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.

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.

Thermoset resin curing simulation using quantum-chemical reaction path calculation and dissipative particle dynamics

Thermoset resin, which is commonly used as a matrix in carbon-fiber-reinforced plastic, requires curing procedures. We propose a curing simulation technique involving a dissipative particle dynamics (DPD) simulation, which can simulate a larger system and longer time period than those of conventional all-atom molecular dynamics (AA-MD) simulations. The proposed curing DPD simulation can represent the thermoset resin exothermic reaction process precisely by considering each reactivity according to the reaction types calculated via quantum-chemical reaction path calculations. The cure reaction process given by the curing DPD simulation agrees well with that given by a conventional curing AA-MD simulation, but with run-time and computational-resource reductions of 1/480 and 1/10 times, respectively. We also conduct reverse mapping, through which the AA-MD system can be reconstructed from the DPD system, to evaluate the structural and thermomechanical properties. The X-ray diffraction pattern and thermomechanical properties of the reconstructed system agree well with those of the systems derived from the curing AA-MD simulation and experimental setup. Therefore, a cured-resin AA-MD system can be obtained from a curing DPD simulation at an extremely low computational cost, and the thermomechanical properties can be evaluated precisely using this system. The proposed curing simulation technique can be applied in high-throughput screening for better materials properties and in large system calculations.

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.

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.

Maximizing the absorption of small cosolutes inside neutral hydrogels: steric exclusion versus hydrophobic adhesion

In this work the equilibrium absorption of nanometric cosolutes (which could represent drugs, reactants, small globular proteins and other kind of biomacromolecules) inside neutral hydrogels is studied. We specially focus on exploring, for different swelling states, the competition between the steric exclusion induced by the cross-linked polymer network constituting the hydrogel, and the solvent-induced short-range hydrophobic attraction between the polymer chains and the cosolute particle. For this purpose, the cosolute partition coefficient is calculated by means of coarse-grained grand canonical Monte Carlo simulations, and the results are compared to theoretical predictions based on the calculation of the excluded and binding volume around the polymer chains. For small hydrophobic attractions or large cosolute sizes, the steric repulsion dominates, and the partition coefficient decreases monotonically with the polymer volume fraction, ϕ_m. However, for large enough hydrophobic attraction strength, the interplay between hydrophobic adhesion and the steric exclusion leads to a maximum in the partition coefficient at certain intermediate polymer density. Good qualitative and quantitative agreement is achieved between simulation results and theoretical predictions in the limit of small ϕ_m, pointing out the importance of geometrical aspects of the cross-linked polymer network, even for hydrogels in the swollen state. In addition, the theory is able to predict analytically the onset of the maximum formation in terms of the details of the cosolute-monomer pair interaction, in good agreement with simulations too. Finally, the effect of the many-body attractions between the cosolute and multiple polymer chains is quantified. The results clearly show that these many-body attractions play a very relevant role determining the cosolute binding, enhancing its absorption in more than one order of magnitude.

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.

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.

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.

Representability and Transferability of Kirkwood-Buff Iterative Boltzmann Inversion Models for Multicomponent Aqueous Systems

We discuss the application of the Kirkwood-Buff iterative Boltzmann inversion (KB-IBI) method for molecular coarse-graining (Ganguly et al. J. Chem. Theory Comput. 2012, 8, 1802) to multicomponent aqueous mixtures. Using a fixed set of effective single-site solvent-solvent potentials previously derived for binary urea-water systems, solute-solvent and solute-solute KB-IBI coarse-grained (CG) potentials have been derived for benzene in urea-water mixtures. Preferential solvation and salting-in coefficients of benzene are reproduced in quantitative agreement with the atomistic force field model. The transferability of the CG models is discussed, and it is shown that free energies of formation of hydrophobic benzene clusters obtained from simulations with the CG model are in good agreement with results obtained from all-atom simulations. The state-point representability of the CG models is discussed with respect to reproducing thermodynamic quantities such as pressure, isothermal compressibility, and preferential solvation. Combined use of KB-IBI and pressure corrections in deriving single-site CG models for pure-water, binary mixtures of urea and water, and ternary mixtures of benzene in urea-water at infinite benzene dilution provides an improved scheme to representing the atomistic pressure and the preferential solvation between the solution components. It is also found that the application of KB-IBI leads to a faster and improved convergence of the pressure and potential energy compared to the IBI method.

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.

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.

Predicting the DNA sequence dependence of nanopore ion current using atomic-resolution Brownian dynamics

It has become possible to distinguish DNA molecules of different nucleotide sequences by measuring ion current passing through a narrow pore containing DNA. To assist experimentalists in interpreting the results of such measurements and to improve the DNA sequence detection method, we have developed a computational approach that has both the atomic-scale accuracy and the computational efficiency required to predict DNA sequence-specific differences in the nanopore ion current. In our Brownian dynamics method, the interaction between the ions and DNA is described by three-dimensional potential of mean force maps determined to a 0.03 nm resolution from all-atom molecular dynamics simulations. While this atomic-resolution Brownian dynamics method produces results with orders of magnitude less computational effort than all-atom molecular dynamics requires, we show here that the ion distributions and ion currents predicted by the two methods agree. Finally, using our Brownian dynamics method, we find that a small change in the sequence of DNA within a pore can cause a large change in the ion current, and validate this result with all-atom molecular dynamics.

Virtual Screening for Dipeptide Aggregation: Toward Predictive Tools for Peptide Self-Assembly

Several short peptide sequences are known to self-assemble into supramolecular nanostructures with interesting properties. In this study, coarse-grained molecular dynamics is employed to rapidly screen all 400 dipeptide combinations and predict their ability to aggregate as a potential precursor to their self-assembly. The simulation protocol and scoring method proposed allows a rapid determination of whether a given peptide sequence is likely to aggregate (an indicator for the ability to self-assemble) under aqueous conditions. Systems that show strong aggregation tendencies in the initial screening are selected for longer simulations, which result in good agreement with the known self-assembly or aggregation of dipeptides reported in the literature. Our extended simulations of the diphenylalanine system show that the coarse-grain model is able to reproduce salient features of nanoscale systems and provide insight into the self-assembly process for this system.

Hybrid simulations: combining atomistic and coarse-grained force fields using virtual sites

Hybrid simulations, in which part of the system is represented at atomic resolution and the remaining part at a reduced, coarse-grained, level offer a powerful way to combine the accuracy associated with the atomistic force fields to the sampling speed obtained with coarse-grained (CG) potentials. In this work we introduce a straightforward scheme to perform hybrid simulations, making use of virtual sites to couple the two levels of resolution. With the help of these virtual sites interactions between molecules at different levels of resolution, i.e. between CG and atomistic molecules, are treated the same way as the pure CG-CG interactions. To test our method, we combine the Gromos atomistic force field with a number of coarse-grained potentials, obtained through several approaches that are designed to obtain CG potentials based on an existing atomistic model, namely iterative Boltzmann inversion, force matching, and a potential of mean force subtraction procedure (SB). We also explore the use of the MARTINI force field for the CG potential. A simple system, consisting of atomistic butane molecules dissolved in CG butane, is used to study the performance of our hybrid scheme. Based on the potentials of mean force for atomistic butane in CG solvent, and the properties of 1:1 mixtures of atomistic and CG butane which should exhibit ideal mixing behavior, we conclude that the MARTINI and SB potentials are particularly suited to be combined with the atomistic force field. The MARTINI potential is subsequently used to perform hybrid simulations of atomistic dialanine peptides in both CG butane and water. Compared to a fully atomistic description of the system, the hybrid description gives similar results provided that the dielectric screening of water is accounted for. Within the field of biomolecules, our method appears ideally suited to study e.g. protein-ligand binding, where the active site and ligand are modeled in atomistic detail and the rest of the protein, together with the solvent, is coarse-grained.

Multiscale coarse-graining of the protein energy landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.

Biological function originates from the dynamical motions of proteins in response to cellular stimuli. Protein dynamics arise from physical interactions that are well-predicted by detailed atomistic simulations. In order to examine large protein complexes on long timescales of biological importance, however, coarse-grained simulation approaches are needed to complement experiment. Previous coarse-grained models have proved successful for investigations involving a given protein's native structure, including protein folding and structure prediction. We construct a model capable of simulating proteins regardless of their sequence or structure. The present coarse-grained model was, however, developed rigorously from the underlying atomistic forces as opposed to knowledge-based or ad hoc parameterizations. Examination of the model predictions on various accessible timescales reveals successes and limitations of the model. While functionally relevant conformational transitions can be studied, the coarse-grained representation has some difficulty with the ab initio folding of the peptide chain into its proper structure. Our observations highlight the complex molecular nature of a protein's underlying energy landscape, offering rigorous insight into the information missing in reduced representations of the peptide chain. With these caveats in mind, the physical interaction–based, coarse-grained model will find application in simulations of a wide variety of proteins and continue to guide future coarse-graining efforts.

Versatile Object-Oriented Toolkit for Coarse-Graining Applications

Coarse-graining is a systematic way of reducing the number of degrees of freedom representing a system of interest. Several coarse-graining techniques have so far been developed, such as iterative Boltzmann inversion, force-matching, and inverse Monte Carlo. However, there is no unified framework that implements these methods and that allows their direct comparison. We present a versatile object-oriented toolkit for coarse-graining applications (VOTCA) that implements these techniques and that provides a flexible modular platform for the further development of coarse-graining techniques. All methods are illustrated and compared by coarse-graining the SPC/E water model, liquid methanol, liquid propane, and a single molecule of hexane.