Physics and Chemistry of Biological Systems

Theoretical Foundations of Molecular Dynamics
7.5 CFU

  • Basic concepts of Newtonian dynamics and Statistical Mechanics: energy conservation, time reversibility and phase-space incompressibility, Liouville Theorem, Ergodicity.
  • Integration schemes for molecular dynamics: Verlet, Trotter splitting, Velocity Verlet. Dependence of the results on the time step.
  • Sampling the canonical ensemble with Monte Carlo: Metropolis-Hastings rule, balance and detailed balance, hybrid Monte Carlo.
  • Sampling the canonical ensemble with molecular dynamics: velocity rescaling, Berendsen thermostat, Andersen thermostat, Langevin dynamics, Nosé-Hoover thermostat.
  • Stochastic equations: Itoh rule, Fokker-Planck equation.
  • Derivation of a biomolecular force field: bonded and non bonded terms.
  • Running with longer timesteps: multiple timestepping and constraints.
  • Efficient long-range force calculations: neighbor lists, isotropic corrections, and Ewald methods.
  • Sampling the constant pressure ensemble: Berendsen and Monte Carlo barostats. Introduction to non-equilibrium statistical mechanics: Crooks theorem and Jarzynski equality.
Theoretical lectures are complemented with numerical exercises to be corrected during classes.

The evaluation consist of a traditional oral exam, where the candidate will be required to answer questions on the whole program in such a way as to demonstrate sufficient knowledge of the subject to pass the exam.
Frenkel-Smit, Understanding Molecular Simulation
Allen-Tildesley, Computer Simulation of Liquidsey
Tuckerman, Statistical Mechanics: Theory and Molecular Simulation
Gardiner, Stochastic Methods, A Handbook for the Natural and Social Sciences