Model analysis and parameter estimation in biochemical reaction networks

Abstract

Kinetic models are central in systems biology to describe and analyse metabolic, generic and signalling networks. Kinetic models provide a way to summarize and precisely formulate the current knowledge about the dynamics of biological systems in terms of di erential equations. Therefore computational tools for the analysis and calibration of these type of models are of great interest. In this thesis, rst the concepts of chemical reaction network theory are extended for biochemical reactions. A complex-reaction graph is de ned for the network, in which the nodes are complexes and the edges represent reactions with multiple kinetics. Then, it is shown that the system of dynamic equations of the bio-CRNs can be formulated such that it has a close relationship to this reaction graph. Further, an algorithm is presented to nd a network (a realization) to a given kinetic equation system. The proposed form of the model equations let us formulate optimization problems to nd dynamically equivalent realizations, i.e. multiple networks which can be described by the same kinetic equations. Further, it is shown by the linear conjugacy theorem, that if the scaling of the state variables is allowed, structurally di erent further realizations of the same kinetic system can be found.

In the third part of this work a model reduction method is proposed for large scale kinetic networks. The original mixed integer nonlinear optimization problem is approximated by a nite sequence of mixed integer quadratic optimization problems, which is much cheaper to solve by existing methods. The reduction method sequentially eliminates reactions from the network, such that the trajectories of some important species do not change, i.e. the reduction error in each step is minimized. Further, the kinetic rate parameters are simultaneously tuned in given bounds to guarantee the best t between the original and the reduced model. In the last part of the thesis the calibration of kinetic models to experimental data is considered. Here a global optimization method is proposed together with regularization techniques. We illustrate by seven case studies of increasing complexity, how the presented method overcome the non-convex nature of these calibration problems and results in faster and more reliable convergence than traditional alternatives. Further, the calibrated models are evaluated by out of sample cross-validation, showing that the regularized estimations have better predictive value.