Luca Larini

The multiscale coarse-graining method. VI. Implementation of three-body coarse-grained potentials

Many methodologies have been proposed to build reliable and computationally fast coarse-grained potentials. Typically, these force fields rely on the assumption that the relevant properties of the system under examination can be reproduced using a pairwise decomposition of the effective coarse-grained forces. In this work it is shown that an extension of the multiscale coarse-graining technique can be employed to parameterize a certain class of two-body and three-body force fields from atomistic configurations. The use of explicit three-body potentials greatly improves the results over the more commonly used two-body approximation. The method proposed here is applied to develop accurate one-site coarse-grained water models.

Regulation and aggregation of intrinsically disordered peptides

Significance The microtubule-regulating protein tau is a prototypical intrinsically disordered protein (IDP) that plays an important physiological role in the human body; however, aggregates of tau are a pathological hallmark of Alzheimer’s disease. Here we demonstrate through simulations and experiments with an aggregating tau fragment that cosolvent interactions can significantly affect the balance between hydrogen bonds and salt bridge formation in IDPs, subsequently determining their preferred conformations. These subtle perturbations can dramatically shift IDPs from compact ensembles to extended ones, thereby influencing aggregate formation. These results lend considerable insight into the biophysics of the regulation and aggregation of IDPs. Intrinsically disordered proteins (IDPs) are a unique class of proteins that have no stable native structure, a feature that allows them to adopt a wide variety of extended and compact conformations that facilitate a large number of vital physiological functions. One of the most well-known IDPs is the microtubule-associated tau protein, which regulates microtubule growth in the nervous system. However, dysfunctions in tau can lead to tau oligomerization, fibril formation, and neurodegenerative disease, including Alzheimer’s disease. Using a combination of simulations and experiments, we explore the role of osmolytes in regulating the conformation and aggregation propensities of the R2/wt peptide, a fragment of tau containing the aggregating paired helical filament (PHF6*). We show that the osmolytes urea and trimethylamine N-oxide (TMAO) shift the population of IDP monomer structures, but that no new conformational ensembles emerge. Although urea halts aggregation, TMAO promotes the formation of compact oligomers (including helical oligomers) through a newly proposed mechanism of redistribution of water around the perimeter of the peptide. We put forth a “superposition of ensembles” hypothesis to rationalize the mechanism by which IDP structure and aggregation is regulated in the cell.

Role of β-hairpin formation in aggregation: the self-assembly of the amyloid-β(25-35) peptide.

The amyloid-β(25-35) peptide plays a key role in the etiology of Alzheimers disease due to its extreme toxicity even in the absence of aging. Because of its high tendency to aggregate and its low solubility in water, the structure of this peptide is still unknown. In this work, we sought to understand the early stages of aggregation of the amyloid-β(25-35) peptide by conducting simulations of oligomers ranging from monomers to tetramers. Our simulations show that although the monomer preferentially adopts a β-hairpin conformation, larger aggregates have extended structures, and a clear transition from compact β-hairpin conformations to extended β-strand structures occurs between dimers and trimers. Even though β-hairpins are not present in the final architecture of the fibril, our simulations indicate that they play a critical role in fibril growth. Our simulations also show that β-sheet structures are stabilized when a β-hairpin is present at the edge of the sheet. The binding of the hairpin to the sheet leads to a subsequent destabilization of the hairpin, with part of the hairpin backbone dangling in solution. This free section of the peptide can then recruit an extra monomer from solution, leading to further sheet extension. Our simulations indicate that the peptide must possess sufficient conformational flexibility to switch between a hairpin and an extended conformation in order for β-sheet extension to occur, and offer a rationalization for the experimental observation that overstabilizing a hairpin conformation in the monomeric state (for example, through chemical cross-linking) significantly hampers the fibrillization process.

Double Resolution Model for Studying TMAO/Water Effective Interactions

The structural properties of water molecules surrounding TMAO molecules are studied using a newly developed atomistic force field for TMAO, combined with a multiscale coarse-graining (MS-CG) force field derived from the atomistic simulations. The all-atom force field is parametrized to work with the OPLS force field and with SPC, TIP3P, and TIP4P water models. The dual-resolution modeling enables a complete study of the dynamical and structural properties of the system, with the CG model providing important new physical insights into which interactions are critical in determining the structure of water around TMAO. TMAO is an osmolyte that stabilizes protein structures under conditions of chemical, thermal, and pressure denaturation. This molecule is excluded from the surface of proteins, and its effect on protein stability is mediated through TMAO-water interactions. We find that TMAO strongly binds two to three water molecules and, surprisingly, that methyl groups repel both the other methyl groups of TMAO and water molecules alike. The latter result is important because it shows that methyl groups are not interacting with each other through the expected hydrophobic effect (which would be attractive and not repulsive) and that the repulsion of water molecules forces a clathrate-like hydrogen bond network around them. We speculate that TMAO is excluded from the vicinity of the protein because the peculiar structure of water around TMAO prevents this molecule from coming in close contact with the protein.

Tau Assembly: The Dominant Role of PHF6 (VQIVYK) in Microtubule Binding Region Repeat R3

Self-aggregation of the microtubule-binding protein Tau reduces its functionality and is tightly associated with Tau-related diseases, termed tauopathies. Tau aggregation is also strongly associated with two nucleating six-residue segments, namely PHF6 (VQIVYK) and PHF6* (VQIINK). In this paper, using experiments and computational modeling, we study the self-assembly of individual and binary mixtures of Tau fragments containing PHF6* (R2/wt; (273)GKVQIINKKLDL(284)) and PHF6 (R3/wt; (306)VQIVYKPVDLSK(317)) and a mutant R2/ΔK280 associated with a neurodegenerative tauopathy. The initial stage of aggregation is probed by ion-mobility mass spectrometry, the kinetics of aggregation monitored with Thioflavin T assays, and the morphology of aggregates visualized by transmission electron microscopy. Insights into the structure of early aggregates and the factors stabilizing the aggregates are obtained from replica exchange molecular dynamics simulations. Our data suggest that R3/wt has a much stronger aggregation propensity than either R2/wt or R2/ΔK280. Heterodimers containing R3/wt are less stable than R3/wt homodimers but much more stable than homodimers of R2/wt and R2/ΔK280, suggesting a possible role of PHF6*-PHF6 interactions in initiating the aggregation of full-length Tau. Lastly, R2/ΔK280 binds more strongly to R3/wt than R2/wt, suggesting a possible mechanism for a pathological loss of normal Tau function.

Equilibrated polyethylene single-molecule crystals: molecular-dynamics simulations and analytic model of the global minimum of the free-energy landscape

The crystalline state of a single polyethylene chain with N = 500 monomers is investigated by extensive MD simulations. The polymer is folded in a well defined lamella with ten stems of approximately equal length, arranged into a regular, hexagonal pattern. The study of the microscopic organization of the lamella, which is in an equilibrium condition, evidences that the two caps are rather flat, i.e. the loops connecting the stems are short. An analytic model of the global minimum of the free energy, based on the assumption that the entropic contribution is mainly due to the combinatorics of the stems and loops and neglecting any conformational contribution, is presented. It provides for the first time a quantitative explanation of the MD results on the equilibrium geometry of single-chain crystals.

Initiation of assembly of tau(273-284) and its ΔK280 mutant: an experimental and computational study

The microtubule associated protein tau is essential for the development and maintenance of the nervous system. Tau dysfunction is associated with a class of diseases called tauopathies, in which tau is found in an aggregated form. This paper focuses on a small aggregating fragment of tau, (273)GKVQIINKKLDL(284), encompassing the (PHF6*) region that plays a central role in tau aggregation. Using a combination of simulations and experiments, we probe the self-assembly of this peptide, with an emphasis on characterizing the early steps of aggregation. Ion-mobility mass spectrometry experiments provide a size distribution of early oligomers, TEM studies provide a time course of aggregation, and enhanced sampling molecular dynamics simulations provide atomistically detailed structural information about this intrinsically disordered peptide. Our studies indicate that a point mutation, as well the addition of heparin, lead to a shift in the conformations populated by the earliest oligomers, affecting the kinetics of subsequent fibril formation as well as the morphology of the resulting aggregates. In particular, a mutant associated with a K280 deletion (a mutation that causes a heritable form of neurodegeneration/dementia in the context of full length tau) is seen to aggregate more readily than its wild-type counterpart. Simulations and experiment reveal that the ΔK280 mutant peptide adopts extended conformations to a greater extent than the wild-type peptide, facilitating aggregation through the pre-structuring of the peptide into a fibril-competent structure.

Langevin stabilization of molecular-dynamics simulations of polymers by means of quasisymplectic algorithms

Algorithms for the numerical integration of Langevin equations are compared in detail from the point of view of their accuracy, numerical efficiency, and stability to assess them as potential candidates for molecular-dynamics simulations of polymeric systems. Some algorithms are symplectic in the deterministic frictionless limit and prove to stabilize long time-step integrators. They are tested against other popular algorithms. The optimal algorithm depends on the main goal: accuracy or efficiency. The former depends on the observable of interest. A recently developed quasisymplectic algorithm with great accuracy in the position evaluation exhibits better overall accuracy and stability than the other ones. On the other hand, the well-known BrunGer-Brooks-Karplus [Chem. Phys. Lett. 105, 495 (1982)] algorithm is found to be faster with limited accuracy loss but less stable. It is also found that using higher-order algorithms does not necessarily improve the accuracy. Moreover, they usually require more force evaluations per single step, thus leading to poorer performances.

A manifestation of the Ostwald step rule: molecular-dynamics simulations and free-energy landscape of the primary nucleation and melting of single-molecule polyethylene in dilute solution.

The paper presents numerical results from extensive molecular-dynamics simulations of the crystallization process of a single polyethylene chain with N=500 monomers. The development of the ordered structure is seen to proceed along different routes involving either the global reorganization of the chain or, alternatively, well-separated connected nuclei. No dependence on the thermal history was observed at the late stages of the crystallization. The folding process involves several intermediate ordered metastable states, in strong analogy with the experiments, and ends up in a well-defined long-lived lamella with ten stems of approximately equal length, arranged into a regular, hexagonal pattern. This behavior may be seen as a microscopic manifestation of the Ostwald step rule. Both the metastable states and the long-lived one are evidenced as the local minima and the global one of the free-energy landscape, respectively. The study of the microscopic organization of the lamella evidenced that the two caps are rather flat, i.e., the loops connecting the stems are short. Interestingly, annealing the chain through the different metastable states leaves the average number of monomers per loop nearly unchanged. It is also seen that the chain ends, the so-called cilia, are localized on the surface of the lamella, in agreement with the experiments, and that structural fluctuations take place on the lamella surface, as noted by recent Monte Carlo simulations. The study of the melting process evidences that the degree of hysteresis is small.

Coarse-Grained Modeling of Simple Molecules at Different Resolutions in the Absence of Good Sampling

Many problems of interest in modern science originate from the complex network of interactions of different molecular structures, each possessing its own typical length and time scale of relevance. In such materials, nontrivial properties emerge from the different length and time scales involved that could not be predicted from the properties of each individual subunit taken alone. A solution to the formidable theoretical and computational issues raised by these systems involves coarse-graining, a procedure in which multiple atoms are grouped into a few interaction sites. The coarse-grained approach aims at constructing an effective Hamiltonian from available information about the system and then using this Hamiltonian to investigate the behavior of the system on the length and time scales of interest. In this paper, we aim at determining how far we can coarse-grain a system using only the commonly used pairwise, spherically symmetric potentials, as well as assessing the impact of poor initial sampling on the quality of the resulting coarse-grained model. Coarse-graining is performed following the multiscale coarse-graining (MS-CG) methodology, and we use as a model system the N-methylacetamide (NMA) molecule, a simple representation of a peptide bond, which can adopt two conformations, cis and trans. Our simulations reveal that as the coarse-graining becomes more aggressive multibody effects start to emerge and that the initial sampling of conformations can adversely bias the model in the case of heavy coarse-graining.