Converting Metabolic Reconstructions into Kinetic and Dynamic Models
Due to its complex temporal organization, a living cell is never in a steady state. Understanding its temporal changes is impossible without mathematical simulation using ordinary differential equations (ODE). To avoid "the curse" of the enormous complexity of biological systems, a number of simplifying assumptions have to be made.
The most important of these are asymptotic transitions widely used in applied mathematics: slowly changing variables must be "frozen", to be considered as "parameters", while fast variables have to be assumed as quasi-stationary ones. These two transitions reduce the order of the ODE models to a relatively small number of essential variables: from unmanageable thousands to less than ten (for mathematical details see reviews by Vasilieva and Hunter).
Choosing the right time domain for a model is indispensable for defining essential variables, as opposed to "parameters" and quasi-stationary algebraic unknowns. In fact, this choice should be made in the very beginning of research projects that target metabolic reconstruction and its mathematical simulation. It narrows the focus of commercial projects to selected biological processes, and makes it possible to use partial reconstructions and models, which saves time and money, and makes the whole genome sequencing, reconstruction and simulation unnecessary.
Breaking up fast reaction networks into equivalent reactions, sources and sinks of reactants can help reduce the model complexity.
Evolutionary considerations and comparative analysis offer effective methods of simplifying models of large metabolic networks. It was theoretically shown and experimentally confirmed that purely stoichiometric models describing unregulated metabolism can predict fundamental properties of the living networks.
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