Atomistic Markov Chain Monte Carlo simulations (MC) offer an interesting and complementary approach to Molecular Dynamics (MD) in the study of long time scale biophysical phenomena. MC simulations follow well established techniques to obtain a statistical physics description of a system using the potential energy function, but without solving the equations of motion. While a temporal description of the simulated process is sacrificed, questions about probabilities, temperature dependence, effects of prevailing conditions etc. can often be answered at a minuscule fraction of  the computing cost (and hence also the energy cost and carbon footprint) of an adequately long MD simulation. We have previously used replica exchange MC simulations to describe the folding of a complex 92 residue alpha + beta protein with an experimental folding time of about one second. We have also applied MC techniques to study intrinsically disordered proteins, peptide aggregation and the influence of macro-molecular crowding on protein behaviour. We believe that MC techniques are severely underused in biophysical research, owing to the dearth of exposure to the technique in contrast to MD within the community. Our tutorial is an effort to introduce researchers in the field to MC techniques in sufficient detail for them to use it in their own research.

1. Basic theory
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- Energy landscapes, time scales, sampling with simulations
- Monte Carlo fundamentals
- Markov Chain Monte Carlo simulations
- Ergodicity, detailed balance and MCMC move set
- Energy barriers and strategies to overcome them
- Comparison between MD and MC simulations
- Hybrid MC

2. MC simulations with ProFASi
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- A minimal protein folding simulation
- Visualisation and interpretation of ProFASi output
- Specifying composition, starting conditions, temperature and measurements
- Multi-molecule MC simulations: peptide aggregation

3. Generalized ensemble simulations
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- Simulated Tempering
- Replica Exchange Monte Carlo (REMC) for protein folding
- Quality checks, statistics
- Analysis and post-processing of REMC results
* Histogram reweighting
* Optimizing the temperature ladder for replica exchange
- Multi-canonical simulations
- The Wang-Landau method
- Applications to the study of intrinsically disordered proteins

4. Protein interactions
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- Protein folding with macromolecular crowding
* Restricting MC sampling with energy and move set restraints
* Representing small non-protein molecules (ions, ligands)
- Deformed energy landscapes (e.g. mechanical pulling)
- Specifying interaction terms for non-standard residues and non-protein molecules

5. ProFASi as a software library
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- Dependencies, installation, updates
- Supported hardware platforms and parallelisation models
- The python/bash script component
- A few important C++ classes in ProFASi
- ProFASi's plug-in interface
- New energy terms, conformational updates, simulated entities through plugins
- Example: Coarse grained crowders (e.g. hard spheres) implemented in a plugin, interacting with atomically represented proteins in a ProFASi REMC simulation
- Writing your own plugin