Abstract
The human body is composed of a large collection of cells,\the building blocks of life". In
each cell, complex networks of biochemical processes contribute in maintaining a healthy
organism. Alterations in these biochemical processes can result in diseases. It is therefore
of vital importance to know how these biochemical networks function. Simple reasoning
is not su±cient to comprehend life's complexity. Mathematical models have to be used
to integrate information from various sources for solving numerous biomedical research
questions, the so-called systems biology approach, in which quantitative data are scarce
and qualitative information is abundant.
Traditional mathematical models require quantitative information. The lack in ac-
curate and su±cient quantitative data has driven systems biologists towards alternative
ways to describe and analyze biochemical networks. Their focus is primarily on the anal-
ysis of a few very speci¯c biochemical networks for which accurate experimental data are
available. However, quantitative information is not a strict requirement. The mutual
interaction and relative contribution of the components determine the global system dy-
namics; qualitative information is su±cient to analyze and predict the potential system
behavior. In addition, mathematical models of biochemical networks contain nonlinear
functions that describe the various physiological processes. System analysis and parame-
ter estimation of nonlinear models is di±cult in practice, especially if little quantitative
information is available.
The main contribution of this thesis is to apply qualitative information to model and
analyze nonlinear biochemical networks. Nonlinear functions are approximated with two
or three linear functions, i.e., piecewise-a±ne (PWA) functions, which enables qualitative
analysis of the system. This work shows that qualitative information is su±cient for the
analysis of complex nonlinear biochemical networks. Moreover, this extra information can
be used to put relative bounds on the parameter values which signi¯cantly improves the
parameter estimation compared to standard nonlinear estimation algorithms. Also a PWA
parameter estimation procedure is presented, which results in more accurate parameter
estimates than conventional parameter estimation procedures. Besides qualitative analysis
with PWA functions, graphical analysis of a speci¯c class of systems is improved for
a certain less general class of systems to yield constraints on the parameters. As the
applicability of graphical analysis is limited to a small class of systems, graphical analysis
is less suitable for general use, as opposed to the qualitative analysis of PWA systems.
The technological contribution of this thesis is tested on several biochemical networks
that are involved in vascular aging. Vascular aging is the accumulation of changes respon-
sible for the sequential alterations that accompany advancing age of the vascular system
and the associated increase in the chance of vascular diseases. Three biochemical networks
are selected from experimental data, i.e., remodeling of the extracellular matrix (ECM),
the signal transduction pathway of Transforming Growth Factor-¯1 (TGF-¯1) and the
unfolded protein response (UPR).
The TGF-¯1 model is constructed by means of an extensive literature search and con-
sists of many state equations. Model reduction (the quasi-steady-state approximation)
reduces the model to a version with only two states, such that the procedure can be visual-
ized. The nonlinearities in this reduced model are approximated with PWA functions and
subsequently analyzed. Typical results show that oscillatory behavior can occur in the
TGF-¯1 model for speci¯c sets of parameter values. These results meet the expectations
of preliminary experimental results. Finally, a model of the UPR has been formulated and
analyzed similarly. The qualitative analysis yields constraints on the parameter values.
Model simulations with these parameter constraints agree with experimental results.
Original language | English |
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Qualification | Doctor of Philosophy |
Awarding Institution |
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Supervisors/Advisors |
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Award date | 18 Sep 2007 |
Place of Publication | Eindhoven |
Publisher | |
Print ISBNs | 978-90-386-1564-6 |
DOIs | |
Publication status | Published - 2007 |