@article{DonatiKeller2018, author = {Donati, Luca and Keller, Bettina G.}, title = {Girsanov reweighting for metadynamics simulations}, volume = {149}, journal = {The Journal of Chemical Physics}, number = {7}, doi = {10.1063/1.5027728}, pages = {072335}, year = {2018}, abstract = {Metadynamics is a computational method to explore the phase space of a molecular system. Gaussian functions are added along relevant coordinates on the fly during a molecular-dynamics simulation to force the system to escape from minima in the potential energy function. The dynamics in the resulting trajectory are however unphysical and cannot be used directly to estimate dynamical properties of the system. Girsanov reweighting is a recent method used to construct the Markov State Model (MSM) of a system subjected to an external perturbation. With the combination of these two techniques—metadynamics/Girsanov-reweighting—the unphysical dynamics in a metadynamics simulation can be reweighted to obtain the MSM of the unbiased system. We demonstrate the method on a one-dimensional diffusion process, alanine dipeptide, and the hexapeptide Val-Gly-Val-Ala-Pro-Gly (VGVAPG). The results are in excellent agreement with the MSMs obtained from direct unbiased simulations of these systems. We also apply metadynamics/Girsanov-reweighting to a β-hairpin peptide, whose dynamics is too slow to efficiently explore its phase space by direct simulation}, language = {en} } @article{DonatiHartmannKeller2017, author = {Donati, Luca and Hartmann, Carsten and Keller, Bettina G.}, title = {Girsanov reweighting for path ensembles and Markov state models}, volume = {146}, journal = {The Journal of Chemical Physics}, number = {24}, doi = {10.1063/1.4989474}, pages = {244112}, year = {2017}, abstract = {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.}, language = {en} } @article{HassanDonatiStensitzkietal.2018, author = {Hassan, Irtaza and Donati, Luca and Stensitzki, Till and Keller, Bettina G and Heyne, Karsten and Imhof, Petra}, title = {The vibrational spectrum of the hydrated alanine-leucine peptide in the amide region from IR experiments and first principles calculations}, volume = {698}, journal = {Chemical Physics Letters}, doi = {10.1016/j.cplett.2018.03.026}, pages = {227 -- 233}, year = {2018}, abstract = {We have combined infrared (IR) experiments with molecular dynamics (MD) simulations in solution at finite temperature to analyse the vibrational signature of the small floppy peptide Alanine-Leucine. IR spectra computed from first-principles MD simulations exhibit no distinct differences between conformational clusters of -helix or -sheet-like folds with different orientations of the bulky leucine side chain. All computed spectra show two prominent bands, in good agreement with the experiment, that are assigned to the stretch vibrations of the carbonyl and carboxyl group, respectively. Variations in band widths and exact maxima are likely due to small fluctuations in the backbone torsion angles.}, language = {en} } @article{DonatiWeberKeller2022, author = {Donati, Luca and Weber, Marcus and Keller, Bettina G.}, title = {A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models}, volume = {63}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, doi = {10.1063/5.0127227}, pages = {123306-1 -- 123306-21}, year = {2022}, abstract = {Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential U(x) from trajectories that have been generated at a different potential V(x). In this article, we present Girsanov reweighting and Square Root Approximation (SqRA): the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov State Models (MSMs) to reweight transition probabilities; the second method was originally developed to discretize the Fokker-Planck operator into a transition rate matrix, but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods, then present two applications relevant to Molecular Dynamics (MD), highlighting their strengths and weaknesses.}, language = {en} }