Selective Neutrality

Many enzymes in intermediary metabolism manifest saturation kinetics in which flux is a concave function of enzyme activity and often of the MichaelisMenten form. The result is that, when natural selection favors increased enzyme activity so as to maximize flux, a point of diminishing returns will be attained in which any increase in flux results in a disproportionately small increase in fitness. Enzyme activity ultimately will reach a level at which the favorable effect of an increase in activity is of the order 1/(4N8) or smaller, where Ne is the effective population number. At this point, many mutations that result in small changes in activity will result in negligible changes in fitness and will be selectively nearly neutral. We propose that this process is a mechanism whereby conditions for the occurrence of nearly neutral mutations and gene substitutions can be brought about by the long-continued action of natural selection. Evidence for the hypothesis derives from metabolic theory, direct studies of flux, studies of null and other types of alleles in Drosophila melanogaster and chemostat studies in Escherichia coli. Limitations and complications of the theory include changes in environment or genetic background, enzymes with sharply defined optima of activity, overdominance, pleiotropy, multifunctional enzymes and branched metabolic pathways. We conclude that the theory is a useful synthesis that unites many seemingly unrelated observations. The principal theoretical conclusion is that the conditions for the occurrence of neutral evolution can be brought about as an indirect result of the action of natural selection. HE neutral theory of molecular evolution (KIMURA 1968) has provided much insight for understanding the rates and patterns of change in macromolecules through evolutionary time, and also for understanding the role of mutation and random genetic drift in the maintenance of contemporary genetic polymorphisms (KIMURA 1983a,b). At the same time the theory has been highly controversial. In some commentaries the neutral theory is even regarded as anti-Darwinian. However, as has been demonstrated in an epigraph (DYKHUIZEN and HARTL 1980), Darwin was well aware of the possibility of selectively neutral variants and evidently did not consider their existence a challenge to his theory. When considered from a certain perspective, the superficial inconsistency between Darwinian selection and neutral evolution disappears completely. InGenetics 111: 655-674 November, 1985. 656 D. L. HARTL, D. E. DYKHUIZEN AND A. M. DEAN deed, the theories are not only consistent, but there is an important connection between the theories that we propose to explore in this paper. We shall develop arguments based on considerations of general characteristics of metabolic enzymes. Among the class of gene products for which the considerations are valid, the rather surprising conclusion is that the long-continued action of Darwinian natural selection may, itself, result in a situation in which many mutations are selectively neutral or nearly neutral. SATURATION KINETICS IN METABOLIC PATHWAYS Many biochemical reactions and metabolic pathways exhibit some type of saturation kinetics in which the reaction velocity or flux through the pathway converges asymptotically to a plateau as the activity of an enzyme increases, until a point is reached after which a further increase in enzyme activity results in a negligible increase in reaction velocity or flux (KACSER and BURNS 1973; CROWLEY 1975; ALBERY and KNOWLES 1976; CORNISH-BOWDEN 1976; PRICE and STEVENS 1982). Saturation behavior is expected in cases in which reaction velocity or flux is limited by substrate availability (MICHAELIS and MENTEN 1913; BRIGGS and HALDANE 1925), or in linear metabolic pathways with fixed inputs of the type studied by KACSER and BURNS (1973, 1979). Saturation kinetics also provides the framework for the molecular theory of dominance (WRIGHT 1934; KACSER and BURNS 1981), and it justifies the assumption that fitness functions are generally concave (GILLESPIE 1976; MIDDLETON and KACSER 1983; WATT 1985). With regard to the modulation and control of complex metabolic networks, many of the corollaries of saturation kinetics have been deduced (KACSER and BURNS 1973, 1979; HEINRICH and RAPOPORT 1974, 1983), and the development of a general theory of metabolic processes is regarded as being of profound importance in cell biology and physiology (PORTEOUS 1983). However, saturation kinetics also has important implications for the evolution of enzymes and of entire metabolic pathways, and several of the implications run contrary to intuitive notions but are supported by observed data. The implications of saturation kinetics for molecular evolution are considered in this paper. Although the arguments will be discussed primarily in the context of enzyme function and evolution, the ideas are supposed to apply rather more generally to structural and regulatory gene products. THE SATURATION MODEL Saturation kinetics may be illustrated by a function of the type in Figure 1 . The exact shape of the curve is largely immaterial to the arguments to be developed, and we shall use an equation of the type F = AF,,,/(KA + A) , where F represents the flux through a metabolic pathway (or rate of reaction), and A represents the amount (or activity) of an enzyme in the pathway. The quantities F,,,,, and K A represent, respectively, the maximum possible value of flux and the amount of enzyme at which flux attains one-half of its maximum value. The two-parameter saturation equation follows from simple MICHAELIS-MENSATURATION THEORY 657 a FIGURE 1 .-Standardized Michaelis-Menten saturation equationf(a) = a / ( l + a ) scaled to equal 1 at a = 30. TEN (1913) or BRIGGS-HALDANE (1925) enzyme kinetics when A is limiting to flux; it appears in the MONOD (1950) model of bacterial growth in a chemostat, and similar kinds of equations emerge from theoretical analysis of multienzyme metabolic pathways (KACSER and BURNS 1973, 1979; SAVAGEAU 1976). Defining f = F/F,,, and a = A/KA yields a parameter-free version of the saturation equation, namely f = a/(l + a), which is the curve illustrated in Figure 1. The curve rises sharply at first, but then increases more gradually to a plateau. We suppose a situation in which the fitness (f) of an organism is proportional to flux and can therefore be represented by means of a saturation curve, with the quantity a representing the amount of an enzyme or other gene product. Concave fitness functions of the general type in Figure 1 have been assumed by WRIGHT (1 934), GILLESPIE (1 976) and KACSER and BURNS (1981). The genotype of an organism (or an entire population) may be represented as a point on the curve, and barring such phenomena as overdominance, natural selection is expected to operate in such a manner that a population moves gradually upward on the curve, as illustrated by the arrows. The following sections concern the implications of natural selection when evolution occurs along the trajectory of a saturation curve. ASYMMETRY OF SELECTIVE EFFECTS Figure 2 illustrates the selection coefficient resulting from a mutation that changes a by a fixed positive or negative amount in the case a0 = 30. For a change in a from a. to a l , the selection coefficient is given by s = 1 [ f (ao)/ f ( a l ) ] , with s greater than or less than 0 as a1 is greater or less than ao, respectively. For a fixed but small Aa = al ao, the selection coefficient is equal in magnitude but opposite in sign because the f (a) is continuous and differentiable. However, for Aa not infinitesimal, the magnitude of the selec658 D. L. HARTL, D. E. DYKHUIZEN AND A. M. DEAN