Realization Theory and Functional Model Reduction in Biochemical Networks

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Eccs-0802008BamiehObjectiveOne of the central problems in the emerging field of Systems Biology is the analysis and functional classification of large complex biochemical reaction networks. Such networks are increasingly being scrutinized and their individual components painstakingly investigated in detail. However, a general methodology for inferring dynamical and functional behavior from the detailed network description is still sorely lacking. We propose methodologies by which large components of such networks can be replaced by components of much smaller state dimension that have similar functionality. We term this problem Functional Model Reduction to emphasize distinctions with traditional model reduction techniques. The enabling ideas behind this methodology consist of understanding how dynamical systems that are designed for prescribed functions (such as logical or hybrid operations) can be implemented with dynamical networks constrained to have specific types of building blocks. We investigate it in the specific context of building blocks that are available from basic biochemical kinetics. Enabled with this analysis, we pose the problem of carrying out this analysis in reverse, that is, given networks with specific types of building blocks, we ask what type of functional behavior they represent, and whether it is possible to mirror that behavior with dynamical system of much lower dimension. Our goal is not to develop a general nonlinear model reduction technique, but rather one that is particularly tailored to the differential equations that result from biochemical kinetics. Some novel aspects of systems theory will need to be developed such as realizations with prespecified network components as well as functional objectives for model reduction.Intellectual MeritUncovering and classification of function from the detailed description of biochemical reaction networks is a central problem in systems biology and dynamical systems theory. The proposed work will contribute techniques that are particularly tailored to the dynamical network that arise from biochemical kinetics. A new paradigm for model reduction based on network function will be developed.Broader ImpactThe broader impacts of this work include the application of the model reduction techniques developed in this project to a high order complex model of ischemic stroke that is being developed, which will make possible new understanding of this disease and new treatments for it. The multi-disciplinary nature of this work will ensure that graduate students from dynamical systems and control and those from the life sciences will develop new skill sets from the other disciplines and will help create graduates who are comfortable working at the boundary of their disciplines.