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Stochastic reaction timings that lead to Poisson-distributed counts

Stochastic reaction timings that lead to Poisson-distributed counts. Stochastic transcription with stochastic degradation. Stochastic transcription with deterministic degradation. Many (usually unproductive) attempts at mRNA transcription. 1 transcription event. =. many unproductive attempts.

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Stochastic reaction timings that lead to Poisson-distributed counts

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  1. Stochastic reaction timings that lead to Poisson-distributed counts Stochastic transcription with stochastic degradation Stochastic transcription with deterministic degradation

  2. Many (usually unproductive) attempts at mRNA transcription 1 transcription event = many unproductive attempts 1 spin represents bunch of attempts Poisson-distributed # transcriptions during Poisson-distributed copy # of mRNA at + tSURVIVE tCOUNT tSURVIVE

  3. Stochastic reaction timings that lead to Poisson-distributed counts Stochastic transcription with stochastic degradation Stochastic transcription with deterministic degradation

  4. Combine stochastic transcription with stochastic degradation 1 transcription event = many unproductive attempts 1 spin represents bunch of attempts Survives many attempts at degradation tSURVIVE

  5. Transcription as a Poisson process tCOUNT

  6. Exponential distribution of survival times tSOURCE tCOUNT

  7. Exponential distribution of survival times tSOURCE tCOUNT

  8. Probability of survival illustrated by reverse exponential decay tSOURCE tCOUNT

  9. Probability of survival illustrated by reverse exponential decay tSOURCE tCOUNT

  10. Probability of survival illustrated by reverse exponential decay tSOURCE tEARLIER tCOUNT

  11. Probability of survival illustrated by reverse exponential decay tSOURCE tLATER tCOUNT

  12. Probability of survival illustrated by reverse exponential decay tCOUNT Survival Transcription

  13. Prob. transcribed xProb. Survived =Prob. counted pCOUNT tCOUNT Counted pSURVIVE = 1/3 = Survival X pTRANSCR = 1/20 Transcription

  14. Multiple “inefficient” wheels look like single “efficient” wheel ≈ Copies of A: Counted F1 E9 E8 E7 E6 E5 E4 E3 E2 E1 D3 D2 D1 C2 C1 B A = Survival X Transcription

  15. Finite number of “effective” wheels . . . Cannot make 6th copy of A ≈ Copies of A: Counted F1 E9 E8 E7 E6 E5 E4 E3 E2 E1 D3 D2 D1 C2 C1 B A Yellow icing on blue cake = Survival Not enough frosting X Transcription

  16. Same statistics for wheels uneven and even in time ≈ Stochastic transcription with stochastic degradation Poisson-distributed number of events associated with passing of time Poisson-distributed instantaneous copy number + Stochastic transcription with deterministic degradation

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