Fluctuating reaction rates and their application to problems of gene expression.
A reduced description is presented for noisy chemical reactions in small systems, such as cells. We show that, even when the number of molecules of a chemical species is small, its elimination from the description is possible provided that its characteristic time scale is short. The resulting effective chemical reaction has a reaction rate which fluctuates in time. The strength of the fluctuations depends on the time scale of the eliminated species as well as its variance. We derive the master equation of the reduced system, which includes additional terms of a diffusive kind, yielding a contribution towards fluctuations from the eliminated species. The stochastic kinetic equation for the reduced system is also derived. Finally, these results are applied to some problems of gene expression.
Shibata
Tatsuo
T
Department of Mathematical and Life Sciences, University of Hiroshima, 1-3-1, Kagamiyama, Higashi-Hiroshima, Japan. shibata@hiroshima-u.ac.jp
D001671:Biochemistry / Q000379:methods; D001692:Biological Transport; D001703:Biophysics / Q000379:methods*; D004058:Diffusion; D015870:Gene Expression; D005786:Gene Expression Regulation; D007700:Kinetics; D008956:Models, Chemical; D008957:Models, Genetic; D015233:Models, Statistical; D008962:Models, Theoretical; D016011:Normal Distribution; D011506:Proteins / Q000737:chemistry; D012333:RNA, Messenger / Q000378:metabolism; D013269:Stochastic Processes; D013997:Time Factors; D014158:Transcription, Genetic
D011506:Proteins; D012333:RNA, Messenger