1. Growth
2. Differentiation
A. Basic Model
Aumptions:
1. Without control elements, A:B=A%:B% in the stable state ??
(1) No control element.
x – concentration of repressor 1(CI)
y – concentration of repressor 2(434)
a1,2 – effective rate of synthesis of x,y b, – cooperativity of repression from
promoter 1(PCI), promoter 2(P434
Parameters
a1=a2=100
b=g=2 (b, g>1)
- three steady states; one unstable, two stable – bistability
- in the case of b, g=1
there is one stable steady state
Bistability requires:
- a1, a2 do not differ greatly
- b,g are not drastically different
- how “drastic” difference of a1 vs. a2 is tolerated depends on the magnitude of b and g
B. Improved Model
RNAP(t) + Proi(t) →ki Proi (t + τ1) + RNAP(t + τ2) + ni × ri (t + τ3) ------ (1)
RNAP(t) + Pro1(t) k1 Pro1(t + τ1) + RNAP(t + τ2) + n1 × r1(t + τ3) ------ (2)
RNAP(t) + Pro2(t) k2 Pro2(t + τ1) + RNAP(t + τ2) + n2 × r2(t + τ3) ------ (3)
r2(t) + Pro1(t) k3 Pro1r2(t) ---------------------------------------------------------------------- (4)
r1(t) + Pro2(t) k4 Pro2r1(t) ---------------------------------------------------------------------- (5)
Pro2r1(t) (5) Pro1r2(t) + I nd1(t) k5 Pro1(t) + r2(t) + I nd1(t) --------------- (6)
Pro2r1(t) + I nd2(t) k6 Pro2(t) + r1(t) + I nd2(t) -------------------------------------- (7)
r1(t) →k7 ---------------------------------------------------------------------------------------------------- (8)
r2(t) →k8 ---------------------------------------------------------------------------------------------------- (9)
Equation(2) and (3) represent the chemical processes of gene expression.Reactions (4) and (5) are pressing processes of the promoters by forming Pro1r1 (PCI) and Pro2r1(P434), and (6) and (7) reactivate the promoters’ expression ability with inducers Ind1 ( in our program, Ind2=0) and Ind1(pluX). The last two reactions, (8) and (9) are the decay processes of the gene expression products (A, B).n1 and n2 equal to 1. In our simulations, the stochastic of all reactions are equal to 1s-1, except the decay reaction, with a stochastic rate constant of 0.001 s-1.RNAP=50, Pro1=1, Pro2=1 and Ind1=1.(Without control element Ind2=0).
With control element , inducer 1 is present.That is removed about time 100s.
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