Cybernetic Modeling and Regulation of Metabolic Pathways. Growth on Complementary Nutrients

Microbial growth requires the presence of several complementary nutrients within the growth medium. Each of these nutrients supplies a different nutritional requirement, e. g., carbon or nitrogen. Furthermore, nutrients that supply the same nutritional requirement, i. e., substitutable nutrients or (substrates), may also be present. As the limiting substrate is altered, a microorganism's internal structure is also altered by preferentially invoking different metabolic pathways for the utilization of the limiting substrate. Transitions between different pathways are moderated by processes associated with metabolic regulation. The present paper describes an objective-oriented approach to account for such regulatory processes. Ramkrishna and co-workers [Kompala, D. S.; et al. Biotechnol. Bioeng. 1986, 28, 1044–1055; Ramkrishna, D.; et al. Biotechnol. Prog. 1987, 3, 121–126; Turner, B. G.; et al. Biotechnol. Bioeng. 1989, 34, 252–261] have developed a cybernetic or goal-seeking modeling perspective that accounts for metabolic regulation in a simple manner by utilizing the optimal behavior of microorganisms when presented with a set of substitutable carbon sources. A single, consistent framework that addresses both substitutable and complementary nutrients is presented. Rather than consider all possible substrate combinations, a topological analysis of metabolic pathways is discussed that suggests that pathways may be derived from three structural types: linear processes, branch points, and cycles. Optimal objectives, from which appropriate metabolic regulation in the form of control variables can be derived, are stated for each of these structures. A complete analysis, however, is presented for only two branch point structures. We derive regulation for convergent branch points or substitutable processes, which is equivalent to the original cybernetic framework, as well as regulation for divergent branch points or complementary processes. The present approach greatly reduces the number of alternatives that must be considered since a process perspective can be easily abstracted. The regulation of substrates that are present in excess is also developed. Finally, the expanded cybernetic modeling framework is applied to a simple, model microbial system developed for the utilization of two complementary substrates under steady-state conditions. Within the model system, structural components such as biosynthetic intermediates and biopolymers are incorporated. The combined polymer concentration represents the biomass concentration. Only processes that ultimately result in polymer synthesis are considered, i. e., no maintenance processes are incorporated. Without defining the two complementary substrates as interactive or noninteractive, the proposed model is capable of exhibiting interactive, noninteractive, and intermediate behavior between these two extremes. Results indicate that the incorporated regulatory structures, i. e., cybernetic or control variables, preferentially activate the synthesis of the biosynthetic intermediate, which limits the specific growth rate. The proposed model is also capable of describing variable cell yields as the status of each of the two complementary substrates changes from limiting to nonlimiting. The resulting variable cell yields are in quantitative agreement with experimental data previously reported in the literature. Furthermore, the degree of interaction between two complementary substrates is predicted to be a function of the medium composition. The presence of biosynthetic intermediates in the model is shown to be capable of converting an interactive system to a noninteractive system; however, conditions for the reverse transition, i. e., a noninteractive to an interactive system, have not been identified at this time.