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<h1 class="top">The Basis of Dominance</h1>
<p class="header">This page is the third of a series of four containing Chapter 1
<q>The basis of dominance</q> by
Athel Cornish-Bowden & Vidyanand Nanjundiah (2006), pp. 1–16 in
<cite>The Biology of Genetic Dominance</cite>
(ed. R. A. Veitia)
Landes Bioscience, Georgetown, Texas.
<h2 class="framed">Effect of high saturation of enzymes</h2>
<div class ="centred">
<h4><img src="images/vidyaf2.gif" width="738"
height="436" alt="Typical dependence of flux on the activity
of any enzyme"></h4></div>
<p class="legend"> 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
<i>AA</i>. If this represents the activity of an enzyme in the normal homozygote, then
the point <i>aa</i> represents an abnormal homozygote in which the enzyme activity is
entirely lacking, and the point labelled <i>Aa</i> represent the heterozygote. The
corresponding phenotypes are related to the fluxes through the pathway, and can
be estimated as the ordinate values labelled <i>J<sub>AA</sub></i>, <i>J<sub>aa</sub></i> and <i>J<sub>Aa</sub></i>. Note that the
heterozygote phenotype is much closer to that of the normal homozygote than to
that of the abnormal homozygote. The point labelled <i>AA (hexokinase D)</i> refers to
a special case discussed at the end of the chapter.
<div class="sidebar-medium">
<p class="ref-in-sidebar"> 9. Kacser H, Burns JA. The molecular basis of dominance. Genetics 1981;
97:639–666
<p class="ref-in-sidebar">23. Cornish-Bowden A. Dominance is not inevitable. <acronym class="deja" title="Journal of Theoretical Biology">J Theor Biol</acronym> 1987;
125:333–338.
<p class="ref-in-sidebar">24. Kacser H. Dominance not inevitable but very likely. <acronym class="deja" title="Journal of Theoretical Biology">J Theor Biol</acronym> 1988;
126:505–506.
</div>
<p>Before the theory of Kacser and Burns<sup>9</sup> 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,<sup>23</sup> 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
Kacser<sup>24</sup> was justified in entitling his response to it <q>Dominance not
inevitable but very likely</q>.
<div class ="centred">
<h4><img src="images/vidyaf3.gif" width="719"
height="423" alt="All enzymes are
close to saturation"></h4></div>
<p class="legend"> 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.
<div class="sidebar-medium">
<p class="ref-in-sidebar"> 23. Cornish-Bowden A. Dominance is not inevitable. <acronym class="deja" title="Journal of Theoretical Biology">J Theor Biol</acronym> 1987;
125:333–338.
<p class="ref-in-sidebar"> 25. Atkinson DE. Regulation of enzyme function. <acronym class="deja" title="Annual Review of Microbiology">Annu Rev Microbiol</acronym> 1969;
23:47–68.
<p class="ref-in-sidebar"> 26. Grossniklaus U, Madhusudhan MS, Nanjundiah V. Nonlinear enzyme kinetics
can lead to high metabolic flux control coefficients: implications for the
evolution of dominance. <acronym class="deja" title="Journal of Theoretical Biology">J Theor Biol</acronym> 1996; 182:299–302.
</div>
<p>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 0.1<i>V</i>, 10% of the
limit, with a substrate concentration equal to 0.1<i>K</i><sub>m</sub>, the rate is
correspondingly far below the limit, about 0.09<i>V</i> 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 0.18<i>V</i> would imply an easily sustainable
increase in substrate concentration to 0.22<i>K</i><sub>m</sub>: barely more than doubled.
<p>Matters are quite different for an enzyme operating at 0.95<i>V</i>: 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.<sup>26</sup> examined a broader range of models
than that considered by Cornish-Bowden,<sup>23</sup> 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.
<h2 class="framed"><a name="hum"></a>Dominant genes in humans: an exceptional species?</h2>
<p>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 <q>MODY</q> (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.
<p>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.
<h2 class="framed"><a name="hkd"></a>The hexokinase D (<q>glucokinase</q>) gene in humans </h2>
<div class="sidebar-medium">
<p class="ref-in-sidebar">27. Cárdenas ML. In: <q>Glucokinase</q>: its regulation and role in liver
metabolism, Austin: RG Landes 1995.
</div>
<p>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 <q>glucokinase</q> 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.
<div class="sidebar-medium">
<p class="ref-in-sidebar">28. Hofmeyr JHS, Cornish-Bowden A. Regulating the cellular economy of supply
and demand. <acronym class="deja" title="FEBS (Federation of European Biochemical Societies) Letters">FEBS Lett</acronym> 2000; 476:47–51.
<p class="ref-in-sidebar">29. Reyes A, Cárdenas ML. All hexokinase isoenzymes coexist in rat
hepatocytes. <acronym class="deja" title="Biochemical Journal">Biochem J</acronym> 1984; 221:303–309.
<p class="ref-in-sidebar">30. Agius L, Peak M, Newgard CB et al. Evidence for a role of glucoseinduced
translocation of glucokinase in the control of hepatic glycogen synthesis.
<acronym class="deja" title="Journal of Biological Chemistry">J Biol Chem</acronym> 1996; 271:30479–30486.
<p class="ref-in-sidebar"> 31. Fajans SS. Maturity onset diabetes of the young (MODY). Diabetes Metab Rev
1989; 5:579–606.
</div>
<p>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.<sup>28</sup> 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,<sup>29</sup> and control of
glycogen synthesis is concentrated almost entirely in hexokinase D.<sup>30</sup> 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 <q>symptomless disease</q>, 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.<sup>31</sup> 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.
<p class="navigation"><a href="vidya4.htm">Continued...</a>
<div class="sidebar-tail">
<p class="in-tail">
Page created on 30 January 2006<br>
Last update: 22 December 2008<br>
Last significant update: 28 October 2008<br>
<em>Comments to <a href="mailto:acornish@ifr88.cnrs-mrs.fr">Athel Cornish-Bowden</a></em><br>
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