Quantitative assessment of regulation in metabolic systems

Abstract

We show how metabolic regulation as commonly understood in biochemistry can be described in terms of metabolic control analysis. The steady-state values of the variables of metabolic systems (fluxes and concentrations) are determined by a set of parameters. Some of these parameters are concentrations that are set by the environment of the system; they can act as external regulators by communicating changes in the environment to the metabolic system. How effectively a system is regulated depends both on the degree to which the activity of the regulatory enzyme with which a regulator interacts directly can be altered by the regulator (its regulability) and on the ability of the regulatory enzyme to transmit the changes to the rest of the system (its regulatory capacity). The regulatory response of a system also depends on its internal organisation around key variable metabolites that act as internal regulators. The regulatory performance of the system can be judged in terms of how sensitively the fluxes respond to the external stimulus and to what degree homeostasis in the concentrations of the internal regulators is maintained. We show how, on the level of both external and internal regulation, regulability can be quantified in terms of an elasticity coefficient and regulatory capacity in terms of a control coefficient. Metabolic regulation can therefore be described in terms of metabolic control analysis. The combined response relationship of control analysis relates regulability and regulatory capacity and allows quantification of the regulatory importance of the various interactions of regulators with enzymes in the system. On this basis we propose a quantitative terminology and analysis of metabolic regulation that shows what we should measure experimentally and how we should interpret the results. Analysis and numerical simulation of a simple model system serves to demonstrate our treatment.Since the discovery of the phenomenon of end-product inhibition in cellular metabolism 11, 21 and the formulation of the first definite ideas on metabolic regulation [3], a vast amount of research has yielded many intricate ways in which enzyme activity and concentration can be changed : cooperative and allosteric effects 14-61, covalent modification cascades [7], genetic mechanisms of induction and repression [S], to mention a few. The terms 'regulation' and 'control' have been applied indiscriminately to all of these phenomena, even to man-made manipulations, so much so that they have almost become devoid of any specific, and therefore useful, meaning. Being terms that are also used, often uncritically, in everyday life, they are admittedly difficult to define qualitatively, and even more so quantitatively, in a specific context such as metabolism, although notable exceptions exist [9 -111. Quantitative definition of control and regulation implies the use of a suitable mathematical framework. Such a framework, called metabolic control analysis, has been under development during the last two decades [12, 131. In this p...

Protein phosphorylation can regulate metabolite concentrations rather than control flux: The example of glycogen synthase

“…In a supply-demand system such as the one treated here, as stated above, the distribution of flux control depends on the ratio of the supply and demand elasticities to G6P: the lower the ratio the more control shifts to the supply. On the other hand, the degree of homeostatic maintenance of this linking metabolite, when either the supply or the demand block is activated, depends on the G6P concentration control coefficients of the two blocks, which are inversely proportional to the sum of the supply and demand elasticities (4)(5)(6). Hence, the greater this sum, the smaller the impact of activation on G6P concentration, and the better the homeostasis.…”

“…Given the success of the glycogen synthetic pathway at coordinating internal and external homeostasis, it seems likely that there are analogous arrangements in other pathways, at least in storage pathways that concentrate flux control on the supply side to coordinate storage with nutrient availability. [Such organization seems less likely in biosynthetic pathways that tend to locate flux control in the final steps to coordinate control with demand (5).] Specifically, we predict the following as a general mechanism for the linkage of internal and external homeostasis at a variety of time scales, particularly for supply-controlled pathways.…”

“…As MCA has matured, it has expanded into associated areas. One of particular interest has been the mechanism of metabolite control, in which the central question is how metabolite homeostasis, the constancy of metabolite concentrations, is maintained during changes in flux (5)(6)(7)(8)(9). One well known example of such metabolite homeostasis comes from the study of fluxes through the energetic pathway of glucose oxidation.…”

Product dependence and bifunctionality compromise the ultrasensitivity of signal transduction cascades

“…Here, it is assumed that the concentrations directly affecting the rate (represented by ''X'') are maintained at constant levels when p is changed. The response coefficient is related to the -elasticity coefficient through the response theorem (1,25,38,39):…”

“…To some alterations in their environment, they do not respond at all. To other such alterations, they respond by little changes in some, and strong changes in other molecular activities; i.e., by homeostasis and adaptive functional changes, respectively (1). The subtlety and diversity of the responses may explain why the functions of many signal-transformation mechanisms are incompletely understood.…”