To increase the in vivo output of a chosen metabolite requires the increase of a number of enzyme concentrations. The enzymes are identified as those leading directly from output back to the input(s). This identification will reveal a number of branch points leading to other parts of metabolism which should not be perturbed. A simple calculation gives the enzyme multipliers, factors by which the identified enzyme concentrations should be increased to generate a given increase in the output flux. The net result of this procedure will be to extract any desired increase in flux while leaving the rest of metabolism to growth and other important functions of the cell unchanged. The method is entirely general.Traditional selection regimes have been used for a long time for the improvement of animal and plant traits as well as for the increased production of metabolites in microorganisms. Such methods have had considerable success in the past but, after the initial advances, this success is beginning to diminish. It is well known that the rates of improvement are decreasing and, in most cases, are approaching a plateau. Even in cases where new variation can be introduced (by mutagenesis), traditional rounds of mutation and selection do not shown significant progress. To maintain fitness of the organism and to improve output appear to be two processes which counteract each other. The subject of selection limits is large and is by no means resolved (Barton and Turelli, 1989; Dykhuizen, 1990) although the phenomenon is real. The greater insight into the molecular basis of genetic variation which we now possess, promises to give a new approach to the problem. Accordingly, the increase in production or yield of certain primary or seconary metabolites has become the aim of many biotechnologists. This has received a great stimulus by recent developments in molecular biology which makes it possible to target genes specifying particular enzymes by genetic manipulation. The cloning of these genes and the availability of useful vectors can result in the overproduction of enzymes involved in the pathways leading to the desired product.Two problems arise from attempts to apply such an approach. The first is to identify which enzymes to overproduce and, hence, which genes to overexpress. The search for the 'rate-limiting enzyme', i. e. the one whose increase in concentration results in a corresponding increase in flux, has been undertaken by many experimentalists -with singular lack of success. Previous studies (Schaaff et al., 1989;Skatrud et al., 1989;Cremer et al., 1991; Niederberger et al., 1992) have shown, that for more than 20 instances of overproduction of individual enzymes, in a variety of microorga-

Covalent modification cycles are ubiquitous. Theoretical studies have suggested that they serve to increase sensitivity. However, this suggestion has not been corroborated experimentally in vivo. Here, we demonstrate that the assumptions of the theoretical studies, i.e., irreversibility and absence of product inhibition, were not trivial: when the conversion reactions are close to equilibrium or saturated by their product, ''zero-order'' ultrasensitivity disappears. For high sensitivities to arise, not only substrate saturation (zero-order) but also high equilibrium constants and low product saturation are required. Many covalent modification cycles are catalyzed by one bifunctional 'ambiguous' enzyme rather than by two independent proteins. This makes high substrate concentration and low product concentration for both reactions of the cycle inconsistent; such modification cycles cannot have high responses. Defining signal strength as ratios of modified (e.g., phosphorylated) over unmodified protein, signal-to-signal response sensitivity equals 1: signal strength should remain constant along a cascade of ambiguous modification cycles. We also show that the total concentration of a signalling effector protein cannot affect the signal emanating from a modification cycle catalyzed by an ambiguous enzyme if the ratio of the two forms of the effector protein is not altered. This finding may explain the experimental result that the pivotal signal transduction protein PII plus its paralogue GlnK do not control steady-state N-signal transduction in Escherichia coli. It also rationalizes the absence of strong phenotypes for many signal-transduction proteins. Emphasis on extent of modification of these proteins is perhaps more urgent than transcriptome analysis.

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Two usual assumptions of the treatment of metabolism are: (a) the rates of isolated enzyme reactions are additive, i.e. that rate is proportional to enzyme concentration; (b) in a system, the rates of individual enzyme reactions are not influenced by interactions with other enzymes, i. e. that they are acting independently, except by being coupled through shared metabolites. On this basis, control analysis has established theorems and experimental methods for studying the distribution of control. These assumptions are not universally true and it is shown that the theorems can be modified to take account of such deviations. This is achieved by defining additional elasticity coefficients, designated by the symbol n, which quantify the effects of homologous and heterologous enzyme interactions. Here we show that for the case of non-proportionality of rate with enzyme concentration, (xi # l), the summation theorems are given byThe example of monomer-oligomer equilibria is used to illustrate non-additive behaviour and experimental methods for their study are suggested.In the classical study of the control of metabolism, two fundamental assumptions are usually made regarding the properties of the enzymes which constitute metabolic systems. The first is that the reaction rate of an isolated enzyme is first order with respect to enzyme concentration and the second assumption is that all enzymes are independently acting cataThe first assumption, that of additivity, (i.e. rate K E ) is based on the observations of the kinetics of a wide range of extracted enzymes. However, there are a number of instances where additivity may not apply [l]. For example, if an enzyme monomer-oligomer equilibrium exists and if the overall specific activity of the mix of monomer and homologous oligomer varies with the proportions of the two forms, then deviations from additivity will occur. Similar deviations could occur if the total concentration of a particular enzyme is partitioned between the free enzyme and enzyme bound to a catalytically inert substratum, such as a membrane or cytoskeleton, present in constant amount. If the bound enzyme has different kinetics from the free enzyme, then nonadditivity would be observed. Similar arguments apply to enzymes operating in cascades.The second assumption, that of independence, is usually represented by each enzyme catalysing one step without the enzyme associating with any other. Such associations between some enzymes, however, are known to take place. Nevertheless, there would be no functional consequences of such association if the catalytic activities of the enzymes in the heterologous complex were the same as those of the free lysts.