stochastic reaction timings that lead to poisson-distributed counts 1 stochastic transcription with...
TRANSCRIPT
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Stochastic reaction timings that lead to Poisson-distributed counts
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Stochastic transcription with stochastic degradation
Stochastic transcription with deterministic degradation
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Many (usually unproductive) attempts at mRNA transcription
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1 transcription event
many unproductive attempts=
1 spin represents bunch of attempts
tSURVIVE
tCOUNTtSURVIVEPoisson-distributed # transcriptions during
Poisson-distributed copy #of mRNA at
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Stochastic transcription with stochastic degradation
Stochastic transcription with deterministic degradation
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Stochastic reaction timings that lead to Poisson-distributed counts
Combine stochastic transcription with stochastic degradation
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1 transcription event
many unproductive attempts=
1 spin represents bunch of attempts
Survives many attempts at degradation
tSURVIVE
Transcription as a Poisson process
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tCOUNT
Exponential distribution of survival times
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tCOUNTtSOURCE
Exponential distribution of survival times
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tCOUNTtSOURCE
Probability of survival illustrated by reverse exponential decay
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tCOUNTtSOURCE
Probability of survival illustrated by reverse exponential decay
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tCOUNTtSOURCE
Probability of survival illustrated by reverse exponential decay
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tCOUNTtSOURCEtEARLIER
Probability of survival illustrated by reverse exponential decay
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tCOUNTtSOURCEtLATER
Probability of survival illustrated by reverse exponential decay
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Tran
scrip
tion
Surv
ival
tCOUNT
Prob. transcribed x Prob. Survived = Prob. counted
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Tran
scrip
tion
Surv
ival
Coun
ted
X=
pTRANSCR = 1/20
pSURVIVE = 1/3
pCOUNT tCOUNT
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Multiple “inefficient” wheels look like single “efficient” wheel
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Tran
scrip
tion
Surv
ival
Coun
ted
X=
≈
ABC2 C1D1D2D3E1E2
Copies of A:
E3E4E5E6E7E8E9F1
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ABC2 C1D1D2D3E1E2E3E4E5E6E7E8E9F1
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Tran
scrip
tion
Surv
ival
Coun
ted
X=
≈
Yellow icingon
blue cake
Copies of A:Cannot make 6th copy of A
Not enoughfrosting
. . .
Finite number of “effective” wheels
Same statistics for wheels uneven and even in time
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≈
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𝑡Stochastic transcription with stochastic degradation
Stochastic transcription with deterministic degradation
Poisson-distributed number of eventsassociated with passing of time
Poisson-distributedinstantaneous copy number
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