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

Abstract

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 biosynthet...

A hybrid model of anaerobic E. coli GJT001: Combination of elementary flux modes and cybernetic variables

“…In adapting the framework to a large network, Varner and Ramkrishna 12,13 developed an approach requiring identification of metabolic subunits each comprising elementary pathways as conceived by Straight and Ramkrishna. 14 The subunits were postulated to compete for the total resources available for synthesizing enzymes. Global objectives were combined with local objectives to determine what the authors referred to as ''complete'' cybernetic variables for each reaction in the network representing a hierarchy of resource distribution.…”

Bioprocess modelling for the design and optimization of lignocellulosic biomass fermentation

“…continuous fermentation of lignocellulosic biomass (Straight and Ramakrishna 1994;Ko et al 2010;Murthy et al 2012). …”

Microbial growth on substitutable substrates: Characterizing the consumer-resource relationship

“…The microorganism is viewed as an optimal system in which the regulatory processes implement optimal strategies, and the outcome of these strategies modifies the intrinsic process kinetics through cybernetic or control variables. Cybernetic models (Baloo and Ramkrishna, 1991;Kompala et al, 1986;Straight and Ramkrishna, 1994;Turner et al, 1988) have successfully described diauxic growth in bath cultures (Kompala et al, 1986) transient behavior in perturbed fedbatch (Turner et al, 1988) and continuous cultures (Baloo and Ramkrishna, 1991) under multiple nutrient limitations and growth in carbon-nitrogen limitations (Straight and Ramkrishna, 1994). Ramakrishna et al (1996) have developed a model based on the same cybernetic principles, to describe a spectrum of growth patterns observed with growth on mixtures of carbon-energy sources.…”

“…The cybernetic variables that describe the regulation of the substitutable processes for the synthesis of M 1 and M 2 are formulated as derived by Straight and Ramkrishna (1994 …”