5. Expansions of the present treatment
5.1. Why mutating one enzyme in a metabolic pathway may alter more than one trait; and mutating more than one enzyme may annul these changes in more than one trait
If the explanation for the origin of dominant and recessive traits depends on realising that fluxing metabolic pathways generate the molecular components of all traits, and that mutating any one enzyme in these pathways alters the flux and the concentrations of those normal metabolic products that are molecular components of a trait, other genetic phenomena could perhaps also be explained. Only two of the thirteen texts surveyed [1] gave a definition, in their glossaries, of pleiotropy and epistasis. Both agreed that pleiotropy was a phenomenon where a change at one gene locus brought about a change in more than one trait. Both attributed epistasis to an interaction between genes or their alleles. Neither of these descriptions of pleiotropy and epistasis is particularly revealing.
The following account, like those preceding it, does not depend on the fiction that all mutations generate inactive enzymes. Figure 1 is elaborated as shown in Figure 4. One pathway, like that shown in Figure 1, is now coupled to another analogous pathway by the conserved metabolite pair (p, q). The sum of the concentrations of (p) and (q) is constant (is conserved) but the ratio of the two concentrations (p/q) is a free variable. All the characteristics of the metabolic system in Figure 1 (Section 2), apply to each of the two fluxing pathways in Figure 4. Claims in the biochemical literature in the past that changes in the ratio (p/q) controlled metabolic fluxes were and remain untenable; one variable of a system cannot be said to control another variable of the system.
Figure 1 may also be elaborated as shown in Figure 5. An input flux from X1 to S4 divides into two output fluxes [16]. Of the input flux, a proportion (α) enters one of the two output fluxes (Ja) and a proportion (1-α) enters the other output flux (Jb). The magnitude of (α) is determined by the magnitudes of the activities of all the enzymes of the metabolic system; (α) is a systemic characteristic [17]. Again, all the characteristics of the model metabolic system in Figure 1 (Section 2), apply to each of the two pathways that generate fluxes Ja and Jb shown in Figure 5.
5.2. The origin of pleiotropy explained
It will be obvious that a mutation of any one enzyme in either of the two pathways of Figure 4 will cause changes in the fluxes through both of the coupled pathways (and the concentrations of metabolites in both pathways). Similarly, a mutation in any one enzyme of the input flux of Figure 5 will affect the concentrations of metabolites in both output fluxes Ja and Jb. Pleiotropy (a change in more than one trait as a consequence of a single mutation), when it is detected, is thus seen to depend on mutating an enzyme within a metabolic pathway, on the consequential changes in metabolite concentrations, and on the structure and interdependence of biochemical pathways. Only if one of the enzymes in the input pathway shows zero activity will both output fluxes (Ja and Jb) cease (Figure 5).
5.3. The origin of epistasis explained
Given a steady input flux from X1 to S4 (Figure 5), a mutation of one of the enzymes (E5a, E6a or any other enzyme in this output limb) would decrease flux Ja and increase flux Jb. The concentrations of metabolites in pathway Ja would decrease and those in pathway Jb would increase, a further example of a pleiotropic response to a single mutation. But suppose that, following the mutation of E5a, a mutation occurred in E6b or any other enzyme in this alternative output limb. Clearly, the effect of the first mutation on the cell characteristics would be at least partly nullified by the second mutation – a phenomenon known as epistasis and sometimes attributed in genetic texts to an interaction between genes but shown here to depend on mutations of one or more enzymes, and on the structure and interdependence of metabolic pathways. Only if the activity of one of the enzymes in one of the two output pathways is diminished to zero by mutation, will the products of that output limb downstream from the mutation be lost.
If the fluxes proceeded in the opposite direction to that shown in Figure 5 (so that two pathways merged into one), mutation of an enzyme in one of the input fluxes followed by a mutation of an enzyme in the other input pathway could again elicit epistatic responses in the system.
5.4. Are pleiotropy and epistasis always detectable?
Particular but common metabolic structures (Figures 4, 5) provide the potential for pleiotropy and epistasis; i.e. changes in concentrations of normal metabolites when an enzyme is mutated within a metabolic pathway. Whether pleiotropy or epistasis is detected, or not, will depend on the severity of the mutation and on the nature of the flux response plots (Figures 2, 3) as demonstrated in section 2.
5.5. Biochemistry and genetics are not separable topics
Beadle and Tatum [18] isolated a series of mutants of Neurospora crassa and tested their ability to grow on basal medium or on basal medium supplemented with different metabolites or cofactors. Wild-type Neurospora crassa grew on basal medium. Different isolated mutants would grow only if the basal medium was supplemented with the specific product of an enzyme rendered partially or fully inactive in one of the mutants. These brilliant observations led to the paradigm "one gene, one function" [19,20], later to "one gene, one enzyme". These observations [18] made explicit what was implied by the observations of Garrod [21-24]] on inborn errors of metabolism namely: metabolism is catalysed by a sequence (or system) of different enzymes; and a sufficient decrease (by mutation) in the activity of any one enzyme may cause a change in the trait(s) or characteristic(s) of the system (e.g. the ability to grow, to accumulate cell mass [18]).
Beadle [20] expressed surprise that Garrod's work had received so little attention. He wrote: "It is a fact both of interest and historical importance that for many years Garrod's book had little influence on genetics. It was widely known and cited by biochemists, and many geneticists in the first two decades of the century knew of it and the cases so beautifully described in it. Yet in the standard textbooks written in the twenties and thirties - - - - few mention its cases or even give a reference to it. I have often wondered why this was so. I suppose most geneticists were not yet inclined to think of hereditary traits in chemical terms. Certainly, biochemists with a few notable exceptions such as the Onslows, Gortner and Haldane were not keenly aware of the intimate way in which genes direct the reactions of living systems that were the subject of their science."
This lack of attention to the implications of Garrod's work is all the more surprising when it is recalled that Bateson [[25], p.133] pointed out that alkaptonuria (a change in concentration of the normal metabolite, homogentisic acid, and one of Garrod's inborn errors of metabolism) was an example of a Mendelian recessive trait or character; see also [[26], p.19]. In other words, some important aspects of genetics depended on recognising the role of changes in an enzyme activity, within a metabolic system, in effecting a change in a trait.
The aphorism "one gene, one enzyme" was refined to "one allele, one polypeptide" after the elucidation of the structure of DNA [27,28] and the rapid advances made in the next 10 or 15 years in elucidating the mechanisms of expression of diploid alleles as pairs of polypeptides or proteins [29-32]] most of which are enzymes [3,4]. These more recent discoveries (Figure 6) emphasise what was implied by the work of Beadle and Tatum [18]: the molecular components of dominant and recessive traits or characteristics, in all biological forms, are generated by fluxing metabolic pathways catalysed by sequences or systems of enzymes. Dominant and recessive traits are not the direct product of the expression of alleles as suggested by the currently favoured explanation of Mendel's observations (Figure 2 in Reference [1]); they are produced indirectly by a system of enzymes (Figures 1, 4, 5, 6).
Figure 6 depicts the direct relationship between any one gene (g1, g2, g3, g4) and the synthesis of individual polypeptides (P1, P2, P3, P4) most of which, but not all, are enzymes (E1, E2, E3, E4). All polypeptides, catalytic and non-catalytic, are synthesised in this way.
X1, X2 and X3 in Figure 6 are immediately identified as extracellular parameters of a cell system. X3 stands for those substrates that lead, through a series of enzyme-catalysed reactions, to the synthesis of nucleoside triphosphates (NTPs) and their subsequent incorporation into mRNA. Note that mRNA is a terminal product of this pathway. It is a coding entity, a proxy for DNA. Each mRNA specifies the order of incorporation of individual amino acids into a polypeptide, but no individual mRNA molecule participates as a substrate in the subsequent steps of the catalysed formation of a polypeptide. The control of the overall expression of a gene as a polypeptide is therefore necessarily treated in Metabolic Control Analysis as a cascade of two fluxing metabolic pathways, one that starts at X3, the other that starts at X2 [33].
X2 stands for those extracellular substrates that lead, through a series of enzyme-catalysed reactions, to the synthesis de novo of amino acids (AAs) and their subsequent incorporation, along with any existing amino acids, into a polypeptide (P). In a haploid cell, one polypeptide is synthesised from each gene locus. In a diploid, one polypeptide is synthesised from each of two alleles at a gene locus. If these pairs of polypeptides are catalytically active, each enzyme in a diploid cell (E1, E2, E3, etc) consists of a pair of allozymes, one of each pair specified by the allele derived from the male parent, the other specified by allele derived from the female parent. Each pair of allozymes, whether normal or mutated, exhibits only one measurable activity (v) at a catalytic locus in a metabolic pathway. If the pairs of polypeptides (P) synthesised by a diploid cell are not catalytically active they will not, of course, play a direct role in catalysing a metabolic pathway. They may have other important functions (e.g. as hormones) and may be components of traits.
X1 stands for all those initial extracellular substrates feeding the matrix of inter-dependent biochemical pathways that typify all functioning cells. It is these pathways that generate the non-protein, non-polyribonucleotide, molecular products of all cell traits.
Each of these three major fluxing pathways (Figure 6) is catalysed by a succession of enzyme-catalysed reactions as shown in Figure 1. The flux through any one of these pathways will respond to a mutation of any one enzyme in the pathway as shown in Figures 2, 3; any change in these fluxes could change the concentrations of the intermediate metabolites or the final product (section 2.3); but, provided mutations do not alter the specificity of an enzyme, they will not change the existing molecular structure or composition of these metabolites.
Most attention is concentrated on the pathway initiated by X1 for the simple reason that this pathway stands for all the matrix of interdependent biochemical fluxes that generate such a wide range of the non-protein (and non-polyribonucleotide) molecular components of cell traits (e.g. skin pigments, membrane lipids, chlorophyll, xanthocyanins, non-peptide hormones, neural transmitters, chitin, serum cholesterol, peptidoglycans, etc, etc).
If any one of the three major pathways shown in Figure 6 is coupled to another pathway (Figure 4) or contains a branch (Figure 5) there will be, potentially detectable, pleiotropic and epistatic responses to mutations of any of the pathway enzymes (section 5.3). Such pathway coupling and branching is a common feature of the pathways that start with one of the extracellular substrates typified by X1.
If the implications of the work of Beadle and Tatum [18] were not fully realised at the time, Figure 6 might have suggested that a fresh approach to an understanding of the origins of dominant and recessive traits was needed. The currently favoured explanation for Mendel's findings ([1], Figure 2) does not take account of the biochemical pathways of the synthesis of enzymes (Figure 6) established 30–40 years ago, does not acknowledge that the molecular components of all traits are synthesised by systems of enzymes, does not take account of the change in concentration of molecular components of traits when any one enzyme is mutated, and fails to distinguish the system parameters (alleles) from the system variables (traits).
Note that changes in the concentrations of external metabolites (whether they are substrates like X1, X2, X3in Figure 6, or extracellular inhibitors or activators of intracellular enzymes) may effect changes in intracellular metabolism and consequently modify the effects of a mutation. This topic is not immediately relevant in the present article but is a notable feature of Metabolic Control Analysis. Descriptions of the role of the Combined Response Coefficient (R) in permitting extracellular effectors to modulate intracellular metabolism (and thus the effects of a mutation) will be found elsewhere [11,34-36].
If pleiotropic and epistatic responses to a mutation are as common as is suggested (sections 5.1–5.4), the question then arises: how do we account for Mendelian segregation of traits during sexual reproduction? The answer lies in the fact that a mutation at a biochemical locus, within the matrix of interdependent pathways, has its most obvious effect on the most closely associated pathways. Distant pathways (on the scale of cellular dimensions) will be less obviously affected. Kacser and Burns (Reference [3], p.649) pointed out that "This apparent independence of most characters makes simple Mendelian genetics possible, but conceals the fact that there is universal pleiotropy. All characters should be viewed as 'quantitative' since, in principle, variation anywhere in the genome affects every character." Section 3 in the present article emphasised the importance of quantitative changes in cell traits. The considerations in this paragraph are germane to the apparent absence of a detectable change of phenotype in some so-called 'knock-out' experiments.
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