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Transcription in E.coli by the numbers •Size of typical gene = 1kb •Typical number of mRNAs = 10 •Typical rate of mRNA production = 10 min-1 •Typical mRNA degradation rate = 1 min-1 mRNA production in E.coli Golding et al. ‘05 hmi r=1/7min °=ln2/50min dhm i dt = r ¡ ° hmi Master equation for mRNA production Master equation for p(m,t): @p(m ;t ) @t = r p(m ¡ 1; t) + ° (m + 1)p(m + 1; t) ¡ r p(m; t) ¡ ° mp(m; t) Steady state: ³ @p( m ;t ) @t ´ = 0 p(m) = m ¡ ¹ ¹ e m! Poisson distribution with mean ¹ = r ° Variance of the mRNA number var(m) = 4 <m> Poisson: var(m) = <m> Poisson Inconsistent with unregulated transcription model Single cell trajectories ¢n Transcription occurs in bursts! Genetic switch Gardner, Cantor and Collins ‘00 Flipping the genetic switch Bistability! Nullclines and flow field Phase portrait of the genetic switch Repressilator Elowitz and Leibler ‘00 The Poisson distribution Probability What is the distribution of people per square? Histogram Poisson people/unit area