These pages contain the full text of the following chapter: María Luz Cárdenas (1997) "Metabolic Cascades: an Evolutionary Strategy for an Integrated and Sensitive Response to Multiple Signals" pp. 159–172 in New Beer in an Old Bottle: Eduard Buchner and the Growth of Biochemical Knowledge (ed. A. Cornish-Bowden), Universitat de València, Valencia, Spain. A PDF file is also available.
Eduard Buchner (1897) is rightly regarded as the founder of modern biochemistry, because his observation that alcoholic fermentation could proceed in a cell-free extract of yeast supplied the final nail in the coffin of the vitalism that dominated physiological thinking in the 19th Century. His work can also be regarded as the beginning of enzymology, but although he regarded his "zymase" as a single enzyme it became clear in the years that followed his discovery that it is really a mixture of several enzymes, all of them necessary if fermentation is to proceed. His experiments can equally well, therefore, be regarded as the first study of the behaviour of a multi-enzyme system, a topic that has taken nearly a century to be taken up again seriously. In this chapter I shall consider one particular type of multi-enzyme system, in which the combined effects of at least three different enzymes allow regulatory properties that would not be possible with just one.
The modern study of metabolic regulation can be regarded as having started in the 1950s with the discovery of feedback inhibition (Yates and Pardee, 1956; Umbarger, 1956) and the recognition, a little later, that cooperativity is not just a special property of haemoglobin but is crucial in the regulatory design of many pathways (Monod et al., 1963). Cooperativity, or unusually high sensitivity, often occurs together with inhibition or activation by a molecule that does not bear any necessary structural similarity to the substrate and products of the reaction catalysed, which is called allosteric inhibition or activation. The importance of cooperativity is that it allows a much more sensitive response to a signal than is possible with an enzyme obeying Michaelis–Menten kinetics: in the latter case an 81-fold change in inhibitor concentration is necessary to bring the reaction rate from 90% to 10% of its uninhibited value, but a cooperative enzyme can manage the same transformation with a much smaller ratio of concentrations, though rarely smaller than three-fold. A cooperative response often has its origin in cooperative binding, and the degree of cooperativity (degree of sensitivity) is then a function of the number of binding sites and of the strength of interaction between the sites. As the interaction is never infinitely strong the degree of cooperativity expressed as the Hill coefficient is usually smaller than the number of sites, and no higher than four. This is well illustrated by haemoglobin, which has four binding sites for oxygen and a Hill cofficient of 2.8; the case of CTP synthetase, with four binding sites and a Hill coefficient of 3.8, is rather exceptional.
Probably because of structural constraints, it appears to have been impossible to evolve enzymes offering much more sensitivity than this. Certain oxygen binding proteins from invertebrates have a very large Hill coefficient in the middle of the range, but they are unable to maintain this over a wide range, and on average are no more sensitive than haemoglobin. Moreover, they require interactions between very large numbers of binding sites, and are in consequence very large proteins.
Kinetic factors may also contribute to generate responses more sensitive than is provided by Michaelis–Menten kinetics. They are at the origin of cooperativity in monomeric enzymes (Cornish-Bowden and Cárdenas, 1987), though in these cases the Hill coefficient is normally lower than 2.0. If binding and kinetic cooperativity both operate in a multimeric protein the joint contribution of both could generate responses of higher sensitivity than is expected from the number of sites. This appears to be rare, however, though it probably explains why phosphofructokinase shows a Hill coefficient of the order of 6 to 8, greater than 4.0, the number of binding sites.
In practice, therefore, a three-fold change in stimulus to span the middle 80% range of responses is about the best that a single enzyme can do (corresponding to a Hill coefficient of 4). Yet a three-fold change in inhibitor (or activator) concentration is by no means negligible, and the concentrations of many metabolites need to be maintained within much narrower limits; it would thus be an exaggeration to claim that a cooperative enzyme allows a system to respond as if to a switch. Clearly, therefore, in some circumstances living organisms require a greater degree of sensitivity than any single enzyme can offer, and they obtain this by use of energy-consuming systems of interconvertible enzymes.
Such systems have been known for more than half a century, since Cori and Green (1943) discovered that glycogen phosphorylase exists in two forms, a catalytically active phosphorylated form, phosphorylase a, and an inactive dephosphorylated form, phosphorylase b. Since then a great many other similar cases have been found, with functions ranging from regulation of metabolic pathways to control of the cell cycle (Chock et al., 1980; Cohen, 1982; Boyer and Krebs, 1986). Their contribution to metabolic regulation was studied quantitatively and in detail by Chock and Stadtman (1977), Stadman and Chock (1977) and Goldbeter and Koshland (1982). The latter authors discovered that when the enzymes responsible for catalysing the conversions between inactive and active forms operated close to saturation, a condition they called "zero-order ultrasensitivity", the cycle as a whole is capable of providing an output response with much more sensitivity to a change in stimulus than the hyperbolic (Michaelis– Menten) equation. Thus, even though none of the enzymes in the cycle may show cooperative behaviour the cycle can generate a more sensitive response than a single cooperative enzyme can offer. The high sensitivity comes at a price, however, because unlike a cooperative enzyme the cycle requires continuous hydrolysis of ATP (or a similar process) to maintain itself in a steady state (Goldbeter and Koshland, 1987). The comparison of an effector acting on a single allosteric and cooperative enzyme with one acting on the simplest kind of cycle of interconvertible enzymes is illustrated in Fig. 1, for the typical case where one reaction is a phosphorylation, catalysed by a protein kinase, and the other is a hydrolysis (dephosphorylation), catalysed by a protein phosphatase.
Fig. 1. Comparison between direct allosteric action of an effector G on a target enzyme that catalyses the conversion of a metabolite X to a metabolite Y (left), and indirect action through inhibitory and activatory effects on the converter enzymes Em1 and Em2 that catalyse the reactions between the active and inactive forms of the target enzyme (right). For purposes of illustration Em1 and Em2 are assumed to be a protein phosphatase and a protein kinase respectively, but other possibilities exist. The allosteric enzyme is less complicated, requiring only one protein rather than three (top row); even at optimum sensitivity it offers only a mildly sigmoid dependence of activity on effector concentration whereas the interconvertible enzymes offer virtually unlimited "switch-like" sensitivity (middle row); however, the allosteric enzyme consumes no energy whereas maintaining the cycle in operation requires continuous hydrolysis of ATP (bottom row).
It is sometimes implied that high sensitivity is an automatic consequence of the existence of a cycle such as that illustrated in Fig. 1, but this is not correct. The mere existence of a cycle does not guarantee high sensitivity, and if a number of conditions are not met the cycle may provide no more sensitivity than can be obtained from a Michaelis–Menten enzyme obeying the classical equations for inhibition or activation, and may even be less (Cárdenas and Cornish-Bowden, 1989). The first condition was discovered by Goldbeter and Koshland (1981, 1982), and has been noted already: the two modifier (or converter) enzymes, Em1 and Em2 in the symbols of Fig. 1, must bind their substrates, Eb and Ea respectively, so tightly that at the concentrations of these substrates in the cell they are close to saturation at all times. This condition appears to be satisfied in some systems, such as phosphorylase b kinase and phosphorylase a phosphatase from muscle (Meinke et al., 1986), but not in others. In any case, we have shown that if other conditions are satisfied, about 30% saturation may be sufficient for a highly sensitive response. Two other conditions appear equally important (Cárdenas and Cornish-Bowden, 1989): the allosteric effector G should act on the limiting rates of the converter enzymes rather than on their specificity constants, and do so with different affinity: the modifier enzyme that is activated should require much higher concentrations of the effector than the enzyme that is inhibited. If the effector acts on only one of the converter enzymes, is still possible to have a highly sensitive response if the catalytic constant is affected (Cárdenas and Cornish-Bowden, 1989). If it acts on both converter enzymes, affecting only the specificity constant and not the limiting rate, there can be no higher sensitivity than that given by the Michaelis–Menten equation. Action of an effector at several points in the pathway, for example on both converter enzymes, has been called "multistep effects" (Goldbeter and Koshland 1984), and it contributes to an increase in sensitivity, which can be amplified in certain conditions if there is more than one cycle.
A cascade with a single cycle can generate responses with extremely high Hill coefficients (about 800) if the three conditions for high sensitivity are satisfied: (i) modifier enzymes near saturation; (ii) catalytic rather than specific effects; and (iii) inhibition stronger than activation (Cárdenas and Cornish-Bowden, 1989, 1990). Furthermore, analysis according to the methods of metabolic control analysis give very high response coefficients (Szedlacsek et al., 1992). Even if the conditions are only partially satisfied the monocyclic system can still generate very sensitive responses.
These requirements for high sensitivity are perhaps unintuitive. It is often assumed (albeit with little direct evidence) that most enzymes operate in vivo at about half-saturation, i.e. that physiological substrate concentrations are similar to the relevant Michaelis constants, and saturation is likely to be rare for an enzyme involved in intermediary metabolism. Likewise, specific (competitive) inhibition and activation appear to be much more common than their catalytic (uncompetitive) counterparts, and in any case in normal laboratory conditions are not very different from one another (and hence are often not clearly distinguished). However, enzymes are usually studied under conditions where the concentrations are determined by the experimenter and the rates that result are measured, whereas in the cell most enzymes operate under more complex conditions that are closer to constant-flux than to constant-concentration. This is important, because at constant flux specific and catalytic effects become drastically different from one another: in the one case a slight adjustment of the system is sufficient to counteract even quite a large concentration of inhibitor; in the other a small amount of inhibitor is sufficient to raise the substrate concentration without limit, converting an apparently stable steady state into a state where no steady state is possible (Cornish-Bowden, 1986).
Finally, the need for the activated modifier enzyme to respond to higher effector concentrations than the inhibited enzyme can often lead to the unwarranted conclusion that even if such activation occurs it has no physiological significance. A clear example came to light when we studied data for the response of muscle fibre tension to the toxin okadaic acid (Takai et al., 1987): myosin phosphatase is strongly inhibited by okadaic acid, with a mixed type of inhibition (catalytic and specific effects), the concentration for half-inhibition is around 0.01 µM, but the concentration for half-maximal muscle tension is very much higher, around 0.5 µM; moreover, the curve for the effect on muscle tension is much steeper (more cooperative) than that for the effect on myosin phosphatase. Although these discrepancies could easily be regarded as anomalous, they are better interpreted as evidence that the effect on muscle tension derives not solely from the effect on myosin phosphatase but also from activation of the corresponding kinase at much higher and supposedly unphysiological concentrations. We have discussed this example in more detail elsewhere (Cárdenas and Cornish-Bowden, 1990).
Much of the discussion to this point is based on theoretical analysis, and Newsholme and Walsh (1992) pointed out that our suggestion (Cárdenas and Cornish-Bowden, 1989) that regulation of kinase-phosphatase cycles ought to involve catalytic effects did not correspond to what were thought to be the experimental facts in relation to glycogen phosphorylase kinase, that effectors such as calcium ions acted only on binding, with no effects on limiting rates. However, they did not simply dismiss our analysis as the typically unreal ideas of theoretically inclined biochemists, but undertook the necessary experiments to determine the truth; we were gratified to read their conclusion that our predictions were correct and that the "facts" were not.
For a cascade mechanism to be of physiological importance the transition from one steady state to another in response to an effector must occur within a reasonable interval of time. This appears to be the case, as analysis of the kinetics have shown that the switch from one activity level to the other can occur within physiologically significant time intervals matching those observed experimentally for some systems (Goldbeter and Koshland, 1981). For example, when the known experimental constants are inserted into a model for glycogen synthesis it appears that about 3–4 minutes are sufficient for phosphorylase a to be completely inactivated and glycogen synthase a to be more than 50% activated by an increase in glucose concentration from 5 mM to 60 mM (Cárdenas and Goldbeter, 1996), corresponding almost exactly with the experimental observations (Stalmans et al., 1974).