Coarse-grained Free Energy Research Articles

The effect of polymer coating on nanoparticles' interaction with lipid membranes studied by coarse-grained molecular dynamics simulations.

Nanoparticles' (NPs) permeation through cell membranes, whether it happens via passive or active transport, is an essential initial step for their cellular internalization. The NPs' surface coating impacts the way they translocate through the lipid bilayer and the spontaneity of the process. Understanding the molecular details of NPs' interaction with cell membranes allows the design of nanosystems with optimal characteristics for crossing the lipid bilayer: computer simulations are a powerful tool for this purpose. In this work, we have performed coarse-grained molecular dynamics simulations and free energy calculations on spherical titanium dioxide NPs conjugated with polymer chains of different chemical compositions. We have demonstrated that the hydrophobic/hydrophilic character of the chains, more than the nature of their terminal group, plays a crucial role in determining the NPs' interaction with the lipid bilayer and the thermodynamic spontaneity of NPs' translocation from water to the membrane. We envision that this computational work will be helpful to the experimental community in terms of the rational design of NPs for efficient cell membrane permeation.

Hierarchical Machine Learning of Low-Resolution Coarse-Grained Free Energy Potentials.

A force-matching-based method for supervised machine learning (ML) of coarse-grained (CG) free energy (FE) potentials─known as multiscale coarse-graining via force-matching (MSCG/FM)─is an efficient method to develop microscopically informed CG models that are thermodynamically and statistically equivalent to the reference microscopic models. For low-resolution models, when the coarse-graining is at supramolecular scales, objective-oriented clustering of nonbonded particles is required and the reduced description becomes a function of the clustering algorithm. In the present work, we explore the dependence of the ML of the CG Helmholtz FE potential on the clustering algorithm. We consider coarse-graining based on partitional (k-means, leading to Voronoi diagram) and hierarchical agglomerative (bottom-up) clustering algorithms common in unsupervised ML and develop theory connecting the MSCG/FM learned CG Helmholtz potential and the clustering statistics. By combining the agglomerative clustering and the MSCG/FM learning in a recursive manner, we propose an efficient ML methodology to develop the fine-to-low resolution hierarchies of the CG models. The methodology does not suffer from degrading accuracy or increased computational cost to construct larger hierarchies and as such does not impose an upper size limitation of the CG particles resulting from the extended hierarchies. The utility of the methodology is demonstrated by obtaining the bottom-up agglomerative hierarchy for liquid nitromethane from all-atom molecular dynamics (MD) simulations. For agglomerative hierarchies, we prove the existence of renormalization group transformations that indicate self-similarity and allow for learning the low-resolution MSCG/FM potentials at low computational cost by rescaling and renormalizing the certain finer-resolution members of the hierarchy. The hierarchies of the CG models can be used to carry out simulations under constant-pressure conditions.

Brownian Motion in an N-Scale Periodic Potential

We study the problem of Brownian motion in a multiscale potential. The potential is assumed to have N+1 scales (i.e. N small scales and one macroscale) and to depend periodically on all the small scales. We show that for nonseparable potentials, i.e. potentials in which the microscales and the macroscale are fully coupled, the homogenized equation is an overdamped Langevin equation with multiplicative noise driven by the free energy, for which the detailed balance condition still holds. This means, in particular, that homogenized dynamics is reversible and that the coarse-grained Fokker–Planck equation is still a Wasserstein gradient flow with respect to the coarse-grained free energy. The calculation of the effective diffusion tensor requires the solution of a system of N coupled Poisson equations.

Microscopic mechanism of nanoscale shear bands in an energetic molecular crystal (α-RDX): A first-order structural phase transition

Nanoscale shear bands formed in many energetic molecular crystals upon shock compression [including 1,3,5-trinitro-$s$-triazine (RDX)] are considered as a defect-free mechanism for formation and growth of hot spots which control detonation initiation. Using classical molecular dynamics, we predict the formation of similar nanoscale shear bands in the \ensuremath{\alpha}-RDX crystal subjected to quasistatic isothermal uniaxial compression indicating a common mechanism of shear strain localization under both shock and quasistatic conditions. In the framework of the Ginzburg-Landau phenomenology coupled with the coarse-grained (CG) Helmholtz free energy of the crystal from first principles, we explore the thermodynamics of stress-induced lattice transformations under quasistatic uniaxial load. We show that the shear banding exhibits a critical behavior associated with a first-order structural phase transition with bands of localized twinning strain as transient microstructure. Analysis of the CG Helmholtz free energy suggests that the stress-induced core softening of the effective intermolecular interaction is a fundamental mechanism for a structural phase transition leading to the nanoscale shear bands.

Inositol Hexakisphosphate (IP6) Accelerates Immature HIV-1 Gag Protein Assembly toward Kinetically Trapped Morphologies.

During the late stages of the HIV-1 lifecycle, immature virions are produced by the concerted activity of Gag polyproteins, primarily mediated by the capsid (CA) and spacer peptide 1 (SP1) domains, which assemble into a spherical lattice, package viral genomic RNA, and deform the plasma membrane. Recently, inositol hexakisphosphate (IP6) has been identified as an essential assembly cofactor that efficiently produces both immature virions in vivo and immature virus-like particles in vitro. To date, however, several distinct mechanistic roles for IP6 have been proposed on the basis of independent functional, structural, and kinetic studies. In this work, we investigate the molecular influence of IP6 on the structural outcomes and dynamics of CA/SP1 assembly using coarse-grained (CG) molecular dynamics (MD) simulations and free energy calculations. Here, we derive a bottom-up, low-resolution, and implicit-solvent CG model of CA/SP1 and IP6, and simulate their assembly under conditions that emulate both in vitro and in vivo systems. Our analysis identifies IP6 as an assembly accelerant that promotes curvature generation and fissure-like defects throughout the lattice. Our findings suggest that IP6 induces kinetically trapped immature morphologies, which may be physiologically important for later stages of viral morphogenesis and potentially useful for virus-like particle technologies.

Analytical solution of surface tension of quark-hadron phase transition

By using the finite temperature field theory, the one-loop effective potential and the dynamics of the quantum chromodynamics deconfinement phase transition in the framework of Friedberg-Lee model are studied at finite temperature and density. Our results show that there is a first-order deconfinement phase transition for the full phase diagram, and the critical temperature is about 119.8 MeV for a zero chemical potential whereas the critical chemical is around 256.4 MeV when the temperature is fixed at <i>T</i> = 50 MeV. Moreover, in the thin-wall approximation, we investigate the dynamics of a strong first-order quark-hadron transition via homogeneous bubble nucleation in the Friedberg-Lee model. Under an appropriate boundary condition, the equation of motion for the <inline-formula><tex-math id="M3">\begin{document}$ \sigma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M3.png"/></alternatives></inline-formula> field is solved, then the evolutions of the bubble critical configuration with radius <inline-formula><tex-math id="M4">\begin{document}$ r $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M4.png"/></alternatives></inline-formula> at different temperatures and densities are calculated. The surface tension, the typical radius of the critical bubble and the shift in the coarse-grained free energy each as a function of temperature and chemical potential are obtained. In order to gain the reliability and advantages of the thin-wall approximation, our analytical results based on the thin-wall approximation are compared with those obtained by the exact numerical method accordingly. Finally, some consequences and possible applications of our results in the quark meson model and Polyakov quark meson model are also presented in the end of this paper.

Association Mechanism of Peptide-Coated Metal Nanoparticles with Model Membranes: A Coarse-Grained Study.

Functionalized metal nanoparticles (NPs) hold great promise as innovative tools in nanomedicine. However, one of the main challenges is how to optimize their association with the cell membrane, which is critical for their effective delivery. Recent findings show high cellular uptake rates for NPs coated with the polycationic cell-penetrating peptide gH625-644 (gH), although the underlying internalization mechanism is poorly understood. Here, we use extended coarse-grained simulations and free energy calculations to study systems that simultaneously include metal NPs, peptides, lipids, and sterols. In particular, we investigate the first encounter between multicomponent model membranes and 2.5 nm metal NPs coated with gH (gHNPs), based on the evidence from scanning transmission electron microscopy. By comparing multiple membrane and (membranotropic) NP models, we found that gHNP internalization occurs by forming an intermediate state characterized by specific stabilizing interactions formed by peptide-coated nanoparticles with multicomponent model membranes. This association mechanism is mainly characterized by interactions of gH with the extracellular solvent and the polar membrane surface. At the same time, the NP core interacts with the transmembrane (cholesterol-rich) fatty phase.

Bubble dynamics in a strong first-order quark-hadron transition * *Supported in part by National Natural Science Foundation of China (NSFC) (11675048)

We investigate the dynamics of a strong first-order quark-hadron transition driven by cubic interactions via homogeneous bubble nucleation in the Friedberg-Lee model. The one-loop effective thermodynamic potential of the model and the critical bubble profiles have been calculated at different temperatures and chemical potentials. By taking the temperature and the chemical potential as variables, the evolutions of the surface tension, the typical radius of the critical bubble, and the shift in the coarse-grained free energy in the presence of a nucleation bubble are obtained, and the limit on the reliability of the thin-wall approximation is also addressed accordingly. Our results are compared to those obtained for a weak first-order quark-hadron phase transition; in particular, the spinodal decomposition is relevant.

Structure and position-dependent properties of inhomogeneous suspensions of responsive colloids.

Responsive particles, such as biomacromolecules or hydrogels, display a broad and polymodal distribution of conformations and have thus the ability to change their properties (e.g., size, shape, charge density, etc.) substantially in response to external fields or to their local environment (e.g., mediated by cosolutes or pH). Here we discuss the basic statistical mechanics for a model of responsive colloids (RCs) by introducing an additional "property" degree of freedom as a collective variable in a formal coarse-graining procedure. The latter leads to an additional one-body term in the coarse-grained (CG) free energy, defining a single-particle property distribution for an individual polydisperse RC. We argue that in the equilibrium thermodynamic limit such a CG system of RCs behaves like a conventional polydisperse system of nonresponsive particles. We then illustrate the action of external fields, which impose local (position-dependent) property distributions leading to nontrivial effects on the spatial one-body property and density profiles, even for an ideal (noninteracting) gas of RCs. We finally apply density-functional theory in the local density approximation to discuss the effects of particle interactions for specific examples of (i) a suspension of RCs in an external field linear in both position and property, (ii) a suspension of RCs with highly localized properties (sizes) confined between two walls, and (iii) a two-component suspension where an inhomogeneously distributed (nonresponsive) cosolute component, as found, e.g., in the studies of osmolyte- or salt-induced collapse or swelling transitions of thermosensitive polymers, modifies the local properties and density of the RC liquid.

Aggregation and pressure effects of asphaltene and resin molecules at oil–water interfaces: a coarse-grained molecular dynamics and free energy study

ABSTRACT Coarse-grained molecular dynamics simulations were used to investigate the aggregation of asphaltene and resin molecules in oils and their deposition to oil–water interfaces. Resin, “interfacially-active” asphaltenes, and “bulk-like” asphaltenes are considered as solutes in organic phases consisting of aromatics or saturates. Resins and asphaltenes formed aggregates with a spacing of 0.46 nm between stacked polycyclic sheets. Whether in the aromatic or saturated solvent, resin molecules did not interact with the interface, but its aggregates remained in the bulk. The degree of surface activity of asphaltenes was found to increase with the polarity of their chemical groups, and decrease with the aromatics content of the solvent. Axial stress profiles were measured to calculate the interfacial tension of each system. The tension of interfaces of crude oil with water was found to depend on aromatics content. The free energy of deposition of asphaltenes and resin molecules to the interface was measured using well-tempered metadynamics, in which it was found that “interfacially-active” asphaltenes possess greater stability at the oil-water interface than “bulk-like” asphaltenes, and the organic solvent influences the favorability of deposition.

Back-mapping based sampling: Coarse grained free energy landscapes as a guideline for atomistic exploration.

One ongoing topic of research in MD simulations is how to enable sampling to chemically and biologically relevant time scales. We address this question by introducing a back-mapping based sampling (BMBS) that combines multiple aspects of different sampling techniques. BMBS uses coarse grained (CG) free energy surfaces (FESs) and dimensionality reduction to initiate new atomistic simulations. These new simulations are started from atomistic conformations that were back-mapped from CG points all over the FES in order to sample the entire accessible phase space as fast as possible. In the context of BMBS, we address relevant back-mapping related questions like where to start the back-mapping from and how to judge the atomistic ensemble that results from the BMBS. The latter is done with the use of the earth mover's distance, which allows us to quantitatively compare distributions of CG and atomistic ensembles. By using this metric, we can also show that the BMBS is able to correct inaccuracies of the CG model. In this paper, BMBS is applied to a just recently introduced neural network (NN) based approach for a radical coarse graining to predict free energy surfaces for oligopeptides. The BMBS scheme back-maps these FESs to the atomistic scale, justifying and complementing the proposed NN based CG approach. The efficiency benefit of the algorithm scales with the length of the oligomer. Already for the heptamers, the algorithm is about one order of magnitude faster in sampling compared to a standard MD simulation.

Machine Learning of Coarse-Grained Molecular Dynamics Force Fields.

Atomistic or ab initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force-matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multibody terms that emerge from the dimensionality reduction.

Universality of domain growth in antiferromagnets with spin-exchange kinetics.

We study phase ordering kinetics in symmetric and asymmetric binary mixtures, undergoing an order-disorder transition below the critical temperature. Microscopically, we model the kinetics via the antiferromagnetic Ising model with Kawasaki spin-exchange kinetics. This conserves the composition while the order parameter (staggered magnetization) is not conserved. The order-parameter correlation function and structure factor show dynamical scaling, and the scaling functions are independent of the mixture composition. The average domain size shows a power-law growth: [Formula: see text]. The asymptotic growth regime has [Formula: see text], though there can be prolonged transients with [Formula: see text] for asymmetric mixtures. Our unambiguous observation of the asymptotic universal regime is facilitated by using an accelerated Monte Carlo technique. We also obtain the coarse-grained free energy from the Hamiltonian, as a function of two order parameters. The evolution of these order parameters is modeled by using Model C kinetics. As for the microscopic dynamics, the average domain size of the nonconserved order-parameter (staggered magnetization) field exhibits a power-law growth: [Formula: see text] at later times, irrespective of the mean value of the conserved order-parameter (composition) field.

Influence of the mode of deformation on recrystallisation kinetics in Nickel through experiments, theory and phase field model

In this paper, we report the influence of the mode of deformation on recrystallisation kinetics through experiments, theory and a phase field model. Ni samples of 99.6% purity are subjected to torsion and rolling at two equivalent plastic strains and the recrystallisation kinetics and microstructure are compared experimentally. Due to significant differences in the distributions of the nuclei and stored energy for the same equivalent strain, large differences are observed in the recrystallisation kinetics of rolled and torsion-tested samples. Next, a multi-phase field model is developed in order to understand and predict the kinetics and microstructural evolution. The coarse-grained free energy parameters of the phase field model are taken to be a function of the stored energy. In order to account for the observed differences in recrystallisation kinetics, the phase field mobility parameter is a required constitutive input. The mobility is calculated by developing a mean field model of the recrystallisation process assuming that the strain free nuclei grow in a uniform stored energy field. The activation energy calculated from the mobilities obtained from the mean field calculation compares very well with the activation energy obtained from the kinetics of recrystallisation. The recrystallisation kinetics and microstructure as characterised by grain size distribution obtained from the phase field simulations match the experimental results to good accord. The novel combination of experiments, phase field simulations and mean field model facilitates a quantitative prediction of the microstructural evolution and kinetics.

A molecular modeling based method to predict elution behavior and binding patches of proteins in multimodal chromatography

Multimodal (MM) chromatography provides a powerful means to enhance the selectivity of protein separations by taking advantage of multiple weak interactions that include electrostatic, hydrophobic and van der Waals interactions. In order to increase our understanding of such phenomena, a computationally efficient approach was developed that combines short molecular dynamics simulations and continuum solvent based coarse-grained free energy calculations in order to study the binding of proteins to Self Assembled Monolayers (SAM) presenting MM ligands. Using this method, the free energies of protein-MM SAM binding over a range of incident orientations of the protein can be determined. The resulting free energies were then examined to identify the more “strongly bound” orientations of different proteins with two multimodal surfaces. The overall free energy of protein-MM surface binding was then determined and correlated to retention factors from isocratic chromatography. This correlation, combined with analytical expressions from the literature, was then employed to predict protein gradient elution salt concentrations as well as selectivity reversals with different MM resin systems. Patches on protein surfaces that interacted strongly with MM surfaces were also identified by determining the frequency of heavy atom contacts with the atoms of the MM SAMs. A comparison of these patches to Electrostatic Potential and hydrophobicity maps indicated that while all of these patches contained significant positive charge, only the highest frequency sites also possessed hydrophobicity. The ability to identify key binding patches on proteins may have significant impact on process development for the separation of bioproduct related impurities.

Directional Force Originating from ATP Hydrolysis Drives the GroEL Conformational Change

Protein functional mechanisms usually require conformational changes, and often there are known structures for the different conformational states. However, usually neither the origin of the driving force nor the underlying pathways for these conformational transitions is known. Exothermic chemical reactions may be an important source of forces that drive conformational changes. Here we investigate this type of force originating from ATP hydrolysis in the chaperonin GroEL, by applying forces originating from the chemical reaction. Specifically, we apply directed forces to drive the GroEL conformational changes and learn that there is a highly specific direction for applied forces to drive the closed form to the open form. For this purpose, we utilize coarse-grained elastic network models. Principal component analysis on 38 GroEL experimental structures yields the most important motions, and these are used in structural interpolation for the construction of a coarse-grained free energy landscape. In addition, we investigate a more random application of forces with a Monte Carlo method and demonstrate pathways for the closed-open conformational transition in both directions by computing trajectories that are shown upon the free energy landscape. Initial root mean square deviation (RMSD) between the open and closed forms of the subunit is 14.7 Å and final forms from our simulations reach an average RMSD of 3.6 Å from the target forms, closely matching the level of resolution of the coarse-grained model.

Membrane Perforation Thermodynamics of a Pore-Forming Toxin Explored by Molecular Dynamics Simulations

Pore-forming toxins constitute one of the most spectacular attack weapons of bacteria. Secreted in soluble form, they undergo large conformational changes after different stimuli, allowing them to create a pore in the host's membrane. For instance, upon endocytosis, the pentameric TcA proteins experience a large conformational change due to the acidification of the endosome. The contraction of a 60-residues-long linker peptide is proposed to drive the syringe-like injection of a helical domain into the membrane, which subsequently opens to create a pore. Unfortunately, the thermodynamics behind this process are poorly understood. Here, we used molecular dynamics and free energy calculations to characterize the thermodynamics associated with the membrane perforation of TcdA1 toxin from Photorhabdus luminescens. Our all-atom free energy calculations showed that the contraction of each linker peptide in the pentamer is associated with a gain of ∼10 kcal/mol. Interestingly, this change is largely independent from pH, suggesting that the acidification of the endosome is only required to initiate the conformational change. In addition, we performed coarse-grained free energy calculations of the syringe-like perforation of a POPC model membrane. The results show that the process is favorable by ∼8 kcal/mol. However, a barrier of ∼35 kcal/mol, originated by the opening of the outer leaflet of the membrane, acts against membrane perforation. Combined, this suggests that the effect of the linker contraction is mainly kinetic, decreasing the effective barrier for the perforation process. Interestingly, our all-atoms simulations of the membrane-embedded protein show that several lipidic head groups from the lower leaflet intercalate between the helices of the protein, stabilizing the open conformation. Taken together, this suggest that the pore opening is induced by the interaction of the protein with the membrane, and occurs only upon full perforation.

Ginzburg-Landau free energy for molecular fluids: Determination and coarse-graining

Using molecular simulation, we determine Ginzburg-Landau free energy functions for molecular fluids. To this aim, we extend the Expanded Wang-Landau method to calculate the partition functions, number distributions and Landau free energies for Ar,CO2 and H2O. We then parametrize a coarse-grained free energy function of the density order parameter and assess the performance of this free energy function on its ability to model the onset of criticality in these systems. The resulting parameters can be readily used in hybrid atomistic/continuum simulations that connect the microscopic and mesoscopic length scales.

Conformational Changes in the Epidermal Growth Factor Receptor: Role of the Transmembrane Domain Investigated by Coarse-Grained MetaDynamics Free Energy Calculations.

The epidermal growth factor receptor (EGFR) is a dimeric membrane protein that regulates key aspects of cellular function. Activation of the EGFR is linked to changes in the conformation of the transmembrane (TM) domain, brought about by changes in interactions of the TM helices of the membrane lipid bilayer. Using an advanced computational approach that combines Coarse-Grained molecular dynamics and well-tempered MetaDynamics (CG-MetaD), we characterize the large-scale motions of the TM helices, simulating multiple association and dissociation events between the helices in membrane, thus leading to a free energy landscape of the dimerization process. The lowest energy state of the TM domain is a right-handed dimer structure in which the TM helices interact through the N-terminal small-X3-small sequence motif. In addition to this state, which is thought to correspond to the active form of the receptor, we have identified further low-energy states that allow us to integrate with a high level of detail a range of previous experimental observations. These conformations may lead to the active state via two possible activation pathways, which involve pivoting and rotational motions of the helices, respectively. Molecular dynamics also reveals correlation between the conformational changes of the TM domains and of the intracellular juxtamembrane domains, paving the way for a comprehensive understanding of EGFR signaling at the cell membrane.

Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers.

The nematic twist-bend (NTB) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase - the first distinct nematic variant discovered in many years. The NTB phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The NTB structure thus provides another fascinating example of spontaneous chiral symmetry breaking in nature. The order parameter driving the formation of the heliconical state has been theoretically conjectured to be a polarization field, deriving from the bent conformation of the dimers, that rotates helically with the same nanoscale pitch as the director field. It therefore presents a significant challenge for experimental detection. Here we report a second harmonic light scattering (SHLS) study on two achiral, NTB-forming LCs, which is sensitive to the polarization field due to micron-scale distortion of the helical structure associated with naturally-occurring textural defects. These defects are parabolic focal conics of smectic-like "pseudo-layers", defined by planes of equivalent phase in a coarse-grained description of the NTB state. Our SHLS data are explained by a coarse-grained free energy density that combines a Landau-deGennes expansion of the polarization field, the elastic energy of a nematic, and a linear coupling between the two.