Modeling the regulation of bacterial genes producing proteins that strongly influence growth

Dynamic responses of protein homeostatic regulatory mechanisms to perturbations from steady state

Nineteen hypothetical protein homeostatic regulatory mechanisms were constructed and analysed in terms of the rate at which they recovered from a perturbation in the steady-state concentration of any component. Systems were constructed to symbolize transcription/translation processes of the average protein from Escherichia coli (1000 copies of protein P along with 1 gene G per cell). In some model systems, G catalysed the synthesis of P directly, while in others G catalysed the synthesis of mRNA (called M), and M catalysed the synthesis of P in a subsequent step. Recovery rates for each regulatory mechanism were obtained by generating the corresponding system of differential equations, linearizing the system about the steady state, and determining eigenvalues of the associated coefficient matrix. The optimal rate of recovery for a given mechanism, R(D), was determined by combining random and gradient search approaches to find rate constants for which the system recovered fastest. Regulatory elements that improved dynamic regulation were identified. These consisted of negative feedback relationships that involved P binding to either G (to shut off the synthesis of P) or M (to stimulate its degradation). Regulation improved as increasing numbers of P's bound to either G or M; however, the binding to M was more effective. In other mechanisms PP dimers bound G. Dimer-binding mechanisms were roughly twice as effective in terms of regulation as those that bound P monomers. The effect of linking two regulatory "modules" was also investigated. Linking had no effect on R(D), but optimal rate constants for the linked system were similar to those of the unlinked modules, suggesting that it may be feasible to construct regulatory networks by linking individual modules of this type.

Analysis of protein homeostatic regulatory mechanisms in perturbed environments at steady state

Nine different protein homeostatic regulatory mechanisms were analysed for their ability to maintain a generic protein P within a specified range of a set-point steady-state concentration while perturbed by external processes that altered the rates at which P was produced and/or consumed. Steady state regulatory effectiveness was defined by the area within a rectangular region of "perturbation space", where axes correspond to rates of positive and negative perturbations. The size of this region differed in accordance with the regulatory elements composing the homeostatic mechanism. Such elements included basic negative feedback control of transcription (in which P, at some high concentration relative to its set-point value, binds to the gene G that encodes it, thereby inhibiting transcription), multiple sequential binding of a feedback effector (two P's bind sequentially to G), and dimerization of a feedback effector (a P(2) dimer binds to G). Two homeostatic mechanisms included a cascade structure, one with and one without translational feedback control. Another mechanism included feedback control of P degradation. Finally, two mechanisms illustrated the limits of regulatory systems. One lacked all regulatory elements (and included only an invariant rate of P synthesis and degradation) while the other assumed perfect (Boolean) regulation, in which transcription is completely inhibited at [P]>[P](sp) and is fully active at [P]<[P](sp). All of the systems evaluated are known, but the analytical expressions developed here allow quantitative comparisons between them. These expressions were evaluated at values typical of the average protein in Escherichia coli. A method for building regulatory networks by linking semi-independent regulatory modules is discussed.

Modeling and simulation: tools for metabolic engineering

Mathematical modeling is one of the key methodologies of metabolic engineering. Based on a given metabolic model different computational tools for the simulation, data evaluation, systems analysis, prediction, design and optimization of metabolic systems have been developed. The currently used metabolic modeling approaches can be subdivided into structural models, stoichiometric models, carbon flux models, stationary and nonstationary mechanistic models and models with gene regulation. However, the power of a model strongly depends on its basic modeling assumptions, the simplifications made and the data sources used. Model validation turns out to be particularly difficult for metabolic systems. The different modeling approaches are critically reviewed with respect to their potential and benefits for the metabolic engineering cycle. Several tools that have emerged from the different modeling approaches including structural pathway synthesis, stoichiometric pathway analysis, metabolic flux analysis, metabolic control analysis, optimization of regulatory architectures and the evaluation of rapid sampling experiments are discussed.

Analysis and modeling of substrate uptake and product release by prokaryotic and eukaryotic cells

Translocation of molecules and ions across cell membranes is an important step for a complete description of the metabolic network in terms of kinetics, energetics and control. With a few exceptions, most molecules cross the permeability barrier of the membrane with the aid of membrane-embedded carrier proteins. Uptake of nutrients (carbon, energy and nitrogen sources as well as supplements) and excretion of the majority of products are thus carrier-mediated transport processes. Consequently, they are characterized by particular kinetic properties of the respective carrier systems, they depend on energy sources (driving forces) which must be provided by the cell, and they are subject to regulation both on the level of activity and expression. They are thus fully integrated into the functional and regulatory networks of the cell. Structural (primary structure, conformation and topology) and functional properties (kinetics, energetics and regulation) of the different classes of carrier systems from both prokaryotic and eukaryotic membranes are summarized. The methodical requirements for a quantitative measurement of their function and possible pitfalls in transport studies are described, both for determination using isolated cells and for analysis in a bioreactor. The significance of transport reactions for biotechnological processes in general and for metabolic design in particular is discussed, with respect to nutrient uptake, product excretion and the occurrence of energy wasting combinations of transport reactions (futile cycles). Some examples are given where transport reactions have been incorporated into modeling approaches with respect to metabolic control, to flux analysis, to kinetic properties and to energetic demands.