Mathematical and Experimental Studies of Microbial Processes with Lag Effects

Citation

Wang, Nam Sun (1989) Mathematical and Experimental Studies of Microbial Processes with Lag Effects. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7mez-bd45. https://resolver.caltech.edu/CaltechETD:etd-06112007-143619

Abstract

Unlike most chemical reaction dynamics, microbial behavior depends not only on the present state of the environment surrounding a microorganism but, more importantly, on its past history as well. Herein lies a major obstacle in the modeling of a biological process with a simple set of equations. By incorporating a culture's past history in the form of a time-lag kernel, a novel approach to bioprocess identification and modeling is formulated. A time-lag kernel is included in the state equations, and a generalized method of mathematical simplification via the transformation of an integro-differential equation to a set of first-order ODE's is developed. The time-lag convolution integral arises during the process of transforming a structured, mechanistic model into an equivalent unstructured model as a result of lumping. The resulting model possesses the combined advantages of the simplicity of an unstructured, lumped-parameter model and the predictive power of a complex structured model. The experimental determination of the kernel is performed by cultivating Saccharomyces cerevisiae in a chemically defined medium of either glucose or ethanol as the limiting carbon source and in a tightly controlled environment of temperature and pH. All the model parameters can be feasibly resolved with a simple set of experiments. The validity of the time-lag modeling approach is clearly demonstrated experimentally by its superior capability in predicting the various transient responses under different modes of operation. Seemingly unreproducible experiments are shown to be united when time-lag effects are taken into consideration. This modeling work fits within the general framework of on-line computer parameter estimation, control, and optimization of a biochemical reactor. As such, the proposed modeling approach to biological systems identifies the cause-effect relationship more clearly and is well suited for process control purposes.

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