Development of New Transferable Coarse-Grained Models of Hydrocarbons

Effects of charge asymmetry on the liquid-liquid phase separation of polyampholytes and their condensate properties

Liquid-liquid phase separation (LLPS) is the mechanism underlying the formation of bio-molecular condensates which are important compartments regulating intra- and extra-cellular functions. Electrostatic interactions are some of the important driving forces of the LLPS behaviors of biomolecules. However, the understanding of the electrostatic interactions is still limited, especially in the mixtures of biomolecules with different charge patterns. Here, we focus on the electrostatic interactions in mixtures of charge-asymmetric and charge-symmetric polyampholytes and their roles in the phase separation behaviors. We build charge-asymmetric and charge-symmetric model proteins consisting of both glutamic acid (E, negatively charged) and lysine (K, positively charged), i.e. polyampholytes of E35K15 (charge asymmetric) and E25K25 (charge symmetric). Pure E25K25 can undergo LLPS. To investigate the effects of charge-asymmetric polyampholytes on the mixtures of E25K25/E35K15, we perform coarse-grained simulations to determine their phase separation. The charge-asymmetric polyampholyte E35K15 is resistant to the LLPS of the mixtures of E25K25/E35K15. The condensate density decreases with the molar fraction of E35K15 increasing to 0.4, and no LLPS occurs at the molar fraction of 0.5 and above. This can be attributed to the electrostatic repulsion between the negatively charged E35K15 polymers. We further investigate the effects of charge asymmetry on the conformations and properties of the condensates. The E35K15 polymers in the condensates exhibit a more collapsed state as the molar fraction of E35K15 increases. However, the conformation of E25K25 polymers changes slightly across different condensates. The surface tensions of condensates decline with the increase of the molar fraction of E35K15 polymers, while the diffusivity of polymers in the condensed phases is enhanced. This work elucidates the role of charge-asymmetric polyampholytes in determining the LLPS behaviours of binary mixtures of charge-symmetric and charge-asymmetric proteins as well as the properties of condensed phases.

Evaluation of Sampling Algorithms Used for Bayesian Uncertainty Quantification of Molecular Dynamics Force Fields

New Bayesian parameter estimation methods have the capability to enable more physically realistic and reliable molecular dynamics (MD) simulations by providing accurate estimates of uncertainties of force-field (FF) parameters and associated properties. However, the choice of which Bayesian parameter estimation algorithm to use has not been widely investigated, despite its impact on the effective exploration of parameter space. Here, using a case example of the Embedded Atom Method (EAM) FF parameters, we investigated the ramifications of several of the algorithm choices. We found that Ensemble Slice Sampling (ESS) and Affine-Invariant Ensemble Sampling (AIES) demonstrate a new level of superior performance, culminating in more accurate parameter and property estimations with tighter uncertainty bounds, compared to traditional methods such as Metropolis-Hastings (MH), Gradient Search (GS), and Uniform Random Sampler (URS). We demonstrate that Bayesian Uncertainty Quantification with ESS and AIES leads to significantly more accurate and reliable predictions of the FF parameters and properties. The results suggest that ESS and AIES should be used to obtain more accurate parameter and uncertainty estimations while providing deeper physical insights.

Branching in molecular structure enhancement of solubility in CO2

Most compounds of some 1,000 amu molecular weight (MW) and higher are poorly soluble in carbon dioxide (CO2). Only at very high pressure, there may be mild solubility. This limits the use of CO2 as a solvent and modifications of CO2 properties through additives. We have developed a coarse-grained molecular model to investigate the dependency of the solubility of hydrocarbon oligomers (MW of ∼1,000 amu) in CO2 and on the molecular structure. The coarse-grained model is optimized by the particle swarm optimization algorithm to reproduce density, surface tension, and enthalpy of vaporization of a highly branched hydrocarbon oligomer (poly-1-decene with six repeating units). We demonstrate that branching in molecular structure of oligomers significantly increases solubility in CO2. The branching in molecular structure results in up to 270-time enhancement of solubility in CO2 than an n-alkane with the same MW. The number of structural edges (methyl group) is a key in improved CO2-philicity. The solubility of poly-1-decene with nine repeating units (MW of 1,264.4 amu) is higher in CO2 than poly-1-dodecene with six repeating units (MW of 1,011.93 amu) because it has more structural edges (10 vs. 7). These results shed light on the enhancement of CO2-philicity by altering molecular structure rather than modifying chemical composition in compounds.

Structural and thermodynamic properties of bulk triglycerides and triglyceride/water mixtures reproduced using a polarizable coarse-grained model

Triglycerides (TGs) play important roles in renewable energies, food production, medicine, and metabolism in organisms. Here, we developed a novel coarse-grained (CG) force field (FF) for triglycerides to reproduce both the structural and thermodynamic properties of bulk TGs, TG/air interfaces, and TG/water mixtures using molecular dynamics (MD) simulations. We rigorously optimized the bonded and nonbonded force parameters between the CG beads of TGs and nonbonded force parameters between TG beads and polarizable CG water beads by employing an efficient meta-multilinear interpolation parameterization algorithm recently developed by us. This CG FF performs very well in reproducing the percolating network of the TG bulk phase self-assembled in water and a variety of molecular conformations predicted by all-atom MD simulations. More importantly, it also correctly reproduces multiple experimentally measurable macroscopic thermodynamic properties, including the density and surface tensions of both the TG/air and TG/water interfaces. This paves the way for studying more complicated systems involving TGs on a large scale.

A coarse-grained model for capturing the helical behavior of isotactic polypropylene

Understanding the process-property relations of helical polymers using molecular simulations has been an attractive research field over the years. Specifically, isotactic polypropylene still remains a challenge for current computational experimentation, as it exhibits phenomena such as crystallization that emerge on large spatial and temporal scales. Coarse-graining is an efficient technique for approaching such phenomena, although previous coarse-grained models lack in preserving important atomistic and structural details. In this paper we develop a new coarse-grained model, based on the popular MARTINI force field, that is able to reproduce the helical behavior of isotactic polypropylene. To test the model, the predicted statistical and structural properties (characteristic ratio, density, entanglement molecular weight, solubility parameter in the melt) are compared with previous simulation results and available experimental data. For the development of the new coarse-grained force field, a single unperturbed chain Monte Carlo algorithm has been implemented: an efficient algorithm which samples conformations representative of a melt by simulating just a single chain.

Molecular simulation of linear octacosane via a CG10 coarse grain scheme

Following our previous work on the united-atom simulation on octacosane (C₂₈H₅₈) (Dai et al., Phys. Chem. Chem. Phys., 2021, 23, 21262-21271), we developed a coarse grain scheme (CG10), which is able to reproduce the pivotal phase characteristics of octacosane with highly improved computational efficiency. The CG10 octacosane chain was composed of 10 consecutive beads, maintaining the fundamental zigzag chain morphology. When the potential functions were set up and the coefficients were parameterized, our CG10 models yielded solid phase diagrams and transitions during an annealing process. We also detected the melting point by various means: direct observation, bond order, density tracking, and an enthalpy plot. Furthermore, our CG10 successfully reproduced the liquid density with only 2% underestimation, indicating its applicability across the solid and liquid phases. Therefore, with the ability to reproduce critical structure and property characteristics, our CG10 scheme provides an effective means of numerically modelling octacosane with highly improved computational efficiency.

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

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

Development of accurate coarse-grained force fields for weakly polar groups by an indirect parameterization strategy

Coarse-grained (CG) molecular dynamics simulations are widely used to predict morphological structures and interpret mechanisms of mesoscopic behavior between the scope of traditional experiments and all-atom simulations. However, most current CG force fields (FFs) are not precise enough, especially for polar molecules or functional groups. A main obstacle in developing accurate CG FFs for polar molecules is the freezing problem met at room temperature. In this work, we introduce an indirect parametrization strategy for weakly polar groups by considering their short-chain homologs to avoid freezing. Here, a polar group containing three to four heavy atoms is mapped into one CG bead that is connected to one alkyl bead composed of three or four carbons. The CG beads interact via 4-parameter nonbonded Morse potentials and harmonic bonded potentials. An efficient meta-multilinear interpolation parameterization algorithm, as recently developed by us, is used to rigorously optimize the force parameters. Satisfactory accuracy is witnessed in terms of the density, heat of vaporization, surface tension, and solvation free energy of the homologs of twelve polar molecules, all deviating from the experiment by less than 5%. The transferability of the current FF is indicated by the predicted density, heat of vaporization, and end-to-end distance distributions of fatty acid methyl esters composed of multiple functional groups parameterized in this work.

Development of coarse-grained force field for alcohols: an efficient meta-multilinear interpolation parameterization algorithm

Coarse-grained (CG) molecular dynamics are powerful tools to access a mesoscopic phenomenon and simultaneously record microscopic details, but currently the CG force fields (FFs) are still limited by low parameterization efficiency and poor accuracy especially for polar molecules. In this work, we developed a Meta-Multilinear Interpolation Parameterization (Meta-MIP) algorithm to optimize the CG FFs for alcohols. This algorithm significantly boosts parameterization efficiency by constructing on-the-fly local databases to cover the global optimal parameterization path. In specific, an alcohol molecule is mapped to a heterologous model composed of an OH bead and a hydrocarbon portion which consists of alkane beads representing two to four carbon atoms. Non-bonded potentials are described by soft Morse functions that have no tail-corrections but can still retain good continuities at truncation distance. Nearly all of the properties in terms of density, heat of vaporization, surface tension, and solvation free energy for alcohols predicted by the current FFs deviate from experimental values by less than 7%. This Meta-MIP algorithm can be readily applied to force field development for a wide variety of molecules or functional groups, in many situations including but not limited to CG FFs.

Evidence of information limitations in coarse-grained models

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

Is preservation of symmetry necessary for coarse-graining?

This work investigates if preserving the symmetry of the underlying molecular graph of a given molecule when choosing a coarse-grained (CG) mapping significantly affects the CG model accuracy.

Assessing the transferability of common top-down and bottom-up coarse-grained molecular models for molecular mixtures

Assessing the performance of top-down and bottom-up coarse-graining approaches.

Machine-Learning Enabled New Insights into the Coil-to-Globule Transition of Thermosensitive Polymers Using a Coarse-Grained Model

We present a computational framework that integrates coarse-grained (CG) molecular dynamics (MD) simulations and a data-driven machine-learning (ML) method to gain insights into the conformations of polymers in solutions. We employ this framework to study conformational transition of a model thermosensitive polymer, poly( N-isopropylacrylamide) (PNIPAM). Here, we have developed the first of its kind, a temperature-independent CG model of PNIPAM that can accurately predict its experimental lower critical solution temperature (LCST) while retaining the tacticity in the presence of an explicit water model. The CG model was extensively validated by performing CG MD simulations with different initial conformations, varying the radius of gyration of chain, the chain length, and the angle between the adjacent monomers of the initial configuration of PNIPAM (total simulation time = 90 μs). Moreover, for the first time, we utilize the nonmetric multidimensional scaling (NMDS) method, a data-driven ML approach, to gain further insights into the mechanisms and pathways of this coil-to-globule transition by analyzing CG MD simulation trajectories. NMDS analysis provides entirely new insights and shows multiple metastable states of PNIPAM during its coil-to-globule transition above the LCST.