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Lumping analysis of biochemical reaction systems with time scale separation
1Department of Chemical Engineering, University of Wisconsin-Madison, Madison, Wisconsin.
Abstract:
Due to the complexity of the systems, successful modelling of intracellular reaction networks must rely on lumping techniques which systematically reduce the number of variables and parameters. Fortunately, the time scale separation characteristics of biochemical systems provide opportunities for eliminating unnecessary details. Through the proper interpretation of eigenvalues and eigenvectors, this article presents a theoretical basis for systematic model reduction. Results are generalized as a semiheuristic basis for lumping systems without complete kinetic information. It is also illustrated that the simplified system can yield new insight which is otherwise unavailable.
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Rate-Determining Steps
In a multistep reaction mechanism, one of the elementary steps progresses significantly slower than the others. This slowest step is called the rate-limiting step (or rate-determining step). A reaction cannot proceed faster than its slowest step, and hence, the rate-determining step limits the overall reaction rate.
The concept of rate-determining step can be understood from the analogy of a 4-lane freeway with a short-stretch of traffic-bottleneck caused due to...

