Cellular Translocation of Biomolecules using Ratcheting
The translocation of biopolymers through nanopores is a crucial process in cellular biology . Such processes have been modelled by means of a Brownian ratchet .
However, as described by , the translocation of proteins into the Endoplasmatic Reticulum (ER) is based on the random binding of an ATPase to the protein inside the ER lumen. Thus the movement of the protein into the ER depends on the process of binding and unbinding of ATPases.
Brownian ratchet models have been used to describe polymerization of actin filaments against a barrier. While these processes have been thoroughly studied [2,4], the understanding of ratchet models for translocation with random target sites is not complete. The most important question is: What is the average velocity of a biomolecule depending on binding and unbinding rates of target molecules?
Andrej Depperschmidt and Peter Pfaffelhuber
 T. Ambjornsson, M. A. Lomholt and R. Metzler, Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins. Journal of Physics: Condensed Matter, 2005, 17, S3945-S3964.
 C. S. Peskin, G. M. Odell and G. F. Oster, Cellular motions and thermal fluctuations: the Brownian ratchet. Biophys J, 1993, 65, 316-324.
 W. Liebermeister, T. A. Rapoport and R. Heinrich, Ratcheting in post-translational protein translocation: A mathematical model. J Mol Biol, 2001, 305, 643-656.
 H. Qian, A stochastic analysis of a Brownian ratchet model for actin-based motility. Mech Chem Biosyst, 2004, 1, 267-278.
Aging and the loss of telomere sequences
Eucaryotic DNA is organized linearly and is replicated when a cell proliferates. The replication mechanism is not perfect in that telomeres are shortened by each round of DNA replication. This mechanism has been suggested to play a role in cellular aging: if the length of the telomere falls below the Hayflick constant the cell loses its ability to replicate, a phenomenon known as replicative senescence.
Katharina Surovcik and Peter Pfaffelhuber
 M. Z. Levy, R. C. Allsopp, A. B. Futcher, C. W. Greider and C. B. Harley, Telomere end-replication problem and cell aging. J Mol Biol, 1992, 225, 951-960.
 O. Arino, M. Kimmel and G. F. Webb, Mathematical modeling of the loss of telomere sequences. J Theor Biol, 1995, 177, 45-57.
 N. Arkus, A mathematical model of cellular apoptosis and senescence through the dynamics of telomere loss. J Theor Biol, 2005, 235, 13-32.
 T. Antal, K. B. Blagoev, S. A. Trugman and S. Redner, Aging and immortality in a cell proliferation model. J Theor Biol, 2007, 248, 411-417.
 H. Mahmoud. Evolution of Random Search Trees. Wiley, 1992.
 D. Aldous and P. Shields, A diffusion limit for a class of randomly-growing binary trees. Probability Theory and Related Fields, 1988, 79, 509-542.
Spatial Phenomena in Systems Biology
Heinz Weisshaupt and Peter Pfaffelhuber
 J. D. Murray, Mathematical Biology I + II, Springer Verlag
 K. Ball, T.G. Kurtz, L. Popovic, G. Rempala, Asymptotic Analysis of Multiscale Approximations to Reaction Networks. The Annals of Applied Probability, 2006, Vol. 16, No. 4, 1925–1961.
Autoinducer signalling in rhizobia
Katharina Surovcik and Peter Pfaffelhuber,