Research Activities

Enhanced Sampling of Complex Systems: From Thermodynamics to Kinetics

The study of the free energy landscape (FEL) of nature-inspired systems is of paramount importance in understanding complex interaction mechanisms. The idea is that a global overview of the systems' energy surface is useful for a quantitative understanding of the relationships between structure, dynamics, stability, and functional behaviours. Thanks to the continuous increase of the computing power and of the reliability of empirical force fields, molecular dynamics (MD) simulations have become a widely employed computational technique to simulate the dynamics of complex systems. Under the assumption of ergodicity, the equilibrium properties can be derived as time averages of the corresponding observables along the MD trajectories and the associated FEL can be computed. However, most phenomena of interest can take place on time scales that are orders of magnitude larger than the accessible time that can be currently simulated with classical MD simulations.

Since the seminal work of Hendrik A. Kramers in 1940, the study of these so-called rare events has been a subject of considerable interest to several scientific communities. These events are rare because the systems have to overcome significant barriers, which can either be of an energetic or an entropic nature. In the context of rare events, the systems can present different free-energy minima, each one trapping the dynamics for a time that can be long compared to fast bond vibrations, until a thermally activated jump is eventually performed toward another metastable or global minima. To address this issue, a variety of enhanced statistical and numerical methods are now routinely employed to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive MD simulations. They exploit methodologies based on constrained MD, such as Metadynamics and Umbrella sampling. These numerical methods can be combined with Markov state model analysis, which allows for the convenient combination of multiple MD trajectories into a single kinetic network model, for which more accurate time scale information of the slowest processes in the system can be obtained.

• F. Sicard*, V. Koskin, A. Annibale, and E. Rosta, Position-Dependent Diffusion from Biased Simulations and Markov State Model Analysis, J. Chem. Theory Comput. 17 (4), 2022-2033 (2021)

• F. Sicard*, Computing Transition Rates for Rare Events: When Kramers Theory meets Free Energy Landscape, Phys. Rev. E 98 (5), 052408 (2018)

• F. Sicard* and P. Senet, Reconstructing the free energy landscape of Met-enkephalin using dihedral principal component analysis and metadynamics, J. Chem. Phys. 138, 235101 (2013)

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