Table 5 A bistable biochemical network with multiple timescales and spontaneous escape

S1 + P → S1:P

k₁

∅→ E^f

k₄

S2 + P → S2:P

k₁

E^f→∅

k₅

S3 + P → S3:P

k₁

∅→ E^f

k₆

S4 + P → S4:P

k₁

E^f→∅

k₇

S1:P + S2:P → S1:P₂:S2

k₁

E^f + P → E^f:P

k₈

S1:P + S3:P → S1:P₂:S3

k₁

E^f:P → E^f + P

k_-8

S1:P + S4:P → S1:P₂:S4

k₁

E^f:P → E^f + P*

k₈^cat

S2:P + S3:P → S2:P₂:S3

k₁

E^b + P → E^b:P

k₉

S2:P + S4:P → S2:P₂:S4

k₁

E^b:P → E^b + P

k_-9

S3:P + S4:P → S3:P₂:S4

k₁

E^b:P → E^b + P*

k₉^cat

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:

0^th order: k₆ = 200 [molecules/sec]

1^st order: k_-1 = 50, k_-2 = k_-3 = 0.2, k₇ = 3.5, k_-8 = k_-9 = 1, k₈^cat = 150, k₉^cat = 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]

2^nd 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

3^rd 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: #P_o = #P* _o = 4000, #S1_o = #S2_o = #S3_o = #S4_o = 1500, #Rib_o = 300, #RNAP_o = 180, #Ef_o = #Eb_o = 250, otherwise 0 [Molecules]