# Stochastic processes in cell biology

This course takes place in the winter term 2005/06 every Tuesday from 11:15 - 12:45. It started on Nov 8 with an overview in the seminar room Philosophenweg 19. As suggested by the participants, on Nov 22 we moved to the Neuenheimer Feld, first to the seminar room 215 at INF 293 (Universitäres Rechenzentrum), and on Jan 10 to the seminar room 14 at INF 350 (Otto-Meyerhof-Zentrum).

The course is divided into two parts. The first part offers a detailed introduction into the theory of stochastic processes, similar to the first chapters of the textbook by Honerkamp, but supplemented by more recent developments and the special requirements for applications to biophysics. The following subjects are covered:
• Fundamental concepts: random variables, probability distribution, moments and cumulants, central limit theorem, conditional probability, stochastic (Markov) processes, white and colored noise, Chapman-Kolmogorov equation
• Examples for probability distributions: binomial, Gauss, Poisson
• Equations for stochastic processes: Fokker-Planck, master, Langevin
• Additive versus multiplicative noise, Ito versus Stratonovich interpretation, equivalence of Fokker-Planck and Langevin equations
• Examples for stochastic processes: random walks, radioactive decay, chemical reactions, birth and death processes
• Advanced subjects: first passage time problems, Kramers theory, bistable systems, noise-induced transitions, fluctuation-dissipation theorem, detailed balance, Kramers-Moyal expansion, fluctuation theorems and Jarzynski equation
The second part deals with modelling of stochastic processes in cell biology. Here we follow mainly the recent literature. The following subjects are covered:
• Biomolecular bonds under force: cohesion in biological systems is provided by biomolecular bonds with relatively small interaction energies; because they have to compete with thermal energy, lifetime is always finite and stochastic; we discuss: mean first passage time in one-dimensional energy landscape, escape over a transition state barrier, Kramers theory, coupling to an external force, adiabatic approximation and Bell equation, master equation for cooperative processes, Jarzynski equation; in particular we discuss models for clusters of adhesion bonds, clusters of molecular motors and multidomain proteins
• Ion channels: these proteins allow ions to pass through biomembranes and are the basis for neuronal excitability; opening and closing is stochastic and can be modelled with mean first passage time methods
• Molecular motors: these proteins are responsible for force production and transport in cells, eg myosin II in muscle and kinesin for axonal transport; they move stochastically and different kinds of models have been developed to describe their motion, including ratchet models and the asymmetric exclusion process (ASEP)

# Literature

## Textbooks stochastic processes

• J. Honerkamp, Stochastische Dynamische Systeme, VCH 1990
• N.G. van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier 1992

## Textbooks biophysics

• H. C. Berg, Random Walks in Biology, Princeton University Press 1993
• P. Nelson, Biological Physics, Freeman 2003
• C. P. Fall, E. S. Marland, J.M.- Wagner and J.J. Tyson, editors, Computational Cell Biology, Springer 2002

## Textbooks cell biology

• Bruce Alberts et al., Molecular biology of the cell, 4th edition, Garland Science 2002
• Thomas Pollard and William Earnshaw, Cell Biology, Saunders 2004
• Harvey Lodish et al., Molecular cell biology, 5th edition, Freeman 2003

## Noise in biology in general

• C.V. Rao, D.W. Wolf und A.P. Arkin, Control, exploitation and tolerance of intracellular noise, Nature 420:231 (2002)
• E. Frey und K. Kroy, Brownian motion: a paradigm of soft matter and biological physics, Annalen der Physik 14:20 (2005) [übersetzter Auszug erschienen als: Im Zickzack zwischen Physik und Biologie, Physik-Journal 4:61 (2005)]

## Noise-induced transitions and stochastic resonance

• W. Horsthemke und R. Lefever, Noise-induced transitions. Theory and Applications in Physics, Chemistry, and Biology, Springer 1984
• L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni, Stochastic resonance, Reviews of Modern Physics 70: 223-287 (1998)

## Biomolecular bonds under force

• E. Evans und K. Ritchie, Dynamic strength of molecular adhesion bonds, Biophysical Journal 72: 1541-1555 (1997)
• J. Shillcock und U. Seifert, Escape from a metastable well under a time-ramped force, Physical Review E 57: 7301-7304 (1998)
• T. Erdmann and U. S. Schwarz, Stochastic dynamics of adhesion clusters under shared constant force and with rebinding, J. Chem. Phys., 121:8997-9017 (2004)
• O. Braun and U. Seifert, Force spectroscopy on single multidomain biopolymers: a master equation approach, Eur. Phys. J. E, 18: 1-13 (2005)
• S. Klumpp and R. Lipowsky, Cooperative cargo transport by several molecular motors, PNAS 102: 17284-17289 (2005)

## Jarzynski equation

• F. Ritort, Work fluctuations, transient violations of the second law and free-energy recovery methods: perspectives in theory and experiment, edited by Jean Dalibard, Bertrand Duplantier, Vincent Rivasseau, Poincare Seminar 2, pages 195-229, Birkhäuser Verlag Basel, 2003.
• C. Jarzynski, Nonequilibrium equality for free energy differences, Phys Rev Lett 14: 2690-2693 (1997)
• G. E. Crooks, Entropy production flutuation theorem and the nonequilibrium work relation for free energy differences, Phys Rev E 60: 2721-2726 (1999)
• G. Hummer and A. Szabo, Free energy reconstruction from nonequilibrium single-molecule pulling experiments, PNAS 98: 3658-3661 (2001)
• Liphardt J, Dumont S, Smith SB, Tinoco I Jr, Bustamante C. Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality. Science. 2002 Jun 7;296(5574):1832-5.

## Molecular motors

• F. Jülicher, A. Ajdari and J. Prost, Modeling molecular motors, Reviews of Modern Physics 69: 1269 (1997)
• P. Reimann, Brownian Motors: Noisy Transport far from Equilibrium, Phys. Rep. 361: 57 (2002)
• A. Parmeggiani, T. Franosch and E. Frey, Totally asymmetric simple exclusion process with Langmuir kinetics, Phys Rev E 70: 046101 (2004)
• R. Lipowsky and S. Klumpp, 'Life is motion': multiscale motility of molecular motors, Physica A 352:53 (2005)

## Ion channels

• I. Goychuk and P. Hänggi. Ion channel gating: a first-passage time analysis of the Kramers type. PNAS 99:3552-3556 (2002)
• I. Goychuk and P. Hänggi. The role of conformational diffusion in ion channel gating. Physica A 325: 9-18 (2003)

Zuletzt geändert am Fr Feb 10 13:55:56 CET 2006