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Course, academic year 2023/2024
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Simulation and Theory of Biological and Soft Matter Systems I - Biopolymers, Ions and Small Molecules - NMMO567
Title: Simulation and Theory of Biological and Soft Matter Systems I - Biopolymers, Ions and Small Molecules
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: yes / unlimited
Key competences: 4EU+ Flagship 3
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Christoph Allolio, Ph.D.
Class: M Mgr. MOD > Volitelné
Classification: Mathematics > Mathematical Modeling in Physics
Annotation -
An introduction to simulation techniques and theoretical concepts relevant for biological systems. The lecture takes a molecular view and connects this approach to statistical physics. The course is given in English and is suitable for master students at MFF UK and PřF UK.
Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.06.2020)

Tuckerman, Mark: Statistical Mechanics: Theory and Molecular Simulation.

Ben-Naim, Aryeh: Molecular Theory of Solutions.

van Kampen, N.: Stochastic Processes in Physics and Chemistry.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.06.2020)


  • Molecular building blocks of biology (Overview)
  • Water, small molecules and ions
  • Polymers and their monomers
  • Proteins, aminoacids
  • DNA, RNA, Nucleobases and their derivatives
  • Cellulose, starch and other sugars
  • Lipids, surfactants and self-assembled systems
  • Basic theory
  • Notions of stochastic processes
  • Brownian motion, Wiener process
  • Langevin equation, diffusion
  • Markov property
  • Remembering thermodynamics
  • Molecular and bulk systems
  • Thermodynamics of aqueous solutions
  • Osmotic pressure, chemical potential, ideal solutions
  • Thermodynamics of ions in solution
  • Simple polymer models
  • Entropic elasticity, persistence length
  • Polymer solutions
  • Introduction to molecular simulations
  • Molecular dynamics and statistical physics
  • Notion of phase space, Liouville theorem
  • Empirical forcefields
  • Potential form and parametrization
  • Basic algorithms of molecular dynamics
  • Integration of the equations of motion
  • Thermostats and barostats (NVT and NPT ensembles)
  • Monte Carlo as an alternative
  • Analyzing molecular simulations
  • Energies and their partition
  • Distribution functions and their interpretation
  • Kirkwood-Buff theory
  • Fluctuation-Dissipation Theorem, linear response
  • obtaining bulk elastic and transport properties from

molecular simulation

  • Microscopic stress tensor
  • Free energies and biased sampling
  • Umbrella sampling
  • Thermodynamic integration
  • Free-Energy perturbation and Bennett acceptance ratio
  • Simulating proteins

Means of Instruction:

The entire class, its materials as the final exercise will be provided online for those students that wish to take the course online. The course

will be weekly from the start of the winter semester. To acquire the credits, students will need to successfully complete an exercise project at home.


This course aims to provide a solid understanding of statistical thermodynamics and selected non-equilibrium processes, thus enabling students

to independently conduct molecular simulations of soft matter systems. Technical instructions on how to perform these simulations on current

hardware will be provided.

Molecular simulations generate a large amount of data. Their analysis by statistical methods is very instructive for

other data-driven applications. In this way, the course will increase the data literacy of the students.

Last update: Allolio Christoph, Ph.D. (28.07.2021)
Entry requirements

Basic knowledge of thermodynamics, mechanics, statistical physics and algorithms. No knowledge of chemistry or biology required.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.06.2020)
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