Coarse-grained Implicit Solvent Research Articles

Influence of the Dielectric Constant on the Ionic Current Rectification of Bipolar Nanopores.

In this paper, we investigate how the dielectric constant, ϵ, of an electrolyte solvent influences the current rectification characteristics of bipolar nanopores. It is well recognized that bipolar nanopores with two oppositely charged regions rectify current when exposed to an alternating electric potential difference. Here, we consider dilute electrolytes with NaCl only and with a mixture of NaCl and charged nanoparticles. These systems are studied using two levels of description, all-atom explicit water molecular dynamics (MD) simulations and coarse-grained implicit solvent MD simulations. The charge density and electric potential profiles and current-voltage relationship predicted by the implicit solvent simulations with ϵ = 11.3 show good agreement with the predictions from the explicit water simulations. Under nonequilibrium conditions, the predictions of the implicit solvent simulations with a dielectric constant closer to the one of bulk water are significantly different from the predictions obtained with the explicit water model. These findings are closely aligned with experimental data on the dielectric constant of water when confined to nanometric spaces, which suggests that ϵ decreases significantly compared to its value in the bulk. Moreover, the largest electric current rectification is observed in systems containing nanoparticles when ϵ = 78.8. Using enhanced sampling, we have shown that this larger rectification arises from the presence of a significantly deeper minimum in the free energy of the system with a larger ϵ, and when a negative voltage bias is applied. Since implicit solvent models and mean-field continuum theories are often used to design Janus membranes based on bipolar nanopores, this work highlights the importance of properly accounting for the effects of confinement on the dielectric constant of the electrolyte solvent. The results presented here indicate that the dielectric constant in implicit solvent simulations may be used as an adjustable parameter to approximately account for the effects of nanometric confinement on aqueous electrolyte solvents.

Investigating lipid bilayer self-assembly and formation of ripple phase: Insights from a coarse-grained implicit solvent model

In this study, we present a comprehensive exploration of the formation of different phases in lipid molecules using a coarse-grained implicit solvent model, where each lipid molecule is presented as a rigid, three-bead, rod-like structure. Our study not only successfully replicates the spontaneous self-assembly of lipid bilayers but also elucidates the intricate phase transitions between the gel phase, the liquid phase, and the elusive ripple phase (Pβ). Specifically, we uncover the pivotal role of molecular rigidity in promoting the formation of the ripple phase. The significance of our findings lies in their potential to reshape our understanding of lipid bilayer dynamics and phase transitions. By shedding light on the ripple phase, a phase previously difficult to simulate convincingly, the insights gained from this study have the potential to guide future investigations into the behavior of biological membranes and their role in cellular processes.

Single-chain and condensed-state behavior of hnRNPA1 from molecular simulations.

Intrinsically disordered proteins (IDPs) are essential components for the formation of membraneless organelles, which play key functional and regulatory roles within biological systems. These complex assemblies form and dissolve spontaneously over time via liquid-liquid phase separation of IDPs. Mutations in their amino acid sequence can alter their phase behavior, which has been linked to the emergence of severe diseases. We study the conformation and phase behavior of a low-complexity domain of heterogeneous nuclear ribonucleoprotein A1 (hnRNPA1), using coarse-grained implicit solvent molecular dynamics simulations. We systematically analyze how these properties are affected by the number of aromatic residues within the examined sequences. We find a significant compaction of the chains and an increase in the critical temperature with increasing number of aromatic residues. The local persistence length is determined in single-chain simulations, revealing strong sequence-specific variations along the chain contour. Comparing single-chain and condensed state simulations, we find much more collapsed polymer conformations in the dilute systems, even at temperatures near the estimated theta temperature of the solution. These observations strongly support the hypothesis that aromatic residues play a dominant role for condensation, which is further corroborated by a detailed analysis of the intermolecular contacts, and conversely that important properties of condensates are captured in coarse-grained simulations. Interestingly, we observe density inhomogeneities within the condensates near criticality, which are driven by electrostatic interactions. Finally, we find that the relatively small fraction of hydrophobic residues in the IDPs results in interfacial tensions which are significantly lower compared to typical combinations of immiscible simple liquids.

Single-chain and condensed-state behavior of hnRNPA1 from molecular simulations.

Intrinsically disordered proteins (IDPs) are essential components for the formation of membraneless organelles, which play key functional and regulatory roles within biological systems. These complex assemblies form and dissolve spontaneously over time via liquid-liquid phase separation of IDPs. Mutations in their amino acid sequence can alter their phase behavior, which has been linked to the emergence of severe diseases. We study the conformation and phase behavior of a low-complexity domain of heterogeneous nuclear ribonucleoprotein A1 (hnRNPA1) using coarse-grained implicit solvent molecular dynamics simulations. We systematically analyze how these properties are affected by the number of aromatic residues within the examined sequences. We find a significant compaction of the chains and an increase in the critical temperature with an increasing number of aromatic residues. The local persistence length is determined in single-chain simulations, revealing strong sequence-specific variations along the chain contour. Comparing single-chain and condensed-state simulations, we find many more collapsed polymer conformations in the dilute systems, even at temperatures near the estimated θ-temperature of the solution. These observations strongly support the hypothesis that aromatic residues play a dominant role in condensation, which is further corroborated by a detailed analysis of the intermolecular contacts, and conversely that important properties of condensates are captured in coarse-grained simulations. Interestingly, we observe density inhomogeneities within the condensates near criticality, which are driven by electrostatic interactions. Finally, we find that the relatively small fraction of hydrophobic residues in the IDPs results in interfacial tensions, which are significantly lower compared to typical combinations of immiscible simple liquids.

Cross-correlation corrected friction in generalized Langevin models: Application to the continuous Asakura-Oosawa model.

The development of dynamically consistent coarse-grained models for molecular simulations is often based on generalized Langevin equations, motivated by the application of the projection operator formalism (Mori-Zwanzig theory). While Mori's projection operator yields linear generalized Langevin equations that can be computationally efficiently implemented in numerical simulations, the downside is that Mori's generalized Langevin equation does not encompass the multi-body potential of mean force required to correctly encode structural and thermodynamic properties in coarse-grained many-body systems. Zwanzig's projection operator yields nonlinear generalized Langevin equations including the multi-body potential of mean force, while the remaining force contributions are not as cheap to implement in molecular simulation without making it formally hard to justify approximations. For many-particle coarse-grained models, due to computational and conceptual simplicity, an often used approach is to combine nonlinear conservative interactions with linear expressions to model dissipation. In a previous study [V. Klippenstein and N. F. A. van der Vegt, J. Chem. Phys. 154, 191102 (2021)], we proposed a method to parameterize such models to achieve dynamic consistency in coarse-grained models, allowing us to reconcile Mori's and Zwanzig's approach for practical purposes. In the current study, by applying the same strategy, we develop coarse-grained implicit solvent models for the continuous Asakura-Oosawa model, which under certain conditions allows us to develop very accurate coarse-grained potentials. By developing coarse-grained models for different reference systems with varying parameters, we test the broader applicability of the proposed procedure and demonstrate the relevance of accurate coarse-grained potentials in bottom-up derived dissipative models. We study how different system parameters affect the dynamic representability of the coarse-grained models. In particular, we find that the quality of the coarse-grained potential is crucial to correctly model the backscattering effect due to collisions on the coarse-grained scale. As hydrodynamic interactions are not explicitly modeled in the presented coarse-graining approach, deviations are observed in the long-time dynamics. The Asakura-Oosawa model allows for the tuning of system parameters to gain an improved understanding of this limitation. We also propose three new iterative optimization schemes to fine-tune the generalized Langevin thermostat to exactly match the reference velocity-autocorrelation function.

Diverse Aggregation Kinetics Predicted by a Coarse-Grained Peptide Model.

Protein and peptide aggregation is a ubiquitous phenomenon with implications in medicine, pharmaceutical industry, and materials science. An important issue in peptide aggregation is the molecular mechanism of aggregate nucleation and growth. In many experimental studies, sigmoidal kinetics curves show a clear lag phase ascribed to nucleation; however, experimental studies also show downhill kinetics curves, where the monomers decay continuously and no lag phase can be seen. In this work, we study peptide aggregation kinetics using a coarse-grained implicit solvent model introduced in our previous work. Our simulations explore the hypothesis that the interplay between interchain attraction and intrachain bending stiffness controls the aggregation kinetics and transient aggregate morphologies. Indeed, our model reproduces the aggregation modes seen in experiment: no observed aggregation, nucleated aggregation, and rapid downhill aggregation. We find that the interaction strength is the primary parameter determining the aggregation mode, whereas the stiffness is a secondary parameter modulating the transient morphologies and aggregation rates: more attractive and stiff chains aggregate more rapidly and the transient morphologies are more ordered. We also explore the effects of the initial monomer concentration and the chain length. As the concentration decreases, the aggregation mode shifts from downhill to nucleated and no-aggregation. This concentration effect is in line with an experimental observation that the transition between downhill and nucleated kinetics is concentration-dependent. We find that longer peptides can aggregate at conditions where short peptides do not aggregate at all. It supports an experimental observation that the elongation of a homopeptide, e.g., polyglutamine, can increase the aggregation propensity.

Binding, unbinding and aggregation of crescent-shaped nanoparticles on nanoscale tubular membranes.

Using molecular dynamics simulations of a coarse-grained implicit solvent model, we investigate the binding of crescent-shaped nanoparticles (NPs) on tubular lipid membranes. The NPs adhere to the membrane through their concave side. We found that the binding/unbinding transition is first-order, with the threshold binding energy being higher than the unbinding threshold, and the energy barrier between the bound and unbound states at the transition that increases with increasing the NP's arclength Lnp or curvature mismatch μ = Rc/Rnp, where Rc and Rnp are the radii of curvature of the tubular membrane and the NP, respectively. Furthermore, we found that the threshold binding energy increases with increasing either Lnp or μ. NPs with curvature larger than that of the tubule (μ > 1) lie perpendicularly to the tubule's axis. However, for μ smaller than a specific arclength-dependent mismatch μ*, the NPs are tilted with respect to the tubule's axis, with the tilt angle that increases with decreasing μ. We also investigated the self-assembly of the NPs on the tubule at relatively weak adhesion strength and found that for μ > 1 and high values of Lnp, the NPs self-assemble into linear chains, and lie side-by-side. For μ < μ* and high Lnp, the NPs also self-assemble into chains, while being tilted with respect to the tubule's axis.

Coarse-grained implicit solvent lipid force field with a compatible resolution to the Cα protein representation.

Biological membranes have been prominent targets for coarse-grained (CG) molecular dynamics simulations. While minimal CG lipid models with three beads per lipid and quantitative CG lipid models with >10 beads per lipid have been well studied, in between them, CG lipid models with a compatible resolution to residue-level CG protein models are much less developed. Here, we extended a previously developed three-bead lipid model into a five-bead model and parameterized it for two phospholipids, POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine). The developed model, iSoLF, reproduced the area per lipid, hydrophobic thickness, and phase behaviors of the target phospholipid bilayer membranes at the physiological temperature. The model POPC and DPPC membranes were in liquid and gel phases, respectively, in accordance with experiments. We further examined the spontaneous formation of a membrane bilayer, the temperature dependence of physical properties, the vesicle dynamics, and the POPC/DPPC two-component membrane dynamics of the CG lipid model, showing some promise. Once combined with standard Cα protein models, the iSoLF model will be a powerful tool to simulate large biological membrane systems made of lipids and proteins.

(Invited) Multiscale Modeling of Formation and Properties of Solid-Electrolyte Interphases in Li-Ion Batteries

In this talk we will discuss recent efforts on multiscale modeling of solid-electrolyte interphase (SEI) and cathode-electrolyte interphases(CEI). The complexity and multiscale phenomena operating at electrode/electrolyte interfaces do not allow to access all necessary length and time scales using a single modeling approach. Combining information from high-level ab initio and DFT calculations, polarizable atomistic molecular dynamics simulations, coarse-grained implicit solvent simulations and continuum level modeling, we focus on understanding the mechanisms of formation of SEI/CEI layers, mechanisms of Li-ion transport, and mechanical and failure properties of SEI during charging/discharging processes.

Discontinuous wrapping transition of spherical nanoparticles by tensionless lipid membranes.

We present a numerical study of the wrapping of spherical nanoparticles by tensionless lipid membranes using molecular dynamics simulations of a coarse-grained implicit solvent model. We found that the degree of wrapping of small nanoparticles increases continuously with the adhesion strength for nanoparticles with diameter less than or about 15 nm. In contrast, the increase in the degree of wrapping becomes discontinuous for larger nanoparticles and exhibits a clear hysteresis when upward and downward annealing scans with respect to adhesion strength are performed. The gap in the degree of wrapping increases with the increase in the diameter of nanoparticles. These results are in qualitative agreement with the mean field prediction that large nanoparticles are either unbound or completely wrapped by tensionless lipid membranes.

Dual-potential approach for coarse-grained implicit solvent models with accurate, internally consistent energetics and predictive transferability.

The dual-potential approach promises coarse-grained (CG) models that accurately reproduce both structural and energetic properties, while simultaneously providing predictive estimates for the temperature-dependence of the effective CG potentials. In this work, we examine the dual-potential approach for implicit solvent CG models that reflect large entropic effects from the eliminated solvent. Specifically, we construct implicit solvent models at various resolutions, R, by retaining a fraction 0.10 ≤ R ≤ 0.95 of the molecules from a simple fluid of Lennard-Jones spheres. We consider the dual-potential approach in both the constant volume and constant pressure ensembles across a relatively wide range of temperatures. We approximate the many-body potential of mean force for the remaining solutes with pair and volume potentials, which we determine via multiscale coarse-graining and self-consistent pressure-matching, respectively. Interestingly, with increasing temperature, the pair potentials appear increasingly attractive, while the volume potentials become increasingly repulsive. The dual-potential approach not only reproduces the atomic energetics but also quite accurately predicts this temperature-dependence. We also derive an exact relationship between the thermodynamic specific heat of an atomic model and the energetic fluctuations that are observable at the CG resolution. With this generalized fluctuation relationship, the approximate CG models quite accurately reproduce the thermodynamic specific heat of the underlying atomic model.

Mechanisms underlying interactions between PAMAM dendron-grafted surfaces with DPPC membranes.

Biofouling is a pervasive problem which demands the creation of smart, antifouling surfaces. Towards this end, we examine the interactions between a dipalmitoylphosphatidylcholine (DPPC) lipid bilayer and a polyamidoamine (PAMAM) dendron-grafted surface. In addition, we investigate the impact of dendron generation on the system behavior. To resolve the multiscale dynamical processes occurring over a large spatial scale, we employ Molecular Dynamics simulations with a coarse-grained implicit solvent force field. Our results demonstrate the transient and equilibrium system dynamics to be determined by the PAMAM dendron generation along with the underlying mechanisms. Higher generation dendrons are observed to favor penetration of the DPPC molecules into the dendron branches, thereby enabling sustained interactions between the membrane and the dendron-grafted surface. Under equilibrium, the membrane adopts a bowl-shaped morphology whose dimensions are determined by the dendron generation and density of interactions. The results from our study can be used to guide the design of novel surfaces with selective antifouling properties which can prevent the adsorption of microorganisms onto lipid membranes.

Static polarizability effects on counterion distributions near charged dielectric surfaces: A coarse-grained Molecular Dynamics study employing the Drude model

Coarse-grained implicit solvent Molecular Dynamics (MD) simulations have been used to investigate the structure of the vicinal layer of polarizable counterions close to a charged interface. The classical Drude oscillator model was implemented to describe the static excess polarizability of the ions. The electrostatic layer correction with image charges (ELCIC) method was used to include the effects of the dielectric discontinuity between the aqueous solution and the bounding interfaces for the calculation of the electrostatic interactions. Cases with one or two charged bounding interfaces were investigated. The counterion density profile in the vicinity of the interfaces with different surface charge values was found to depend on the ionic polarizability. Ionic polarization effects are found to be relevant for ions with high excess polarizability near surfaces with high surface charge.

A Coarse-Grained Implicit Solvent Model for Poly(ethylene oxide), CnEm Surfactants, and Hydrophobically End-Capped Poly(ethylene oxide) and Its Application to Micelle Self-Assembly and Phase Behavior

We parametrize a molecular dynamics force field for poly(ethylene oxide) (PEO) within the Dry Martini coarse-grained (CG) implicit solvent model and show that it yields similar distributions of bond lengths, angles and torsional angles, and a similar dependence of radius of gyration on PEO chain length as those obtained from atomistic and explicit-solvent CG simulations. We apply these new parameters to simulate self-assembly of long-chain single-end-capped CnEm surfactants and double-end-capped telechelic polymers CnEmCn, where n is the number of alkane carbons and m the number of ethylene oxide monomers. We determine that the average equilibrium micelle aggregation number at high concentrations is around 23 hydrophobes for C12E100, C12E100C12, and C12E200C12, consistent with experimental/theoretical results. However, for EO block less than 200 monomers at 300 K, for example, for C12E45C12 and C12E136C12, telechelic polymers phase separate to form a polymer dense phase at low concentrations due to the fo...

Structures and Thermodynamics of Alzheimer’s Amyloid-β Aβ(16−35) Monomer and Dimer by Replica Exchange Molecular Dynamics Simulations: Implication for Full-Length Aβ Fibrillation

Many proteins display a strand-loop-strand motif in their amyloid fibrillar states. For instance, the amyloid beta-protein, Abeta1-40, associated with Alzheimer's disease, displays a loop at positions 22-28 in its amyloid fibril state. It has been suggested that this loop could appear early in the aggregation process, but quantitative information regarding its presence in small oligomers remains scant. Because residues 1-15 are disordered in Abeta1-42 fibrils and Abeta10-35 forms fibrils in vitro, we select the peptide Abeta16-35, centered on residues 22-28 and determine the structures and thermodynamics of the monomer and dimer using coarse-grained implicit solvent replica exchange molecular dynamics simulations. Our simulations totalling 5 mus for the monomer and 12 micros for the dimer show no sign of strong secondary structure signals in both instances and the significant impact of dimerization on the global structure of Abeta16-35. They reveal however that the loop 22-28 acts as a quasi-independent unit in both species. The loop structure ensemble we report in Abeta16-35 monomer and dimer has high similarity to the loop formed by the Abeta21-30 peptide in solution and, to a lesser extent, to the loop found in Abeta1-40 fibrils. We discuss the implications of our findings on the assembly of full-length Abeta.

Replica Exchange Molecular Dynamics Simulations of Coarse-grained Proteins in Implicit Solvent

Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.

Supramolecular Self-Organization in PEO-Modified C60 Fullerene/Water Solutions: Influence of Polymer Molecular Weight and Nanoparticle Concentration

Utilizing a first-principles-based coarse-grained implicit solvent model, we have investigated the self-association of C(60) fullerenes that have been symmetrically modified with six grafted poly(ethylene oxide) (PEO) chains in aqueous solution. Despite the highly symmetric nature of the pair interactions between PEO-grafted fullerenes, their supramolecular assemblies are highly anisotropic and resemble the linear clusters formed in Stockmayer fluids. The dipole-like interaction between these symmetrically modified fullerenes results from the shielding of the C(60) fullerenes by PEO, favoring the addition of more PEO-grafted fullerenes to the linear clusters at the relatively unprotected ends. At low nanoparticle concentrations, self-association is dominated by the formation of stable dimers and trimers resulting from fullerene-fullerene contact and favorable PEO-fullerene interactions. With increasing nanoparticle concentration, larger clusters become increasingly probable. The molecular weight of the PEO tethers can be treated as a temperature-like analogue, with a reduction in average cluster size with increasing chain length due to increased steric repulsion, which is qualitatively similar to effects observed in Stockmayer fluids with increasing temperature. The role of PEO in supramolecular self-organization in PEO-modified C(60) fullerene/water solutions is complex, contributing not only to steric stabilization but also to favorable energetic interactions, nanoparticle shielding, and depletion-driven aggregation.

Molecular Dynamics Simulation Study of the Influence of Cluster Geometry on Formation of C60 Fullerene Clusters in Aqueous Solution

We have performed atomistic molecular dynamics simulations of linear (1-dimensional), planar (2-dimensional), and icosahedral (3-dimensional) clusters of C60 fullerenes in aqueous solution in order to investigate the influence of cluster geometry on their free energy of formation. As was found in our previous study of the potential of mean force (PMF) as a function of separation for a single pair of fullerenes in aqueous solution, the interaction between fullerenes for all cluster geometries was dominated by direct fullerene-fullerene interactions and not by water-induced hydrophobic interactions. A coarse-grained implicit solvent (CGIS) potential, given by the PMF for the fullerene pair in water obtained from atomistic simulations, was found to describe well the free energy of formation of the linear cluster, indicating that many-body effects, i.e., the influence of neighboring fullerenes on the water-induced interaction between a fullerene pair, are negligible for the 1-dimensional geometry. For the 2-dimensional and particularly the 3-dimensional geometry, however, many-body effects were found to strongly influence hydration, leading to complete dehydration of the central fullerene at close fullerene-fullerene separations for the icosahedral cluster. This strong influence of geometry on hydration translates into water-induced interactions that, while remaining repulsive, as is found for the fullerene pair, are not well described by the two-body CGIS potential obtained from the isolated fullerene pair, particularly for the 3-dimensional geometry.

Multiscale Modeling of Poly(ethylene oxide)-Poly(propylene oxide)-Poly(ethylene oxide) Triblock Copolymer Micelles in Aqueous Solution.

We present a multiscale modeling approach for simulation of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer micelles in aqueous solution. We rely on systematic elimination of computationally expensive degrees of freedom yet retain implicitly their influence on the remaining degrees freedom in a coarser-grained model. Quantum chemistry (QC) calculations, atomistic explicit solvent (AES) molecular dynamics (MD) simulations, and coarse-grained implicit solvent (CGIS) simulations have been applied to investigate physical properties of these important self-assembling triblock copolymers. High-level QC calculations have been used to parametrize classical atomistic force fields that implicitly take into account and reproduce the important energetic and structural features due to correlations of electronic degrees of freedom. AES MD simulations utilizing the QC-based force fields have been used to provide structural and conformational properties of polymers in aqueous solution which were subsequently used for parametrization of the CGIS model using the Inverted Boltzmann method. The CGIS simulations were then employed to investigate structural properties of two PEO-PPO-PEO micelles (EO13-PO30-EO13 and EO99-PO65-EO99 also known as Pluronic L64 and F127, respectively) in aqueous solution.