Multiscale, Multiresolution Coarse-Grained Model via a Hybrid Approach: Solvation, Structure, and Self-Assembly of Aromatic Tripeptides

Short aromatic peptides have been observed to assemble into diverse nanostructures, including fibers, tubes, and vesicles, using computational techniques. However, the computational studies have employed top-down coarse-grained (CG) models, which are unable to capture the assembly along with the conformation, packing, and organization of the peptides within the aggregates in a manner that is consistent with the all atom (AA) representation of the molecules. In this study, a hybrid structure- and force-based approach is adapted to develop a bottom-up CG force field of triphenylalanine using reference data from AA trajectories. This approach follows a flexible methodology to approximate the chemical complexity of the underlying AA representation with the chosen CG representation. Two CG models are developed with distinct representations of the aromatic side chains. The first uses a simple single-bead representation, while the second uses a three-bead representation to more accurately represent the planarity of the ring. The one-bead model yields nanorods, while the three-bead model results in nanospheres. The role of different chemical groups in the assembly of nanostructures is identified, along with the importance of steric effects on the packing of the peptides within assemblies.

Machine Learning-Guided Adaptive Parametrization for Coupling Terms in a Mixed United-Atom/Coarse-Grained Model for Diphenylalanine Self-Assembly in Aqueous Ionic Liquids

Precise regulation of the peptide self-assembly into ordered nanostructures with intriguing properties has attracted intense attention. However, predicting peptide assembly at atomic resolution is a challenge due to both the structural flexibility of peptides and the associated huge computational costs. A machine learning-guided adaptive parametrization method was proposed for developing a mixed atomic and coarse-grained (CG) model through a multiobjective optimization strategy. Our model incorporates the united-atom (UA) model for diphenylalanine (P) and the polarizable electrostatic-variable coarse-grained (VaCG) model for aqueous ionic liquid [BMIM]+[BF4]- solution. In this mixed model, the coupling van der Waals (vdW) interaction is addressed by introducing virtual sites (VS) in the UA model to interact with solvent CG beads. The coupling parameters, including the electrostatic parameter and vdW parameters, are automatically optimized through ML-guided adaptive parametrization. The performance of this model was tested by some microstructural properties, e.g., the average number of P-P intermolecular hydrogen bonds (HBs) and radius distribution functions (RDFs) between P and different fragments of IL, in comparison with all-atom (AA) simulations. The computational cost is significantly reduced using such a parametrization scheme, which could search tens of thousands of force-field parameter sets, while needing only a small fraction of them to be assessed with molecular dynamics (MD) simulations. We used such a mixed resolution model to investigate the self-assembly in IL-water mixtures with variants of IL concentration (X). The long-range-ordered fibril structure is formed in a pure water system (X = 0). With an increase of IL concentrations, the formation of an ordered self-assembly nanostructure is prohibited, instead forming branched fibril at X = 2 mol % or amorphous aggregates when X > 10 mol %, resulting from the interplay between π-stacking and HB interactions between P and IL. The qualitative agreement between the simulated structures and the observed morphologies in experiments indicates the applicability of ML-guided parametrization strategy in the study of complex systems, such as polymers, lipid bilayers, and polysaccharides.

Integrating Machine Learning in the Coarse-Grained Molecular Simulation of Polymers

Machine learning (ML) is having an increasing impact on the physical sciences, engineering, and technology and its integration into molecular simulation frameworks holds great potential to expand their scope of applicability to complex materials and facilitate fundamental knowledge and reliable property predictions, contributing to the development of efficient materials design routes. The application of ML in materials informatics in general, and polymer informatics in particular, has led to interesting results, however great untapped potential lies in the integration of ML techniques into the multiscale molecular simulation methods for the study of macromolecular systems, specifically in the context of Coarse Grained (CG) simulations. In this Perspective, we aim at presenting the pioneering recent research efforts in this direction and discussing how these new ML-based techniques can contribute to critical aspects of the development of multiscale molecular simulation methods for bulk complex chemical systems, especially polymers. Prerequisites for the implementation of such ML-integrated methods and open challenges that need to be met toward the development of general systematic ML-based coarse graining schemes for polymers are discussed.

A hybrid approach for coarse-graining helical peptoids: Solvation, secondary structure, and assembly

Protein mimics such as peptoids form self-assembled nanostructures whose shape and function are governed by the side chain chemistry and secondary structure. Experiments have shown that a peptoid sequence with a helical secondary structure assembles into microspheres that are stable under various conditions. The conformation and organization of the peptoids within the assemblies remains unknown and is elucidated in this study via a hybrid, bottom-up coarse-graining approach. The resultant coarse-grained (CG) model preserves the chemical and structural details that are critical for capturing the secondary structure of the peptoid. The CG model accurately captures the overall conformation and solvation of the peptoids in an aqueous solution. Furthermore, the model resolves the assembly of multiple peptoids into a hemispherical aggregate that is in qualitative agreement with the corresponding results from experiments. The mildly hydrophilic peptoid residues are placed along the curved interface of the aggregate. The composition of the residues on the exterior of the aggregate is determined by two conformations adopted by the peptoid chains. Hence, the CG model simultaneously captures sequence-specific features and the assembly of a large number of peptoids. This multiscale, multiresolution coarse-graining approach could help in predicting the organization and packing of other tunable oligomeric sequences of relevance to biomedicine and electronics.

Coarse-Grained Model Incorporating Short- and Long-Range Effective Potentials for the Fast Simulation of Micelle Formation in Solutions of Ionic Surfactants

A coarse-grained model comprising short- and long-range effective potentials, parametrized with the iterative Boltzmann inversion (IBI) method, is presented for capturing micelle formation in aqueous solutions of ionic surfactants using as a model system sodium dodecyl sulfate (SDS). In the coarse-grained (CG) model, each SDS molecule is represented as a sequence of four beads while each water molecule is modeled as a single bead. The proposed CG scheme involves ten potential energy functions: four of them describe bonded interactions and control the distribution functions of intramolecular degrees of freedom (bond lengths, valence angles, and dihedrals) along an SDS molecule while the other six account for intermolecular interactions between pairs of SDS and water beads and control the radial distribution functions. The nonbonded effective potentials between coarse-grained SDS molecules extend up to about 12 nm and capture structural and morphological features of the micellar solution both at short and long distances. The long-range component of these potentials, in particular, captures correlations between surfactant molecules belonging to different micelles and is essential to describe ordering associated with micelle formation. A new strategy is introduced for determining the effective potentials through IBI by using information (target distribution functions) extracted from independent atomistic simulations of a micellar reference system (a salt-free SDS solution at total surfactant concentration c_T equal to 103 mM, temperature T equal to 300 K, and pressure P equal to 1 atm) obtained through a multiscale approach described in an earlier study. It employs several optimization steps for bonded and nonbonded interactions and a gradual parametrization of the short- and long-range components of the latter, followed by reparametrization of the bonded ones. The proposed CG model can reproduce remarkably accurately the microstructure and morphology of the reference system within only a few hours of computational time. It is therefore very promising for future studies of structural and morphological behavior of various liquid surfactant formulations.

Molecular Simulation Approaches to the Study of Thermotropic and Lyotropic Liquid Crystals

Over the last decade, the availability of computer time, together with new algorithms capable of exploiting parallel computer architectures, has opened up many possibilities in molecularly modelling liquid crystalline systems. This perspective article points to recent progress in modelling both thermotropic and lyotropic systems. For thermotropic nematics, the advent of improved molecular force fields can provide predictions for nematic clearing temperatures within a 10 K range. Such studies also provide valuable insights into the structure of more complex phases, where molecular organisation may be challenging to probe experimentally. Developments in coarse-grained models for thermotropics are discussed in the context of understanding the complex interplay of molecular packing, microphase separation and local interactions, and in developing methods for the calculation of material properties for thermotropics. We discuss progress towards the calculation of elastic constants, rotational viscosity coefficients, flexoelectric coefficients and helical twisting powers. The article also covers developments in modelling micelles, conventional lyotropic phases, lyotropic phase diagrams, and chromonic liquid crystals. For the latter, atomistic simulations have been particularly productive in clarifying the nature of the self-assembled aggregates in dilute solution. The development of effective coarse-grained models for chromonics is discussed in detail, including models that have demonstrated the formation of the chromonic N and M phases.

A hybrid coarse-grained model for structure, solvation and assembly of lipid-like peptides

Reconstituted photosynthetic proteins which are activated upon exposure to solar energy hold enormous potential for powering future solid state devices and solar cells. The functionality and integration of these proteins into such devices has been successfully enabled by lipid-like peptides. Yet, a fundamental understanding of the organization of these peptides with respect to the photosynthetic proteins and themselves remains unknown and is critical for guiding the design of such light-activated devices. This study investigates the relative organization of one such peptide sequence V₆K₂ (V: valine and K: lysine) within assemblies. Given the expansive spatiotemporal scales associated with this study, a hybrid coarse-grained (CG) model which captures the structure, conformation and aggregation of the peptide is adopted. The CG model uses a combination of iterative Boltzmann inversion and force matching to provide insight into the relative organization of V₆K₂ in assemblies. The CG model reproduces the structure of a V₆K₂ peptide sequence along with its all atom (AA) solvation structure. The relative organization of multiple peptides in an assembly, as captured by CG simulations, is in agreement with corresponding results from AA simulations. Also, a backmapping procedure reintroduces the AA details of the peptides within the aggregates captured by the CG model to demonstrate the relative organization of the peptides. Furthermore, a large number of peptides self-assemble into an elongated micelle in the CG simulation, which is consistent with experimental findings. The coarse-graining procedure is tested for transferability to longer peptide sequences, and hence can be extended to other amphiphilic peptide sequences.

Ultra-coarse-graining of homopolymers in inhomogeneous systems

We develop coarse-grained (CG) models for simulating homopolymers in inhomogeneous systems, focusing on polymer films and droplets. If the CG polymers interact solely through two-body potentials, then the films and droplets either dissolve or collapse into small aggregates, depending on whether the effective polymer-polymer interactions have been determined from reference simulations in the bulk or at infinite dilution. To address this shortcoming, we include higher order interactions either through an additional three-body potential or a local density-dependent potential (LDP). We parameterize the two- and three-body potentials via force matching, and the LDP through relative entropy minimization. While the CG models with three-body interactions fail at reproducing stable polymer films and droplets, CG simulations with an LDP are able to do so. Minor quantitative differences between the reference and the CG simulations, namely a slight broadening of interfaces accompanied by a smaller surface tension in the CG simulations, can be attributed to the deformation of polymers near the interfaces, which cannot be resolved in the CG representation, where the polymers are mapped to spherical beads.

Atomistic simulation studies of ionic cyanine dyes: self-assembly and aggregate formation in aqueous solution

Cyanine dyes are known to form large-scale aggregates of various morphologies via spontaneous self-assembly in aqueous solution, akin to chromonic liquid crystals. Atomistic molecular dynamics simulations have been performed on four cyanine dyes: pseudoisocyanine chloride (PIC), pinacyanol chloride (PCYN), 5,5',6,6'-tetrachloro-1,1',3,3'-tetraethylbenzimidazolylcarbocyanine chloride (TTBC) and 1,1'-disulfopropyl-3,3'-diethyl-5,5',6,6'-tetrachloro-benzimidazolylcarbocyanine sodium salt (BIC). Simulations employed an optimised general AMBER force field and demonstrate the organisation of the dyes into stacked structures at dilute concentrations. The thermodynamics of self-assembly was studied by calculating potentials of mean force for n-mers (n = 2, 3 or 4), from which the free energies of association are determined. We report binding free energies in the range of 8 to 15k_BT for dimerisation, concordant with typical values for ionic chromonics (7 to 14k_BT), and examine the enthalpic and entropic contributions to the aggregation process. The self-assembly of these dyes yields two distinct classes of structures. We observe the formation of H-aggregate stacks for PCYN, with further complexity in these assemblies for PIC; where the aggregates contain shift and Y junction defects. TTBC and BIC associate into a J-aggregate sheet structure of unimolecular thickness, and is composed of a brickwork arrangement between molecules. These sheet structures are characteristic of the smectic chromonic mesophase, and such assemblies provide a route to the emergence of nanoscale tubular architectures.

Aggregation of the Dipeptide Leu-Gly in Alcohol-Water Binary Solvents Elucidated from the Solvation Structure for Each Moiety

The aggregation of a dipeptide, l-leucine-glycine (Leu-Gly), at 100 mmol dm^-3 has been observed in 1,1,1,3,3,3-hexafluoroisopropanol (HFIP)-water and 2-propanol (2-PrOH)-water solvents at various alcohol mole fractions, x_A, using the dynamic light scattering technique and molecular dynamics (MD) simulations. Leu-Gly was dissolved into the HFIP solvents at the concentration over the entire x_A range, while the dipeptide was not dissolved in the 2-PrOH solvents above x_A = 0.6. Interestingly, the MD snapshots showed different shapes of Leu-Gly aggregates in the HFIP and 2-PrOH solvents. A linear-shaped aggregate forms in the former; in contrast, a spherical-shaped aggregate is generated in the latter. The solvation structure of each moiety of Leu-Gly in the HFIP and 2-PrOH solvents was observed using experimental and theoretical techniques,¹H and ¹³C NMR, IR, and ¹⁹F-¹H HOESY measurements and MD simulations. These results gave us the reasons for the different shapes of Leu-Gly aggregates in both solvents. In the HFIP solvents, most of the moieties of the dipeptide are easily solvated by HFIP. This induces the elongated structure of Leu-Gly, leading to the electrostatic interaction between the N- (NH₃⁺ group) and C- (COO^- group) terminals of dipeptide molecules. On the other hand, in the 2-PrOH solvents, water molecules that initially solvate the moieties of Leu-Gly, such as the N- and C-terminals and the peptide linkage, are not easily eliminated even as the x_A is close to 0.6. The water molecules can bridge such moieties of Leu-Gly to form spherical-shaped aggregates. The diffusion coefficients of Leu-Gly in both alcohol-water binary solvents were experimentally determined by NMR DOSY to estimate the geometries of the aggregates in the solvents. The sizes of Leu-Gly aggregates obtained by DOSY for both solvent systems were consistent with those estimated from the MD snapshots.

Self-assembly of Alanine-Isoleucine and Isoleucine-Isoleucine Dipeptides through Atomistic Simulations and Experiments

A detailed investigation of the structural and conformational properties of alanine-isoleucine (Ala-Ile) and isoleucine-isoleucine (Ile-Ile) dipeptides is presented in water and in methanol solvents. We propose a consistent combination of complementary simulation and experimental methods, covering a broad range of length and time scales, from the very short (i.e., atomic level), via all-atom molecular dynamics (MD) simulations, up to the macroscopic one, via scanning electron microscopy (SEM) experiments. The examined samples from both simulations and experiment cover a board range of concentrations since these are usually in different concentration windows (i.e., high values in simulations vs low values in experiments). In the present study, there is an overlapping concentration regime and a qualitative agreement between simulation and experimental results is observed. The effect of temperature on the formed structures is found to be small, from both simulation and experiments, when temperature varies from 278 to 300 K. Furthermore, the differences of Ala-Ile and Ile-Ile dipeptides from dialanine (Ala-Ala) and diphenylalanine (Phe-Phe) dipeptides in similar conditions are highlighted. Based on various measures, the strength of the self-assembly propensity of the four dipeptides in aqueous solutions attains the following order: Phe-Phe > Ala-Ile > Ala-Ala > Ile-Ile.

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.

Molecular Modeling Investigations of Sorption and Diffusion of Small Molecules in Glassy Polymers

With a wide range of applications, from energy and environmental engineering, such as in gas separations and water purification, to biomedical engineering and packaging, glassy polymeric materials remain in the core of novel membrane and state-of the art barrier technologies. This review focuses on molecular simulation methodologies implemented for the study of sorption and diffusion of small molecules in dense glassy polymeric systems. Basic concepts are introduced and systematic methods for the generation of realistic polymer configurations are briefly presented. Challenges related to the long length and time scale phenomena that govern the permeation process in the glassy polymer matrix are described and molecular simulation approaches developed to address the multiscale problem at hand are discussed.

Toward Multiscale Modeling of Proteins and Bioagglomerates: An Orientation-Sensitive Diffusion Model for the Integration of Molecular Dynamics and the Discrete Element Method

Most processes involved in biological and biotechnological systems spread over many scales in space and time. For example, the interaction of multiple enzymes in heterogeneous enzymatic agglomerates or clusters, necessary for efficient enzymatic conversion, is of high interest for research and enzyme engineering. In order to understand and predict their overall behavior and performance, it is important to describe these scales as completely as possible, known as multiscale modeling. While many different approaches have been presented in recent years, knowledge about protein formation and bioagglomeration at the micro scale is still very limited. In an attempt to address such systems, we propose a bottom- up multiscale modeling methodology, bridging the gaps between molecular dynamics (MD) with an explicit solvent and the larger scale discrete element method (DEM) using an implicit solvent and abstracting macromolecules (e.g., proteins) as objects with anisotropic properties. We term this approach the molecular discrete element method (MDEM). For this, we present an orientation-sensitive diffusion model for DEM, which describes the dynamics of anisotropic translational and rotational diffusion, while implicitly considering solvent molecules and enforcing a canonical ensemble. A general-purpose model and parametrization approach is presented, which can be used to simulate any process involving diffusion of discrete particles. Effects of temperature and viscosity changes can be considered, and guidance is provided concerning time step selection. This model is generally applicable and serves as a precondition to enforce the proper dynamics (i.e., diffusion characteristics and canonical ensemble, similar to a thermostat in MD) for the proposed multiscale modeling methodology with anisotropic properties. Thereby, it presents a first step toward modeling at the micro scale and is integral to enforcing dynamics of such systems and therefore extensively validated. As a next step, interaction models are to be defined and added to the presented model. In comparison to atomistic and coarse-grained (CG) MD, a speedup of 5-7 orders of magnitude can be achieved. The approach is demonstrated on multiple components of the pyruvate dehydrogenase enzyme complex, a multienzymatic machinery that involves very different types of enzymes and is of high value to further elucidate the mechanisms of bioagglomeration and metabolic channeling.

Guiding principles for peptide nanotechnology through directed discovery

Life's diverse molecular functions are largely based on only a small number of highly conserved building blocks - the twenty canonical amino acids. These building blocks are chemically simple, but when they are organized in three-dimensional structures of tremendous complexity, new properties emerge. This review explores recent efforts in the directed discovery of functional nanoscale systems and materials based on these same amino acids, but that are not guided by copying or editing biological systems. The review summarises insights obtained using three complementary approaches of searching the sequence space to explore sequence-structure relationships for assembly, reactivity and complexation, namely: (i) strategic editing of short peptide sequences; (ii) computational approaches to predicting and comparing assembly behaviours; (iii) dynamic peptide libraries that explore the free energy landscape. These approaches give rise to guiding principles on controlling order/disorder, complexation and reactivity by peptide sequence design.

Molecular simulations of self-assembling bio-inspired supramolecular systems and their connection to experiments

In bionanotechnology, the field of creating functional materials consisting of bio-inspired molecules, the function and shape of a nanostructure only appear through the assembly of many small molecules together. The large number of building blocks required to define a nanostructure combined with the many degrees of freedom in packing small molecules has long precluded molecular simulations, but recent advances in computational hardware as well as software have made classical simulations available to this strongly expanding field. Here, we review the state of the art in simulations of self-assembling bio-inspired supramolecular systems. We will first discuss progress in force fields, simulation protocols and enhanced sampling techniques using recent examples. Secondly, we will focus on efforts to enable the comparison of experimentally accessible observables and computational results. Experimental quantities that can be measured by microscopy, spectroscopy and scattering can be linked to simulation output either directly or indirectly, via quantum mechanical or semi-empirical techniques. Overall, we aim to provide an overview of the various computational approaches to understand not only the molecular architecture of nanostructures, but also the mechanism of their formation.

Reconstruction of Atomistic Structures from Coarse-Grained Models for Protein-DNA Complexes

While coarse-grained (CG) simulations have widely been used to accelerate structure sampling of large biomolecular complexes, they are unavoidably less accurate and thus the reconstruction of all-atom (AA) structures and the subsequent refinement is desirable. In this study we developed an efficient method to reconstruct AA structures from sampled CG protein-DNA complex models, which attempts to model the protein-DNA interface accurately. First we developed a method to reconstruct atomic details of DNA structures from a three-site per nucleotide CG model, which uses a DNA fragment library. Next, for the protein-DNA interface, we referred to the side chain orientations in the known structure of the target interface when available. The other parts are modeled by existing tools. We confirmed the accuracy of the protocol in various aspects including the structure deviation in the self-reproduction, the base pair reproducibility, atomic contacts at the protein-DNA interface, and feasibility of the posterior AA simulations.

Local bond order parameters for accurate determination of crystal structures in two and three dimensions

Local order parameters for the characterization of liquid and different two- and three-dimensional crystalline structures are presented.

Molecular simulations of peptide amphiphiles

This review describes recent progress in the area of molecular simulations of peptide assemblies, including peptide-amphiphiles and drug-amphiphiles. The ability to predict the structure and stability of peptide self-assemblies from the molecular level up is vital to the field of nanobiotechnology. Computational methods such as molecular dynamics offer the opportunity to characterize intermolecular forces between peptide-amphiphiles that are critical to the self-assembly process. Furthermore, these computational methods provide the ability to computationally probe the structure of these supramolecular assemblies at the molecular level, which is a challenge experimentally. Herein, we briefly highlight progress in the areas of all-atomistic and coarse-grained simulation studies investigating the self-assembly process of short peptides and peptide amphiphiles. We also discuss recent all-atomistic and coarse-grained simulations of the self-assembly of a drug-amphiphile into elongated filaments. Next, we discuss how these computational methods can provide further insight into the pathway of cylindrical nanofiber formation and predict their biocompatibility by studying the interaction of these peptide-amphiphile nanostructures with model cell membranes.

Molecular Structuring and Percolation Transition in Hydrated Sulfonated Poly(ether ether ketone) Membranes

The extent of phase separation and water percolation in sulfonated membranes are the key to their performance in fuel cells. Toward this, the effect of hydration on the morphology and transport characteristics of sulfonated poly(ether ether ketone), sPEEK, membrane is investigated using atomistic molecular dynamics simulation at various hydration levels(λ: number of water molecules per sulfonate group). The evolution of local morphology is investigated using structural correlations and minimum pair distances. Transport properties are probed using mean squared displacements and diffusion coefficients. The water-sulfonate interaction in sPEEK is found to be stronger than that in Nafion, as observed in experiments. Analyses indicate the presence of narrow connected path of water and hydronium at λ = 4 and large domains, spanning half the simulation box, at λ = 15. The behavior of membrane water remains far from bulk as indicated by its diffusion coefficient. The persistence of small isolated water clusters demonstrates the extent of phase separation in sPEEK to be lesser than that in Nafion. Analyses at molecular and collective levels suggest the occurrence of a percolation transition between λ = 8 and 10, which leads to a connected network of water channels in the membrane, thereby boosting the hydronium mobility.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

Mesoscale Simulation of Asphaltene Aggregation

Asphaltenes constitute a heavy aromatic crude oil fraction with a propensity to aggregate and precipitate out of solution during petroleum processing. Aggregation is thought to proceed according to the Yen-Mullins hierarchy, but the molecular mechanisms underlying mesoscopic assembly remain poorly understood. By combining coarse-grained molecular models parametrized using all-atom data with high-performance GPU hardware, we have performed molecular dynamics simulations of the aggregation of hundreds of asphaltenes over microsecond time scales. Our simulations reveal a hierarchical self-assembly mechanism consistent with the Yen-Mullins model, but the details are sensitive and depend on asphaltene chemistry and environment. At low concentrations asphaltenes exist predominantly as dispersed monomers. Upon increasing concentration, we first observe parallel stacking into 1D rod-like nanoaggregates, followed by the formation of clusters of nanoaggregates associated by offset, T-shaped, and edge-edge stacking. Asphaltenes possessing long aliphatic side chains cannot form nanoaggregate clusters due to steric repulsions between their aliphatic coronae. At very high concentrations, we observe a porous percolating network of rod-like nanoaggregates suspended in a sea of interpenetrating aliphatic side chains with a fractal dimension of ∼2. The lifetime of the rod-like aggregates is described by an exponential distribution reflecting a dynamic equilibrium between coagulation and fragmentation.

Investigation of interphase effects in silica-polystyrene nanocomposites based on a hybrid molecular-dynamics-finite-element simulation framework

A recently developed hybrid method is employed to study the mechanical behavior of silica-polystyrene nanocomposites (NCs) under uniaxial elongation. The hybrid method couples a particle domain to a continuum domain. The region of physical interest, i.e., the interphase around a nanoparticle (NP), is treated at molecular resolution, while the surrounding elastic continuum is handled with a finite-element approach. In the present paper we analyze the polymer behavior in the neighborhood of one or two nanoparticle(s) at molecular resolution. The coarse-grained hybrid method allows us to simulate a large polymer matrix region surrounding the nanoparticles. We consider NCs with dilute concentration of NPs embedded in an atactic polystyrene matrix formed by 300 chains with 200 monomer beads. The overall orientation of polymer segments relative to the deformation direction is determined in the neighborhood of the nanoparticle to investigate the polymer response to this perturbation. Calculations of strainlike quantities give insight into the deformation behavior of a system with two NPs and show that the applied strain and the nanoparticle distance have significant influence on the deformation behavior. Finally, we investigate to what extent a continuum-based description may account for the specific effects occurring in the interphase between the polymer matrix and the NPs.

Thermodynamics of the self-assembly of non-ionic chromonic molecules using atomistic simulations. The case of TP6EO2M in aqueous solution

Atomistic molecular dynamic simulations have been performed for the non-ionic chromonic liquid crystal 2,3,6,7,10,11-hexa-(1,4,7-trioxa-octyl)-triphenylene (TP6EO2M) in aqueous solution. TP6EO2M molecules consist of a central poly-aromatic core (a triphenylene ring) functionalized by six hydrophilic ethyleneoxy (EO) chains, and have a strong tendency to aggregate face-to-face into stacks even in very dilute solution. We have studied self-assembly of the molecules in the low concentration range corresponding to an isotropic solution of aggregates, using two force fields GAFF and OPLS. Our results reveal that the GAFF force field, even though it was successfully used previously for modelling of ionic chromonics, overestimates the attraction of TP6EO2M molecules in water. This results in an aggregation free energy which is too high, a reduced hydration of EO chains and, therefore, molecular self-assembly into compact disordered clusters instead of stacks. In contrast, use of the OPLS force field, leads to self-assembly into ordered stacks in agreement with earlier experimental studies of triphenylene-based chromonics. The free energy of association follows a "quasi-isodesmic" pattern, where the binding free energy of two molecules to form a dimer is of the order of 2.5 RT larger than the corresponding energy of addition of a molecule into a stack. The obtained value for the binding free energy, ΔG=-12 RT, is found to be in line with the published values for typical ionic chromonics (-7 to -12 RT), and agrees reasonably well with the experimental results for this system. The calculated interlayer distance between the molecules in a stack is 0.37 nm, which is at the top of the range found for typical chromonics (0.33-0.37 nm). We suggest that the relatively large layer spacing can be attributed to the repulsion between EO side chains.

Simulation of metal–organic framework self-assembly

Spontaneous growth of metal–organic frameworks (MOFs) composed of metal ions and 4,4′-bipyridine ligands was successfully demonstrated by molecular dynamics simulations, starting from a random initial placement of the metals and the ligands.

Conformational dynamics and aggregation behavior of piezoelectric diphenylalanine peptides in an external electric field

Aromatic peptides including diphenylalanine (FF) have the capacity to self-assemble into ordered, biocompatible nanostructures with piezoelectric properties relevant to a variety of biomedical applications. Electric fields are commonly applied to align FF nanotubes, yet little is known about the effect of the electric field on the assembly process. Using all-atom molecular dynamics with explicit water molecules, we examine the response of FF monomers to the application of a constant external electric field over a range of intensities. We probe the aggregation mechanism of FF peptides, and find that the presence of even relatively weak fields can accelerate ordered aggregation, primarily by facilitating the alignment of individual molecular dipole moments. This is modulated by the conformational response of individual FF peptides (e.g., backbone stretching) and by the cooperative alignment of neighboring FF and water molecules. These observations may facilitate future studies on the controlled formation of nanostructured aggregates of piezoelectric peptides and the understanding of their electro-mechanical properties.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Triphenylalanine peptides self-assemble into nanospheres and nanorods that are different from the nanovesicles and nanotubes formed by diphenylalanine peptides

Understanding the nature of the self-assembly of peptide nanostructures at the molecular level is critical for rational design of functional bio-nanomaterials. Recent experimental studies have shown that triphenylalanine(FFF)-based peptides can self-assemble into solid plate-like nanostructures and nanospheres, which are different from the hollow nanovesicles and nanotubes formed by diphenylalanine(FF)-based peptides. In spite of extensive studies, the assembly mechanism and the molecular basis for the structural differences between FFF and FF nanostructures remain poorly understood. In this work, we first investigate the assembly process and the structural features of FFF nanostructures using coarse-grained molecular dynamics simulations, and then compare them with FF nanostructures. We find that FFF peptides spontaneously assemble into solid nanometer-sized nanospheres and nanorods with substantial β-sheet contents, consistent with the structural properties of hundred-nanometer-sized FFF nano-plates characterized by FT-IR spectroscopy. Distinct from the formation mechanism of water-filled FF nanovesicles and nanotubes reported in our previous study, intermediate bilayers are not observed during the self-assembly process of FFF nanospheres and nanorods. The peptides in FFF nanostructures are predominantly anti-parallel-aligned, which can form larger sizes of β-sheet-like structures than the FF counterparts. In contrast, FF peptides exhibit lipid-like assembly behavior and assemble into bilayered nanostructures. Furthermore, although the self-assembly of FF and FFF peptides is mostly driven by side chain-side chain (SC-SC) aromatic stacking interactions, the main chain-main chain (MC-MC) interactions also play an important role in the formation of fine structures of the assemblies. The delicate interplay between MC-MC and SC-SC interactions results in the different nanostructures formed by the two peptides. These findings provide new insights into the structure and self-assembly pathway of di-/tri-phenylalanine peptide assemblies, which might be helpful for the design of bioinspired nanostructures.

Short peptide based self-assembled nanostructures: implications in drug delivery and tissue engineering

Self-assembling peptides with many potential biomedical applications.

Coarse-Grained Models for Protein-Cell Membrane Interactions

The physiological properties of biological soft matter are the product of collective interactions, which span many time and length scales. Recent computational modeling efforts have helped illuminate experiments that characterize the ways in which proteins modulate membrane physics. Linking these models across time and length scales in a multiscale model explains how atomistic information propagates to larger scales. This paper reviews continuum modeling and coarse-grained molecular dynamics methods, which connect atomistic simulations and single-molecule experiments with the observed microscopic or mesoscale properties of soft-matter systems essential to our understanding of cells, particularly those involved in sculpting and remodeling cell membranes.

Effect of solvent on the self-assembly of dialanine and diphenylalanine peptides

Diphenylalanine (FF) is a very common peptide with many potential applications, both biological and technological, due to a large number of different nanostructures which it attains. The current work concerns a detailed study of the self-assembled structures of FF in two different solvents, an aqueous (H2O) and an organic (CH3OH) through simulations and experiments. Detailed atomistic molecular dynamics (MD) simulations of FF in both solvents have been performed, using an explicit solvent model. The self-assembling propensity of FF in water is obvious while in methanol a very weak self-assembling propensity is observed. We studied and compared structural properties of FF in the two different solvents and a comparison with a system of dialanine (AA) in the corresponding solvents was also performed. In addition, temperature-dependence studies were carried out. Finally, the simulation predictions were compared to new experimental data, which were produced in the framework of the present work. A very good qualitative agreement between simulation and experimental observations was found.

Mixing MARTINI: electrostatic coupling in hybrid atomistic-coarse-grained biomolecular simulations

Hybrid molecular dynamics simulations of atomistic (AA) solutes embedded in coarse-grained (CG) environment can substantially reduce the computational cost with respect to fully atomistic simulations. However, interfacing both levels of resolution is a major challenge that includes a balanced description of the relevant interactions. This is especially the case for polar solvents such as water, which screen the electrostatic interactions and thus require explicit electrostatic coupling between AA and CG subsystems. Here, we present and critically test computationally efficient hybrid AA/CG models. We combined the Gromos atomistic force field with the MARTINI coarse-grained force field. To enact electrostatic coupling, two recently developed CG water models with explicit electrostatic interactions were used: the polarizable MARTINI water model and the BMW model. The hybrid model was found to be sensitive to the strength of the AA-CG electrostatic coupling, which was adjusted through the relative dielectric permittivity εr(AA-CG). Potentials of mean force (PMFs) between pairs of amino acid side chain analogues in water and partitioning free enthalpies of uncharged amino acid side chain analogues between apolar solvent and water show significant differences between the hybrid simulations and the fully AA or CG simulations, in particular for charged and polar molecules. For apolar molecules, the results obtained with the hybrid AA/CG models are in better agreement with the fully atomistic results. The structures of atomistic ubiquitin solvated in CG water and of a single atomistic transmembrane α-helix and the transmembrane portion of an atomistic mechanosensitive channel in CG lipid bilayers were largely maintained during 50-100 ns of AA/CG simulations, partly due to an overstabilization of intramolecular interactions. This work highlights some key challenges on the way toward hybrid AA/CG models that are both computationally efficient and sufficiently accurate for biomolecular simulations.

Reduced atomic pair-interaction design (RAPID) model for simulations of proteins

Increasingly, theoretical studies of proteins focus on large systems. This trend demands the development of computational models that are fast, to overcome the growing complexity, and accurate, to capture the physically relevant features. To address this demand, we introduce a protein model that uses all-atom architecture to ensure the highest level of chemical detail while employing effective pair potentials to represent the effect of solvent to achieve the maximum speed. The effective potentials are derived for amino acid residues based on the condition that the solvent-free model matches the relevant pair-distribution functions observed in explicit solvent simulations. As a test, the model is applied to alanine polypeptides. For the chain with 10 amino acid residues, the model is found to reproduce properly the native state and its population. Small discrepancies are observed for other folding properties and can be attributed to the approximations inherent in the model. The transferability of the generated effective potentials is investigated in simulations of a longer peptide with 25 residues. A minimal set of potentials is identified that leads to qualitatively correct results in comparison with the explicit solvent simulations. Further tests, conducted for multiple peptide chains, show that the transferable model correctly reproduces the experimentally observed tendency of polyalanines to aggregate into β-sheets more strongly with the growing length of the peptide chain. Taken together, the reported results suggest that the proposed model could be used to succesfully simulate folding and aggregation of small peptides in atomic detail. Further tests are needed to assess the strengths and limitations of the model more thoroughly.

Systematic methods for structurally consistent coarse-grained models

This chapter provides a primer on theories for coarse-grained (CG) modeling and, in particular, reviews several systematic methods for determining effective potentials for CG models. The chapter first reviews a statistical mechanics framework for relating atomistic and CG models. This framework naturally leads to a quantitative criterion for CG models that are "consistent" with a particular atomistic model for the same system. This consistency criterion is equivalent to minimizing the relative entropy between the two models. This criterion implies that a many-body PMF is the appropriate potential for a CG model that is consistent with a particular atomistic model. This chapter then presents a unified exposition of the theory and numerical methods for several approaches for approximating this many-body PMF. Finally, this chapter closes with a brief discussion of a few of the outstanding challenges facing the field of systematic coarse-graining.

Probing the self-assembly mechanism of diphenylalanine-based peptide nanovesicles and nanotubes

Nanostructures, particularly those from peptide self-assemblies, have attracted great attention lately due to their potential applications in nanotemplating and nanotechnology. Recent experimental studies reported that diphenylalanine-based peptides can self-assemble into highly ordered nanostructures such as nanovesicles and nanotubes. However, the molecular mechanism of the self-organization of such well-defined nanoarchitectures remains elusive. In this study, we investigate the assembly pathway of 600 diphenylalanine (FF) peptides at different peptide concentrations by performing extensive coarse-grained molecular dynamics (MD) simulations. Based on forty 0.6-1.8 μs trajectories at 310 K starting from random configurations, we find that FF dipeptides not only spontaneously assemble into spherical vesicles and nanotubes, consistent with previous experiments, but also form new ordered nanoarchitectures, namely, planar bilayers and a rich variety of other shapes of vesicle-like structures including toroid, ellipsoid, discoid, and pot-shaped vesicles. The assembly pathways are concentration-dependent. At low peptide concentrations, the self-assembly involves the fusion of small vesicles and bilayers, whereas at high concentrations, it occurs through the formation of a bilayer first, followed by the bending and closure of the bilayer. Energetic analysis suggests that the formation of different nanostructures is a result of the delicate balance between peptide-peptide and peptide-water interactions. Our all-atom MD simulation shows that FF nanostructures are stabilized by a combination of T-shaped aromatic stacking, interpeptide head-to-tail hydrogen-bonding, and peptide-water hydrogen-bonding interactions. This study provides, for the first time to our knowledge, the self-assembly mechanism and the molecular organization of FF dipeptide nanostructures.