Statistical and Biological Physics

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TVI: Theoretical Biological Physics (Prof. Erwin Frey)

This lecture is intended as an introduction to the theoretical concepts used in describing biological systems and biologically relevant soft materials such as polymers and membranes. It builds on the course "thermodynamics and statistical mechanics". The course starts with an introduction into the the theories of stochastic processes and nonlinear systems. These methods are of particular importance in the molecular world of cellular systems but have broad range of applications far beyond biologically relevant systems. Building on these theoretical concepts the course will cover a range of topics:
  • Theory of Stochastic Processes and Brownian Motion
  • Nonlinear Dynamics
  • Brownian Dynamics Simulations
  • Hydrodynamics at Low Reynolds Number
  • Entropic Forces
  • Molecular Machines and Enzymes
  • Polymers and Membranes
  • Population Genetics and Gene Regulation
  • Reaction Diffusion Models and Pattern Formation
  • Game Theory and Evolution
  • System Theory and Networks


  • 4- stündig, Mo 9 - 11 Uhr, Do 11 - 13 Uhr
  • Sommerfeld Raum 348/349, Theresienstr. 37, 3. Stock

Begleitendes Seminar & Übungen:

  • 2- stündig, Mi 13 - 15 Uhr, Sommerfeld Raum (Beginn am 26. Oktober)

Seminar Schedule:

  • 26.10.   Wolfram Möbius: How to generate random numbers
  • 02.11.   Jonas Kraus: The Ehrenfest model and the Jarzynski relation
  • 16.11.   Stephanie Kappler: Delbrück-Luria Experiment
  • 30.11.   Benjamin Terjung: Stochastic Gene Expression in Fluctuating Environments
  • 07.12.   Axel Kammerer: Intrinsic noise in gene regulatory networks
  • 07.12.   Borysova Elina: Polymerization Ratchets
  • 14.12.   Special Sommerfeld Lectures
  • 20.12.   Anton Winkler: Forced Thermal Ratchets
  • 11.01.   Boris Schäfer: Fluctuation Driven Ratchets: Molecular Motors
  • 11.01.   Louis Reese: Fluctuation-Driven Molecular Transport through an asymmetric Membrane Channel
  • 18.01.   Tobias Reichenbach: Stochastic Resonance in Biology
  • 18.01.   Gerald Raoul Ryseck: Models of Circadian Rhythms
  • 25.01.   Stephanie Kappler: Statistical Fluctuations in Autocatalytic Reactions
  • 25.01.   Karen Winkler: Kinetic Proofreading
  • 02.02.   Michael Hecht: Distribution Function of Semiflexible Polymers
  • 02.02.   Daniel Nicklas: Voltage Gated Ion Channels
  • 08.02.   Georg Fritz: Stochastic description of gene regulatory mechanisms
  • 08.02.   Matthias Schmitt: Force Spectroscopy on Single Macromolecules

Topics for Seminar Talks:


  1. Introduction
  2. Script
please report any errors and typos in the script to Jan-Timm Kuhr

Supplementary material:

  1. Supplement_1 (password required)
  2. Numerical recipes in C
  3. Gambler's Ruin Java Applet
  4. Random Walk Notebook for Mathematica
  5. P.A. Pury, Asymmetry and convergence in the central limit theorem: An approach for physicists, Am. J. Phys. 58, 62 (1990) [Article]
  6. E. Frey and K. Kroy, Im Zickzack zwischen Physik und Biologie [Article]
  7. E. Frey and K. Kroy, Brownian motion: a paradigm of soft matter and biological physics, Annalen der Physik (Leipzig) 14, 20 (2005). [Article]
  8. E. Frey, Physics in Cell Biology: On the physics of Biopolymers and Molecular Motors, ChemPhysChem 3, 270 (2002). [Article]
  9. E. Frey, Physikalische Fragestellungen aus der Zellbiologie, Physikalische Blätter 57, 63 (2001). [PDF]
  10. Poisson Process - Notebook for Mathematica
  11. Yule Process - Notebook for Mathematica
  12. Molecular motors - pdf slides
  13. Supplement 2 (password required)
  14. Malthus-Verhulst Gillespie simulation - Notebook for Mathematica
  15. Methode der Charakteristiken (password required)
  16. Introduction to Biopolymers and Biomembranes (password required)
  17. Ideal chains (password required)


  • L.J.S. Allen, Stochastic Processes with Applications to Biology
  • C.W. Gardiner, Handbook of Stochastic Methods

Sprechstunde Prof. Dr. Frey:

  • Fr 13.30 - 15 Uhr, Raum 335, Theresienstr. 37