Aug 2026· Journal of Chemical Physics· Vol 165 6· 0 citations· 77 references
Medicine
TL;DR
This work introduces an analytical framework for computing continuous-space committor functions directly from molecular dynamics trajectories using a Liouville propagator formulated in a basis-function representation that provides a versatile foundation for analyzing dynamics in biomolecular systems and other complex dynamical processes.
Abstract
Many biomolecular processes are governed by rare transitions between metastable states on complex free-energy landscapes. The committor function, the probability that a trajectory initiated from a given configuration reaches one metastable state before another, is regarded as the optimal reaction coordinate for describing such transitions. Committor functions are often computed using Transition Path Theory (TPT) combined with Markov State Models (MSMs), which discretize configuration space into states and, therefore, limit spatial resolution. Here, we introduce an analytical framework for computing continuous-space committor functions directly from molecular dynamics trajectories using a Liouville propagator formulated in a basis-function representation. The key insight is that the slow eigenmodes of the propagator can be represented as linear combinations of basis functions, yet the resulting committor equations do not depend explicitly on the unknown expansion coefficients. Consequently, the Liouville propagator and committor functions can be constructed directly from an arbitrary set of basis functions without explicitly solving for eigenfunctions. This formulation enables continuous committor functions, iso-committor surfaces, and other kinetic quantities such as mean first passage times to be computed without discretizing configuration space. Applications to a two-dimensional model potential, alanine dipeptide, and the FIP35 WW domain demonstrate that the resulting committor functions agree with MSM-TPT results while providing substantially higher spatial resolution, enabling precise identification of transition states. Because our theoretical framework accommodates general basis representations, including polynomial or Fourier expansions of physical coordinates, tensor-based collective variables (CVs), and machine-learning-derived CVs, it provides a versatile foundation for analyzing dynamics in biomolecular systems and other complex dynamical processes.
The committor is the optimal reaction coordinate for a rare transition: it pinpoints the transition state and fixes the rate, and it governs events from protein folding to crystal nucleation. It minimises a Dirichlet energy, whose value at the minimum is the reactive flux, over functions that vanish on the reactant state and equal one on the product state. In high dimensions such a trial space is very hard to build. Here we rewrite the variational principle so that the boundary conditions are replaced by a normalisation of one boundary observable, the fidelity. Any trial function is then admissible, including functions that cannot satisfy the boundary values at all. On this basis we estimate the high-dimensional committor and rates from one-dimensional profiles along projected coordinates, taking as input only pre-existing equilibrium or reweighted configurations, a diffusion constant estimate, and the two state definitions. The optimum has a closed form that is cheap to evaluate. We obtain committors for AIB9 and villin HP-35 in full torsion space, and folding and unfolding rates for chignolin from umbrella sampling alone.
M. Petersen, Simon M. Lichtinger, Roberto Covino· 0 citations
PHASE (Protein Hamiltonians for Sampling of Ensembles), a system-specific framework that converts atomistic conformational ensembles into an explicit and interpretable statistical model, is introduced.
Daniele Angioletti, Marco S. Nobile, Matteo Carli et al.· 0 citations
Many molecular dynamics simulations aim at studying transitions between two states (from reactants to products). In this context, the committor function (which gives for a given molecular configuration the probability to reach the product state before the reactant state) is a pivotal quantity, in particular because it is the optimal importance function for rare event simulation methods such as importance sampling or splitting techniques. These methods are used to sample the reactive path ensemble, and estimate for example the transition rate. However, learning such a function is generally a challenging task due to the high dimensionality of the configuration space. In this work, after reviewing the existing methodologies to construct approximate committor functions, a new loss function based on the application of It\={o}'s formula is proposed to learn the committor function with a minimization procedure on the parameters of a neural network. After comparing this novel approach to existing procedures on the M\"uller--Brown potential, we introduce a coupling strategy with the Adaptive Multilevel Splitting method to better approximate the committor function using a better sampling of the reactive trajectories. This methodology in which the committor function is iteratively learned only requires initially the knowledge of the reactant and product states.
Thomas Pigeon, Gabriel Stoltz, T. Lelièvre· 0 citations
The present work revisits the methods within CP2K that turn electronic structure into dynamics, transport, and spectroscopic response, highlighting CP2K's unique capability to unify quantum chemistry with quantum and statistical mechanics within a versatile, holistic simulation environment.
Jan Wilhelm, Anna-Sophia Hehn, Hossam Elgabarty et al.· 1 citation· ⚡1
Molecular dynamics (MD) simulations are powerful tools for investigating the dynamic behavior of complex biomolecular systems at atomistic resolution. However, the size and complexity of the configuration space pose substantial challenges to this exploration. Key cellular processes often depend on rare events, where a system must overcome energy barriers to spontaneously switch between metastable states. Extensively sampling those rare transitions, thus achieving ergodicity, is practically unfeasible for conventional, physically unbiased MD simulations. Even if we could dedicate enough computational power to this goal, we would produce massive, mostly redundant trajectory data of difficult interpretation—unless guided by prior knowledge.
A more effective strategy is to carefully select the starting configurations of the simulations. In doing so, we split the problem of obtaining a long equilibrium trajectory into the more manageable task of sampling many shorter, meaningful paths. But how can we identify optimal starting configurations? Artificial intelligence (AI) offers an attractive solution. Using AI to both guide MD simulations and interpret the results is a core realization of the simulation intelligence paradigm and a foundational principle of this thesis. This work focused on both method development and applications to biologically relevant systems involving protein-protein and membrane-protein interactions. By combining rigorous path sampling with AI in an active learning framework, we demonstrated that accurate thermodynamic, kinetic, and mechanistic insights can be obtained with reasonable resource usage, even for processes occurring on time scales far beyond the reach of conventional MD simulations.
In the first part of this work, we investigated the role of the amphipathic helix (AH) of the ATG3 protein in promoting LC3 lipidation on the phagophore membrane. Unsupervised machine learning (ML) revealed structural features that distinguish ATG3 AH from other membrane-sensing helices and guided the identification of an AH mutant that retains phagophore binding but compromises LC3 lipidation in vivo. Generative AI provided biologically relevant initial configurations for multiple unbiased MD simulations. Through supervised analysis and strategic reinitialization, we mapped the conformational landscape of the membrane-bound ATG3~LC3 complex and characterized the structural and dynamical differences between wild-type and mutant AHs. Based on these results, we proposed a speculative model describing the fine-tuned interplay between the AH, the lipids, and the rest of the complex. However, despite months of computation, the MD trajectories were not sufficiently long to extract comprehensive quantitative information, limiting our analysis to qualitative insights.
For the remainder of this thesis, we addressed the sampling and interpretation challenges in systems shaped by rare-event transitions by adopting the AI for Molecular Mechanism Discovery (AIMMD) framework. At its core, AIMMD employs an iterative cycle where a ML model of the committor enhances path sampling simulations by orchestrating the selection of starting configurations—the shooting points (SPs)—from previously generated data. At the same time, the method uses the simulation results to train the model, further improving sampling efficiency. The committor function serves as the optimal reaction coordinate and, together with the sampled paths, can be analyzed to uncover the transition mechanism. What sets AIMMD apart from other AI-based enhanced sampling techniques is its minimal reliance on prior knowledge, its solid statistical mechanics foundations, its limited yet effective AI intervention in the simulations (still evolving from previous configurations under unbiased dynamics), and its strong emphasis on interpretability, all of which contribute to the method's robustness.
In the second part of this work, we expanded the scope of AIMMD to obtain accurate free energy and transition rates estimates without the need for additional enhanced sampling simulations. To this end, we reintegrated all simulated excursions, previously considered failed attempts at generating transitions, in our sampling. We developed a data-efficient path reweighting algorithm incorporating free simulations around metastable states. Again, we relied on the committor model for optimal performance. We validated the updated method on the folding/unfolding of the mini protein chignolin, highlighting the computational advantages over standard MD simulations and the benefits of accessing the full equilibrium path ensemble.
In the third part of this work, we demonstrated AIMMD's effectiveness in fully characterizing EGFR transmembrane dimerization and dissociation. In this way, we extended its applicability to a broader class of processes characterized by a single basin of attraction, where the transition is rare in only one direction. We emphasized the importance of dimer stability in triggering downstream signaling pathways and proposed AIMMD as a valuable tool for detecting stability changes under varying system conditions. Additionally, we further improved the method and its code implementation by parallelizing the computational effort, augmenting the committor training set, exploring path sampling alternatives to the original AI-guided TPS scheme, and streamlining the reweighting algorithm to improve its robustness and efficiency.
In the fourth and final part of this work, we introduced an optimal rejection-free path sampling (RFPS) scheme by shifting our perspective to sampling a SP distribution.
%an optimal path sampling scheme with no more rejected trials in the Markov chain.
As a result, we could use all sampled paths for selecting SPs, enhancing exploration without compromising exploitation. RFPS integrates naturally into AIMMD, resulting in the updated RFPS-AIMMD algorithm, where free energy estimates are incorporated directly into the iterative cycle. RFPS-AIMMD improved committor learning through better training set coverage and demonstrated notable robustness on chignolin. This theoretical development bears broader implications for path sampling methods beyond AIMMD. Overall, the updated AIMMD framework offers a practical, interpretable, and computationally efficient alternative to long, unbiased MD simulations, with strong potential for further improvements and applications to more complex systems.
We present Hamiltonian Replica Exchange Transition Interface Sampling (HRETIS), a path sampling framework designed to efficiently sample rare events in systems with complex potential energy landscapes. HRETIS introduces a helper potential within a Hamiltonian replica exchange scheme, which enhances exploration of path space when the underlying potential is not well suited for conventional path sampling approaches. This is particularly advantageous for systems exhibiting multiple pathways separated by orthogonal barriers such as in drug (un)binding, where standard algorithms often show slow convergence since they become trapped within specific pathways. By exchanging Hamiltonians between the path ensembles, HRETIS overcomes these limitations and increases the decorrelation between subsequent paths in the Monte Carlo chain. We demonstrate that HRETIS provides robust and accurate kinetics in several systems, including coarse-grained simulations of amino acid permeation through a dipalmitoylphosphatidylcholine (DPPC) membrane. Moreover, HRETIS is found to improve sampling efficiency and convergence, illustrating its potential as a powerful tool for rare event sampling in complex molecular systems.
Sina Safaei, P. Rezaee, An Ghysels· 0 citations
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