Acceleration with Interpretability: A Surrogate Model-Based Collective Variable for Enhanced Sampling

Most enhanced sampling methods facilitate the exploration of molecular free energy landscapes by applying a bias potential along a reduced dimensional collective variable (CV) space. The success of these methods depends on the ability of the CVs to follow the relevant slow modes of the system. Intuitive CVs, such as distances or contacts, often prove inadequate, particularly in biological systems involving many coupled degrees of freedom. Machine learning algorithms, especially neural networks (NN), can automate the process of CV discovery by combining a large number of molecular descriptors and often outperform intuitive CVs in sampling efficiency. However, their lack of interpretability and high cost of evaluation during trajectory propagation make NN-CVs difficult to apply to large biomolecular processes. Here, we introduce a surrogate model approach using lasso regression to express the output of a neural network as a linear combination of an automatically chosen subset of the input descriptors. We demonstrate successful applications of our surrogate model CVs in the enhanced sampling simulation of the conformational landscape of alanine dipeptide and chignolin mini-protein. In addition to providing mechanistic insights due to their explainable nature, the surrogate model CVs showed a negligible loss in efficiency and accuracy, compared to the NN-CVs, in reconstructing the underlying free energy surface. Moreover, due to their simplified functional forms, these CVs are better at extrapolating to unseen regions of the conformational space, e.g., saddle points. Surrogate model CVs are also less expensive to evaluate compared to their NN counterparts, making them suitable for enhanced sampling simulation of large and complex biomolecular processes.