Path probability ratios for Langevin dynamics-Exact and approximate.

Path reweighting is a principally exact method to estimate dynamic properties from biased simulations-provided that the path probability ratio matches the stochastic integrator used in the simulation. Previously reported path probability ratios match the Euler-Maruyama scheme for overdamped Langevin dynamics. Since molecular dynamics simulations use Langevin dynamics rather than overdamped Langevin dynamics, this severely impedes the application of path reweighting methods. Here, we derive the path probability ratio ML for Langevin dynamics propagated by a variant of the Langevin Leapfrog integrator. This new path probability ratio allows for exact reweighting of Langevin dynamics propagated by this integrator. We also show that a previously derived approximate path probability ratio Mapprox differs from the exact ML only by O(ξ4Δt4) and thus yields highly accurate dynamic reweighting results. (Δt is the integration time step, and ξ is the collision rate.) The results are tested, and the efficiency of path reweighting is explored using butane as an example.

Girsanov reweighting for path ensembles and Markov state models.

The sensitivity of molecular dynamics on changes in the potential energy function plays an important role in understanding the dynamics and function of complex molecules. We present a method to obtain path ensemble averages of a perturbed dynamics from a set of paths generated by a reference dynamics. It is based on the concept of path probability measure and the Girsanov theorem, a result from stochastic analysis to estimate a change of measure of a path ensemble. Since Markov state models (MSMs) of the molecular dynamics can be formulated as a combined phase-space and path ensemble average, the method can be extended to reweight MSMs by combining it with a reweighting of the Boltzmann distribution. We demonstrate how to efficiently implement the Girsanov reweighting in a molecular dynamics simulation program by calculating parts of the reweighting factor "on the fly" during the simulation, and we benchmark the method on test systems ranging from a two-dimensional diffusion process and an artificial many-body system to alanine dipeptide and valine dipeptide in implicit and explicit water. The method can be used to study the sensitivity of molecular dynamics on external perturbations as well as to reweight trajectories generated by enhanced sampling schemes to the original dynamics.

Molecular dynamics simulations data of the twenty encoded amino acids in different force fields.

We present extensive all-atom Molecular Dynamics (MD) simulation data of the twenty encoded amino acids in explicit water, simulated with different force fields. The termini of the amino acids have been capped to ensure that the dynamics of the Φ and ψ torsion angles are analogues to the dynamics within a peptide chain. We use representatives of each of the four major force field families: AMBER ff-99SBILDN [1], AMBER ff-03 [2], OPLS-AA/L [3], CHARMM27 [4] and GROMOS43a1 [5], [6]. Our data represents a library and test bed for method development for MD simulations and for force fields development. Part of the data set has been previously used for comparison of the dynamic properties of force fields (Vitalini et al., 2015) [7] and for the construction of peptide basis functions for the variational approach to molecular kinetics [8].

A Basis Set for Peptides for the Variational Approach to Conformational Kinetics.

Although Markov state models have proven to be powerful tools in resolving the complex features of biomolecular kinetics, the discretization of the conformational space has been a bottleneck since the advent of the method. A recently introduced variational approach, which uses basis functions instead of crisp conformational states, opened up a route to construct kinetic models in which the discretization error can be controlled systematically. Here, we develop and test a basis set for peptides to be used in the variational approach. The basis set is constructed by combining local residue-centered kinetic modes that are obtained from kinetic models of terminally blocked amino acids. Using this basis set, we model the conformational kinetics of two hexapeptides with sequences VGLAPG and VGVAPG. Six basis functions are sufficient to represent the slow kinetic modes of these peptides. The basis set also allows for a direct interpretation of the slow kinetic modes without an additional clustering in the space of the dominant eigenvectors. Moreover, changes in the conformational kinetics due to the exchange of leucine in VGLAPG to valine in VGVAPG can be directly quantified by comparing histograms of the basis set expansion coefficients.

Dynamic properties of force fields.

Molecular-dynamics simulations are increasingly used to study dynamic properties of biological systems. With this development, the ability of force fields to successfully predict relaxation timescales and the associated conformational exchange processes moves into focus. We assess to what extent the dynamic properties of model peptides (Ac-A-NHMe, Ac-V-NHMe, AVAVA, A10) differ when simulated with different force fields (AMBER ff99SB-ILDN, AMBER ff03, OPLS-AA/L, CHARMM27, and GROMOS43a1). The dynamic properties are extracted using Markov state models. For single-residue models (Ac-A-NHMe, Ac-V-NHMe), the slow conformational exchange processes are similar in all force fields, but the associated relaxation timescales differ by up to an order of magnitude. For the peptide systems, not only the relaxation timescales, but also the conformational exchange processes differ considerably across force fields. This finding calls the significance of dynamic interpretations of molecular-dynamics simulations into question.

Maxillary dental arch dimensions following pharyngeal-flap surgery.

Pharyngeal-flap surgery (PFS) is a surgical procedure utilized in the treatment of hypernasal speech. The purpose of this study was to evaluate the effect of PFS on the maxillary dental arch. Sixteen patients who had undergone PFS between the ages of 5 and 7 years were selected from the longitudinal growth study of the Lancaster Cleft Palate Clinic. Eight points were marked on the occlusal surfaces of serial maxillary dental models to determine arch width and length. These data were compared to a matched sample of patients from the same growth study who did not undergo PFS. The flap group demonstrated significant reduction in both arch width (at cuspids and molars) and arch length development compared to the control sample, following PFS. These results are not inconsistent with an hypothesis of dental-arch form changes related to possible airway obstruction following PFS, although data on the latter were not available on this sample.