I will first cover the Metropolis Monte Carlo method. This method reproduces the canonical ensemble, which is based on Boltzmann weight factors. Generalized-ensemble algorithms greatly enhance configurational sampling through the use of non-Boltzmann weight factors. Examples of generalized-ensemble algorithms are replica-exchange, simulated tempering, multicanonical algorithms, etc. After a single generalized-ensemble simulation, we can reproduce thermodynamic quantities in canonical ensemble by using reweighting techniques. In this lecture I will explain these methods.

Topics

• What is the best method for your problem?
• Alchemical transformations.
• Reaction coordinates and collective variables.
• Introduction to transition path sampling.
• Geometric transformations.
• How to determine binding affinities?
• Accuracy and precision. Error estimates.

This course will provide an introduction to the principal theory and computational methodology developed in the Wales group in Cambridge over the last two decades. The corresponding computer programs are:

1. GMIN for global optimisation and structure prediction. GMIN can also perform parallel tempering calculations and basin-sampling to treat systems with broken ergodicity.
2. OPTIM for characterising transition states and pathways between local minima on the potential energy surface.
3. PATHSAMPLE to distribute and organise OPTIM jobs on cluster computers. PATHSAMPLE also performs rate constant and committor probability analysis for the resulting kinetic transition networks.

References at the Wales group web site

This course will cover robotics-inspired algorithms to sample conformations and transition paths of flexible molecules

• Brief introduction to robot modeling and motion-planning algorithms.
• Modeling proteins as robots to enhance conformational sampling.
• Cost-based motion-planning algorithms to efficiently compute transition paths of highly flexible molecules: application to peptides.

The potential energy landscape (PEL) plays a fundamental role in understanding the meta-stable states of a system as well as transitions between them. Novel methods will be presented for modeling a sampled PEL and its associated transition graph (including frustration), and for comparing two PELs obtained, for example, from two different simulation runs. Software tools implementing these methods will also be presented and used in analyzing example systems.