Information Technology Reference
In-Depth Information
details will likely have a similar qualitative behavior as the 15-gene regulatory net-
work that has been uncovered. This is supported by the fact that the present model
has been overall validated with simulations of several mutants and it has been able
to make predictions that have been later conrmed with additional experimental
data. For example, we had predicted that AG, one of the GRN nodes, should have
a positive direct or indirect feedback loop and this has been conrmed in a recent
paper [Gomez-Mena et al. (2005)].
5.5.2. Noisy dynamics
In this paper, we use this GRN to explore the response of a biological network
to random perturbations. This is a follow up of a study, that we have recently
published which demonstrates that when this GRN is subject to noise the sequence
of attractor visitation recovered mimics that observed in nature. In particular, is
the same as that observed for the ABC functions. The A genes are turned rst, then
the B ones dening the A to AB transition, and then the C, dening the AB to BC
and C transitions [Alvarez-Buylla et al. (2008)]. We explore here in a systematic
way the complex response of the network to noise. We also relate the complexity
of the dynamical output signal to the exibility that the system has to explore the
set of deterministic attractors.
First of all, we look at the noisy dynamics of the original network with the rules
experimentally obtained [Alvarez-Buylla et al. (2008)]. However, in this contribu-
tion we do so from the point of view of the complexity of the generated time series.
We plot the time series of the state of the system, as dened by Eq. (5.2), and we
can observe the dierent behavior for dierent noise intensities in Fig. 5.7. For a
low noise intensity, the system stays most of the time in a subset of the available
attractors. On the other hand, for a large noise intensity the system is not able to
reside for a long a time close to any of the attractors and the dynamics is clearly
dominated by noise. However, for an intermediate value (around 3%) the system
jumps between the dierent attractors and stays for a reasonable time in most of
them. The latter behavior is the required mixture of robustness and exibility in
many biological system. When applying the DFA to the time series we see in Fig. 5.8
how the dynamical behavior turns into precise values of the exponent. Thus, for
low noise intensity we obtain Brownian noise, for a large noise intensity white noise,
and for the intermediate value we get 1=f noise. This is in fact a very remarkable
result that relates the correlations of the uctuations with the observed robustness
and exibility in the dynamics of the model around the attractors. In Fig. 5.9 (top
set of points) we have plotted the dependence of the exponent on the intensity of
the noise, and we can see that only for intermediate values this exponent is close
to 1.
In order to check the biological relevance of the observed rules, we have re-
peated the previous analysis on the network preserving the topology but allowing
for changes in the way the units process the information, i.e. altering the logical
