
Stochastic processes in cell biology
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, 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
 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
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; 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, PhysikJournal 4:61 (2005)]
Noiseinduced transitions and stochastic resonance
 W. Horsthemke und R. Lefever, Noiseinduced 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: 223287 (1998)
Biomolecular bonds under force
 E. Evans und K. Ritchie, Dynamic strength of molecular adhesion
bonds, Biophysical Journal 72: 15411555 (1997)
 J. Shillcock und U. Seifert, Escape from a metastable well under a timeramped force, Physical Review E 57: 73017304 (1998)
 T. Erdmann and U. S. Schwarz, Stochastic dynamics of adhesion clusters under shared constant force and with rebinding, J. Chem. Phys., 121:89979017 (2004)
 O. Braun and U. Seifert, Force spectroscopy on single multidomain biopolymers: a master equation approach, Eur. Phys. J. E, 18: 113 (2005)
 S. Klumpp and R. Lipowsky, Cooperative cargo transport by several
molecular motors, PNAS 102: 1728417289 (2005)
Jarzynski equation
 F. Ritort, Work fluctuations, transient violations of the second law and freeenergy recovery methods: perspectives in theory and experiment, edited by Jean Dalibard, Bertrand Duplantier, Vincent Rivasseau, Poincare Seminar 2, pages 195229, Birkhäuser Verlag Basel, 2003.
 C. Jarzynski, Nonequilibrium equality for free energy differences, Phys Rev Lett 14: 26902693 (1997)
 G. E. Crooks, Entropy production flutuation theorem and the nonequilibrium work relation for free energy differences, Phys Rev E 60: 27212726 (1999)
 G. Hummer and A. Szabo, Free energy reconstruction from
nonequilibrium singlemolecule pulling experiments, PNAS 98: 36583661
(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):18325.
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 firstpassage time analysis of the Kramers type. PNAS 99:35523556 (2002)
 I. Goychuk and P. Hänggi. The role of conformational diffusion in ion channel gating. Physica A 325: 918 (2003)
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