A theoretical metabolic-control-analysis approach has been used to study aspects of glycolytic-flux control and carbon-metabolite regulation, particularly the role of ATP demand (ATPase), in order to determine what general features of the regulation of energy metabolism would be consistent with good carbon-metabolite homeostasis in the face of large changes in carbon flux. On the basis of a semiquantitative control-analysis model, incorporating estimates of substrate, product and effector actions on the enzymes, the experimentally observed characteristics of glycolytic-flux changes prove to impose constraints on the feasible ranges of these estimates. This leads to the identification of several features of energy metabolism, each of which is necessary but not sufficient to explain the observations; although most of these have been advocated previously (such as AMP activation of phosphofructokinase (PFK), ADP inhibition of ATPase and the role of energy charge or ATP/ADP ratio), our analysis allows their relative importance to be assessed. In the model, the distribution of flux control depends primarily on ADP inhibition of ATPase, and on the activation of PFK by AMP; increase in ADP inhibition of ATPase increases the control on PFK; increase in AMP activation of PFK increases control on ATPase. PFK exerts greater flux control than does ATPase over approximately 50% of the ranges (parameter space) studied, but its control is sufficiently high to achieve sizeable flux increases over less than 20% of the space. Furthermore, control by alteration in PFK activity is shown to result in poor glycolytic metabolite homeostasis over the entire parameter space studied. However, over a large proportion of the parameter space, control by activation of ATPase can lead to large flux changes, i.e. high flux control, coupled with excellent glycolytic-metabolite homeostasis, similar to that observed in working muscle. As well as altering the relative degrees of flux control invested in PFK and ATPase, ADP inhibition of ATPase and AMP activation of PFK have pronounced effects on the homeostatic properties of the system. Stronger ADP inhibition of ATPase results in improved homeostasis of glycolytic metabolites, ATP and ADP in response to PFK activation, whereas stronger activation of PFK by AMP improves the homeostasis of these three quantities in response to ATPase activation. The results are further evidence of the potential for physiological ATP demand to exert control over glycolytic flux, but additionally show that the known effector interactions, in addition to their previously known role in ATP regulation, could contribute to the remarkable homeostasis of glycolytic-metabolite levels observed in vivo. They further indicate that quantitative characterisation of likely domains of behaviour of metabolic systems can be achieved by an algebraic analysis that is not highly dependent on a full and precise knowledge of the molecular details of the kinetic/regulatory properties of the enzymes, but that still allows an assessment of w...