Table 5.

A bistable biochemical network with multiple timescales and spontaneous escape

Reactions	Kinetics	Reactions	Kinetics
S1 + P → S1:P	k1	∅→ Ef	k4
S2 + P → S2:P	k1	Ef→∅	k5
S3 + P → S3:P	k1	∅→ Ef	k6
S4 + P → S4:P	k1	Ef→∅	k7
S1:P + S2:P → S1:P2:S2	k1	Ef + P → Ef:P	k8
S1:P + S3:P → S1:P2:S3	k1	Ef:P → Ef + P	k-8
S1:P + S4:P → S1:P2:S4	k1	Ef:P → Ef + P*	k8cat
S2:P + S3:P → S2:P2:S3	k1	Eb + P → Eb:P	k9
S2:P + S4:P → S2:P2:S4	k1	Eb:P → Eb + P	k-9
S3:P + S4:P → S3:P2:S4	k1	Eb:P → Eb + P*	k9cat
S1:P → S1 + P	k-1	P:O + RNAP → P:O:RNAP	k10
S2:P → S2 + P	k-1	P:O:RNAP → P:O + RNAP	k-10
S3:P → S3 + P	k-1	P:O:RNAP → P:O + RNAP:DNA	k11
S4:P → S4 + P	k-1	P:O + (S1:P2:S2)3→ P:O*	k12
S1:P2:S2 → S1:P + S2:P	k-1	P:O* → P:O + (S1:P2:S2)3	k-12
S1:P2:S3 → S1:P + S3:P	k-1	P:O* + RNAP → P:O*:RNAP	k13
S1:P2:S4 → S1:P + S4:P	k-1	P:O*:RNAP → P:O* + RNAP	k-13
S2:P2:S3 → S2:P + S3:P	k-1	P:O*:RNAP → P:O* + RNAP:DNA	k14
S2:P2:S4 → S2:P + S4:P	k-1	RNAP:DNA → RNAP + mRNA	k15, N15
S3:P2:S4 → S3:P + S4:P	k-1	mRNA + Rib → Rib:mRNA	k16
2 S1:P2:S2 → (S1:P2:S2)2	k2	Rib:mRNA → mRNA+Rib:mRNA1	k17
S1:P2:S2 + (S1:P2:S2)2→ (S1:P2:S2)3	k3	Rib:mRNA1 → Rib + P	k18, N18
(S1:P2:S2)2→ 2 S1:P2:S2	k-2	mRNA →∅	k19
(S1:P2:S2)3→ S1:P2:S2 + (S1:P2:S2)2	k-3	P →∅	k20
Rate Laws & Kinetic Constants:
0th order: k6 = 200 [molecules/sec]
1st order: k-1 = 50, k-2 = k-3 = 0.2, k7 = 3.5, k-8 = k-9 = 1, k8cat = 150, k9cat = 50, k-10 = k-13 = 0.1, k11 = 0.01, k-12 = 1.155e-3, k14 = 0.2, k17 = 33, k19 = 2.31e-3, k20 = 1.1155e-3 [1/sec]
2nd order: k1 = 0.025, k2 = 1e-3, k3 = 1e-5, k4 = 0.015 (mono-molecular), k8 = 2.5e-4, k9 = 8.47e-5, k10 = 0.05, k12 = 0.01, k13 = 0.1, k16 = 5e-3 [molecules sec]-1
3rd order: k5 = 1e-4 (mono-molecular) [molecules2 sec]-1
Gamma-distributed events: k15 = 30 nt/sec, N15 = 1200 nt, k18 = 33 aa/sec, N18 = 400 aa
Initial Conditions: #Po = #P* o = 4000, #S1o = #S2o = #S3o = #S4o = 1500, #Ribo = 300, #RNAPo = 180, #Efo = #Ebo = 250, otherwise 0 [Molecules]

The computational times of a large-scale system benchmark using the fixed Euler-Maruyama (EM) and Milstein implementations of the HyJCMSS algorithm and the Next Reaction variant of the stochastic simulation algorithm (SSA). ND: Not Determined