Self-consistent calculation of protein folding pathways.

We introduce an iterative algorithm to efficiently simulate protein folding and other conformational transitions, using state-of-the-art all-atom force fields. Starting from the Langevin equation, we obtain a self-consistent stochastic equation of motion, which directly yields the reaction pathways. From the solution of this set of equations we derive a stochastic estimate of the reaction coordinate. We validate this approach against the results of plain MD simulations of the folding of a small protein, which were performed on the Anton supercomputer. In order to explore the computational efficiency of this algorithm, we apply it to generate a folding pathway of a protein that consists of 130 amino acids and has a folding rate of the order of s-1.

Computing Reaction Pathways of Rare Biomolecular Transitions using Atomistic Force-Fields.

The Dominant Reaction Pathway (DRP) method is an approximate variational scheme which can be used to compute reaction pathways in conformational transitions undergone by large biomolecules (up to ~10(3) amino-acids) using realistic all-atom force fields. We first review the status of development of this method. Next, we discuss its validation against the results of plain MD protein folding simulations performed by the DE-Shaw group using the Anton supercomputer. Finally, we review a few representative applications of the DRP approach to study reactions which are far too complex and rare to be investigated by plain MD, even on the Anton machine.

Variational scheme to compute protein reaction pathways using atomistic force fields with explicit solvent.

We introduce a variational approximation to the microscopic dynamics of rare conformational transitions of macromolecules. Within this framework it is possible to simulate on a small computer cluster reactions as complex as protein folding, using state of the art all-atom force fields in explicit solvent. We test this method against MD simulations of the folding of an α and a ß protein performed with the same all-atom force field on the Anton supercomputer. We find that our approach yields results consistent with those of MD simulations, at a computational cost orders of magnitude smaller.

Quantum diffusive dynamics of macromolecular transitions.

We study the role of quantum fluctuations of atomic nuclei in the real-time dynamics of non-equilibrium macro-molecular transitions. To this goal we introduce an extension of the dominant reaction pathways formalism, in which the quantum corrections to the classical overdamped Langevin dynamics are rigorously taken into account to order h(2). We first illustrate our approach in simple cases, and compare with the results of the instanton theory. Then we apply our method to study the C7(eq) → C7(ax) transition of alanine dipeptide. We find that the inclusion of quantum fluctuations can significantly modify the reaction mechanism for peptides. For example, the energy difference which is overcome along the most probable pathway is reduced by as much as 50%.

Communications: Ab initio dynamics of rare thermally activated reactions.

We introduce a framework to investigate ab initio the dynamics of rare thermally activated reactions, which cannot be studied using the existing techniques. The electronic degrees of freedom are described at the quantum-mechanical level in the Born-Oppenheimer approximation, while the nuclear degrees of freedom are coupled to a thermal bath, through a classical Langevin equation. This method is based on the path integral representation for the stochastic dynamics and yields the time evolution of both nuclear and electronic degrees of freedom, along the most probable reaction pathways, without spending computational time to explore metastable states. As a first illustrative application, we characterize the dominant pathway in the cyclobutene-->butadiene reaction, using the semiempirical Parametrized Model 3 (PM3) approach.

Local thermal expansion in a cuprite structure: the case of Ag(2)O.

The local thermal behavior of the Ag(2)O framework structure has been studied by extended x-ray absorption fine structure. The average Ag-O nearest-neighbor distance expands upon heating, while the Ag-Ag next-nearest-neighbor distance contracts. An original implementation of the cumulant analysis shows that the Ag-O expansion is a joint effect of potential anharmonicity and geometrical deformation of the Ag(4)O basic tetrahedral units. Accordingly, the negative thermal expansion of the lattice parameter in Ag(2)O cannot be explained uniquely in terms of rigid unit modes.