Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths
This addresses the challenge of sampling molecular transitions without requiring expert-selected CVs, making it applicable to larger systems where traditional methods fail, though it is incremental as it builds on existing stochastic optimal control frameworks.
The paper tackles the problem of sampling molecular transition paths between metastable states, which is difficult with standard methods due to high energy barriers and reliance on collective variables (CVs). It proposes a machine learning method called PIPS that eliminates the need for CVs and successfully generates low-energy transitions for proteins like Alanine Dipeptide, Polyproline, and Chignolin.
We consider the problem of sampling transition paths between two given metastable states of a molecular system, e.g. a folded and unfolded protein or products and reactants of a chemical reaction. Due to the existence of high energy barriers separating the states, these transition paths are unlikely to be sampled with standard Molecular Dynamics (MD) simulation. Traditional methods to augment MD with a bias potential to increase the probability of the transition rely on a dimensionality reduction step based on Collective Variables (CVs). Unfortunately, selecting appropriate CVs requires chemical intuition and traditional methods are therefore not always applicable to larger systems. Additionally, when incorrect CVs are used, the bias potential might not be minimal and bias the system along dimensions irrelevant to the transition. Showing a formal relation between the problem of sampling molecular transition paths, the Schrödinger bridge problem and stochastic optimal control with neural network policies, we propose a machine learning method for sampling said transitions. Unlike previous non-machine learning approaches our method, named PIPS, does not depend on CVs. We show that our method successful generates low energy transitions for Alanine Dipeptide as well as the larger Polyproline and Chignolin proteins.