with atomic fragments and subsequent relaxation or parametrized models to propose atomic coordinates separately and independently for each coarse-grain structure. These approaches neglect information from previous trajectory frames that is critical to ensuring temporal coherence of the backmapped trajectory, while also offering information potentially helpful to producing higher-fidelity atomic reconstructions. In this work, we present a deep learning-enabled data-driven approach for temporally coherent backmapping that explicitly incorporates information from preceding trajectory structures. Our method trains a conditional variational autoencoder to nondeterministically reconstruct atomistic detail conditioned on both the target coarse-grain configuration and the previously reconstructed atomistic configuration. We demonstrate our backmapping approach on two exemplar biomolecular systems: alanine dipeptide and the miniprotein chignolin. We show that our backmapped trajectories accurately recover the structural, thermodynamic, and kinetic properties of the atomistic trajectory data.

A Core-Shell Approach for Systematically Coarsening Nanoparticle-Membrane Interactions: Application to Silver Nanoparticles

The continuous release of engineered nanomaterial (ENM) into the environment may bring about health concerns following human exposure. One important source of ENMs are silver nanoparticles (NPs) that are extensively used as anti-bacterial additives. The introduction of ENMs into the human body can occur via ingestion, skin uptake or the respiratory system. Therefore, evaluating how NPs translocate over bio-membranes is essential in assessing their primary toxicity. Unfortunately, data regarding membrane-NP interaction is still scarce, as is theoretical and in silico insight into what governs adhesion and translocation for the most relevant NPs and membranes. Coarse-grained (CG) molecular descriptions have the potential to alleviate this situation, but are hampered by the absence of a direct link to NP materials and membrane adhesion mechanisms. Here, we interrogate the relationship between the most common NP representation at the CG level and the adhesion characteristics of a model lung membrane. We find that this representation for silver NPs is non-transferable, meaning that a proper CG representation for one size is not suited for other sizes. We also identify two basic types of primary adhesion-(partial) NPs wrapping by the membrane and NP insertion into the membrane-that closely relate to the overall NP hydrophobicity and significantly differ in terms of lipid coatings. The proven non-transferability of the standard CG representation with size forms an inspiration for introducing a core-shell model even for bare NPs that are uniform in composition. Using existing all-atom molecular dynamics (MD) data as a reference, we show that this extension does allow us to reproduce size-dependent NP adhesion properties and lipid responses to NP binding at the CG level. The subsequent CGMD evaluation for 10 nm Ag NPs provides new insight into membrane binding for relevant NP sizes and into the role of water in trapping NPs into defected mixed monolayer-bilayer states. This development will be instrumental for simulating NP-membrane adhesion towards more experimentally relevant length and time scales for particular NP materials.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Roughness Volumes: An Improved RoughMob Concept for Predicting the Increase of Molecular Mobility upon Coarse-Graining

The reduced number of degrees of freedom in a coarse-grained molecular model compared to its parent atomistic model not only makes it possible to simulate larger systems for longer time scales but also results in an artificial mobility increase. The RoughMob method [Meinel, M. K. and Müller-Plathe, F. J. Chem. Theory Comput. 2020, 16, 1411.] linked the acceleration factor of the dynamics to the loss of geometric information upon coarse-graining. Our hypothesis is that coarse-graining a multiatom molecule or group into a single spherical bead smooths the molecular surface and, thus, leads to reduced intermolecular friction. A key parameter is the molecular roughness difference, which is calculated via a numerical comparison of the molecular surfaces of both the atomistic and coarse-grained models. Augmenting the RoughMob method, we add the concept of the region where the roughness acts. This information is contained in four so-called roughness volumes. For 17 systems of homogeneous hydrocarbon fluids, simple one-bead coarse-grained models are derived by the structure-based iterative Boltzmann inversion. They include 13 different homogeneous aliphatic and aromatic molecules and two different mapping schemes. We present a simple way to correlate the roughness volumes to the acceleration factor. The resulting relation is able to a priori predict the acceleration factors for an extended size and shape range of hydrocarbon molecules, with different mapping schemes and different densities.

Coarse-Grained Model of Thiol-Epoxy-Based Alternating Copolymers in Explicit Solvents

The cosolvent method has been widely used in the self-assembly of amphiphilic alternating copolymers (ACPs), but the role of good and selective solvents is rarely investigated. Here, we have developed a coarse-grained (CG) model for the widely studied thiol-epoxy-based amphiphilic ACPs and a three-bead CG model for tetrahydrofuran (THF) as the good solvent, which is compatible with the MARTINI water model. The accuracy of both the CG polymer and THF models was validated by reproducing the structural and thermodynamic properties obtained from experiments or atomistic simulation results. Density in bulk, the radius of gyration, and solvation free energy in water or THF showed a good agreement between CG and atomistic models. The CG models were further employed to explore the self-assembly of ACPs in THF/water mixtures with different compositions. Chain folding and liquid-liquid phase separation behaviors were found with increasing water fractions, which were the key steps of the self-assembly process. This work will provide a basic platform to explore the self-assembly of amphiphilic ACPs in solvent mixtures and to reveal the real role of different solvents in self-assembly.

Selective solvent conditions influence sequence development and supramolecular assembly in step-growth copolymerization

Sequence control in synthetic copolymers remains a tantalizing objective in polymer science due to the influence of sequence on material properties and self-organization. A greater understanding of sequence development throughout the polymerization process will aid the design of simple, generalizable methods to control sequence and tune supramolecular assembly. In previous simulations of solution-based step-growth copolymerizations, we have shown that weak, non-bonding attractions between monomers of the same type can produce a microphase separation among the lengthening nascent oligomers and thereby alter sequence. This work explores the phenomenon further, examining how effective attractive interactions, mediated by a solvent selective for one of the reacting species, impact the development of sequence and the supramolecular assembly in a simple A-B copolymerization. We find that as the effective attractions between monomers increase, an emergent self-organization of the reactants causes a shift in reaction kinetics and sequence development. When the solvent-mediated interactions are selective enough, the simple mixture of A and B monomers oligomerize and self-assemble into structures characteristic of amphiphilic copolymers. The composition and morphology of these structures and the sequences of their chains are sensitive to the relative balance of affinities between the comonomer species. Our results demonstrate the impact of differing A-B monomer-solvent affinities on sequence development in solution-based copolymerizations and are of consequence to the informed design of synthetic methods for sequence controlled amphiphilic copolymers and their aggregates.

A hybrid coarse-grained model for structure, solvation and assembly of lipid-like peptides

Reconstituted photosynthetic proteins which are activated upon exposure to solar energy hold enormous potential for powering future solid state devices and solar cells. The functionality and integration of these proteins into such devices has been successfully enabled by lipid-like peptides. Yet, a fundamental understanding of the organization of these peptides with respect to the photosynthetic proteins and themselves remains unknown and is critical for guiding the design of such light-activated devices. This study investigates the relative organization of one such peptide sequence V₆K₂ (V: valine and K: lysine) within assemblies. Given the expansive spatiotemporal scales associated with this study, a hybrid coarse-grained (CG) model which captures the structure, conformation and aggregation of the peptide is adopted. The CG model uses a combination of iterative Boltzmann inversion and force matching to provide insight into the relative organization of V₆K₂ in assemblies. The CG model reproduces the structure of a V₆K₂ peptide sequence along with its all atom (AA) solvation structure. The relative organization of multiple peptides in an assembly, as captured by CG simulations, is in agreement with corresponding results from AA simulations. Also, a backmapping procedure reintroduces the AA details of the peptides within the aggregates captured by the CG model to demonstrate the relative organization of the peptides. Furthermore, a large number of peptides self-assemble into an elongated micelle in the CG simulation, which is consistent with experimental findings. The coarse-graining procedure is tested for transferability to longer peptide sequences, and hence can be extended to other amphiphilic peptide sequences.

Determining Sequence-Dependent DNA Oligonucleotide Hybridization and Dehybridization Mechanisms Using Coarse-Grained Molecular Simulation, Markov State Models, and Infrared Spectroscopy

A robust understanding of the sequence-dependent thermodynamics of DNA hybridization has enabled rapid advances in DNA nanotechnology. A fundamental understanding of the sequence-dependent kinetics and mechanisms of hybridization and dehybridization remains comparatively underdeveloped. In this work, we establish new understanding of the sequence-dependent hybridization/dehybridization kinetics and mechanism within a family of self-complementary pairs of 10-mer DNA oligomers by integrating coarse-grained molecular simulation, machine learning of the slow dynamical modes, data-driven inference of long-time kinetic models, and experimental temperature-jump infrared spectroscopy. For a repetitive ATATATATAT sequence, we resolve a rugged dynamical landscape comprising multiple metastable states, numerous competing hybridization/dehybridization pathways, and a spectrum of dynamical relaxations. Introduction of a G:C pair at the terminus (GATATATATC) or center (ATATGCATAT) of the sequence reduces the ruggedness of the dynamics landscape by eliminating a number of metastable states and reducing the number of competing dynamical pathways. Only by introducing a G:C pair midway between the terminus and the center to maximally disrupt the repetitive nature of the sequence (ATGATATCAT) do we recover a canonical "all-or-nothing" two-state model of hybridization/dehybridization with no intermediate metastable states. Our results establish new understanding of the dynamical richness of sequence-dependent kinetics and mechanisms of DNA hybridization/dehybridization by furnishing quantitative and predictive kinetic models of the dynamical transition network between metastable states, present a molecular basis with which to understand experimental temperature jump data, and furnish foundational design rules by which to rationally engineer the kinetics and pathways of DNA association and dissociation for DNA nanotechnology applications.

Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.

Coarse grained simulation of the aggregation and structure control of polyethylene nanocrystals

Polyethylene (PE) telechelics with carboxylate functional groups at both ends have been shown to assemble into hexagonal nanocrystal platelets with a height defined by their chain length in basic CsOH-solution. In this coarse grained (CG) simulation study we show how properties of the functional groups alter the aggregation and crystallization behavior of those telechelics. Systematic variation of the parameters of the CG model showed that important factors which control nanoparticle stability and structure are the PE chain length and the hydrophilicity and the steric demand of the head groups. To characterize the aggregation process we analyzed the number and size of the obtained aggregates as well as intramolecular order and intermolecular alignment of the polymer chains. By comparison of CG and atomistic simulation data, it could be shown that atomistic simulations representing different chemical systems can be emulated with specific, different CG parameter sets. Thus, the results from the (generic) CG simulation models can be used to explain the effect of different head groups and different counterions on the aggregation of PE telechelics and the order of the obtained nanocrystals.

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.

Introducing Memory in Coarse-Grained Molecular Simulations

Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori-Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.

Force probe simulations using an adaptive resolution scheme

Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In force probe molecular dynamics (FPMD) simulations, one pulls one end of the molecule with a constant velocity in order to induce the relevant conformational transitions. Since the extended configuration of the system has to fit into the simulation box together with the solvent such simulations are very time consuming. Here, we apply a hybrid scheme in which the solute is treated with atomistic resolution and the solvent molecules far away from the solute are described in a coarse-grained manner. We use the adaptive resolution scheme (AdResS) that has very successfully been applied to various examples of equilibrium simulations. We perform FPMD simulations using AdResS on a well studied system, a dimer formed from mechanically interlocked calixarene capsules. The results of the multiscale simulations are compared to all-atom simulations of the identical system and we observe that the size of the region in which atomistic resolution is required depends on the pulling velocity, i.e. the particular non-equilibrium situation. For large pulling velocities a larger all atom region is required. Our results show that multiscale simulations can be applied also in the strong non-equilibrium situations that the system experiences in FPMD simulations.

Dynamically consistent coarse-grain simulation model of chemically specific polymer melts via friction parameterization

Coarse-grained (CG) models of polymers involve grouping many atoms in an all-atom (AA) representation into single sites to reduce computational effort yet retain the hierarchy of length and time scales inherent to macromolecules. Parameterization of such models is often via "bottom-up" methods, which preserve chemical specificity but suffer from artificially accelerated dynamics with respect to the AA model from which they were derived. Here, we study the combination of a bottom-up CG model with a dissipative potential as a means to obtain a chemically specific and dynamically correct model. We generate the conservative part of the force-field using the iterative Boltzmann inversion (IBI) method, which seeks to recover the AA structure. This is augmented with the dissipative Langevin thermostat, which introduces a single parameterizable friction factor to correct the unphysically fast dynamics of the IBI-generated force-field. We study this approach for linear polystyrene oligomer melts for three separate systems with 11, 21, and 41 monomers per chain and a mapping of one monomer per CG site. To parameterize the friction factor, target values are extracted from the AA dynamics using translational monomer diffusion, translational chain diffusion, and rotational chain motion to test the consistency of the parameterization across different modes of motion. We find that the value of the friction parameter needed to bring the CG dynamics in line with AA target values varies based on the mode of parameterization with short-time monomer translational dynamics requiring the highest values, long-time chain translational dynamics requiring the lowest values, and rotational dynamics falling in between. The friction ranges most widely for the shortest chains, and the span narrows with increasing chain length. For longer chains, a practical working value of the friction parameter may be derived from the rotational dynamics, owing to the contribution of multiple relaxation modes to chain rotation and a lack of sensitivity of the translational dynamics at these intermediate levels of friction. A study of equilibrium chain structure reveals that all chains studied are non-Gaussian. However, longer chains better approximate ideal chain dimensions than more rod-like shorter chains and thus are most closely described by a single friction parameter. We also find that the separability of the conservative and dissipative potentials is preserved.

Development of Coarse-Grained Models for Poly(4-vinylphenol) and Poly(2-vinylpyridine): Polymer Chemistries with Hydrogen Bonding

In this paper, we identify the modifications needed in a recently developed generic coarse-grained (CG) model that captured directional interactions in polymers to specifically represent two exemplary hydrogen bonding polymer chemistries-poly(4-vinylphenol) and poly(2-vinylpyridine). We use atomistically observed monomer-level structures (e.g., bond, angle and torsion distribution) and chain structures (e.g., end-to-end distance distribution and persistence length) of poly(4-vinylphenol) and poly(2-vinylpyridine) in an explicitly represented good solvent (tetrahydrofuran) to identify the appropriate modifications in the generic CG model in implicit solvent. For both chemistries, the modified CG model is developed based on atomistic simulations of a single 24-mer chain. This modified CG model is then used to simulate longer (36-mer) and shorter (18-mer and 12-mer) chain lengths and compared against the corresponding atomistic simulation results. We find that with one to two simple modifications (e.g., incorporating intra-chain attraction, torsional constraint) to the generic CG model, we are able to reproduce atomistically observed bond, angle and torsion distributions, persistence length, and end-to-end distance distribution for chain lengths ranging from 12 to 36 monomers. We also show that this modified CG model, meant to reproduce atomistic structure, does not reproduce atomistically observed chain relaxation and hydrogen bond dynamics, as expected. Simulations with the modified CG model have significantly faster chain relaxation than atomistic simulations and slower decorrelation of formed hydrogen bonds than in atomistic simulations, with no apparent dependence on chain length.

Quantitative Synaptic Biology: A Perspective on Techniques, Numbers and Expectations

Synapses play a central role for the processing of information in the brain and have been analyzed in countless biochemical, electrophysiological, imaging, and computational studies. The functionality and plasticity of synapses are nevertheless still difficult to predict, and conflicting hypotheses have been proposed for many synaptic processes. In this review, we argue that the cause of these problems is a lack of understanding of the spatiotemporal dynamics of key synaptic components. Fortunately, a number of emerging imaging approaches, going beyond super-resolution, should be able to provide required protein positions in space at different points in time. Mathematical models can then integrate the resulting information to allow the prediction of the spatiotemporal dynamics. We argue that these models, to deal with the complexity of synaptic processes, need to be designed in a sufficiently abstract way. Taken together, we suggest that a well-designed combination of imaging and modelling approaches will result in a far more complete understanding of synaptic function than currently possible.

Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.

Dynamical self-consistent field theory captures multi-scale physics during spinodal decomposition in a symmetric binary homopolymer blend

We study the spinodal decomposition in a symmetric, binary homopolymer blend using our recently developed dynamical self-consistent field theory. By taking the extremal solution of a dynamical functional integral, the theory reduces the interacting, multi-chain dynamics to a Smoluchowski equation describing the statistical dynamics of a single, unentangled chain in a self-consistent, time-dependent, mean force-field. We numerically solve this equation by evaluating averages over a large ensemble of replica chains, each one of which obeys single-chain Langevin dynamics, subject to the mean field. Following a quench from the disordered state, an early time spinodal instability in the blend composition develops, before even one Rouse time elapses. The dominant, unstable, growing wavelength is on the order of the coil size. The blend then enters a late-time, t, scaling regime with a growing domain size that follows the expected Lifshitz-Slyozov-Wagner t^1/3 power law, a characteristic of a diffusion-driven coarsening process. These results provide a satisfying test of this new method, which correctly captures both the early and late time physics in the blend. Our simulation spans five orders-of-magnitude in time as the domains coarsen to 20 times the coil size, while remaining faithful to the dynamics of the microscopic chain model.

Performance of Coarse Graining in Estimating Polymer Properties: Comparison with the Atomistic Model

Combining atomistic and coarse-grained (CG) models is a promising approach for quantitative prediction of polymer properties. However, the gaps between the length and time scales of atomistic and CG models still need to be bridged. Here, the scale gaps of the atomistic model of polyethylene melts, the bead–spring Kremer–Grest model, and dissipative particle dynamics with the slip-spring model were investigated. A single set of spatial and temporal scaling factors was determined between the atomistic model and each CG model. The results of the CG models were rescaled using the set of scaling factors and compared with those of the atomistic model. For each polymer property, a threshold value indicating the onset of static or dynamic universality of polymers was obtained. The scaling factors also revealed the computational efficiency of each CG model with respect to the atomistic model. The performance of the CG models of polymers was systematically evaluated in terms of both the accuracy and computational efficiency.

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

Recent Advances in Coarse-Grained Models for Biomolecules and Their Applications

Molecular dynamics simulations have emerged as a powerful tool to study biological systems at varied length and timescales. The conventional all-atom molecular dynamics simulations are being used by the wider scientific community in routine to capture the conformational dynamics and local motions. In addition, recent developments in coarse-grained models have opened the way to study the macromolecular complexes for time scales up to milliseconds. In this review, we have discussed the principle, applicability and recent development in coarse-grained models for biological systems. The potential of coarse-grained simulation has been reviewed through state-of-the-art examples of protein folding and structure prediction, self-assembly of complexes, membrane systems and carbohydrates fiber models. The multiscale simulation approaches have also been discussed in the context of their emerging role in unravelling hierarchical level information of biosystems. We conclude this review with the future scope of coarse-grained simulations as a constantly evolving tool to capture the dynamics of biosystems.