Puckering free energy of pyranoses: A NMR and metadynamics-umbrella sampling investigation.

We present the results of a combined metadynamics-umbrella sampling investigation of the puckered conformers of pyranoses described using the GROMOS 45a4 force field. The free energy landscape of Cremer-Pople puckering coordinates has been calculated for the whole series of α and ß aldohexoses, showing that the current force field parameters fail in reproducing proper puckering free energy differences between chair conformers. We suggest a modification to the GROMOS 45a4 parameter set which improves considerably the agreement of simulation results with theoretical and experimental estimates of puckering free energies. We also report on the experimental measurement of altrose conformer populations by means of NMR spectroscopy, which show good agreement with the predictions of current theoretical models.

On the calculation of puckering free energy surfaces.

Cremer-Pople puckering coordinates appear to be the natural candidate variables to explore the conformational space of cyclic compounds and in literature different parametrizations have been used to this end. However, while every parametrization is equivalent in identifying conformations, it is not obvious that they can also act as proper collective variables for the exploration of the puckered conformations free energy surface. It is shown that only the polar parametrization is fit to produce an unbiased estimate of the free energy landscape. As an example, the case of a six-membered ring, glucuronic acid, is presented, showing the artifacts that are generated when a wrong parametrization is used.

Dominant reaction pathways in high-dimensional systems.

This paper is devoted to the development of a theoretical and computational framework denominated dominant reaction pathways (DRPs) to efficiently sample the statistically significant thermally activated reaction pathways, in multidimensional systems. The DRP approach is consistently derived from the Langevin equation through a systematic expansion in the thermal energy, k(B)T. Its main advantage with respect to existing simulation techniques is that it provides a natural and rigorous framework to perform the path sampling using constant displacement steps, rather than constant time steps. In our previous work, we have shown how to obtain the set of most probable reaction pathways, i.e., the lowest order in the k(B)T expansion. In this work, we show how to compute the corrections to the leading order due to stochastic fluctuations around the most probable trajectories. We also discuss how to obtain predictions for the evolution of arbitrary observables and how to generate conformations, which are representative of the transition state ensemble. We illustrate how our method works in practice by studying the diffusion of a point particle in a two-dimensional funneled external potential.