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A study of T cell proliferation in response to stimulation by the cytokine
IL2 inferred the interactions among co-expressed gene clusters. The authors
consider
all possible networks matching the data instead
of requiring enough data
to infer a unique network (Martin
et al.
2007). 99.4% of the total inferred
networks had a single fixed point (steady-state). In the remaining 0.6% of the
cases the cyclin-dependent kinase inhibitor was observed to fluctuate, leading to
a three-step cycle. The resulting network topology elucidated the regulation
between early, intermediate and late genes activated upon IL2 stimulation. A
regulatory network involved in embryonic segmentation and muscle development
in
D. melanogaster
was recently produced (Zhao
et al.
2006) using an inference
method combining minimum description length principle (MDL) (Rissanen
1978) with a probabilistic Boolean method. MDL reduces the search space of
possible networks, which is usually high in PBNs, giving a good trade-off
between modeling complexity and data-fitting. The algorithm developed in (Zhao
et al.
2006) is useful for inferring temporal regulation and analyzing time-series
datasets. Thus probabilistic Boolean networks are attractive in that they maintain
the large-scale inference ability of standard Boolean methods while relaxing the
determinism of the basic method.
4.6. Dynamic Boolean Models: Examples in Plant Biology, Developmental
Biology and Immunology
While inference methods extract a network of interactions based on the observed
data, such networks serve as an input to dynamic models. Inputs to a dynamic
model include (i) the interactions and regulatory relationships between
components (i.e. the network), (ii) how the strength of the interactions depends
on the state of the interacting components (i.e. the state transfer functions) and
(iii) the initial state of each component in the system. Given these, the model will
output the time evolution of the state of the system.
To analyze the dynamics of a system of interest we can either use inferred
networks or assemble a network from independent studies. In case of the latter,
the topology can be verified by performing known perturbations and comparing
the outcome to the result of the experimentally known mutant. In the process
of network assembly inference rules need to be employed to represent the
regulatory relationships concluded by various independent experimental
observations since the experimentally observed relationship is often not a direct
interaction (Fig. 4.6) (Li
et al.
2006).
