Alchemical Move: Chasing Rabbits, Trusting Turtles a Institute of Biomedical Engineering and Technology, Biophysical Models for Medical Applications group (BioMMedA), Ghent University, Ghent B9000, Belgium Parham Rezaeea, Sina Safaeia, An Ghyselsa
[email protected] biommeda.ugent.be Parham Rezaee Introduction Objective Conclusion & future work Method Rare Events: Key biological processes (e.g., ligand binding, membrane permeation) are rare and occur on long timescales. Molecular Dynamics (MD): Simulates biomolecular systems at atomistic resolution. Accurate but inefficient for capturing rare events due to timescale limitations. Monte Carlo sampling: It helps to sample phase points from the phase space. Transition Interface Sampling (TIS): Uses Monte Carlo sampling by dividing phase space into interfaces to sample rare event transitions efficiently. Alchemical method is an algorithm that turns the rapid search into reliable transitions by swapping lowand high-level forcefields (Ulow and Uhigh) in the simulation system. The main aims of alchemical move are: Enhanced exploration of phase space Avoidance of trapping in local minima Reduction in computational cost The algorithm of alchemical move starts by one path from Ulow and the other one from Uhigh forcefield. I. Phase points selection: Randomly select phase points from the existing paths. II. Forcefield swap: Exchange the forcefields between the two systems and compute the energy difference ΔΔU. III. Forward/backward integration: For each swapped phase point, integrate the equations of motion backward until the trajectory reaches the reactant boundary λA , and forward until it reaches either λA or the product boundary λB , using the current (postswap) forcefield. IV. Accept or reject generated paths: Accept the newly generated path according to the prescribed acceptance-probability criterion. References Our preliminary results, including crossing probabilities, and paths length obtained from both pure Uhigh and alchemical move algorithm which the forcefield swapped between Uhigh and Ulow, demonstrate that the proposed pipeline works as intended. To fully establish its efficiency and robustness, further systematic investigations are required. Future work will focus on: ✵ 1D test cases (e.g., cosine bump potentials with varying heights or displacements). ✵ 2D test cases (e.g., maze potentials, systems with two or multiple transition channels). ✵ All-atom simulations (e.g., peptide diffusion through a membrane under different forcefields, ligand–receptor binding). ✵ Algorithmic refinement, such as optimizing acceptance probabilities to improve the yield of accepted paths. These steps will allow us to rigorously validate the method and expand its applicability to increasingly complex systems. select phase points swap forcefields integrate backward and forward in both systems Test cases We performed simulations of a dummy atom crossing a potential barrier, and measured the crossing probabilities and average paths length. Reference simulations used only Uhigh (flat, single-bump cosine, and double-bump cosine), while comparative runs applied the alchemical move by swapping between a Ulow (flat potential) and the same set of Uhigh. The alchemicalmove results show excellent agreement with those from the pure Uhigh simulations, validating the method’s accuracy. 1. Falkner, S., Coretti, A. & Dellago, C. Enhanced sampling of configuration and path space in a generalized ensemble by shooting point exchange.= Phys. Rev. Lett .=132, 128001 (2024). 2. Vervust, W., Zhang, D. T., Riccardi, E., van Erp, T. S. & Ghysels, A. Path sampling challenges in large biomolecular systems: RETIS and REPPTIS for ABL-imatinib kinetics.= Biophys. J .=(2025). 3. Ghysels, A., Roet, S., Davoudi, S. & van Erp, T. S. Exact non-Markovian permeability from rare event simulations.= Phys. Rev. Res .=3, (2021). The generated path is rejected if it reaches λB in both directions. start with two paths in low and high level forcefield Ulow Uhigh Ulow Uhigh new generated paths paths are rejected reject Potential Alchem. Alg. Ref (high level) flat 5.16×10-1 ± 1% 5.05×10-1 ± 2% one bump 3.16×10-1 ± 2% 3.23×10-1 ± 3% two bump 2.40×10-1 ± 4% 2.45×10-1 ± 2% Crossing probability Potential Alchem. Alg. Ref (high level) flat 2534 ± 0.8% 2463 ± 1.3% one bump 810 ± 0.7% 805 ± 0.7% two bump 1637 ± 1.7% 1664 ± 1.3% Average path length in [0+] Potential Alchem. Alg. Ref (high level) flat 636 ± 0.9% 631 ± 0.8% one bump 620 ± 0.8% 636 ± 0.9% two bump 630 ± 1% 621 ± 1.6% Average path length in [0-] accept check generated paths Alchemical Move “ Alchemy was an ancient protoscientific and philosophical tradition that emerged in Hellenistic Egypt, particularly in Alexandria, and later spread to Iran, India, China, and Europe. Its main pursuits were the transmutation of base metals into gold, the search for universal cures, and the quest for longevity ”. In this work, a rabbit (Ulow) investigates the phase space and a turtle (Uhigh) refines the transition pathway. To achieve this, they swapped their place. rlow rhigh rlow rhigh rlow rhigh Uhigh Uhigh Uhigh Ulow Ulow Ulow Ulow = Uhigh Ulow Ulow Uhigh Uhigh Uhigh Uhigh Ulow Ulow rlow rlow rhigh rhigh
