I will discuss the reaction diffusion master equation (RDME) [1] as a
framework for spatially resolved stochastic kinetics. I will also
describe the Next Subvolume Method (NSM)[2] which is a fast algorithm
for sampling exact trajectories of systems modeled by the RDME. The
NSM has for instance been implemented in our software MesoRD [3],
which is freely available at sourceforge.net. I will further describe
two biologically relevant systems where stochastic kinetics results in
phenomena that can not be modeled by conventional deterministic
reaction-diffusion equations. The first is the PE- phenotype of the
Min proteins oscillations in E. coli [4]. The second is the noise
induced domain separation that we observe for a bistable MAPK switch
[2]. Finally, I will present some experimental results from single
protein tracking in living E. coli cells at a time resolution of 10ms
and a spatial precision of 50nm [5]. In particular, I will show that
the YFP fused lac repressor displays normal diffusion over all
measured timescales (10ms-100ms), which partly justifies the simple
RDME approach to in vivo kinetics.
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[1] Nicolis, G. and Prigogine, I.: Self-organization in nonequilibrium
systems. (John Wiley & sons. New York, 1977).
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[2] Elf, J and Ehrenberg, M (2004) Spontaneous separation of bi-stable
biochemical systems into spatial domains of opposite phases Syst Biol
(Stevenage) 1 230-236.
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[3] Hattne J, Fange D, and Elf J (2005) Stochastic reaction-diffusion
simulation with MesoRD Bioinformatics 21(12):2923-4.
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[4] Fange D and Elf J (2006) Noise induced Min phenotypes in E. coli
PLoS computational biology 2(6):e80.
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[5] Elf, Li and Xie (2007) Probing Transcription Factor Dynamics at
the Single Molecule Level a Living Cell Science 316 1191-4