Quantitative evolutionary design

Abstract

The field of quantitative evolutionary design uses evolutionary reasoning (in terms of natural selection and ultimate causation) to understand the magnitudes of biological reserve capacities, i.e. excesses of capacities over natural loads. Ratios of capacities to loads, defined as safety factors, fall in the range 1.2-10 for most engineered and biological components, even though engineered safety factors are specified intentionally by humans while biological safety factors arise through natural selection. Familiar examples of engineered safety factors include those of buildings, bridges and elevators (lifts), while biological examples include factors of bones and other structural elements, of enzymes and transporters, and of organ metabolic performances. Safety factors serve to minimize the overlap zone (resulting in performance failure) between the low tail of capacity distributions and the high tail of load distributions. Safety factors increase with coefficients of variation of load and capacity, with capacity deterioration with time, and with cost of failure, and decrease with costs of initial construction, maintenance, operation, and opportunity. Adaptive regulation of many biological systems involves capacity increases with increasing load; several quantitative examples suggest sublinear increases, such that safety factors decrease towards 1.0. Unsolved questions include safety factors of series systems, parallel or branched pathways, elements with multiple functions, enzyme reaction chains, and equilibrium enzymes. The modest sizes of safety factors imply the existence of costs that penalize excess capacities. Those costs are likely to involve wasted energy or space for large or expensive components, but opportunity costs of wasted space at the molecular level for minor components.

A research program that has been emerging at the interface between physiology and evolutionary biology is the approach termed quantitative evolutionary design. It uses evolutionary reasoning to understand, in terms of ultimate rather than proximate causation, why any particular physiological or anatomical quantity has the numerical value that it does, rather than some higher or lower value. By this approach, physiologists and evolutionary biologists may be able to contribute solutions to each others’ problems. On the one hand, the concepts of ‘ultimate causation’ and ‘evolutionary design’, which I shall discuss below, have been exploited routinely in evolutionary biology but rarely in physiology. On the other hand, physiologists are in a position to measure the evolutionary costs that evolutionary biologists routinely postulate but have rarely have been able to measure.

The two pioneering sets of studies that founded this field have been the theoretical papers by Alexander (1981, 1984, 1997; Alexander et al. 1984), who applied the engineering concept of safety factors to biological systems, and who developed an optimality model for systems consisting of series components; and the long series of experimental papers by Taylor, Weibel and colleagues (e.g. Taylor & Weibel, 1981; Taylor et al. 1996; Weibel et al. 1987, 1991, 1998; Weibel, 2000), whose measurements of the key physiological and anatomical parameters in mammalian systems for aerobic exercise are unique in their comprehensive scope, and who introduced the term ‘symmorphosis’ to describe series systems with safety factors close to 1.0 (see below). Suarez and colleagues (Suarez, 1992, 1996, 1998; Suarez et al. 1996, 1997; Staples & Suarez, 1997) have published insightful studies of animals operating with various metabolic rates and corresponding variation in safety factors, and have also solved the paradox of apparently exorbitantly high safety factors of biochemical reactions operating near equilibrium. My colleagues and I have measured safety factors of intestinal brush-border hydrolases (Weiss et al. 1998; O'Connor & Diamond, 1999; Lam et al. 2002) and nutrient transporters (Buddington & Diamond, 1989; Ferraris & Diamond, 1989; Diamond & Hammond, 1992, 1994; Diamond, 1993; Hammond et al. 1994) in many species, while imposing various metabolic workloads in order to analyse adaptive regulation quantitatively. Biewener and colleagues measured bone safety factors and their behavioural consequences for mammals and birds (Biewener, 1982, 1983a, b, 1989; Perry et al. 1988). Also relevant is the biochemical literature on so-called ‘metabolic control theory’, which uses different terminology but performs similar analyses of enzyme reaction chains (Cornish-Bowden & Cardenas, 1990).

What are safety factors?

As an illustrative example (Weiss et al. 1998), consider a Swiss-Webster mouse consuming a diet whose principal source of calories is the disaccharide sucrose, hydrolysed in the small intestine by the brush border enzyme sucrase to yield the monosaccharides glucose and fructose, which are then taken up across the brush border membrane into the enterocyte by the transporters SGLT1 and GLUT5, respectively. Thus, sucrase operates in series with SGLT1 and GLUT5. The mouse's ad libitum dietary intake is 7.5 mmol sucrose day⁻¹, yielding upon hydrolysis 6 mmol day⁻¹ each of glucose and fructose. The brush border contains enough sucrase to split 19.5 mmol sucrose day⁻¹ (the V_max value for sucrase), and enough SGLT1 to take up 21.5 mmol glucose day⁻¹ (the V_max value for SGLT1), while the V_max value for GLUT5 for fructose uptake has yet to be measured in this system.

One refers to the mouse's maximal abilities to split sucrose and to take up glucose as capacities (C), and one refers to the actual amounts of sucrose split and glucose taken up per day as loads (L). The physiological literature sometimes refers to the excess of capacity over load as reserve capacity (R):

The engineering literature on analogous problems instead defines ratios of capacities to loads as safety factors (SFs):

In the above example, the mouse's reserve capacities are 19.5 — 7.5 = 11.5 mmol day⁻¹ for sucrase, and 21 — 7.5 = 13.5 mmol day⁻¹ for SGLT1, while the corresponding safety factors are 19.5/7.5 = 2.6 and 21/7.5 = 2.8, respectively.

Note that mouse intestine possesses a considerable reserve capacity for both of these proteins. It requires explanation why energy should apparently be wasted on synthesizing and maintaining quantities of both proteins so much in excess of needs, or why (given that there might be some advantage to maintaining reserve capacities) the reserve capacities are not even larger. It also requires explanation why mouse sucrase and SGLT1, operating in series, should have evolved to possess virtually the same capacities and safety factors. These are separate proteins, coded by separate genes and synthesized separately; there is no functional or mechanistic reason why they must have the same capacities, and indeed there are other cases in which series components have evolved different capacities (Alexander, 1997; O'Connor & Diamond, 1999; Lam et al. 2002). Why did the capacities of sucrase and SGLT1 end up closely matched to each other, but not matched to their loads? Analogous questions can be raised for a wide variety of other physiological systems (see Tables 2, 3 and 4 below).

Table 2.

Biological safety factors of structural elements

Structure	Safety factor
Jawbone of biting monkey	7
Wing bones of flying goose	6
Leg bones of running turkey	6
Leg bones of galloping horse	4.8
Leg bones of running elephant	3.2
Leg bones of hopping kangaroo	3
Leg bones of running ostrich	2.5
Leg bones of jumping dog	2.5
Dragline of spider	1.5
Backbone of human weightlifter	1.35
Shell of squid	1.35

From Alexander (1981) and sources cited therein.

Table 3.

Biological safety factors of organ performance

Organ	Function	Safety factor
Human pancreas	Enzyme secretion	10
Human kidneys	Glomerular filtration	4
Human mammary glands	Milk secretion	3
Human small intestine	Absorption	2
Human liver	Metabolism	2
Cow lungs	Aerobic capacity	2
Dog lungs	Aerobic capacity	1.25

From DiMagno et al. (1973), Weibel et al. (1991) and clinical studies of milk production and organ resection. The safety factors for human kidneys, human mammary glands, and cow and dog lungs refer to the paired organs together, not to each kidney or mammary gland or lung separately. Organ resection studies of human kidneys, small intestine and liver show that unassisted survival is difficult, even after adaptive hypertrophy, for patients who have lost 3/4, 1/2 and 1/2 of the original organ mass, respectively.

Table 4.

Biological safety factors of intestinal brush border transporters and enzymes

Transporter or enzyme	Safety factor
Cat arginine transporter	7
Mouse maltase	6.5
Rat lactase	6
Mouse glucose transporter	2.8
Mouse sucrase	2.6
Cat leucine transporter	2
Rat pro line transporter	1.3
Rat glucose transporter	1.2

From papers by my colleagues and me, cited in the references.

Ultimate causation

The ‘why’ questions posed above can be answered at two levels of explanation and causation. The level familiar to physiologists is the proximate level in terms of molecular mechanisms: one would invoke the number of copies of sucrase, its turnover rate, and its synthesis and degradation rates to explain ‘why’ its V_max value ended up as it did. This approach has nothing to say about the relation between that sucrase capacity and the sucrose load; the fact that the ratio turns out to be 2.6 cannot be interpreted.

The other level, familiar to evolutionary biologists, is the ultimate level in terms of natural selection: what are the quantitative evolutionary costs and benefits that caused mice to evolve a safety factor of 2.6, instead of 26 or 1.026, for brush border sucrase? Evidently, mice with either more or less sucrase were at a selective disadvantage compared with mice with enough sucrase to give a safety factor of 2.6. What exactly are the disadvantages of more or less sucrase, and why did natural selection compromise on safety factor of 2.6? This approach has nothing to say about the particular molecular mechanisms setting sucrase's capacity; even if those molecular mechanisms had been completely different, the question about evolutionary costs and benefits would have remained the same. The latter question about ultimate causation is typical of the type of question asked by evolutionary biologists, but in many cases, as here, they lack the tools to solve them. Ironically, physiologists have the tools to solve such questions but almost never ask them.

The distinction between proximate and ultimate causation is worth belabouring, because, in my experience, scientists who study proximate causation (such as physiologists and biochemists) not only do not realize that there are separate questions of ultimate causation but also, when those questions are posed to them, are inclined to dismiss them as speculative and unanswerable. I shall discuss in the last paragraph of this paper how those questions could be answered for brush border membrane proteins like sucrase, but I shall give one example now of how they can be answered in a more obvious case. Consider the non-poisonous, orange-and-black North American butterfly species called the Viceroy, whose colour pattern closely resembles that of the highly poisonous Monarch Butterfly. Why is the Viceroy orange-and-black? A biochemist would provide a proximate explanation in terms of the pigments in the butterfly's wings, the molecular structure of those pigments, and the principles of quantum mechanics according to which those molecular structures yield orange-and-black colours. The function of those colours to the living butterfly is irrelevant and unanswerable to the biochemist. An evolutionary biologist would instead provide an ultimate explanation in terms of Muellerian (or perhaps Batesian) mimicry: the more closely a Viceroy resembles a Monarch, the less likely it is to be eaten by a predator that has learned to recognize the Monarch's colour pattern in order to avoid eating the Monarch because of its unpalatable poisons. Evolutionary biologists test such mimicry-based interpretations in many ways, for example, by measuring differential predation on Viceroys and on non-mimic non-poisonous butterflies; by painting a different colour pattern onto Viceroys and remeasuring predation; by measuring predation on Viceroys by predators with no experience of Monarchs; by comparing colour patterns of Viceroys between geographic areas supporting and lacking Monarchs; and by estimating the cost of synthesis of the Monarch's poisons.

Measured safety factors

Engineers designing human-built structures and machines deal with safety factors constantly (Roark, 1965; Shigley, 1972). They calculate, according to the criteria of Table 5 to be discussed below, what safety factor would be optimal for each component of the structure or machine, and they intentionally manufacture the component to have that safety factor, which often becomes specified by law. Table 1 summarizes some engineered safety factors. For example, the cable that hoists a fast passenger lift is required to be of a strength that will not break until the load is 12 times the load for which the elevator is certified. That is, if you find yourself in an elevator whose sign proclaims ‘certified for 10 passengers or 700 kg’, do not worry about the cable breaking unless the weight of you and your fellow passengers actually exceeds 8400 kg. Freight lifts have lower safety factors (only 7), and dumb waiters (the miniature lifts by which hotels transport your room-service breakfast from the hotel kitchen in the basement up to the guest floors) have an even lower safety factor of 5. Wooden support beams in a building are required to have safety factors of 6, but steel beams need only be twice as strong as the expected load. You may already be able to guess why passenger elevators and wooden buildings are designed more conservatively than are freight elevators and steel buildings; more of this later.

Table 5.

Considerations setting the values of safety factors

+	1.	Coefficient of variation of load
+	2.	Coefficient of variation of capacity
+	3.	Deterioration of capacity with time
+	4.	Cost of failure
−	5.	Cost of initial construction
−	6.	Cost of maintenance
−	7.	Cost of operation
−	8.	Opportunity cost of occupied space

Table 1.

Engineered safety factors

Structure		Safety factor
Elevator cables	Passenger	12
	Freight	7
	Dumb waiter	5
Buildings	Wood	6
	Steel	2

From Roark (1965), Shigley (1972) and Alexander (1981).

The biological safety factors most nearly analogous to these safety factors of human-built structures are those of bones and other load-bearing structural elements. Table 2 shows that these fall within the range 1.35 (for a weightlifter’ s backbone and a squid’ s shell) to 7 (for a monkey's jawbone), similar to those of the human-built structures of Table 1. Why do you think that jawbones, wing bones, and leg bones are relatively over-designed in comparison with a squid's shell?

Some other biological safety factors, which do not refer to load-bearing structures, are summarized in Tables 3 and 4. (Values in Tables 2–4 refer to adults, except that values in Table 4 for cat transporters and rat lactase refer to not-yet-weaned young animals.) The pancreas, kidney, mammary gland, small intestine, and lungs are all capable of (respectively) secreting digestive enzymes, filtering plasma, secreting milk, absorbing the digesta, and taking up oxygen at rates in excess of the maximal rates observed physiologically (Table 3). The highest of those organ safety factors (10) is that of the pancreas: malabsorption, due to decreased absorption of ingested food by pancreatic proteases and lipases, is not observed until pancreatic enzyme output has dropped to only 10 % of normal peak values (DiMagno et al. 1973). That is why pancreatic cancer is so insidiously difficult to detect: patients show no tell-tale symptoms of malabsorption until 90 % of pancreatic function has been destroyed, by which time the cancer has usually metastasized to other organs. Safety factors of intestinal brush border hydrolases and nutrient transporters range from 1.2 to 7, with the highest known value (7) being that of the cat arginine transporter (Table 4): why?

Ultimate factors behind safety factors

One's first impression is that the ranges of safety factors for engineered structures (2-12) and biological structures (1.2-10) are similar. A priori, if someone without experience of the problem had been asked to guess the likely ranges, guesses of 1.0 to 1.1, or 10 to 100, might instead have seemed reasonable. One's second impression is that, in the worlds of both machines and biology, there is much variation to be explained. Why are passenger lifts, the pancreas, and cat arginine transporters so over-designed in comparison with dumb waiters, squid shells, and intestinal glucose transporters? Why, for that matter, are machines designed, and why have biological components evolved, to have any reserve capacity at all? Don't unutilized capacities represent a waste of money or of biosynthetic energy?

The reason for the existence of safety factors is that neither capacities nor loads are precisely predictable. The magnitudes of capacities specified either by blueprints or by genes exhibit some variation in practice. For instance, individual lift cables manufactured in the same factory, or corresponding bones of identical twins, differ somewhat in strength. Also, the loads upon capacity vary. No matter what the sign inside the lift says about ‘certified for 10 passengers or 700 kg’, some extra passengers may crowd into the elevator, and some of them may be 200 kg sumo wrestlers rather than 70 kg physiologists. When a lift cable at the low end of the strength distribution is required to lift a load at the high end of the weight distribution (Fig. 1), the result is a torn cable, lift crash, and risk of passenger deaths.

Figure 1.

Examples of the frequency distribution of a capacity and of the load upon it (ordinate), as a function of load units (abscissa)

The failure zone (shaded) represents the range of load units over which the load exceeds the capacity, so that system performance fails. The ratio of the mean value of capacity to load (A/B) is defined as the safety factor. Upper panel, high coefficients of variation of capacity and load; lower panel, low coefficients of variation. Note that more variable capacities or loads mandate higher safety factors in order to reduce the failure zone to an acceptably low value. Modified from Fig. 1a of Alexander (1981).

From Fig. 1 follows a series of eight guidelines used by engineers in setting values of safety factors (Table 5). The higher the coefficient of variation of the load or capacity, the larger must be the safety factor in order to reduce the overlap zone between exceptionally large loads and exceptionally small capacities to some acceptably low value. Greater deterioration of capacities with time also mandates higher safety factors. (That is why higher safety factors are specified for wooden beams than for steel beams: wooden beams are more variable in strength, and more prone to deterioration, than are steel beams.) High penalties for failure mandate high safety factors: for example, a lift company will be sued for higher damages if the cable snaps on a passenger lift, killing some passengers, than if it snaps on a dumb waiter, spilling some hotel guest's breakfast of scrambled eggs. Conversely, engineers cannot afford to overbuild capacities that cost a lot to build, maintain, or operate, or that occupy too much space.

In designing a building and setting the safety factors of its components, engineers consciously balance these eight conflicting considerations, four of which favour large safety factors while four favour small safety factors. The arbiter for these compromise decisions is the marketplace of consumer choice among competing products: building owners do not like lifts with a reputation for frequent crashes, but they also do not like unnecessarily expensive or large lifts. Consumer choice selects for lift companies whose cables are built with some optimal intermediate safety factor, leaving companies making either crash-prone or overpriced lifts to go bankrupt.

Similar considerations apply in the biological world, except that the selection among different genotypes and phenotypes is not made consciously by an engineer responding to consumer choice, but is made unconsciously by natural selection. Nevertheless, the result is still structures that appear to be well designed for a purpose, so much so that many people remain creationists who take that appearance of design as evidence for the hand of God rather than of natural selection. In analysing animal and plant bodies, evolutionary biologists routinely use the term ‘design’ as shorthand to mean ‘the fit of form to function resulting from natural selection’. In the biological world the penalty for too low a safety factor is obvious: animals with broken bones or incomplete food absorption are likely to die, or to starve and fail to reproduce. As for the penalty for too high a biological safety factor, very big bones or organs would never break or fail, but the energy and body space available to an animal are finite, so that excessive energy or space lavished on one biological element must come at the expense of energy or space that could have been devoted to another element. (I shall consider this argument in more detail in the last five paragraphs of this article.)

Within this framework, the factors setting the compromise value of a safety factor are the same eight for biological components as for machines (Table 5). For instance, loads are unpredictable, and safety factors correspondingly high, for leg bones of animals running over irregular terrain; but loads are highly predictable, and safety factors low, for a spider's dragline (the load is just the spider's own weight), the backbone of a human lifting weights (we select the load ourselves and we lift carefully), and a squid's shell (the load is water pressure varying with ocean depth that the squid chooses itself). Two reasons underlie the higher safety factors of the pancreas than of the kidney, liver and small intestine: like a wooden beam, the pancreas deteriorates with age because it does not regenerate after damage, as do kidney, liver, and small intestine; and the latter three organs have among the highest metabolic rates and maintenance costs, whereas an excess of pancreas is more affordable because its maintenance costs are low. Among intestinal brush border nutrient transporters, the cost of failure (hence the safety factor) is much higher for cat arginine transporter than for mouse or rat glucose transporter, because arginine is a hyperessential nutrient for cats (a single meal without arginine is sufficient to kill a cat) whereas glucose is a non-essential nutrient, the calories derived from which are replaceable by other sources (Buddington & Diamond, 1989).

Adaptive regulation

One difference between engineered and biological safety factors is that most engineered components are not designed to vary their capacity depending on the applied load, but many biological components have evolved to do so. For example, lifts are not designed to close their doors or to unroll another cable if too many sumo wrestlers try to crowd into the cabin. However, phenomena such as protein induction and repression, tissue growth and atrophy, and membrane protein insertion permit many biological capacities to vary with their load; this response is termed adaptive regulation.

Analysis in terms of safety factors can yield quantitative insights into adaptive regulation. For example, when mice increase their food intake because of increased energy requirements for any reason — cold ambient temperature, pregnancy, lactation, expanded litter size, or delayed weaning — the intestine is observed to undergo hypertrophy. Because activities per milligram of tissue generally remain the same after hypertrophy for intestinal brush border nutrient transporters and hydrolases, the result of the hypertrophy is increases of capacity for these proteins, because capacity equals activity times intestinal mass. But the slope for the increase in capacity with load is less than 1.0 (Fig. 2), so that the safety factor declines towards 1.0 (Fig. 3) (Toloza et al. 1991; Hammond & Diamond, 1992, 1994; Hammond et al. 1994, 1996; Weiss et al. 1998; O'Connor & Diamond, 1999; O'Connor et al. 1999; Lam et al. 2002). That is, the function of adaptive regulation is to maintain sufficient capacity in the face of load increases, but a mouse cannot increase its intestinal mass indefinitely, so that reserve capacity must gradually be sacrificed. It will be interesting to analyse graphically other physiological systems undergoing adaptive regulation by the method of Fig. 2 and Fig. 3.

Figure 2.

Intestinal hypertrophy with hyperphagia: mass of a female mouse's small intestine as a function of the mouse's daily load intake, which increases during lactation and at low ambient temperature

Symbols: virgin mice at a temperature of 23 °C (•) or 5 °C (▴); lactating mice at 23 °C (□) or 5 °C (▵). Data are from Hammond & Diamond (1992, 1994) and from Hammond et al. (1994). Note that intestinal mass increases linearly with food intake, but with a slope of less than 1.0.

Figure 3.

The safety factor for the small intestinal brush border glucose transporter SGLT1 of female mice as a function of glucose intake, which increases during lactation, at low ambient temperature, and with increased pup mass

Data are from the experiments of Fig. 2 plus experiments involving increased pup mass. Symbols: virgin mice at a temperature of 23 °C (•) or 5 °C (▪); lactating mice at 23 °C (▿, ⋄) or 5 °C (□); lactating mice at 23 °C with pup mass increased above normal by experimentally prolonging the obligate period of lactation (▵). Note that the safety factor decreases towards 1.0 with increasing glucose intake, because glucose transport (proportional to intestinal mass) increases with glucose intake with a slope less than 1.0 (Fig. 2).

Unsolved questions

Within this framework, I see at least five major questions remaining unsolved.

Series systems.

In a system consisting of components operating in series, does one expect the components’ capacities to be equal to each other? A simple argument in favour of equal capacities is that such a design would avoid wasting energy on high-capacity components whose high capacity could never be utilized because lower-capacity components in series would always limit the performance of the whole system. If one component had a lower capacity than others, that one component would serve as a rate-limiting bottleneck, and increased system performance could be obtained merely by increasing the capacity of that one component.

However, other theoretical considerations besides that simple one apply to the design of series systems. Biochemists have argued that a single rate-limiting step in an enzyme reaction chain is advantageous, because regulation of that single step could then regulate system performance. Alexander (1997) has shown by a theoretical model that, if steps in series differ in coefficient of variation or else in expense of the capacity, and if the resources available for building the system are limited, then system performance is optimized by devoting resources to extra capacity for more variable or cheaper elements.

The experimental evidence available to date makes clear that there will not be one universal answer to this question of capacity matching in series and systems. In the few cases studied, tendons do not have the same capacities as the muscles with which they are in series (Alexander, 1981). Among the series systems of intestinal brush border hydrolases and nutrient transporters that my colleagues and I have studied, the capacities of sucrase and of the glucose transporter SGLT1 are matched in non-reproductive mice consuming a sucrose-based diet, but they differ in lactating mice (the factor for SGLT1 being double that for sucrase) (Weiss et al. 1998), while lactase capacity exceeds SGLT1 capacity in rat pups consuming a lactose-based diet (O'Connor & Diamond, 1999), and maltase capacity exceeds SGLT1 capacity in mice consuming a maltose-based diet (Lam et al. 2002). The question of capacity matching in series systems partly motivated Taylor, Weibel and colleagues to analyse mammalian aerobic exercise quantitatively, and they coined the term ‘symmorphosis’ to describe the case in which series capacities are matched to each other and to the load with safety factors near 1.0. In reality, they found that the heart, skeletal muscle capillaries, and skeletal muscle mitochondria had approximately matched capacities for oxygen transfer, but that the capacity of the lungs was higher (Weibel et al. 1991). We need much more experimental evidence before we shall understand the quantitative evolutionary design of series systems.

Parallel or branched pathways.

Complexities may be introduced into series systems by branching, i.e. a single element leading to two or more elements in parallel. Examples include intestinal brush border maltase activity, which arises from a total of three different active sites on two different proteins (Lam et al. 2002); and substrate pathways during aerobic exercise, comprising parallel carbohydrate and lipid pathways (Taylor et al. 1996).

Elements with multiple functions.

Many biological elements have more than one function. Such an element might possess excess capacity for one function, mandated by the need to have a sufficient quantity of the element present to provide enough capacity for a second function. For instance, each element of the mammalian O₂ transfer system — the heart, lungs, capillaries and mitochondria — does other things besides transferring O₂, such as transferring glucose, other nutrients, metabolic waste, and CO₂. Could a high safety factor and apparently large excess capacity for one of these functions result from the need to maintain a safety factor at least equal to 1.0 for another of these functions (Taylor et al. 1996)? Might the high safety factor for mouse brush border maltase capacity result from the fact that the enzymes responsible for maltase activity also hydrolyse starch (Lam et al. 2002)?

Enzyme reaction chains and equilibrium enzymes.

There is a large and controversial biochemical literature debating whether enzyme reaction chains generally possess a single rate-limiting regulated step, with excess capacities at other steps, as most biochemists believe, or whether they consist of steps with similar capacities. The latter point of view is associated with a school of thought termed metabolic control theory, which is fundamentally similar to the analysis that I have discussed in terms of safety factors, although the terminology employed is different (Cornish-Bowden & Cardenas, 1990). Part of the reason why controversy persists is that enzyme capacities (i.e. V_max values) are usually measured in homogenates under conditions not identical to those prevailing intracellularly under natural conditions, raising questions whether the measured capacities are physiologically realistic.

Another likely reason for the controversy was recognized by Staples & Suarez (1997), who noted that measured nominal safety factors are much higher for enzymes normally operating close to equilibrium (e.g. phosphoglucose isomerase) than for enzymes operating far from equilibrium (e.g. hexokinase). With the former but not the latter enzymes, there is normally a large back reaction so that the net reaction is only a small fraction of the forward reaction, whose safety factor thus appears artefactually high. When Staples & Suarez took this effect into account quantitatively for phosphoglucose isomerase by means of the Haldane equation, the resulting corrected safety factor was modest and reasonable. This interpretation is likely to be of wide relevance in interpreting enzyme safety factors.

What are the costs that penalize excess capacities?

Many capacities vary among individuals of a wild animal population within only narrow limits, with inter-individual coefficients of variation of 20 % or less. This implies strong natural selection against individuals with capacities either much above or much below the mean value. The penalty for too low a capacity is, obviously, performance failure: for example, an animal whose bones are too small and weak is prone to break its bones and be caught by a predator. But what penalty eliminates animals with much-higher-than-average capacities?

The answer frequently proposed is waste of energy or space. This explanation is plausible for elements that consume a large fraction of an animal's energy or body space. The energy available to an individual animal, and the space that its body occupies, are both finite. Excessive energy for synthesis, operation, or maintenance, or else excessive space, squandered on one element necessarily come at the expense of energy or space that could have been devoted to another element. Hence the overall performance of an animal overdesigned in one respect may be poorer than that of an economically designed animal. For instance, the small intestine occupies a large fraction of an animal's body cavity, and the kidney consumes a large fraction of resting blood flow and resting metabolism. These organs could not double in size without severely compromising the rest of the animal.

Cooper et al. (1993) have developed this argument quantitatively to explain the evolutionary reduction of the visual system in cave-dwelling or subterranean animals adapted to a life in darkness. The subterranean mole rat has its eyes reduced to the size of pinheads, its optic nerve reduced to less than 1000 fibres, and its brain area that would be devoted in sighted rodents to visual cortex pre-empted in the blind mole rat by somatosensory cortex. But the retina, brain and visual cortex are among the most expensive body tissues in their metabolism, and the subterranean lifestyle of the blind mole rate mandates expansion of other sensory modalities devoted to touch, smell, sound, seismic signals and magnetic compass orientation. By jettisoning most of its expensive but useless visual system, the blind mole rat frees up 2 % of its whole energy budget for other purposes. In the world of natural selection, a 2 % advantage is enormous and rapidly leads to fixation of alleles from such an advantage.

However, that argument in terms of the whole animal's energy budget or space cannot explain selection against overcapacity for elements consuming only a tiny fraction of the whole energy budget or space. For instance, brush border sucrase constitutes much less than 1 % of the protein in the intestine mucosa, which constitutes in turn much less that 1 % of the mass of the whole body. Measured against the energy or space of the whole animal, the consequences of doubling the amount of intestinal brush border sucrase would be utterly trivial. Why, then, don't mice have twice as much sucrase as they actually do, and why is the coefficient of variation of sucrase activity among individual mice only 10 %?

I hypothesize that the explanation has to do with competition for space at the molecular level. Just as we can see with our naked eyes that an animal's body cavity is crammed full of organs and is not a largely empty space, an electron microscope also shows us that a cell is crammed full of organelles and particles, and the lipid bilayer of biological membranes is crammed with membrane transporters in its interior and with hydrolases and antigens on its surface. A mouse could not afford to pack more sucrase onto its brush border membrane surface without reducing the amount of maltase, amino-oligopeptidase, or other surface enzymes and receptors and thus compromising the function of the whole mouse. Dykhuizen (1978) has suggested a similar argument to explain selection for auxotrophic bacterial mutants in solutions already containing the required substrate, even though — in the system that Dykhuizen studied, tryptophan-synthesizing E. coli — the tryptophan-synthesizing enzymes consume less than 0.01 % of the bacterium's energy budget.

With modern techniques of genetic engineering, this hitherto untestable hypothesis to explain evolutionary elimination of excessive reserve capacities can now at last be tested experimentally. A suggested experiment is to produce overexpression or underexpression of some biological membrane protein in a bacterium or mouse; to measure the resulting effect on the bacterium or mouse's growth rate, or on the bacterium's competitive ability in a chemostat; and thereby actually to calculate the costs of excess capacity in the units of fitness that population geneticists employ when studying natural selection.