biologia - Studia

Atm PROTEIN CAN SWITCH OFF THE DNA DAMAGE SIGNAL IN A p53 MODEL
however, the parameters α
is
, i = 1,2 , which control phosphorylation and
dephosphorylation rate of the Atm protein, are more biologically important.
Meanwhile, because the total amount of the Atm protein and its phosphorylated
form, Atm-p, is assumed to be constantly µ , so we can consider Λ Λ(
k , k )
=
1s
2s
and solve the equation Λ = 0 with respect to k 2 s
and find k
2s
= µ ( µ + k1s
)/ k1s.
This is a curve in plane of k
is
, i = 1,2 , which acts like a switch between two
bifurcation diagrams, that is, down of the curve, the bifurcation diagram is
determined by Ω = 0 , so we call it Ω region, and in above of it, the bifurcation
diagram is determined by ∆ = 0 , so we call it ∆ region. (see figure 1). By putting
*
*
A = µ + k1s
, B = µ k0dk2s,
A = U , B = k0d
( U − U )( U − k1s
),
the equations ∆ = 0 and Ω = 0 are reformulated respectively by
* *
Aα
2s
− Bα1s
= 0, A α
2s
− B α1s
= 0, which are two lines in plane of α
is
,
i = 1,2 . Therefore we can show the bifurcation diagram as figure 2.
Fig. 1. Typical plot for switch curve, here µ = 1.
Fig. 2. Typical bifurcation diagram. Since the space of parameters has dimension upper
than 3, so we have to simplify it as above. Note that the switch curve is in space of k
is
,
α , i = 1,2 .
i = 1,2 and the bifurcation curves are in space of
is
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