CGBack: Diffusion Model for Backmapping Large-Scale and Complex Coarse-Grained Molecular Systems.

Transferability of a coarse-grained atactic polystyrene model: Thermodynamics and structure

<p>The use of computational simulation to study the dynamics and interactions of macromolecules has become an important tool in the field of biochemistry. A common method to perform these simulations is to use all-atom explicit-solvent molecular dynamics (MD). However, due to the limitations in computational power currently available, this method is not practical for simulating large-scale biomolecular systems on long timescales. An alternative is to perform implicit-solvent Brownian dynamics (BD) simulations using a coarse grained (CG) model that allows for increased computational efficiency. However, if simulations using the CG model are not realistic, then the gain in computational efficiency from using a CG model is not worthwhile.</p> <p>This thesis describes the derivation of a set of bonded and nonbonded CG potential functions for use in implicit-solvent BD simulations of proteins derived from all-atom explicit-solvent MD simulations of amino acids. To determine which force field and water model to use in the MD simulations, Chapter II describes 1 Μs all-atom explicit-solvent MD simulations of glycine, asparagine, phenylalanine, and valine solutions at 50, 100, 200 and 300 mg/ml concentrations performed using eight different force field and water model combinations. To evaluate the accuracy of the force fields at high solute concentrations, the density, viscosity, and dielectric increments of the four amino acids were calculated from the simulations and compared to experimental results. Additionally, the change in the strength of hydrophobic and electrostatic interactions with increasing solute concentration was calculated for each force field and water model combination. As a result of this study, the Amber ff99SB-ILDN force field and TIP4P-Ew explicit-solvent water model were chosen for all subsequent MD simulations. Chapter III describes the derivation of CG bonded potential functions from 1 Μs all-atom explicit-solvent MD simulations of each of the twenty amino acids, including a separate simulation for protonated histidine. The angle and dihedral probability distributions sampled during the MD simulations were used to optimize the bonded potential functions using the iterative Boltzmann inversion (IBI) method. Chapter IV describes the derivation of CG nonbonded potential functions from 1 Μs all-atom explicit-solvent MD simulations of every possible pairing of the amino acids (231 different systems). The radial distribution functions calculated from these MD simulations were used to optimize a set of nonbonded CG potential functions using the IBI method. The optimized set of bonded and nonbonded potential functions, which is termed COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins), quantitatively reproduced all of the calculated MD distributions. To determine if COFFDROP would be useful for simulations of bimolecular systems, Chapter V describes the testing of the transferability of the force field. First, COFFDROP was used to simulate concentrated amino acid solutions. The clustering of the solutes in these simulations was directly compared with results from corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. Next, BD simulations of 9.2 mM solutions of the small protein villin headpiece were performed. The proteins aggregated during these simulations, which is in agreement with results from MD simulation but in disagreement with experiment. After scaling the strength of COFFDROP's nonbonded potential functions by a factor of 0.8 and rerunning the BD simulations, the amount of aggregation was comparable to experimental observations. Based on these results, COFFDROP is likely to be applicable in CG BD simulations of large, highly concentrated, biomolecular systems.</p>

We recently developed a dynamic force matching technique for converting a coarse-grained (CG) model of a molecular system, with a CG potential energy function, into a dynamic CG model with realistic dynamics [A. Davtyan et al., J. Chem. Phys. 142, 154104 (2015)]. This is done by supplementing the model with additional degrees of freedom, called "fictitious particles." In that paper, we tested the method on CG models in which each molecule is coarse-grained into one CG point particle, with very satisfactory results. When the method was applied to a CG model of methanol that has two CG point particles per molecule, the results were encouraging but clearly required improvement. In this paper, we introduce a new type (called type-3) of fictitious particle that exerts forces on the center of mass of two CG sites. A CG model constructed using type-3 fictitious particles (as well as type-2 particles previously used) gives a much more satisfactory dynamic model for liquid methanol. In particular, we were able to construct a CG model that has the same self-diffusion coefficient and the same rotational relaxation time as an all-atom model of liquid methanol. Type-3 particles and generalizations of it are likely to be useful in converting more complicated CG models into dynamic CG models.

Coarse-grained (CG) models of biomolecules have been widely used in protein/ribonucleic acid (RNA) three-dimensional structure prediction, docking, drug design, and molecular simulations due to their superiority in computational efficiency. Most of these applications strongly depend on the reasonable estimation of solvation free energy, which requires the accurate calculation of solvent accessible surface area (SASA). Although algorithms for SASA calculations with all-atom protein and RNA structures have been well-established, accurately estimating the SASA based on CG structures is extremely challenging. In this work, we developed a deep learning-based SASA estimator (DeepCGSA), which can provide almost perfect SASA estimation based on CG structures of protein and RNA molecules. Extensive testing analysis showed that for three types of widely used CG protein models, including the Cα-based, Cα-Cβ, and Martini models, the correlation coefficients between the predicted values and the reference values can be as high as 0.95-0.99, which perform dramatically better than available methods. In addition, the new method can be used for CG RNA structures and unfolded protein structures with much improved accuracy. We anticipate that DeepCGSA will be highly useful in the protein/RNA structure prediction, drug design, and other applications, in which accurate estimations of SASA for CG biomolecular structures are critically important.

The coarse grained (CG) model implements the molecular dynamics simulation by simplifying atom properties and interaction between them. Despite losing certain detailed information, the CG model is still the first-thought option to study the large molecule in long time scale with less computing resource. The deep learning model mainly mimics the human studying process to handle the network input as the image to achieve a good classification and regression result. In this work, the TorchMD, a MD framework combining the CG model and deep learning model, is applied to study the protein folding process. In 3D collective variable (CV) space, the modified find density peaks algorithm is applied to cluster the conformations from the TorchMD CG simulation. The center conformation in different states is searched. And the boundary conformations between clusters are assigned. The string algorithm is applied to study the path between two states, which are compared with the end conformations from all atoms simulations. The result shows that the main phenomenon of protein folding with TorchMD CG model is the same as the all-atom simulations, but with a less simulating time scale. The workflow in this work provides another option to study the protein folding and other relative processes with the deep learning CG model.

Molecular simulations provide a versatile tool to study the structure, anion conductivity, and stability of anion-exchange membrane (AEM) materials and can provide a fundamental understanding of the relation between structure and property of membranes that is key for their use in fuel cells and other applications. The quest for large spatial and temporal scales required to model the multiscale structure and transport processes in the polymer electrolyte membranes, however, cannot be met with fully atomistic models, and the available coarse-grained (CG) models suffer from several challenges associated with their low-resolution. Here, we develop a high-resolution CG force field for hydrated polyphenylene oxide/trimethylamine chloride (PPO/TMACl) membranes compatible with the mW water model using a hierarchical parametrization approach based on Uncertainty Quantification and reference atomistic simulations modeled with the Generalized Amber Force Field (GAFF) and TIP4P/2005 water. The parametrization weighs multiple properties, including coordination numbers, radial distribution functions (RDFs), self-diffusion coefficients of water and ions, relative vapor pressure of water in the solution, hydration enthalpy of the tetramethylammonium chloride (TMACl) salt, and cohesive energy of its aqueous solutions. We analyze the interdependence between properties and address how to compromise between the accuracies of the properties to achieve an overall best representability. Our optimized CG model FFcomp quantitatively reproduces the diffusivities and RDFs of the reference atomistic model and qualitatively reproduces the experimental relative vapor pressure of water in solutions of tetramethylammonium chloride. These properties are of utmost relevance for the design and operation of fuel cell membranes. To our knowledge, this is the first CG model that includes explicitly each water and ion and accounts for hydrophobic, ionic, and intramolecular interactions explicitly parametrized to reproduce multiple properties of interest for hydrated polyelectrolyte membranes. The CG model of hydrated PPO/TMACl water is about 100 times faster than the reference atomistic GAFF-TIP4P/2005 model. The strategy implemented here can be used in the parametrization of CG models for other substances, such as biomolecular systems and membranes for desalination, water purification, and redox flow batteries. We anticipate that the large spatial and temporal simulations made possible by the CG model will advance the quest for anion-exchange membranes with improved transport and mechanical properties.

We present a systematic derivation of a coarse grained (CG) model for molecular dynamics (MD) simulations of a liquid crystalline (LC) compound containing an azobenzene mesogen. The model aims at a later use in a multiscale modeling approach to study liquid crystalline phase transitions that are (photo)induced by the trans/cis photoisomerization of the mesogen. One of the major challenges in the coarse graining process is the development of models that are for a given chemical system structurally consistent with for example an all-atom reference model and reproduce relevant thermodynamic properties such as the LC phase behavior around the state point of interest. The reduction of number of degrees of freedom makes the resulting coarse models by construction state point dependent; that is, they cannot easily be transferred to a range of temperatures, densities, system compositions, etc. These are significant challenges, in particular if one wants to study LC phase transitions (thermally or photoinduced). In the present paper we show how one can systematically derive a CG model for a LC molecule that is highly consistent with an atomistic description by choosing an appropriate state point for the reference simulation. The reference state point is the supercooled liquid just below the smectic-isotropic phase transition which is characterized by a high degree of local nematic order while being overall isotropic. With the resulting CG model it is possible to switch between the atomistic and the CG levels (and vice versa) in a seamless manner maintaining values of all the relevant order parameters which describe the smectic A (smA) state. This model will allow us in the future to link large length scale and long time scale CG simulations of the LC state with chemically accurate QM/MM simulations of the photoisomerization process.

In this thesis we address the problem of data-driven coarse-graining, i.e. the process of inferring simplified models, which describe the evolution of the essential characteristics of a complex system, from available data (e.g. experimental observation or simulation data). Specifically, we consider the case where the coarse-grained model can be formulated as a stochastic differential equation. The main part of this work is concerned with data-driven coarse-graining when the underlying complex system is characterised by processes occurring across two widely separated time scales. It is known that in this setting commonly used statistical techniques fail to obtain reasonable estimators for parameters in the coarse-grained model, due to the multiscale structure of the data. To enable reliable data-driven coarse-graining techniques for diffusion processes with multiple time scales, we develop a novel estimation procedure which decisively relies on combining techniques from mathematical statistics and numerical analysis. We demonstrate, both rigorously and by means of extensive simulations, that this methodology yields accurate approximations of coarse-grained SDE models. In the final part of this work, we then discuss a systematic framework to analyse and predict complex systems using observations. Specifically, we use data-driven techniques to identify simple, yet adequate, coarse-grained models, which in turn allow to study statistical properties that cannot be investigated directly from the time series. The value of this generic framework is exemplified through two seemingly unrelated data sets of real world phenomena.

Advances in nanotechnology lead to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators with ultra-high resonant frequencies. The ultra-high-frequency resonators have recently received significant attention for wide-ranging applications such as molecular separation, molecular transportation, ultra-high sensitive sensing, high-frequency signal processing, and biological imaging. It is well known that for micrometer length scale, first-principles technique, the most accurate approach, poses serious limitations for comparisons with experimental studies. For such larger size, classical molecular dynamics (MD) simulations are desirable, which require interatomic potentials. Additionally, a mesoscale method such as the coarse-grained (CG) method is another useful method to support simulations for even larger system sizes. Furthermore, quasi-two-dimensional (Q2D) materials have attracted intensive research interest due to their many novel properties over the past decades. However, the energy dissipation mechanisms of nanomechanical resonators based on several Q2D materials are still unknown. In this work, the addressed main issues include the development of the CG models for molybdenum disulphide (MoS2), investigation of the mechanism effects on black phosphorus (BP) nanoresonators and the application of graphene nanoresonators. The primary coverage and results of the dissertation are as follows: Method development. Firstly, a two-dimensional (2D) CG model for single layer MoS2 (SLMoS2) is analytically developed. The Stillinger-Weber (SW) potential for this 2D CG model is further parametrized, in which all SW geometrical parameters are determined analytically according to the equilibrium condition for each individual potential term, while the SW energy parameters are derived analytically based on the valence force field model. Next, the 2D CG model is further simplified to one-dimensional (1D) CG model, which describes the 2D SLMoS2 structure using a 1D chain model. This 1D CG model is applied to investigate the relaxed configuration and the resonant oscillation of the folded SLMoS2. Owning to the simplicity nature of the 1D CG model, the relaxed configuration of the folded SLMoS2 is determined analytically, and the resonant oscillation frequency is derived analytically. Considering the increasing interest in studying the properties of other 2D layered materials, and in particular those in the semiconducting transition metal dichalcogenide class like MoS2, the CG models proposed in current work provide valuable simulation approaches. Mechanism understanding. Two energy dissipation mechanisms of BP nanoresonators are focused exclusively, i.e. mechanical strain effects and defect effects (including vacancy and oxidation). Vacancy defect is intrinsic damping factor for the quality (Q)-factor, while mechanical strain and oxidation are extrinsic damping factors. Intrinsic dissipation (induced by thermal vibrations) in BP resonators (BPRs) is firstly investigated. Specifically, classical MD simulations are performed to examine the temperature dependence for the Q-factor of the single layer BPR (SLBPR) along the armchair and zigzag directions, where two-step fitting procedure is used to extract the frequency and Q-factor from the kinetic energy time history. The Q-factors of BPRs are evaluated through comparison with those of graphene and MoS2 nanoresonators. Next, effects of mechanical strain, vacancy and oxidation on BP nanoresonators are investigated in turn. Considering the increasing interest in studying the properties of BP, and in particular the lack of theoretical study for the BPRs, the results in current work provide a useful reference. Application. A novel application for graphene nanoresonators, using them to self-assemble small nanostructures such as water chains, is proposed. All of the underlying physics enabling this phenomenon is elucidated. In particular, by drawing inspiration from macroscale self-assembly using the higher order resonant modes of Chladni plates, classical MD simulations are used to investigate the self-assembly of water molecules using graphene nanoresonators. An analytic formula for the critical resonant frequency based on the interaction between water molecules and graphene is provided. Furthermore, the properties of the water chains assembled by the graphene nanoresonators are studied.

Coarse-grained (CG) models provide a computationally efficient method for rapidly investigating the long time- and length-scale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarse-graining (MS-CG) method [J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for the MS-CG models. A CG model that employs such a PMF as a "potential energy function" will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.

In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

Liposomes are common carriers of drug molecules, providing enhanced delivery and accumulation of hydrophilic agents or larger biomolecules. Molecular simulations can be used to estimate key features of the drug molecules upon interaction with the liposomes, such as penetration barriers and localization. Herein, we investigate several aspects of the computational estimation of penetration barriers, viz. the potential of mean force (PMFs) along a vector spanning the membrane. First, we provide an evaluation of the all-atom (AA) and coarse-grained (CG) parametrization of 5-aminolevulinic acid (5-ALA) and two of its alkyl esters by computing n-octanol/water partition coefficients. We find that the CG parametrization of the esters performs significantly better than the CG model of 5-ALA, highlighting the difficulty to coarse-grain small, polar molecules. However, the expected trend in partition coefficients is reproduced also with the CG models. Second, we compare PMFs in a small membrane slab described with either the AA or CG models. Here, we are able to reproduce the all-atom PMF of 5-ALA with CG. However, for the alkyl esters it is unfortunately not possible to correctly reproduce both the depth and the penetration barrier of the PMF seen in the AA simulations with any of the tested CG models. We argue that it is more important to choose a CG parametrization that reproduces the depth of the PMF. Third, we compare, using the CG model, PMFs in the membrane slab with PMFs in a large, realistic liposome. We find similar depths but slightly different penetration barriers most likely due to differences in the lipid density along the membrane axis. Finally, we compute PMFs in liposomes with three different lipid compositions. Unfortunately, differences in the PMFs could not be quantified, and it remains to be investigated to what extent liposome simulations can fully reproduce experimental findings.

Advanced coarse-grained model for fast simulation of nascent polypeptide chain dynamics within the ribosome.

The Lennard-Jones (LJ) energy functions are commonly used to describe the nonbonded interactions in bulk coarse-grained (CG) models, which contribute significantly to the stabilization of a local binding configuration or a self-assembly system. In many cases, systematic development of the LJ interaction parameters in a CG model requires a comprehensive sampling of the objective molecules at the all-atom (AA) level, which is therefore extremely time-consuming for large systems. Inspired by the concept of electrostatic potential (ESP), we define the LJ static potential (LJSP), by which the embedding potential energy surface can be constructed analytically. A semianalytic approach, namely, the LJSP matching method, is developed here to derive the CG parameters by minimizing the LJSP difference between the AA and the CG models, which provides a universal way to derive the CG LJ parameters from the AA models without doing presampling. The LJSP matching method is successful not only in deriving the LJ interaction energy landscape in the CG models for proteins, lipids, and DNA but also in reproducing the critical properties such as intermediate structures and enthalpy contributions as exemplified in simulating the self-assembly process of the dipalmitoylphosphatidylcholine (DPPC) lipids.

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.