| Summary: | <p>Many biological mechanisms can be understood as a complex interaction of chemical reactions. In order to explain the wealth of biochemical phenomena in systems biology, a sophisticated analytic framework for these chemical reaction networks is needed. This thesis investigates the role of extrinsic fluctuations in biochemical reaction mechanisms and develops mathematical tools for the systematic study of extrinsic noise.</p>
<p>The first part of this thesis studies variability in biological processes which
manifests itself as randomised rate constants. This variability can stem
from many sources, such as different cellular environments, or upstream
stochastic effects, which directly influence the reaction network under
study. As variability is often modelled as constant, but unknown parameters, parameter-free algebraic methods are developed in this thesis to
study large classes of chemical reaction networks named families. In particular, these methods allow for parameter-free model rejection, or model
testing and give upper bounds on the algebraic complexity of these tasks.
Further, a parameter-free result on the capability of multistationarity in
infinite classes of networks is proved.</p>
<p>The second part of this thesis studies time-varying extrinsic noise, such as
fluctuating experimental conditions, which directly influences the reaction
rates. A particular focus is on upstream stochastic networks, propagating
their stochasticity into the main network under study. Crucially, as the
stochasticity in the system is imposed externally, the analysis of such models is not subject to the constraints of stochastic methods. While intrinsic
noise imposes rigid restrictions on the modelling process, it is shown how
in extrinsic noise models the deterministic model structure stays intact.
Consequently, in this thesis, algebraic methods for deterministic networks
are extended to be applied to networks subject to extrinsic noise in order
to find oscillations and preclude stochastic switching. The effects of intrinsic stochasticity are also compared to the effects of extrinsic noise and
the framework is extended to correlated (coloured) noise.</p>
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