The Basis of Dominance

Effect of high saturation of enzymes

Fig. 2. Typical dependence of flux through a metabolic pathway on the activity of any enzyme in the pathway. The curve resembles a rectangular hyperbola, but is not exactly one except under rather special circumstances. Most enzymes have low flux control coefficients, which means that they are typically located on a part of the curve where the slope is small, for example at the point labelled AA. If this represents the activity of an enzyme in the normal homozygote, then the point aa represents an abnormal homozygote in which the enzyme activity is entirely lacking, and the point labelled Aa represent the heterozygote. The corresponding phenotypes are related to the fluxes through the pathway, and can be estimated as the ordinate values labelled J_AA, J_aa and J_Aa. Note that the heterozygote phenotype is much closer to that of the normal homozygote than to that of the abnormal homozygote. The point labelled AA (hexokinase D) refers to a special case discussed at the end of the chapter.

Before the theory of Kacser and Burns⁹ is accepted as the full explanation of dominance and recessivity there are some complications that need to be dealt with. The first is the question of whether it is necessarily true that the curve for dependence of metabolic flux on the activity of any enzyme resembles a rectangular hyperbola as closely as the one illustrated in Fig. 2. In fact it is not necessarily true, because it is possible to devise models in which the normal steady state is one in which all of the enzymes in a sequence are close to saturation with their substrates,²³ and in such a case the curve relating flux through the pathway to the activity of any enzyme resembles the one shown in Fig. 3. This differs from a rectangular hyperbola in having much more extended domains of first and second-order dependence, with a more abrupt transition between them, and the enzymes in the homozygote are typically perched as shown near the transition region. In such a case the relationship embodied by eqn. (2) remains true; i.e. it remains true that very small changes in the activity of any enzyme produce even smaller effects on the flux. However, the effects of decreases of the order of 50% are quite different from what is seen in Fig. 2. Now the heterozygote phenotype is very close to halfway between the homozygote phenotypes, as it was assumed to be in early models. We must emphasize, that this was a pathological model constructed to demonstrate that dominance did not follow necessarily from the summation property. It was not intended as a realistic model of how real systems would normally behave, and Kacser²⁴ was justified in entitling his response to it Dominance not inevitable but very likely.

Fig. 3. Dependence of flux on the activity of any enzyme when all enzymes are close to saturation with their substrates. Although it remains true that an enzyme in the normal homozygote is typically located at a point where the slope is small, the slope in this case changes sharply if the activity is decreased, even by a small amount, and for this model the phenotypes of the heterozygote is close to the midpoint between those of the homozygotes.

Even in the absence of any selection, assigning kinetic constants entirely at random to the enzymes in a metabolic pathway would be very unlikely to produce a set generating behaviour similar to that in Fig. 3. If a primitive organism happened to possess such a pathway one could expect its kinetic characteristics to be varied by natural selection towards a more typical behaviour. That is because the model proposed is not only pathological in the modelling sense; it would also be pathological in a living organism, because any enzyme working close to saturation represents a danger for the organism.25 For an enzyme operating far below saturation, for example at 0.1V, 10% of the limit, with a substrate concentration equal to 0.1K_m, the rate is correspondingly far below the limit, about 0.09V for the numerical case considered. In consequence a sudden increase in the flux to the pathway brought about by increased activity of the upstream enzymes would present little problem to the enzyme: doubling the flux to 0.18V would imply an easily sustainable increase in substrate concentration to 0.22K_m: barely more than doubled.

Matters are quite different for an enzyme operating at 0.95V: a mere 5% increase in flux is now sufficient to bring it to a region where no steady state exists, a potential catastrophe. It is reasonable to suppose, therefore, that if any pathway existed in which all enzymes were fluxcontrolling for noninfinitesimal decreases in activity then natural selection would act to moderate such behaviour. Thus we cannot entirely eliminate natural selection from the discussion of dominance and recessivity, but it is a much more physiological and intelligible form of natural selection than what was envisaged by Fisher. Grossniklaus et al.²⁶ examined a broader range of models than that considered by Cornish-Bowden,²³ and found that even when enzymes are not close to saturation substantial deviations from Michaelis–Menten kinetics, especially in cases with a large degree of positive cooperativity, can cause some enzymes to have large flux control coefficients, so that mutations in these enzymes would not be recessive.

Dominant genes in humans: an exceptional species?

As we have seen, the controversy over the explanation of dominance arose from the observation that mutant genes were normally recessive. Until comparatively recently it appeared that this was quite general, observed in all diploid and polyploid species. Remarkably, however, the human species appears to be exceptional, with a high proportion of mutant genes reported to be dominant. How is this to be explained? Must we return to a world view in which the human species is unique unto itself, and quite separate from animals, plants, fungi and bacteria? Clearly not, but the observation appears genuine, and needs a plausible explanation. The most likely one is that this difference between humans and animals (like most differences between humans and animals) owes more to the way in which they are studied than to any inherent differences in the underlying properties. The idea of a symptomless disease would appear absurd in relation to animals or plants, but is applied in all seriousness to human conditions like maturity-onset diabetes of the young, or MODY (infection with human immunodeficiency virus may be a better example, but we shall not enter into that controversy here). In such cases there is no sickness, but biochemical tests indicate abnormal levels of certain metabolites that indicate that a disease is likely to develop later. Applying this idea to other organisms, and bearing in mind the behaviour suggested by Fig. 2, it seems clear that Mendel could have distinguished between homozygotes and heterozygotes of pea plants producing green seeds if he had used modern instruments to measure the exact amounts of green pigment in his samples, rather than relying on his eye to distinguish between green and yellow seeds.

In general, therefore, the apparent difference in heterozygote characteristics between humans and other animals is best explained by the greater detail in which humans are subjected to biochemical tests. Nonetheless, there is at least one example of a dominant gene — first recognized in humans, though probably not a special property of humans — that can serve as an archetype to illustrate when such genes are to be expected. This will be considered next.

The hexokinase D (glucokinase) gene in humans

Hexokinase D is the isoenzyme of hexokinase characteristic of the vertebrate liver (see ref. 27), and like any hexokinase it catalyses the phosphorylation by ATP of glucose and other hexoses, such as fructose and mannose. However, it differs from the other isoenzymes found in mammals in several respects (though not in specificity, as implied by the misleading name glucokinase that is often used for it): it is halfsaturated at much higher glucose concentrations, of the order of the glucose concentration in the blood; it does not follow Michaelis–Menten kinetics with respect to glucose but shows positive cooperativity instead; it is unaffected by its product glucose 6phosphate at physiological concentrations. All of these properties fit it for the role of helping to maintain a constant glucose concentration in the blood: when this increases above the normal level of 5 mM the activity of hexokinase D rises steeply and glucose is stored in the liver as glycogen; when the bloodglucose concentration falls hexokinase D decreases its activity and other enzymes catalyse the mobilization of the glycogen.

These characteristics not only set hexokinase D apart from the other hexokinase isoenzymes; they also set it apart from most enzymes known to have important roles in metabolic regulation, because they imply that conversion of blood glucose to liver glycogen is a supply-driven process, whereas most of the pathways that have been well studied are best understood as demanddriven processes.²⁸ This does not affect the general truth of the summation property expressed by eqn. (2), which is derived without reference to the properties of the specific enzymes considered, but it does affect the way the control is distributed among the terms in the sum. In a typical demand-driven pathway properties such as feedback inhibition act to transfer control away from the supply part of the pathway towards the reactions that consume the endproduct. However, the liver has little demand for glucose 6-phosphate, such little as it has being amply satisfied by the other hexokinase enzymes,²⁹ and control of glycogen synthesis is concentrated almost entirely in hexokinase D.³⁰ This concentration of flux control in hexokinase D means that it is located much further to the left on the curve in Fig. 2 than a typical enzyme, as indicated by the point labelled AA (hexokinase D), and that the argument used previously to conclude that the heterozygote phenotype ought to resemble that of the normal homozygote does not apply to hexokinase D. Instead, heterozygotes for hexokinase D should be much less efficient than homozygotes for maintaining a correct bloodglucose concentration, and should have a readily recognizable hyperglycaemia. In accordance with this expectation, young heterozygotes display a mild hyperglycaemia that is taken as the form of type II (non-insulin-dependent) diabetes known as maturity-onset diabetes of the young, an example of a symptomless disease, as already noted. Later, in adulthood, such heterozygotes usually show increased hyperglycaemia and the pathological symptoms of type II diabetes, thus providing a genuine example of a disease with dominant transmission.³¹ However, it should be clear from this discussion that the dominance is here a consequence of the special properties of hexokinase D, and does not support that notion that dominant mutations are any more common in humans than in other species. It would, in fact, be very surprising if hexokinase D mutants in animals such as dogs and rats did not prove to behave the same way as in humans if the genetics of type II diabetes were studied in as much detail in these animals as it has been in humans.