
Stochastic processes with applications to biological systems
This course takes place in the summer term 2008 every Tuesday from 14:15  15:45 in the large seminar room of the BIOQUANTbuilding (INF 267) and is given jointly with Christian Korn. On April 8 we will have a short meeting discussing content and literature. The first lecture will take place on April 15 and the last one on July 15. The course is given in English and 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, ChapmanKolmogorov equation
 Examples for probability distributions: binomial, Gauss, Poisson
 Equations for stochastic processes: FokkerPlanck, master, Langevin
 Additive versus multiplicative noise, Ito versus Stratonovich
interpretation, equivalence of FokkerPlanck 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, noiseinduced transitions, fluctuationdissipation
theorem, detailed balance, KramersMoyal expansion, fluctuation
theorems and Jarzynski equation
The second part deals with modelling
of biological systems. Here we follow mainly
the recent literature. The following subjects are covered:
 Biomolecular bonds under force: binding in biological systems
is always transient and stochastic; we discuss mean first passage time in
onedimensional 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, bond heterogeneity, models for catch
bonds, analogy to protein folding
 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. We also explain the relation to the famous HodgkinsHuxley model for action potentials.
 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); we also discuss recent models for cooperative transport by many motors, tugofwar in bidirectional transport and mean first passage time problems for the motorbased transport of viruses to the nucleus
 Noise in gene expression: transcription and translation are stochastic events and recently a large body of experimental data has been measured in bacterial systems. For example, it has been shown that increasing cell (=system) size in E. Coli leads to a decreased noise level. We will review these experiments and simple models for this context.
Literature
 J. Honerkamp, Stochastische Dynamische Systeme, VCH 1990
 N.G. van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier 1992
 C.W. Gardiner, Handbook of stochastic methods, Springer 2004
 W. Horsthemke und R. Lefever, Noiseinduced transitions. Theory and Applications in Physics, Chemistry, and Biology, Springer 1984
 H. Risken, The FokkerPlanck Equation, Springer 1996
 H. C. Berg, Random Walks in Biology, Princeton University Press 1993
 P. Nelson, Biological Physics, Freeman 2003
 R. Phillips, J. Kondev and J. Theriot, Physical Biology of the Cell, to appear fall 2008
Presentations
 Introduction
 Random Text
 Molecular motors
 Single molecule experiments
 Noise in gene expression
 Ion channels