This dissertation attempts to answer some of the vital questions involved in the
genetic regulatory networks: inference, optimization and robustness of the mathe-
matical models. Network inference constitutes one of the central goals of genomic
signal processing. When inferring rule-based Boolean models of genetic regulations,
the same values of predictor genes can correspond to di®erent values of the target gene
because of inconsistencies in the data set. To resolve this issue, a consistency-based
inference method is developed to model a probabilistic genetic regulatory network,
which consists of a family of Boolean networks, each governed by a set of regulatory
functions. The existence of alternative function outputs can be interpreted as the
result of random switches between the constituent networks. This model focuses on
the global behavior of genetic networks and re°ects the biological determinism and
stochasticity.
When inferring a network from microarray data, it is often the case that the
sample size is not su±ciently large to infer the network fully, such that it is neces-
sary to perform model selection through an optimization procedure. To this end, the
network connectivity and the physical realization of the regulatory rules should be
taken into consideration. Two algorithms are developed for the purpose. One algo-
rithm ¯nds the minimal realization of the network constrained by the connectivity,
and the other algorithm is mathematically proven to provide the minimally connected network constrained by the minimal realization.
Genetic regulatory networks are subject to modeling uncertainties and perturba-
tions, which brings the issue of robustness. From the perspective of network stability,
robustness is desirable; however, from the perspective of intervention to exert in-
°uence on network behavior, it is undesirable. A theory is developed to study the
impact of function perturbations in Boolean networks: It ¯nds the exact number
of a®ected state transitions and attractors, and predicts the new state transitions
and robust/fragile attractors given a speci¯c perturbation. Based on the theory, one
algorithm is proposed to structurally alter the network to achieve a more favorable
steady-state distribution, and the other is designed to identify function perturbations
that have caused changes in the network behavior, respectively.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1498 |
| Date | 15 May 2009 |
| Creators | Xiao, Yufei |
| Contributors | Dougherty, Edward R. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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