This course provides a graduate level introduction to continuous time stochastic processes suitable for applied mathematicians and theoretical scientists. The aim of the course is to develop the basic foundations of the subject and to apply these to a range of biological problems. We will follow the more physically intuitive approach of Gillespie, Gardiner and van Kampen (see recommended texts). However, we will strive to maintain sufficient rigor throughout by making clear our assumptions and definitions, and highlighting important mathematical issues. Biological applications will be chosen from a variety of topics including, ion channel gating, molecular motors, polymerization, biochemical and gene networks, stochastic neuron models and population dynamics.

Syllabus

Selected papers (molecular motors)

C. S. Peskin, G. M. Odell, and G. F. Osters (1993). Cellular motions and thermal fluctuations: The Brownian ratchet. Biophysical Journal 65: 316-324 PDF

P. Riemann (2002). Brownian motors :noisy transport far from equilibrium. Physics Reports 361:57-265 PDF

S. Klumpp and R. Lipowsky (2005). Cooperative cargo transport by several molecular motors. PNAS 102: 17284-17289 PDF

R. Lipowsky and S. Klumpp (2005). `Life is motion': multiscale motility of molecular motors. Physica A 35: 53-112 PDF

D. Chowdhury et. al. (2005). PHYSICS of TRANSPORT and TRAFFIC PHENOMENA in BIOLOGY: from molecular motors and cells to organisms. Physics of Life Reviews 2: 318-352 PDF

Selected papers (polymerization)

M. Dogterom and S. Leibler (1993). Physical aspects of the growth and regulation of microtubule structures. Phys. Rev. Lett. 70: 1347-1350 PDF

L. E. Keshet and G. B. Ermentrout (1998). Models for the Length Distributions of Actin Filaments: I. Simple Polymerization and Fragmentation. Bulletin of Mathematical Biology 60: 449-475 PDF

T. Antal et al (2007). Dynamics of an idealized model of microtubule growth and catastrophe. Phys. Rev. E. 76:041907 PDF

Selected papers (gene networks)

P. S. Swain, M. B. Elowitz, and E. D. Siggia (2002). Intrinsic and extrinsic contributions to stochasticity in gene expression PNAS 99:12795-12800PDF

J. Elf and M. Ehrenberg (2003) Fast Evaluation of Fluctuations in Biochemical Networks With the Linear Noise Approximation. Genome Res. 13: 2475-2484 PDF

J. Paulsson (2005). Models of stochastic gene expression. Physics of Life Reviews 2: 157-175PDF

N. Maheshri and E. K. OÕShea (2007). Living with noisy genes: how cells function reliably with inherent variability in gene expression. Annu. Rev. Biophys. Biomol. Struct. 36:413-34 PDF