Multiscale Coarse-graining Model Research Articles

A multiscale coarse-grained model of HIV-1 capsid self-assembly

A multiscale coarse-grained model of HIV-1 capsid self-assembly

Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy

In recent years, various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular liquid—liquid phase separation (LLPS) and elucidate the dominant physicochemical driving forces. Here, we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino-acid sequence. The model is parameterised from both atomistic simulations and bioinformatics data and accounts for the dominant role of π–π and hybrid cation–π/π–π interactions and the much stronger attractive contacts established by arginines than lysines.

A multiscale coarse-grained model of the nuclear pore complex and HIV-1 capsid interaction

The docking of the HIV-1 capsid at the nuclear pore complex, penetration of the viral capsid, and subsequent nuclear uncoating kinetics are critical HIV host-cell interactions that are yet to be understood. A particular challenge in this regard, is the computational modeling of the nuclear pore complex (NPC), a large macromolecular complex in the cell that regulates transport into and out of the nucleus. Computer simulations of complete nuclear pore complex can provide theoretical insights into large-scale viral processes pertaining to capsid entry.

Coarse-grained models for local density gradients

Coarse-grained (CG) models provide superior computational efficiency for simulating soft materials. Unfortunately, CG models with conventional pair-additive potentials demonstrate limited transferability between bulk and interfacial environments. Recently, a growing number of CG models have supplemented these pair potentials with one-body potentials of the local density (LD) around each site. These LD potentials can significantly improve the accuracy and transferability of CG models. Nevertheless, it remains challenging to accurately describe interfaces where the LD varies rapidly. In this work, we consider a new class of one-body potentials that depend upon the square of the LD gradient around each site. We investigate the impact of this square gradient (SG) potential upon both top-down dissipative particle dynamics (DPD) models and also bottom-up multiscale coarse-graining (MS-CG) models. We demonstrate that SG potentials can be used to tune the interfacial properties of DPD models without significantly altering their bulk properties. Moreover, we demonstrate that SG potentials can improve the bulk pressure-density equation of state as well as the interfacial profile of MS-CG models for acetic acid. Consequently, SG potentials may provide a useful connection between particle-based top-down models and mean-field Landau theories for phase behavior. Furthermore, SG potentials may prove useful for improving the accuracy and transferability of bottom-up CG models for interfaces and other inhomogeneous systems with significant density gradients.

Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy.

Various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular phase separation and elucidate the dominant physicochemical driving forces. Here, we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino-acid sequence. The model is parameterised from both atomistic simulations and bioinformatics data and accounts for the dominant role of π-π and hybrid cation-π/π-π interactions and the much stronger attractive contacts established by arginines than lysines. We provide a comprehensive set of benchmarks for Mpipi and seven other residue-level coarse-grained models against experimental radii of gyration and quantitative in-vitro phase diagrams; Mpipi predictions agree well with experiment on both fronts. Moreover, it can account for protein-RNA interactions, correctly predicts the multiphase behaviour of a charge-matched poly-arginine/poly-lysine/RNA system, and recapitulates experimental LLPS trends for sequence mutations on FUS, DDX4 and LAF-1 proteins.

Multiscale Coarse-Grained Model for the Stepping of Molecular Motors with Application to Kinesin.

Conventional kinesin, a motor protein that transports cargo within cells, walks by taking multiple steps toward the plus end of the microtubule (MT). While significant progress has been made in understanding the details of the walking mechanism of kinesin, there are many unresolved issues. From a computational perspective, a central challenge is the large size of the system, which limits the scope of time scales accessible in standard computer simulations. Here, we create a general multiscale coarse-grained model for motors that enables us to simulate the stepping process of motors on polar tracks (actin and MT) with a focus on kinesin. Our approach greatly shortens the computation times without a significant loss in detail, thus allowing us to better describe the molecular basis of the stepping kinetics. The small number of parameters, which are determined by fitting to experimental data, allows us to develop an accurate method that may be adopted to simulate stepping in other molecular motors. The model enables us to simulate a large number of steps, which was not possible previously. We show in agreement with experiments that due to the docking of the neck linker (NL) of kinesin, sometimes deemed as the power stroke, the space explored diffusively by the tethered head is severely restricted, allowing the step to be completed in tens of microseconds. We predict that increasing the interaction strength between the NL and the motor head, achievable by mutations in the NL, decreases the stepping time but reaches a saturation value. Furthermore, the full three-dimensional dynamics of the cargo are fully resolved in our model, contributing to the predictive power and allowing us to study the important aspects of cargo-motor interactions.

New and notable: A multiscale coarse-grained model of the SARS-CoV-2 virion

The global corona virus disease 2019 (COVID-19) pandemic has led to intense activity to develop an effective vaccine. In addition, there have been efforts to develop therapeutics to treat symptoms of the disease, reduce the severity of infection, or prevent infection entirely. Inspired by the potential of structure-based therapeutic design, research has led to detailed molecular models of key protein structural components of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virion (1).

Bottom-up coarse-grained models for external fields and interfaces

Bottom-up coarse-grained (CG) models accurately describe the structure of homogeneous systems but sometimes provide limited transferability and a poor description of thermodynamic properties. Consequently, inhomogeneous systems present a severe challenge for bottom-up models. In this work, we examine bottom-up CG models for interfaces and inhomogeneous systems. We first analyze the effect of external fields upon the many-body potential of mean force. We also demonstrate that the multiscale CG (MS-CG) variational principle for modeling the external field corresponds to a generalization of the first Yvon-Born-Green equation. This provides an important connection with liquid state theory, as well as physical insight into the structure of interfaces and the resulting MS-CG models. We then develop and assess MS-CG models for a film of liquid methanol that is adsorbed on an attractive wall and in coexistence with its vapor phase. While pair-additive potentials provide unsatisfactory accuracy and transferability, the inclusion of local-density (LD) potentials dramatically improves the accuracy and transferability of the MS-CG model. The MS-CG model with LD potentials quite accurately describes the wall-liquid interface, the bulk liquid density, and the liquid-vapor interface while simultaneously providing a much improved description of the vapor phase. This model also provides an excellent description of the pair structure and pressure-density equation of state for the bulk liquid. Thus, LD potentials hold considerable promise for transferable bottom-up models that accurately describe the structure and thermodynamic properties of both bulk and interfacial systems.

A multiscale coarse-grained model to predict the molecular architecture and drug transport properties of modified chitosan hydrogels.

Hydrogels constructed with functionalized polysaccharides are of interest in a multitude of applications, chiefly the design of therapeutic and regenerative formulations. Tailoring the chemical modification of polysaccharide-based hydrogels to achieve specific drug release properties involves the optimization of many tunable parameters, including (i) the type, degree (χ), and pattern of the functional groups, (ii) the water-polymer ratio, and (iii) the drug payload. To guide the design of modified polysaccharide hydrogels for drug release, we have developed a computational toolbox that predicts the structure and physicochemical properties of acylated chitosan chains, and their impact on the transport of drug molecules. Herein, we present a multiscale coarse-grained model to investigate the structure of networks of chitosan chains modified with acetyl, butanoyl, or heptanoyl moieties, as well as the diffusion of drugs doxorubicin (Dox) and gemcitabine (Gem) through the resulting networks. The model predicts the formation of different network structures, in particular the hydrophobically-driven transition from a uniform to a cluster/channel morphology and the formation of fibers of chitin chains. The model also describes the impact of structural and physicochemical properties on drug transport, which was confirmed experimentally by measuring Dox and Gem diffusion through an ensemble of modified chitosan hydrogels.

Analysis of local density potentials.

Low resolution coarse-grained (CG) models are widely adopted for investigating phenomena that cannot be effectively simulated with all-atom (AA) models. Since the development of the many-body dissipative particle dynamics method, CG models have increasingly supplemented conventional pair potentials with one-body potentials of the local density (LD) around each site. These LD potentials appear to significantly extend the transferability of CG models, while also enabling more accurate descriptions of thermodynamic properties, interfacial phenomena, and many-body correlations. In this work, we systematically examine the properties of LD potentials. We first derive and numerically demonstrate a nontrivial transformation of pair and LD potentials that leaves the total forces and equilibrium distribution invariant. Consequently, the pair and LD potentials determined via bottom-up methods are not unique. We then investigate the sensitivity of CG models for glycerol to the weighting function employed for defining the local density. We employ the multiscale coarse-graining (MS-CG) method to simultaneously parameterize both pair and LD potentials. When employing a short-ranged Lucy function that defines the local density from the first solvation shell, the MS-CG model accurately reproduces the pair structure, pressure-density equation of state, and liquid-vapor interfacial profile of the AA model. The accuracy of the model generally decreases as the range of the Lucy function increases further. The MS-CG model provides similar accuracy when a smoothed Heaviside function is employed to define the local density from the first solvation shell. However, the model performs less well when this function acts on either longer or shorter length scales.

Ultra-Coarse-Grained Models Allow for an Accurate and Transferable Treatment of Interfacial Systems.

Interfacial systems are fundamentally important in many processes. However, constructing coarse-grained (CG) models for such systems is a significant challenge due to their inhomogeneous nature. This problem is made worse due to the generally nontransferable nature of the interactions in CG models across different phases. In this paper, we address these challenges by systematically constructing ultra-coarse-grained (UCG) models for interfaces, in which the CG sites are allowed to have internal states. We find that a multiscale coarse-grained (MS-CG) representation of a single CG site model fails to identify the directionality of a molecule and is unable to reproduce the correct phase coexistence for aspherical molecules. In contrast with conventional MS-CG models, the UCG methodology allows chemical and environmental changes to be captured by modulating the interactions between internal states. In this work, we design the internal states to depend on local particle density to distinguish different phases in liquid/vapor or liquid/liquid interfaces. These UCG models are able to capture phase coexistence and recapitulate structures, notably at state points in which the MS-CG method yields poor results. Interestingly, effective pairwise forces and potentials from the UCG models are almost identical to those of the bulk liquids that correspond to each phase, indicating that the UCG approach can provide transferable interactions. This approach is expected to be applicable to other systems that exhibit phase coexistence and also to complex macromolecular systems by modulating interactions based on local density or other order parameters to unravel the complex nature underlying heterogeneous system boundaries.

Multiscale mechanics of the lateral pressure effect on enhancing the load transfer between polymer coated CNTs.

While individual carbon nanotubes (CNTs) are known as one of the strongest fibers ever known, even the strongest fabricated macroscale CNT yarns and fibers are still significantly weaker than individual nanotubes. The loss in mechanical properties is mainly because the deformation mechanism of CNT fibers is highly governed by the weak shear strength corresponding to sliding of nanotubes on each other. Adding polymer coating to the bundles, and twisting the CNT yarns to enhance the intertube interactions are both efficient methods to improve the mechanical properties of macroscale yarns. Here, we perform molecular dynamics (MD) simulations to unravel the unknown deformation mechanism in the intertube polymer chains and also local deformations of the CNTs at the atomistic scale. Our results show that the lateral pressure can have both beneficial and adverse effects on shear strength of polymer coated CNTs, depending on the local deformations at the atomistic scale. In this paper we also introduce a bottom-up bridging strategy between a full atomistic model and a coarse-grained (CG) model. Our trained CG model is capable of incorporating the atomistic scale local deformations of each CNT to the larger scale collect behavior of bundles, which enables the model to accurately predict the effect of lateral pressure on larger CNT bundles and yarns. The developed multiscale CG model is implemented to study the effect of lateral pressure on the shear strength of straight polymer coated CNT yarns, and also the effect of twisting on the pull-out force of bundles in spun CNT yarns.

Predicting the Sensitivity of Multiscale Coarse-Grained Models to their Underlying Fine-Grained Model Parameters.

The sensitivity of a coarse-grained (CG) force field to changes in the underlying fine-grained (FG) model from which it was derived provides modeling insight for improving transferability across interaction parameters, transferability across temperature, and the calculation of thermodynamic derivatives. Methods in the literature, such as multi-trajectory finite differences and reweighted finite differences, are either too computationally demanding to calculate within acceptable noise tolerances or are too biased for practical accuracy. This work presents a new reweighting-free, single-simulation formula that allows for practical, high signal-to-noise calculations of CG model sensitivity with respect to FG model interaction parameters and thermodynamic state points. This formula, the self-consistent basis (SCB) single point formula, determines the many-body sensitivity in a single step by approximating the derivative of the many-body potential projected onto the same set of trial functions as the sensitivity. A related diagnostic formula also derived in this paper is the self-consistent iterative (SCI) single point formula, which is useful for identifying the importance of many-body sources of error and verifying CG representability of observables. The SCI formula determines the many-body sensitivity iteratively via a series of partially self-consistent, variational approximations to the complete many-body sensitivity. The new, computationally efficient SCB formula shows substantially less noise than previous methods when applied to single site methanol and solvent-free sodium chloride CG models, though bias can remain a problem. It represents a novel method for calculating alchemical transferability across interaction parameters at low computational cost and with high fidelity, and the results point to new understanding of the current limits of CG model transferability.

Dynamic force matching: A method for constructing dynamical coarse-grained models with realistic time dependence.

Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that the method provides realistic dynamical CG models that have non-Markovian or close to Markovian behavior that is consistent with the actual dynamical behavior of the all-atom system used to construct the CG model. Both the construction and the simulation of such a dynamic CG model have computational requirements that are similar to those of the corresponding MS-CG model and are good candidates for CG modeling of very large systems.

Bottom-Up Coarse-Graining of Peptide Ensembles and Helix-Coil Transitions.

This work investigates the capability of bottom-up methods for parametrizing minimal coarse-grained (CG) models of disordered and helical peptides. We consider four high-resolution peptide ensembles that demonstrate varying degrees of complexity. For each high-resolution ensemble, we parametrize a CG model via the multiscale coarse-graining (MS-CG) method, which employs a generalized Yvon-Born-Green (g-YBG) relation to determine potentials directly (i.e., without iteration) from the high-resolution ensemble. The MS-CG method accurately describes high-resolution models that fluctuate about a single conformation. However, given the minimal resolution and simple molecular mechanics potential, the MS-CG method provides a less accurate description for a high-resolution peptide model that samples a disordered ensemble with multiple distinct conformations. We employ an iterative g-YBG method to develop a CG model that more accurately describes the relevant distribution functions and free energy surfaces for this disordered ensemble. Nevertheless, this more accurate model does not reproduce the cooperative helix-coil transition that is sampled by the high resolution model. By comparing the different models, we demonstrate that the errors in the MS-CG model primarily stem from the lack of cooperative interactions afforded by the minimal representation and molecular mechanics potential. This work demonstrates the potential of the MS-CG method for accurately modeling complex biomolecular structures, but also highlights the importance of more complex potentials for modeling cooperative transitions with a minimal CG representation.

Investigation of Coarse-Grained Mappings via an Iterative Generalized Yvon–Born–Green Method

Low resolution coarse-grained (CG) models enable highly efficient simulations of complex systems. The interactions in CG models are often iteratively refined over multiple simulations until they reproduce the one-dimensional (1-D) distribution functions, e.g., radial distribution functions (rdfs), of an all-atom (AA) model. In contrast, the multiscale coarse-graining (MS-CG) method employs a generalized Yvon-Born-Green (g-YBG) relation to determine CG potentials directly (i.e., without iteration) from the correlations observed for the AA model. However, MS-CG models do not necessarily reproduce the 1-D distribution functions of the AA model. Consequently, recent studies have incorporated the g-YBG equation into iterative methods for more accurately reproducing AA rdfs. In this work, we consider a theoretical framework for an iterative g-YBG method. We numerically demonstrate that the method robustly determines accurate models for both hexane and also a more complex molecule, 3-hexylthiophene. By examining the MS-CG and iterative g-YBG models for several distinct CG representations of both molecules, we investigate the approximations of the MS-CG method and their sensitivity to the CG mapping. More generally, we explicitly demonstrate that CG models often reproduce 1-D distribution functions of AA models at the expense of distorting the cross-correlations between the corresponding degrees of freedom. In particular, CG models that accurately reproduce intramolecular 1-D distribution functions may still provide a poor description of the molecular conformations sampled by the AA model. We demonstrate a simple and predictive analysis for determining CG mappings that promote an accurate description of these molecular conformations.

Dimensional Reduction of a Multiscale Continuum Model of Microtubule Gliding Assays

Microtubule gliding assays, in which molecular motors anchored to a plate drive the gliding motion of filaments in a quasi--two-dimensional fluid layer, have been shown to organize into a variety of large-scale patterns. We derive a fully three-dimensional multiscale coarse-grained model of a gliding assay including the evolution of densities of rigid filaments, bound motors, and free motors, coupled to fluid equations. Our model combines continuum theories of polymeric liquids with the force spreading approach of the immersed boundary method. We use dimensional and asymptotic analysis to derive a reduced two-dimensional model and show that, to leading order, the filaments evolve in a plane, similar to what is experimentally observed. We simulate our model numerically with a GPU-based implementation and observe the same qualitative behavior as in experimental work.

Evaluation of coarse-grained mapping schemes for polysaccharide chains in cellulose

A fundamental understanding of the intermolecular forces that bind polysaccharide chains together in cellulose is crucial for designing efficient methods to overcome the recalcitrance of lignocellulosic biomass to hydrolysis. Because the characteristic time and length scales for the degradation of cellulose by enzymatic hydrolysis or chemical pretreatment span orders of magnitude, it is important to closely integrate the molecular models used at each scale so that, ultimately, one may switch seamlessly between quantum, atomistic, and coarse-grained descriptions of the system. As a step towards that goal, four multiscale coarse-grained models for polysaccharide chains in a cellulose-Iα microfiber are considered. Using the force matching method, effective coarse-grained forces are derived from all-atom trajectories. Performance of the coarse-grained models is evaluated by comparing the intrachain radial distribution functions with those obtained using the all-atom reference data. The all-atom simulation reveals a double peak in the radial distribution function for sites within each glucose residue that arises from the distinct conformations sampled by the primary alcohol group in the glucose residues. The three-site and four-site coarse-grained models have sufficient degrees of freedom to predict this double peak while the one-site and two-site models do not. This is the first time that coarse-grained models have been shown to reproduce such subtle, yet important, molecular features in a polysaccharide chain. The relative orientations between glucose residues along the polysaccharide chain are evaluated and it is found that the four-site coarse-grained model is best at reproducing the glucose-glucose conformations observed in the all-atom simulation. The success of the four-site coarse-grained model underscores the importance of decoupling the pyranose ring from the oxygen atom in the glycosidic bond when developing all-atom to coarse-grained mapping schemes for polysaccharides.

Procedure to construct a multi-scale coarse-grained model of DNA-coated colloids from experimental data

We present a quantitative, multi-scale coarse-grained model of DNA coated colloids. The parameters of this model are transferable and are solely based on experimental data. As a test case, we focus on nano-sized colloids carrying single-stranded DNA of length comparable to the colloids' size. We show that in this regime, the common theoretical approach of assuming pairwise additivity of the colloidal pair interactions leads to quantitatively and sometimes even qualitatively wrong predictions of the phase behaviour of DNA-grafted colloids. Compared to experimental data, we find that our coarse-grained model correctly predicts the equilibrium structure and melting temperature of the formed solids. Due to limited experimental information on the persistence length of single-stranded DNA, some quantitative discrepancies are found in the prediction of spatial quantities. With the availability of better experimental data, the present approach provides a path for the rational design of DNA-functionalised building blocks that can self-assemble into complex, three-dimensional structures.

Concentration and Temperature Dependences of Polyglutamine Aggregation by Multiscale Coarse-Graining Molecular Dynamics Simulations

The solvent-free multiscale coarse-graining model of polyglutamine was employed to study polyglutamine aggregation at different concentrations and temperatures by means of molecular dynamics simulation. The heterogeneity order parameter (HOP) was used to quantify the polyglutamine aggregation. Our simulation results demonstrate that polyglutamine aggregation is sensitive to concentration and temperature changes. In equilibrium states, polyglutamine molecules fluctuate between aggregating tightly and distributing uniformly. The degree of aggregation monotonically increases with decreasing temperature, but the fluctuation of HOP reaches its maximum at an intermediate temperature. With increasing concentration, the distribution of polyglutamines first changes from more uniform to more nonuniform and then changes back to be more uniform, and the HOP has the widest distribution at the turning point. Simulations with different system sizes indicate that the finite-size effect is trivial and do not change the conclusions drawn for the polyglutamine system. In addition, the composition of the potential energies has been analyzed to confirm that the nonbonded interactions dominate the aggregation of polyglutamines. These results can be thermodynamically understood by considering the competition between the system entropy and molecular interactions, and a statistical model based on HOP has been developed to explain the microscopic mechanism of polyglutamine aggregation.