Inference of Calmodulin's Ca²⁺-Dependent Free Energy Landscapes via Gaussian Mixture Model Validation

A free energy landscape estimation method based on the well-known Gaussian mixture model (GMM) is used to compare the efficiencies of thermally enhanced sampling methods with respect to regular molecular dynamics. The simulations are carried out on two binding states of calmodulin, and the free energy estimation method is compared with other estimators using a toy model. We show that GMM with cross-validation provides a robust estimate that is not subject to overfitting. The continuous nature of Gaussians provides better estimates on sparse data than canonical histogramming. We find that diffusion properties determine the sampling method effectiveness, such that diffusion-dominated apo calmodulin is most efficiently sampled by regular molecular dynamics, while holo calmodulin, with its rugged free energy landscape, is better sampled by enhanced sampling methods.