We introduce a coarse-grained model of DNA with bases modeled as rigid-body ellipsoids to capture their anisotropic stereochemistry. Interaction potentials are all physicochemical and generated from all-atom simulation/parameterization with minimal phenomenology. Persistence length, degree of stacking, and twist are studied by molecular dynamics simulation as functions of temperature, salt concentration, sequence, interaction potential strength, and local position along the chain, for both single-and double-stranded DNA where appropriate. The model of DNA shows several phase transitions and crossover regimes in addition to dehybridization, including unstacking, untwisting, and collapse which affect mechanical properties such as rigidity and persistence length. The model also exhibits chirality with a stable right-handed and metastable left-handed helix.

Protein aggregation involves the self-assembly of normally soluble proteins into large supramolecular assemblies. The typical end product of aggregation is the amyloid fibril, an extended structure enriched in β-sheet content. The aggregation process has been linked to a number of diseases, most notably Alzheimer's disease, but fibril formation can also play a functional role in certain organisms. This review focuses on theoretical studies of the process of fibril formation, with an emphasis on the computational models and methods commonly used to tackle this problem.

This Perspective highlights recent computational approaches to protein aggregation, from coarse-grained models to atomistic simulations, using the islet amyloid polypeptide (IAPP) as a case study. We review salient open questions where simulations can make an impact, discuss the successes and challenges met by simulations, and explore new directions.

The aggregation of peptides on a lipid bilayer is studied using coarse-grained molecular dynamics in implicit solvent. Peptides bind to and self-assemble on the membrane surface into β-rich fibrillar aggregates, even under conditions where only disordered oligomers form in bulk solution. Relative to a solid surface, the membrane surface facilitates peptide mobility and a more complex network of morphology transitions as aggregation proceeds. Additionally, final aggregate structures realized on the membrane surface are distinct from those observed on a comparable solid surface. The aggregated fibrils alter the local structure and material properties of the lipid bilayer in their immediate vicinity but have only a modest effect on the overall bending rigidity of the bilayer.

The effect of seeds in templating the morphology of peptide aggregates is examined using molecular dynamics simulations and a coarse-grained peptide representation. Varying the nature of the aggregate seed between β-sheet, amorphous, and β-barrel seeds leads to different aggregation pathways and to morphologically different aggregates. Similar effects are seen by varying the β-sheet propensity of the free peptides. For a fibrillar seed and free peptides of high β-sheet propensity, fibrillar growth occurred by means of direct attachment (without structural rearrangement) of free individual peptides and small ordered oligomers onto the seed. For a fibrillar seed and free peptides of low β-sheet propensity, fibrillar growth occurred through a dock-lock mechanism, in which the free peptides first docked onto the seed, and then locked on, extending and aligning to join the fibril. Amorphous seeds absorbed free peptides into themselves indiscriminately, with any fibrillar rearrangement subsequent to this absorption by means of a condensation-ordering transition. Although the mechanisms observed by varying peptide β-sheet propensity are diverse, the initial pathways can always be broken down into the following steps: (i) the free peptides diffuse in the bulk and attach individually to the seed; (ii) the free peptides diffuse and aggregate among themselves; (iii) the free peptide oligomers collide with the seed; and (iv) the free oligomers merge with the seed and rearrange in a manner dependent on the backbone flexibility of both the free and seed peptides. Our simulations indicate that it is possible to sequester peptides from amorphous aggregates into fibrils, and also that aggregate morphology (and thus cytoxicity) can be controlled by introducing seeds of aggregate-compatible peptides with differing β-sheet propensities into the system.

Mechanisms of peptide aggregation on hydrophobic surfaces are explored using molecular dynamics simulations with a coarse-grained peptide representation. Systems of peptides are studied with varying degrees of backbone rigidity (a measure of β-sheet propensity) and degrees of attraction between their hydrophobic residues and the surface. Multiple pathways for aggregation are observed, depending on the surface attraction and peptide β-sheet propensity. For the case of a single-layered β-sheet fibril forming on the surface (a dominant structure seen in all simulations), three mechanisms are observed: (a) a condensation-ordering transition where a bulk-formed amorphous aggregate binds to the surface and subsequently rearranges to form a fibril; (b) the initial formation of a single-layered fibril in the bulk depositing flat on the surface; and (c) peptides binding individually to the surface and nucleating fibril formation by individual peptide deposition. Peptides with a stiffer chiral backbone prefer mechanism (b) over (a), and stronger surface attractions prefer mechanism (c) over (a) and (b). Our model is compared to various similar experimental systems, and an agreement was found in terms of the surface increasing the degree of fibrillar aggregation, with the directions of fibrillar growth matching the crystallographic symmetry of the surface. Our simulations provide details of aggregate growth mechanisms on scales inaccessible to either experiment or atomistic simulations.

The formation of peptide aggregates mediated by an attractive surface is investigated using replica exchange molecular dynamics simulations with a coarse-grained peptide representation. In the absence of a surface, the peptides exhibit a range of aggregate morphologies, including amorphous aggregates, β-barrels and multi-layered fibrils, depending on the chiral stiffness of the chain (a measure of its β-sheet propensity). In contrast, aggregate morphology in the presence of an attractive surface depends more on surface attraction than on peptide chain stiffness, with the surface favoring fibrillar structures. Peptide-peptide interactions couple to peptide-surface interactions cooperatively to affect the assembly process both qualitatively (in terms of aggregate morphology) and quantitatively (in terms of transition temperature and transition sharpness). The frequency of ordered fibrillar aggregates, the surface binding transition temperature, and the sharpness of the binding transition all increase with both surface attraction and chain stiffness.

We investigate the role of lipid chemical potential on the shape, thickness, and molecular orientation (lipid tilting relative to the monolayer surface normal) of lipid bilayers via a continuum-level model. We predict that decreasing the chemical potential at constant temperature, which is associated with an increase in surface tension via the Gibbs-Duhem relation, leads both to the well known reduction in thermal membrane undulations and also to increasing fluctuation amplitudes for bilayer thickness and molecular orientation. These trends are shown to be in good agreement with molecular simulations, however it is impossible to achieve full quantitative agreement between theory and simulation within the confines of the present model. We suggest that the assumption of lipid volume incompressibility, common to our theoretical treatment and other continuum models in the literature, may be partially responsible for the quantitative discrepancies between theory and simulation.