𝑡
Stochastic reaction timings that lead to Poisson-distributed counts
1
Stochastic transcription with stochastic degradation
Stochastic transcription with deterministic degradation
𝑡
Many (usually unproductive) attempts at mRNA transcription
2
𝑡
1 transcription event
many unproductive attempts=
1 spin represents bunch of attempts
tSURVIVE
tCOUNTtSURVIVEPoisson-distributed # transcriptions during
Poisson-distributed copy #of mRNA at
+
3
𝑡
Stochastic transcription with stochastic degradation
Stochastic transcription with deterministic degradation
𝑡
Stochastic reaction timings that lead to Poisson-distributed counts
Combine stochastic transcription with stochastic degradation
4
1 transcription event
many unproductive attempts=
1 spin represents bunch of attempts
Survives many attempts at degradation
tSURVIVE
Probability of survival illustrated by reverse exponential decay
12
𝑡
Tran
scrip
tion
Surv
ival
tCOUNT
Prob. transcribed x Prob. Survived = Prob. counted
13
Tran
scrip
tion
Surv
ival
Coun
ted
X=
pTRANSCR = 1/20
pSURVIVE = 1/3
pCOUNT tCOUNT
𝑡
Multiple “inefficient” wheels look like single “efficient” wheel
14
𝑡
Tran
scrip
tion
Surv
ival
Coun
ted
X=
≈
ABC2 C1D1D2D3E1E2
Copies of A:
E3E4E5E6E7E8E9F1
𝑡
ABC2 C1D1D2D3E1E2E3E4E5E6E7E8E9F1
15
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