Abstract
The best known genes of microbes, mice and men are those that specify enzymes. Wild type, mutant and heterozygote for variants of such genes differ in the catalytic activity at the step in the enzyme network specified by the gene in question. The effect on the respective phenotypes of such changes in catalytic activity, however, is not defined by the enzyme change as estimated by in vitro determination of the activities obtained from the extracts of the three types. In vivo enzymes do not act in isolation, but are kinetically linked to other enzymes via their substrates and products. These interactions modify the effect of enzyme variation on the phenotype, depending on the nature and quantity of the other enzymes present. An output of such a system, say a flux, is therefore a systemic property, and its response to variation at one locus must be measured in the whole system. This response is best described by the sensitivity coefficient, Z, which is defined by the fractional change in flux over the fractional change in enzyme activity.
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Its magnitude determines the extent to which a particular enzyme "controls" a particular flux or phenotype and, implicitly, determines the values that the three phenotypes will have. There are as many sensitivity coefficients for a given flux as there are enzymes in the system. It can be shown that the sum of all such coefficients equals unity.
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Since n, the number of enzymes, is large, this summation property results in the individual coefficients being small. The effect of making a large change in enzyme activity therefore usually results in only a negligible change in flux. A reduction to 50% activity in the heterozygote, a common feature for many mutants, is therefore not expected to be detectable in the phenotype. The mutant would therefore be described as "recessive". The widespread occurrence of recessive mutants is thus seen to be the inevitable consequence of the kinetic structure of enzyme networks. The ad hoc hypothesis of "modifiers" selected to maximize the fitness of the heterozygote, as proposed by Fisher, is therefore unnecessary. It is based on the false general expectation of an intermediate phenotype in the heterozygote. Wright's analysis, substantially sound in its approach, proposed selection of a "safety factor" in enzyme activity. The derivation of the summation property explains why such safety factors are automatically present in almost all enzymes without selection.
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Selected References
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