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UBC Theses and Dissertations

Application of the extended Kalman filter to enzyme reactions Lai, Henry K. H.

Abstract

In monitoring biological processes, measurement of key variables is often impeded by the lack of reliable on-line measurements of biomass, substrate, and product concentrations, and the difficulty to properly model biological activity in processes that are nonlinear and time-varying. One approach to solving this problem involves the development of state estimation techniques that use available measurements to reconstruct the evolution of state variables or to estimate the bioprocess parameters. The use of filtering theory for state estimation provides a means of incorporating a deterministic model into a method of forecasting future states which includes the probabilistic uncertainties of both the system and the measuring devices. The state estimation technique we use is the discrete extended Kalman filter. This method allows the use of an approximate model and partial measurements of process variables. To study the application of the discrete extended Kalman filter to a biological problem, we used two different enzyme reactions as model systems. The first model problem is a simulation of cellulose hydrolysis with enzyme inactivation. The second model problem is a simulation of the separation of a chiral substance into its respective enantiomers. In the first problem, the hydrolysis of cellulose, a slowly varying parameter is tracked after correctly choosing the model error covariance matrix. In the second problem, we reconstruct the complete composition of the system from a partial set of measurements. Although these model problems are simple cases involving only single enzymes, the extended Kalman filter can be applied to more complex systems of enzymes.

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