Designing transferable transition state guided collective variables via interpretable machine learning models for enhanced sampling: a case study on polymer collapse transition

Enhanced sampling methods enable the mechanistic study of complex biophysical processes at atomistic resolution, addressing the key timescale limitations of brute-force molecular dynamics (MD) simulation. However, selecting appropriate collective variables (CVs) for enhanced sampling simulation to explore the relevant phase space of the system is challenging. In recent years machine learning (ML) algorithms have shown promise in the design of efficient CVs for enhanced sampling and improvements over traditional intuitive order parameters (OPs) in free energy surface (FES) exploration. However, the lack of interpretability and high cost of evaluation make it difficult to apply these ML-based CVs across diverse systems. Moreover, transferability of ML-guided CVs is a critical issue and can't be directly applied in different systems with similar mechanistic details without retraining. In this study, we introduce a surrogate model assisted enhanced sampling method using an elastic net (EN) regression model which expresses the relevance of different OPs as a linear combination locally at the transition state (TS) region. We demonstrate the successful applications of surrogate model-based TS-derived CV in exploring the landscapes of polymer collapse transition with varying lengths. This method shows improvements in achieving a faster free energy convergence within very short simulation time over other OPs tested in this study. Moreover, we demonstrate that this approach is transferable across different lengths of polymer systems without the requirement of large training data for each system. Overall, this study provides a general and interpretable approach to run enhanced sampling simulations with surrogate model-assisted TS-derived CV which can be extrapolated beyond their training system.