In systems biology, models often contain a large number of unknown or only roughly known parameters that must be estimated through the fitting of data. This work examines the question of whether or not these parameters can in fact be estimated from available measurements. Structural or a priori identifiability of unknown parameters in biochemical reaction networks is considered. Such systems consist of continuous time, nonlinear differential equations. Several methods for analyzing identifiability of such systems exist, most of which restate the question as one of observability by expanding the state space to include parameters. However, these existing methods were not developed with biological systems in mind, so do not necessarily address the specific challenges posed by this type of problem. In this work, such methods are considered for the analysis of a representative biological system, the NF-kappaB signal transduction pathway. It is shown that existing observability-based strategies, which rely on finding an analytical solution, require significant simplifications to be applicable to systems biology problems that are seldom feasible. The analytical nature of the solution imposes restrictions on the size and complexity of systems that these methods can handle. This conflicts with the fact that most currently studied systems biology models are rather large networks containing many states and parameters. In this thesis, a new simulation based method using an empirical observability Gramian for determining identifiability is proposed. Computational and numerical sensitivity issues for this method are considered. An algorithm, based on this method, is developed and demonstrated on a simple biological example of microbial growth with Michaelis-Menten kinetics. The new method is applied to the motivating NF-kappaB example to show its suitability for use in systems biology. / Thesis (Master, Chemical Engineering) -- Queen's University, 2008-08-05 22:20:32.561

Stochastic models of biochemical reaction networks are used for understanding the properties of molecular regulatory circuits in living cells. The state of the cell is defined by the number of copies of each molecular species in the model. The chemical master equation (CME) governs the time evolution of the the probability density function of the often high-dimensional state space. The CME is approximated by a partial differential equation (PDE), the Fokker-Planck equation and solved numerically. Direct solution of the CME rapidly becomes computationally expensive for increasingly complex biological models, since the state space grows exponentially with the number of dimensions. Adaptive numerical methods can be applied in time and space in the PDE framework, and error estimates of the approximate solutions are derived. A method for splitting the CME operator in order to apply the PDE approximation in a subspace of the state space is also developed. The performance is compared to the most widely spread alternative computational method.

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