Kinetics from Metadynamics: Principles, Applications, and Outlook

Abstract

Metadynamics is a popular enhanced sampling algorithm for computing the free energy landscape of rare events by using molecular dynamics simulation. Ten years ago, Tiwary and Parrinello introduced the infrequent metadynamics approach for calculating the kinetics of transitions across free energy barriers. Since then, metadynamics-based methods for obtaining rate constants have attracted significant attention in computational molecular science. Such methods have been applied to study a wide range of problems, including protein−ligand binding, protein folding, conformational transitions, chemical reactions, catalysis, and nucleation. Here, we review the principles of elucidating kinetics from metadynamics-like approaches, subsequent methodological developments in this area, and successful applications on chemical, biological, and material systems. We also highlight the challenges of reconstructing accurate kinetics from enhanced sampling simulations and the scope of future developments.

Kinetic View of Enzyme Catalysis from Enhanced Sampling QM/MM Simulations

“…Enhanced sampling methods like infrequent metadynamics, variational flooding, and OPES f have so far been successfully applied to a variety of chemical, material, and biological systems for calculating kinetics. 22 However, to the best of our knowledge, this work first demonstrates the successful application of these techniques to compute the kinetics of an enzymatic reaction. We also take into account the relative stability of the RC of the enzyme/substrate complex using classical force-field-based simulations, leading to a significant increase in computational efficiency.…”

“…Our methodology offers a more precise theoretical framework by directly measuring time scales, rather than deriving kinetic estimates from an approximated barrier height calculated from a free-energy surface. Enhanced sampling methods like infrequent metadynamics, variational flooding, and OPES f have so far been successfully applied to a variety of chemical, material, and biological systems for calculating kinetics . However, to the best of our knowledge, this work first demonstrates the successful application of these techniques to compute the kinetics of an enzymatic reaction.…”

“…Recently, it has been demonstrated that the kinetics of molecular rare events can be calculated directly using adaptive-bias-enhanced sampling algorithms without introducing any assumption of the underlying kinetic model, e.g., transition-state theory. − Examples of such methods include infrequent metadynamics, Gaussian accelerated molecular dynamics, variational flooding, Gaussian mixture based enhanced sampling, and On-the-fly probability enhanced sampling (OPES) flooding (OPES f ) . It is therefore appropriate that such algorithms are used to directly measure the rate constant of the catalytic step instead of the indirect estimation from the free-energy landscape.…”

Collective Variable-Based Enhanced Sampling: From Human Learning to Machine Learning

“…Enhanced sampling techniques − are commonly employed to overcome the time-scale limitations of brute-force MD. Collective variable (CV)-based enhanced-sampling methods, including umbrella sampling, (extended-)­adaptive biasing force, , metadynamics, and temperature accelerated MD, along with their variants, − have been extensively utilized in examining numerous complex (bio)­chemical processes, as discussed in recent literature reviews. ,− …”

Standard Binding Free-Energy Calculations: How Far Are We from Automation?

“…This approach provides valuable structural and energetic data on the paths taken by the ligand to reach the final binding site, thereby aiding in the elucidation of the ligand-binding mechanism and kinetics. In addition to funnel MtD, frequency adaptive MtD can also offer insight into the ligand-binding mechanism, which includes free-energy barriers and consequently kinetics. , These benefits render the geometric approach more desirable and easier to automate compared to the alchemical one when the precise binding pose of the ligand is undetermined or when understanding ligand kinetics is important.…”