A superior theory?

Evolution of Henrik Kacser's thought: Early publications on the organization of the whole system

Although the papers of Kacser and Burns (1973) and Heinrich and Rapoport (1974a,b) are commonly taken as the birth of metabolic control analysis, many of the ideas in them are foreshadowed in earlier papers, from 1956 onwards, when Kacser first argued for taking a systemic view of genetics and biochemistry.

Unresolved boundaries of evolutionary theory and the question of how inheritance systems evolve: 75 years of debate on the evolution of dominance

One of the key issues in the evolution of life is the evolution of inheritance systems. In population genetics, the earliest attempt at addressing the latter problem revolved around Fisher's theory on the evolution of dominance. Fisher's hypothesis was that inheritance systems could be modified during the evolutionary process in such a way that wild-type phenotypes could become dominant with respect to mutant phenotypes. This would result in the buffering of a population against the deleterious effects of mutations. The debate that ensued on this topic has been one of the most longstanding in evolutionary theory. At present, the prevalent view is that dominance cannot evolve as a direct result of selection. Furthermore, it has been argued that due to inherent constraints in biochemical systems, the manifestation of dominance is a default expectation and hence evolutionary explanations are not necessary. This has led to the position that the subject is generally resolved and no further debate is necessary. However, there are also several studies indicating that dominance levels can be modified as a result of changes in the genetic background. Furthermore, other studies have indicated that dominance selection is possible in certain circumstances. To a large degree, conclusions from both of the latter types of studies have been ignored. In this article, the history of several intellectual and methodological traditions that have contributed to this debate are traced, including experimental genetics, theoretical population genetics and theoretical biochemistry. In the light of both old and contemporary works on this topic, it is argued that contrary to the prevalent view, the evolution of dominance is not a resolved issue. A re-examination of this issue is essential, given that dominance evolution is likely to be an important stepping stone towards understanding the evolution of inheritance systems.

Evolution of dominance in metabolic pathways

Dominance is a form of phenotypic robustness to mutations. Understanding how such robustness can evolve provides a window into how the relation between genotype and phenotype can evolve. As such, the issue of dominance evolution is a question about the evolution of inheritance systems. Attempts at explaining the evolution of dominance have run into two problems. One is that selection for dominance is sensitive to the frequency of heterozygotes. Accordingly, dominance cannot evolve unless special conditions lead to the presence of a high frequency of mutant alleles in the population. Second, on the basis of theoretical results in metabolic control analysis, it has been proposed that metabolic systems possess inherent constraints. These hypothetical constraints imply the default manifestation of dominance of the wild type with respect to the effects of mutations at most loci. Hence, some biologists have maintained that an evolutionary explanation is not relevant to dominance. In this article, we put into question the hypothetical assumption of default metabolic constraints. We show that this assumption is based on an exclusion of important nonlinear interactions that can occur between enzymes in a pathway. With an a priori exclusion of such interactions, the possibility of epistasis and hence dominance modification is eliminated. We present a theoretical model that integrates enzyme kinetics and population genetics to address dominance evolution in metabolic pathways. In the case of mutations that decrease enzyme concentrations, and given the mechanistic constraints of Michaelis-Menten-type catalysis, it is shown that dominance of the wild type can be extensively modified in a two-enzyme pathway. Moreover, we discuss analytical results indicating that the conclusions from the two-enzyme case can be generalized to any number of enzymes. Dominance modification is achieved chiefly through changes in enzyme concentrations or kinetic parameters such as k(cat), both of which can alter saturation levels. Low saturation translates into higher levels of dominance with respect to mutations that decrease enzyme concentrations. Furthermore, it is shown that in the two-enzyme example, dominance evolves as a by-product of selection in a manner that is insensitive to the frequency of heterozygotes. Using variation in k(cat) as an example of modifier mutations, it is shown that the latter can have direct fitness effects in addition to dominance modification effects. Dominance evolution can occur in a frequency-insensitive manner as a result of selection for such dual-effects alleles. This type of selection may prove to be a common pattern for the evolution of phenotypic robustness to mutations.

Effects of epistasis on phenotypic robustness in metabolic pathways

It is an open question whether phenomena such as phenotypic robustness to mutation evolve as adaptations or are simply an inherent property of genetic systems. As a case study, we examine this question with regard to dominance in metabolic physiology. Traditionally the conclusion that has been derived from Metabolic Control Analysis has been that dominance is an inevitable property of multi-enzyme systems and hence does not require an evolutionary explanation. This view is based on a mathematical result commonly referred to as the flux summation theorem. However it is shown here that for mutations involving finite changes (of any magnitude) in enzyme concentration, the flux summation theorem can only hold in a very restricted set of conditions. Using both analytical and simulation results we show that for finite changes, the summation theorem is only valid in cases where the relationship between genotype and phenotype is linear and devoid of non-linearities in the form of epistasis. Such an absence of epistasis is unlikely in metabolic systems. As an example, we show that epistasis can arise in scenarios where we assume generic non-linearities such as those caused by enzyme saturation. In such cases dominance levels can be modified by mutations that affect saturation levels. The implication is that dominance is not a necessary property of metabolic systems and that it can be subject to evolutionary modification.

Dosage, deletions and dominance: simple models of the evolution of gene expression

Dominance of the wild-type allele over spontaneous null mutations, such as deletions, can be explained in terms of the effects of changes in enzyme dose on the flux of metabolic pathways. If ever increasing levels of enzyme activity have ever decreasing effects on the flux of the biochemical pathway, then halving of dosage will always have a lesser effect on flux than half the effect of complete removal of gene activity. Furthermore, if gene expression rates are high, then halving of dose can have a negligible effect on flux and dominance will be strong. Given that strong dominance appears to be common, this leaves open the issue of why enzyme activity levels are so high that a halving of expression rates is of minimal effect. Why produce so much surplus enzyme? One explanation, suggested by Haldane, is that selection favoured high expression levels as a defence against mutation. We model this scenario formally and show that protection from mutation is an extremely weak force determining expression levels. The selective coefficients are only of the order of the mutation rate. However, if we suppose a linear mapping of flux with fitness and a monotonic cost to increased gene expression, it follows simply that here exists an optimal level of gene expression. By contrast to the mutational model, doubling of gene expression rates when the system is distant from the optimum is associated with extremely high selective coefficients (orders of magnitude higher than the mutation rate). When the cost of gene expression is slight the optimal rate of expression is such that strong dominance will follow.

Dynamic metabolic control theory. A methodology for investigating metabolic regulation using transient metabolic data

The purposes of the dynamic metabolic control theory are to provide a theoretical basis for estimating the control coefficients using the transient metabolic responses and to gain insights into the metabolic regulation in the transient states. The numerical application of this theory is relatively straightforward: it involves a standard linear regression and a matrix multiplication. Although the equations are exact only for linear kinetics, they yield relatively good estimates of the control coefficients for nonlinear systems.

Metabolic control analysis: a survey of its theoretical and experimental development

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