Date of Award

5-2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

Advisor

Dimitrova, Elena S

Committee Member

Dean , Brian C

Committee Member

Gao , Shuhong

Committee Member

Macauley , Matthew

Abstract

A large influx of experimental data has prompted the development of
innovative computational techniques for modeling and reverse
engineering biological networks. While finite dynamical systems,
in particular Boolean networks, have gained attention as relevant
models of network dynamics, not all Boolean functions reflect the
behaviors of real biological systems. In this work, we focus on two
classes of Boolean functions and study their applicability as
biologically relevant network models: the nested and partially nested
canalyzing functions.
We begin by analyzing the nested canalyzing functions} (NCFs),
which have been proposed as gene regulatory network models due to
their stability properties. We introduce two biologically motivated
measures of network stability, the average height and average cycle
length on a state space graph and show that, on average, networks
comprised of NCFs are more stable than general Boolean networks.
Next, we introduce the partially nested canalyzing functions
(PNCFs), a generalization of the NCFs, and the nested canalyzing
depth, which measures the extent to which it retains a nested
canalyzing structure. We characterize the structure of functions with
a given depth and compute the expected activities and sensitivities of
the variables. This analysis quantifies how canalyzation leads to
higher stability in Boolean networks. We find that functions become
decreasingly sensitive to input perturbations as the canalyzing depth
increases, but exhibit rapidly diminishing returns in
stability. Additionally, we show that as depth increases, the dynamics
of networks using these functions quickly approach the critical
regime, suggesting that real networks exhibit some degree of
canalyzing depth, and that NCFs are not significantly better than
PNCFs of sufficient depth for many applications to biological
networks.
Finally, we propose a method for the reverse engineering of networks
of PNCFs using techniques from computational algebra. Given
discretized time series data, this method finds a network model using
PNCFs. Our ability to use these functions in reverse engineering
applications further establishes their relevance as biological network
models.

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