We construct coarse master equations for peptide folding dynamics from atomistic molecular dynamics simulations. A maximum-likelihood propagator-based method allows us to extract accurate rates for the transitions between the different conformational states of the small helix-forming peptide Ala5. Assigning the conformational states by using transition paths instead of instantaneous molecular coordinates suppresses the effects of fast non-Markovian dynamics. The resulting master equations are validated by comparing their analytical correlation functions with those obtained directly from the molecular dynamics simulations. We find that the master equations properly capture the character and relaxation times of the entire spectrum of conformational relaxation processes. By using the eigenvectors of the transition rate matrix, we are able to systematically coarse-grain the system. We find that a two-state description, with a folded and an unfolded state, roughly captures the slow conformational dynamics. A four-state model, with two folded and two unfolded states, accurately recovers the three slowest relaxation process with time scales between 1.5 and 7 ns. The master equation models not only give access to the slow conformational dynamics but also shed light on the molecular mechanisms of the helix-coil transition.

Accurate force fields are essential for the success of molecular dynamics simulations. In apparent contrast to the conformational preferences of most force fields, recent NMR experiments suggest that short polyalanine peptides in water populate the polyproline II structure almost exclusively. To investigate this apparent contradiction, with its ramifications for the assessment of molecular force fields and the structure of unfolded proteins, we performed extensive simulations of Ala(5) in water ( approximately 5 micros total time), using twelve different force fields and three different peptide terminal groups. Using either empirical or density-functional-based Karplus relations for the J-couplings, we find that most current force fields do overpopulate the alpha-region, with quantitative results depending on the choice of Karplus relation and on the peptide termini. Even after reweighting to match experiment, we find that Ala(5) retains significant alpha- and beta-populations. In fact, several force fields match the experimental data well before reweighting and have a significant helical population. We conclude that radical changes to the best current force fields are not necessary, based on the NMR data. Nevertheless, experiments on short peptides open the way toward the systematic improvement of current simulation models.

Graphical abstract

Filamentous amyloid aggregates are central to the pathology of Alzheimer's disease. We use all-atom molecular dynamics (MD) simulations with explicit solvent and multiple force fields to probe the structural stability and the conformational dynamics of several models of Alzheimer's beta-amyloid fibril structures, for both wild-type and mutated amino acid sequences. The structural models are based on recent solid state NMR data. In these models, the peptides form in-register parallel beta-sheets along the fibril axis, with dimers of two U-shaped peptides located in layers normal to the fibril axis. Four different topologies are explored for stacking the beta-strand regions against each other to form a hydrophobic core. Our MD results suggest that all four NMR-based models are structurally stable, and we find good agreement with dihedral angles estimated from solid-state NMR experiments. Asp23 and Lys28 form buried salt-bridges, resulting in an alternating arrangement of the negatively and positively charged residues along the fibril axis that is reminiscent of a one-dimensional ionic crystal. Interior water molecules are solvating the buried salt-bridges. Based on data from NMR measurements and MD simulations of short amyloid fibrils, we constructed structural models of long fibrils. Calculated X-ray fiber diffraction patterns show the characteristics of packed beta-sheets seen in experiments, and suggest new experiments that could discriminate between various fibril topologies.