biologia - Studia

O. RABIEIMOTLAGH, Z. AFSHARNEZHAD
Fig. 6. Certain behavior of ~ γ ( t ) with respect to all possible plots for G (g)
. Here we can
see the effect of G (g)
on the convergence of ~ γ . In fact, according to the what mentioned
after theorem 2, G (g)
acts like a controller on the DNA healing process .
Dependence on initial values
The part (2) of the theorem 2 states that if Λ > 0 and Ω < 0 then some
compatible solutions converges to N , this means that there may exist compatible
solutions converging to N
w
, for some w∈ R . This fact can be seen through the cases
(d)
and ( f ) in the table A. This is biologically interesting, because, as it is shown in
the figure 6, in these cases, the model forecasts permanent damage for the DNA if the
compatible solutions have simultaneously initial low amount of the DNA damage
signal and the Atm-p protein. But, the compatible solutions which has initially enough
amount of the DNA damage signal, even if they have initially low amount of the Atm-p
protein, converge to N . This may occurs because of the fact that, from the second term
of the third equation of the model (3) , dephosphorylation rate of Atm-p has inverse
relation with amount of the DNA damage signal. Therefore, low amount of the DNA
damage signal can not force the system to provide enough Atm-p which is necessary
for DNA healing process. However, if a compatible solution has enough initial amount
of the Atm-p, then it converges to N , hence DNA will be repaired from damages.
ACKNOWLEDGMENT
This research was supported by Ferdowsi University of Mashhad and partly
supported by the Center for Research in Modeling and Computation Linear and Nonlinear
Systems, Ferdowsi University of Mashhad (Iran).
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