arXiv subjects

Bettina G. Keller

Publications and source records attributed to Bettina G. Keller.

At least 19 recordsLinked to original sources

arXiv2026

$π$-Girsanov: A Generalized Method to Construct Markov State Models from Non-Equilibrium and Multiensemble Biased Simulations

We introduce $π$-Girsanov, a new method for constructing Markov state models from biased enhanced-sampling molecular dynamics simulations based on Girsanov reweighting. The key idea behind this new method is to separate the reweighting of the stationary density from the reweighting of the correlation function. We evaluate the effectiveness of this approach on several analytical potentials and on a model biomolecular system, comparing its performance with the original method. Our results show that $π$-Girsanov not only improves the estimation in a single-ensemble setting, but also resolves key challenges in estimating transition matrices from multiensemble and non-equilibrium biased trajectories. Overall, $π$-Girsanov represents a substantial advance in kinetic reweighting, strengthening the connection between enhanced sampling techniques and Markov state modeling.

physics.bio-ph↗

arXiv2026

A Machine-Learned Symbolic Committor for a Chemical Reaction: Retinal Isomerization

The thermal cis-trans isomerization around the C$_{13}$=C$_{14}$ double bond of retinal is a prototypical high-barrier reaction whose mechanism hinges on subtle out-of-plane bending motions. We apply Artificial Intelligence for Molecular Mechanism Discovery (AIMMD) to N-retinylidene-lysine in vacuum, learning the committor from unbiased molecular dynamics trajectories generated by two-way shooting. Parametrizing the logit of the committor, rather than the committor itself, allows the neural network to resolve the reaction coordinate across the full transition region, not only at the isocommittor surface $p_B(\mathbf{x}) = 0.5$. Holdback input randomization identifies four proper dihedrals around the reactive bond as the informative coordinates, while the improper dihedrals at C$_{13}$ and C$_{14}$ prove unsuitable because reactant, transition, and product states share the same values. Symbolic regression then distills the network into compact analytical expressions and shows that a nonlinear coupling of all four dihedrals is required to reproduce the S-shaped, stepwise pathway seen in the transition path ensemble. This S-shape is absent from the minimum-free-energy path: it arises from the non-equilibrium dynamics of the short ($\sim 0.13$ ps) transition events combined with the mass asymmetry between heavy-atom and hydrogen-bearing dihedrals. An interpretable, machine-learned committor thus exposes dynamical features of the mechanism to which the free-energy surface is blind. The workflow requires no prior assumptions about the reaction coordinate and extends naturally to other isomerizations and to chemical reactions more broadly.

physics.chem-ph↗

arXiv2026

Estimating Solvation Free Energies with Boltzmann Generators

Accurate calculations of solvation free energies remain a central challenge in molecular simulations, often requiring extensive sampling and numerous alchemical intermediates to ensure sufficient overlap between phase-space distributions of a solute in the gas phase and in solution. Here, we introduce a computational framework based on normalizing flows that directly maps solvent configurations between solutes of different sizes, and compare the accuracy and efficiency to conventional free energy estimates. For a Lennard-Jones solvent, we demonstrate that this approach yields acceptable accuracy in estimating free energy differences for challenging transformations, such as solute growth or increased solute-solute separation, which typically demand multiple intermediate simulation steps along the transformation. Analysis of radial distribution functions indicates that the flow generates physically meaningful solvent rearrangements, substantially enhancing configurational overlap between states in configuration space. These results suggest flow-based models as a promising alternative to traditional free energy estimation methods.

cond-mat.stat-mech↗

arXiv2026

Internal Trajectories and Observation Effects in Langevin Splitting Schemes

Langevin integrators based on operator splitting are widely used in molecular dynamics. This work examines Langevin splitting schemes from the perspective of their internal trajectories and observation points, complementing existing generator-based analyses. By exploiting merging, splitting, and cyclic permutation of elementary update operators, formally distinct schemes can be grouped according to identical or closely related trajectories. Accuracy differences arising from momentum updates and observation points are quantified for configurational sampling, free-energy estimates, and transition rates. While modern Langevin integrators are remarkably stable under standard simulation conditions, subtle but systematic biases emerge at large friction coefficients and time steps. These results clarify when accuracy differences between splitting schemes matter in practice and provide an intuitive framework for understanding observation effects.

cond-mat.stat-mech↗

arXiv2026

Implementation of Girsanov Reweighting in CP2K

Dynamical reweighting of path measures is a powerful approach for accurately evaluating slow molecular processes using modified potential energy surfaces used in enhanced sampling methods. Integrating this reweighting framework into the CP2K electronic-structure and molecular-dynamics (MD) software package delivers a robust and widely applicable tool for metadynamics, uncertainty quantification, and force-field optimisation based on both \textit{ab initio} and classical MD simulations. Based on the Girsanov theorem for stochastic dynamical systems, the method is adapted to the Bussi-Donadio-Parrinello velocity-rescaling scheme. This scheme is accessible through the CSVR thermostat and can be interpreted as a Langevin OVRVO/OBABO update scheme requiring two random numbers per integration step. Comprehensive implementation details are provided, including a complete overview of the modified CP2K modules involved in the MD cycle and the computation of reweighting factors. The framework supports multiple sources of bias potentials, enabling reweighting via the PLUMED interface or CP2K-native external potentials and restraints. The feasibility of the implementation is demonstrated through rerun benchmarks, dynamical reweighting of Markov state models (MSMs) and computation of transport properties based on CP2K trajectories, showing excellent agreement with reference simulations.

physics.chem-ph↗

arXiv2025

How Thermostats Influence Dynamics Across Time Scales: A Systematic Study from Fast Motions to Slow Transitions

Reliable dynamical properties from molecular dynamics simulations require careful control of thermostatting artifacts. We systematically assess how NVE, deterministic thermostats, velocity-rescale dynamics, and stochastic Langevin-type thermostats affect time-correlation functions across liquids of varying complexity. The analysis spans vibrational spectra, velocity and pressure autocorrelations, diffusion coefficients, shear viscosities, and Markov state models. Deterministic thermostats and velocity-rescale dynamics closely reproduce NVE reference data over all observables. In contrast, strongly coupled stochastic thermostats (tau less 1 ps) systematically distort dynamical properties. By constrast, moderate stochastic coupling (tau eq. 1 ps) restores near-NVE behavior while maintaining canonical sampling. Our results provide practical guidelines for selecting thermostat schemes when accurate dynamical properties or Markov models are required.

physics.chem-ph↗

arXiv2024

Accuracy of reaction coordinate based rate theories for modelling chemical reactions: insights from the thermal isomerization in retinal

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.

physics.chem-ph↗

arXiv2023

Thermal Isomerization Rates in Retinal Analogues using Ab-Initio Molecular Dynamics

For a detailed understanding of chemical processes in nature and industry, we need accurate models of chemical reactions in complex environments. While Eyring transition state theory is commonly used for modeling chemical reactions, it is most accurate for small molecules in the gas phase. A wide range of alternative rate theories exist that can better capture reactions involving complex molecules and environmental effects. However, they require that the chemical reaction is sampled by molecular dynamics simulations. This is a formidable challenge since the accessible simulation timescales are many orders of magnitude smaller than typical timescales of chemical reactions. To overcome these limitations, rare event methods involving enhanced molecular dynamics sampling are employed. In this work, thermal isomerization of retinal is studied using tight-binding density functional theory. Results from transition state theory are compared to those obtained from enhanced sampling. Rates obtained from dynamical reweighting using infrequent metadynamics simulations were in close agreement with those from transition state theory. Meanwhile, rates obtained from application of Kramers rate equation to a sampled free energy profile along a torsional dihedral reaction coordinate were found to be up to three orders of magnitude higher. This discrepancy raises concerns about applying rate methods to one-dimensional reaction coordinates in chemical reactions.

physics.chem-ph↗

arXiv2023

How chromophore labels shape the structure and dynamics of a peptide hydrogel

Biocompatible and functionalizable hydrogels have a wide range of (potential) medicinal applications. In contrast to conventional hydrogels formed by interconnected or interlocked polymer chains, self-assembled hydrogels form from small building blocks like short peptide chains. This has the advantage that the building blocks can be functionalized separately and then mixed to obtain the desired properties. However, the hydrogelation process for these systems, especially those with very low polymer weight percentage (< 1 wt%), is not well understood, and therefore it is hard to predict whether a given molecular building block will self-assemble into a hydrogel. This severely hinders the rational design of self-assembled hydrogels. In this study, we demonstrate the impact of an N-terminal chromophore label amino-benzoic acid on the self-assembly and rheology of hydrogel hFF03 (hydrogelating, fibril forming) using molecular dynamics simulations, which self-assembles into α-helical coiled-coils. We find that the chromophore and even its specific regioisomers have a significant influence on the microscopic structure and dynamics of the self-assembled fibril, and on the macroscopic mechanical properties. This is because the chromophore influences the possible salt-bridges which form and stabilize the fibril formation. Furthermore we find that the solvation shell fibrils by itself cannot explain the viscoelasticity of hFF03 hydrogels. Our atomistic model of the hFF03 fibril formation enables a more rational design of these hydrogels. In particular, altering the N-terminal chromophore emergesas a design strategy to tune the mechanic properties of these self-assembled peptide hydrogels.

physics.chem-ph↗

arXiv2023

Girsanov reweighting for simulations of underdamped Langevin dynamics. Theory

The critical step in a molecular process is often a rare-event and has to be simulated by an enhanced sampling protocol. Recovering accurate dynamical estimates from such biased simulation is challenging. Girsanov reweighting is a method to reweight dynamic properties formulated as path expected values. The path probability is calculated at the time-step resolution of the molecular-dynamics integrator. But the theory is largely limited to overdamped Langevin dynamics. For underdamped Langevin dynamics, the absolute continuity of the path probability ratio for the biased and unbiased potential is not guaranteed, but it depends on the Langevin integrator. We develop a general approach to derive the path probability ratio for Langevin integrators and to analyze whether absolute continuity is fulfilled. We demonstrate our approach on symmetric splitting methods for underdamped Langevin dynamics. For methods that obey absolute continuity, and thus can be used for Girsanov reweighting, we provide an expression for the relative path probability. %

cond-mat.stat-mech↗

arXiv2022

Clustering -- Basic concepts and methods

We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task? And how can clustering results be validated? Connectivity-based versus prototype-based approaches are reflected in the context of several popular methods: single-linkage, spectral embedding, k-means, and Gaussian mixtures are discussed as well as the density-based protocols (H)DBSCAN, Jarvis-Patrick, CommonNN, and density-peaks.

cs.LG↗

arXiv2022

A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models

Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential $\tilde{V}(x)$ 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.

physics.chem-ph↗

arXiv2022

Grid-based state space exploration for molecular binding

Binding processes are difficult to sample with molecular-dynamics (MD) simulations. In particular, the state space exploration is often incomplete. Evaluating the molecular interaction energy on a grid circumvents this problem but is heavily limited by state space dimensionality. Here, we make the first steps towards a low-dimensional grid-based model of molecular binding. We discretise the state space of relative positions and orientations of the two molecules under the rigid body assumption.The corresponding program is published as the Python package molgri. For the rotational component of the grids, we test algorithms based on Euler angles, polyhedra and quaternions, of which the polyhedra-based are the most uniform. The program outputs a sequence of molecular structures that can be easily processed by standard MD programs to calculate grid point energies. We demonstrate the grid-based approach on two molecular systems: a water dimer and a coiled-coil protein interacting with a chloride anion. For the second system we relax the rigid-body assumption and improve the accuracy of the grid point energies by an energy minimisation. In both cases, oriented bonding patterns and energies confirm expectations from chemical intuition and MD simulations. We also demonstrate how analysis of energy contributions on a grid can be performed and demonstrate that electrostatically-driven association is sufficiently resolved by point-energy calculations. Overall, grid-based models of molecular binding are potentially a powerful complement to molecular sampling approaches, and we see the potential to expand the method to quantum chemistry and flexible docking applications.

physics.chem-ph↗

arXiv2022

GROMACS Stochastic Dynamics and BAOAB are equivalent configurational sampling algorithms

Two of the most widely used Langevin integrators for molecular dynamics simulations are the GROMACS Stochastic Dynamics (GSD) integrator and the splitting method BAOAB. In this letter, we show that the GROMACS Stochastic Dynamics integrator is equal to the less frequently used splitting method BAOA. It immediately follows that GSD and BAOAB sample the same configurations and have the same high configurational accuracy. Our numerical results indicate that GSD/BAOA has higher kinetic accuracy than BAOAB.

physics.comp-ph↗

arXiv2021

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 MD 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 $M_L$ 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 $M_{\mathrm{approx}}$ differs from the exact $M_L$ only by $\mathcal{O}(ξ^4Δt^4)$, and thus yields highly accurate dynamic reweighting results. ($Δt$ is the integration time step, $ξ$ is the collision rate.) The results are tested and the efficiency of path-reweighting is explored using butane as an example.

physics.chem-ph↗

arXiv2020

Markov models from the Square Root Approximation of the Fokker-Planck equation: calculating the grid-dependent flux

Molecular dynamics are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the molecular dynamics 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 molecular dynamics 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 molecular dynamics 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 $\mathcal{O}(10^6)$ states can be obtained within seconds on a single high-performance compute server if regular grids are used.

physics.chem-ph↗

arXiv2019

Dynamical reweighting methods for Markov models

Markov State Models (MSM) 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, for example produced by enhanced sampling techniques, 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.

physics.chem-ph↗

arXiv2017

Estimation of the infinitesimal generator by square-root approximation

For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant subspace projection problem. A certain infinitesimal generator acting on function space is projected to a low-dimensional rate matrix. This projection can be performed in two steps. First, the infinitesimal generator is discretized, then the invariant subspace is approxi-mated and used for the subspace projection. In our approach, the discretization will be based on a Voronoi tessellation of the conformational space. We will show that the discretized infinitesimal generator can simply be approximated by the geometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct correla-tion between the potential energy surface of molecular structures and the transition rates of conformational changes. We present results for a 2d-diffusion process and Alanine dipeptide.

physics.comp-ph↗