Metadynamic sampling of the free energy landscapes of proteins coupled with a Monte Carlo algorithm

Metadynamics is a powerful computational tool to obtain the free energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical.

💡 Research Summary

The paper introduces a hybrid sampling scheme that merges metadynamics with a Monte Carlo (MC) algorithm to efficiently reconstruct the free‑energy landscape (FEL) of simplified protein models. Traditional metadynamics, when coupled with molecular dynamics, provides a powerful way to overcome energy barriers by depositing Gaussian “hills” in the collective‑variable (CV) space, but the associated MD simulations are computationally demanding, especially for large biomolecules. Conversely, MC simulations are cheap and can explore high‑dimensional conformational spaces through stochastic trial moves, yet they struggle to cross deep free‑energy barriers. The authors therefore propose to embed the time‑dependent bias potential generated by metadynamics directly into the Metropolis acceptance criterion of MC moves.

In the proposed algorithm, a set of CVs that capture the overall folding state (e.g., a contact‑based order parameter or radius of gyration) is chosen. At regular intervals τ a Gaussian hill of height w and width σ is added to the bias potential Vbias(CV). When a trial MC move proposes a new configuration, the biased energies Eold+Vbias(old) and Enew+Vbias(new) are computed, and the acceptance probability follows the usual Metropolis form p= min