TY - GEN A1 - Quer, Jannes A1 - Donati, Luca A1 - Keller, Bettina A1 - Weber, Marcus T1 - An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates N2 - In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities. T3 - ZIB-Report - 17-09 KW - Adaptive Importance Sampling KW - Molecular Dynamics KW - Metastability KW - Variance Reduction KW - Non Equilibrium Sampling KW - Metadynamics KW - Girsanov Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62075 SN - 1438-0064 ER - TY - JOUR A1 - Quer, Jannes A1 - Donati, Luca A1 - Keller, Bettina A1 - Weber, Marcus T1 - An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates JF - SIAM Journal on Scientific Computing N2 - In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities. Y1 - 2018 U6 - https://doi.org/10.1137/17m1124772 VL - 40 IS - 2 SP - A653 EP - A670 ER - TY - JOUR A1 - Kieninger, Stefanie A1 - Donati, Luca A1 - Keller, Bettina G. T1 - Dynamical reweighting methods for Markov models JF - Current Opinion in Structural Biology N2 - Conformational dynamics is essential to biomolecular processes. Markov State Models (MSMs) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the state-of-the-art and discuss the methodological differences of these methods, their limitations and recent applications. Y1 - 2020 U6 - https://doi.org/10.1016/j.sbi.2019.12.018 VL - 61 SP - 124 EP - 131 ER - TY - CHAP A1 - Keller, Bettina G. A1 - Aleksić, Stevan A1 - Donati, Luca T1 - Markov State Models in Drug Design T2 - Biomolecular Simulations in Structure‐Based Drug Discovery N2 - This chapter explains the different ways in which Markov State Models (MSMs) can be helpful in structure-based drug design. MSMs are constructed from the time series of molecular dynamics (MD), which can be generated by classical MD simulations. Several features of the MSMs can be utilized for rational drug design. The discretization of a validated MSM is particularly suited to extract meaningful representatives from the conformational ensemble, because the discretization yields a small number of microstates and mirrors the features of the free energy landscape. Long-lived conformations consist of a set of microstates which show high transition rates within the set and low transition rates to microstates outside of the set. The Bayesian agglomerative clustering engine (BACE) algorithm uses the observed transition counts to extract long-lived conformations from an MSM. By iteratively merging microstates according to the Bayes factor and recalculating the Bayes-factor matrix, the algorithm yields an aggregation of the microstates into long-lived conformations. Y1 - 2018 SN - 1865-0562 U6 - https://doi.org/10.1002/9783527806836.ch4 SP - 67 EP - 86 PB - Wiley-Interscience, Weinheim ER - TY - JOUR A1 - Hassan, Irtaza A1 - Donati, Luca A1 - Stensitzki, Till A1 - Keller, Bettina G A1 - Heyne, Karsten A1 - Imhof, Petra T1 - The vibrational spectrum of the hydrated alanine-leucine peptide in the amide region from IR experiments and first principles calculations JF - Chemical Physics Letters N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1016/j.cplett.2018.03.026 VL - 698 SP - 227 EP - 233 ER - TY - JOUR A1 - Ghysbrecht, Simon A1 - Donati, Luca A1 - Keller, Bettina G. T1 - Accuracy of reaction coordinate based rate theories for modelling chemical reactions: insights from the thermal isomerization in retinal JF - Submitted to The Journal of Physical Chemistry A N2 - Modern potential energy surfaces have shifted attention to molecular simulations of chemical reactions. While various methods can estimate rate constants for conformational transitions in molecular dynamics simulations, their applicability to studying chemical reactions remains uncertain due to the high and sharp energy barriers and complex reaction coordinates involved. This study focuses on the thermal cis-trans isomerization in retinal, employing molecular simulations and comparing rate constant estimates based on one-dimensional rate theories with those based on sampling transitions and grid-based models for low-dimensional collective variable spaces. Even though each individual method to estimate the rate passes its quality tests, the rate constant estimates exhibit disparities of up to four orders of magnitude. Rate constant estimates based on one-dimensional reaction coordinates prove challenging to converge, even if the reaction coordinate is optimized. However, consistent estimates of the rate constant are achieved by sampling transitions and by multi-dimensional grid-based models. Y1 - 2023 ER - TY - JOUR A1 - Donati, Luca A1 - Weber, Marcus A1 - Keller, Bettina G. T1 - A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models JF - Journal of Mathematical Physics N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1063/5.0127227 VL - 63 IS - 12 SP - 123306-1 EP - 123306-21 PB - AIP Publishing ER - TY - JOUR A1 - Donati, Luca A1 - Weber, Marcus A1 - Keller, Bettina G. T1 - Markov models from the square root approximation of the Fokker–Planck equation: calculating the grid-dependent flux JF - Journal of Physics: Condensed Matter N2 - Molecular dynamics (MD) are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the MD as a stochastic process and analyses the dominant eigenfunctions of the associated Fokker–Planck operator, or of closely related transfer operators. So far, the calculation of the discretized operators requires extensive MD simulations. The square-root approximation of the Fokker–Planck equation is a method to calculate transition rates as a ratio of the Boltzmann densities of neighboring grid cells times a flux, and can in principle be calculated without a simulation. In a previous work we still used MD simulations to determine the flux. Here, we propose several methods to calculate the exact or approximate flux for various grid types, and thus estimate the rate matrix without a simulation. Using model potentials we test computational efficiency of the methods, and the accuracy with which they reproduce the dominant eigenfunctions and eigenvalues. For these model potentials, rate matrices with up to $\mathcal{O}\left(1{0}^{6}\right)$ states can be obtained within seconds on a single high-performance compute server if regular grids are used. Y1 - 2021 U6 - https://doi.org/10.1088/1361-648X/abd5f7 VL - 33 IS - 11 SP - 115902 ER - TY - JOUR A1 - Donati, Luca A1 - Keller, Bettina G. T1 - Girsanov reweighting for metadynamics simulations JF - The Journal of Chemical Physics N2 - 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 Y1 - 2018 U6 - https://doi.org/10.1063/1.5027728 VL - 149 IS - 7 SP - 072335 ER - TY - JOUR A1 - Donati, Luca A1 - Heida, Martin A1 - Keller, Bettina G. A1 - Weber, Marcus T1 - Estimation of the infinitesimal generator by square-root approximation JF - J. Phys.: Condens. Matter N2 - In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is—from a mathematical point of view—an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system. Y1 - 2018 U6 - https://doi.org/10.1088/1361-648X/aadfc8 VL - 30 IS - 42 SP - 425201 EP - 425201 ER -