Simplicity within Complexity : Understanding dynamics of cellular networks by model reduction

Abstract: Cellular networks composed of interactions between genes, proteins and metabolites, determines the behavioural repertoire of the cell. Recent developments in high-throughput experimental techniques and computational methods allow static descriptions of these networks on a genome scale. There are also several dynamical mathematical models characterizing small subnetworks of the cell such as a signaling cascade or cell division. These networks exhibit a considerable complexity, and mathematical analysis are therefore essential in order to uncover the underlying dynamical core driving the systems. A core description can reveal the relative functional contributions of the various molecular interactions and goes to the heart of what kind of computations biological circuits perform. Partially successful methodologies toward this end includes bifurcation analysis, which only considers a small number of dimensions, and large-scale computer simulations.In this thesis we explore a third route utilizing the inherent biological structure and dynamics of the network as a tool for model simplification. Using the well studied cell cycle, as a model system, we observe that the this network can be divided into dynamical modules displaying a switch-like behaviour. This allows a transformation into a piecewise linear system with delay, the subsequent use of tools from linear systems theory and finally a core dynamical description. Analytical expressions capturing important cell cycle features such as cell mass, as well as necessary constraints for cell cycle oscillations, are thereby retrieved. Finally we use the dynamical core together with large-scale simulations in order to study the balance between robustness and sensitivity.It appears that biological features such as switches, modularity and robustness provide a means to reformulate intractable mathematical problems into solvable ones, as biology appears to suggest a path of simplicity within the realm of mathematical complexity.