Physics and Chemistry of Biological Systems
Advanced Sampling Techniques (AST)

  • General introduction to the "rare events" problem. Introduction to the concepts of free energy, rate constant, mean-first-passage time, separation of time scales, committor distribution, etc.

  • Computing the free energy in complex systems:

    • Thermodynamic integration and umbrella sampling techniques.

    • Ferrenberg and Swendsen method for computing the density of states and weighted-histogram analysis.

    • History-dependent reconstruction of the free energy: metadynamics and Wand-Landau sampling.

  • Techniques for computing the rate constants:

    • Classical transition state theory. Kramers theory and Bennett-Chandler method for computing the recrossing corrections.

    • Methods for finding the saddle point in complex potential energy surfaces: nudged elastic band, eigenvalue following and the dimer method.

    • Path integral formulation of the rare event problem: transition path sampling. Methods for computing the committor distribution (finite-temperature string, etc.).


The successful and proficient attendance of the course will be evaluated by assigning to each student a different problem, that can be solved by numerical simulation implementing one of the approaches discussed in the course. The outcome of the exercise will be discussed in a oral exam.