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Communicated by John R. Roth, University of California, Davis, CA, December 19, 2005 (received for review January 10, 2005)
Abstract
That distinct enzyme activities in an unbranched metabolic pathway are evolutionarily tuned to a single functional requirement is a pervasive assumption. Here we test this assumption by examining the activities of two consecutively acting enzymes in human erythrocytes with an approach to quantitative evolutionary design that avoids the above-mentioned assumption. We previously found that avoidance of NADPH depletion during the pulses of oxidative load to which erythrocytes are normally exposed is the main functional requirement mediating selection for high glucose-6-phosphate dehydrogenase activity. In the present study, we find that, in contrast, the maintenance of oxidized glutathione at low concentrations is the main functional requirement mediating selection for high glutathione reductase activity. The results in this case show that, contrary to the assumption of a single functional requirement, natural selection for the normal activities of the distinct enzymes in the pathway is mediated by different requirements. On the other hand, the results agree with the more general principles that underlie our approach. Namely, that (i) the values of biochemical parameters evolve so as to fulfill the various performance requirements that are relevant to achieve high fitness, and (ii) these performance requirements can be inferred from quantitative systems theory considerations, informed by knowledge of specific aspects of the biochemistry, physiology, genetics, and ecology of the organism.
Although numerous mutations can drastically change the values of biochemical parameters such as enzyme activities, these values are often narrowly distributed in natural populations. This outcome owes largely to the interplay between constraints imposed by physicochemical laws and natural selection for good performance of the organism’s biochemical circuits. The strength of natural selection in shaping the design of living organisms at the molecular level ( 1) is just beginning to be appreciated. In humans, natural selection is strong enough to almost prevent fixation of mutations that decrease fitness by >0.002%. Furthermore, >70% of the amino acid-changing mutations are selected against ( 2, 3). In the many organisms that have larger effective populations, even smaller fitness differentials can drive natural selection. Understanding the quantitative design for biochemical parameters that has been achieved through natural selection (i.e., the qualitative and quantitative functional requirements that mediate their evolutionary tuning) is a goal of systems biology with far-reaching implications. Such understanding would provide valuable insight regarding physiological as well as evolutionary adaptation ( 4, 5) and guidance for metabolic engineering ( 6). However, this type of understanding for parameters such as enzyme activities remains limited.
The assumption that the distinct enzyme activities in a metabolic pathway are evolutionarily tuned to a single functional requirement, often identified with flux capacity, has dominated thinking in this area. In metabolic engineering, this assumption is implicit in approaches ( 7 ⇓– 9) relating enzyme activities to cellular performance, inasmuch as these approaches take for granted that such a relationship is mediated by the effects of the activities on the steady-state fluxes of the pathways in which the enzymes participate. In integrative physiology, attempts to explain the quantitative evolutionary design ∥ of enzyme activities (e.g., refs. 11 ⇓– 13) have also, in general, relied on the assumption in question. Accordingly, ratios greater than one for enzyme activities to flux capacity of the pathway were rationalized as “safety factors” that evolved to avoid failure under exceptionally heavy loads ( 14). However, observed mismatches among activities of sequential enzymes ( 15) are so large that their interpretation as safety factors with respect to flux capacity is implausible ( 16). Evolutionary ( 17, 18), developmental ( 19), and physiological ( 18) adaptations of activities of multiple glycolytic enzymes to conditions requiring increased glycolysis also have been interpreted on the assumption that attainment of the necessary steady-state glycolytic flux was the sole functional requirement justifying the observed changes of the various enzyme activities. However, the observation that the equilibrium enzymes (which are already more abundant and have low influence on flux) are up-regulated to a greater extent than the enzymes that have high influence on flux strongly suggests, instead, that additional performance requirements are at play. Evolutionary ecology studies in Colias butterflies ( 20) have shown that the loci for three enzymes that share a common substrate do experience very different selective pressures. However, these enzymes ( 20) feed different metabolic pathways that are active in different conditions.
A few theoretical analyses have examined unbranched pathways with respect to performance criteria other than flux ( 1, 21). However, these analyses have been in the context of abstract idealized systems (e.g., series of monosubstrate enzymes), and, when multiple criteria were considered ( 1), the influence of the various performance requirements on the activities of each of the different enzymes was not examined. In any case, theoretical analyses based on idealized models that overlook relevant features of real organisms cannot identify the performance requirements that mediate natural selection for each enzyme’s activity. Hence, they cannot prove or disprove the assumption of a common performance requirement or set of requirements. To overcome these limitations, one must examine specific biochemical systems.
To test the assumption that a common performance requirement mediates the evolutionary tuning of all of the distinct enzyme activities in a pathway, we compared the functional requirements mediating natural selection for normal activity of two well studied consecutively acting enzymes in human erythrocytes. The glucose-6-phosphate dehydrogenase (G6PD, EC 1.1.1.49) reaction regenerates NADPH, most of which ( 22) is used in the glutathione reductase (GSR, EC 1.6.4.2) reaction for regenerating reduced glutathione (GSH) that is oxidized to oxidized glutathione (GSSG) in prevention and repair of oxidative damage ( Fig. 1A).
Fig. 1.
Schematic representations of the oxidative part of the hexose–monophosphate shunt and relevant sources of oxidative load (A) and the simplified reaction network that captures the essential features of these pathways (B) (see Supporting Text section 1 for details) and that is used in our analysis. Cat, catalase; G6P, glucose 6-phosphate; GL6P, gluconolactone 6-phosphate; Glc, glucose; GO6P, gluconate 6-phosphate; G6PD, glucose-6-phosphate dehydrogenase; GO6PD, gluconate-6-phosphate dehydrogenase; GRX, glutaredoxin; GSH, reduced glutathione; GSSG, oxidized glutathione; GPx, glutathione peroxidase; GSR, glutathione reductase; HbSH, hemoglobin; HbSSG, glutathionyl-hemoglobin; HK, hexokinase; SOD, superoxide dismutase.
The activities of G6PD and GSR in human erythrocytes are responsive to natural selection: low-activity G6PD mutants (which protect against malaria) are prevalent where malaria is endemic ( 23), and the same has been argued about the prevalence of GSR mutants ( 24). However, despite that many different mutations cause G6PD or GSR deficiency ( 25), erythrocyte G6PD ( 26) and GSR ( 27) activities in human populations are narrowly distributed about the main mode, with typical standard deviations of <17% and <12%, respectively. These observations suggest the occurrence of natural selection against mild deficiencies of these enzymes in populations where malaria has low incidence. Using an approach to quantitative evolutionary design that avoids the assumption mentioned at the beginning of this paragraph, we have shown that the activity of G6PD in human erythrocytes is necessary to avoid NADPH depletion and ensure timely adaptation of NADPH supply during pulses of oxidative load that occur when erythrocytes interact with phagocytes ( 16). Here, we show that the normal activity of glutathione reductase does not significantly influence the homeostasis of NADPH concentrations, and we present strong evidence for the notion that normal GSR activity is necessary to keep the concentration of GSSG low. Taken together, our results identify two different functional requirements, one for each of the sequentially acting enzymes and neither of them related to steady-state flux, that mediate natural selection for the high activities of these enzymes. We argue that similar conclusions likely apply to many other systems.
Model Formulation and Strategy for Analysis
We base our analysis on the model shown schematically in
Fig. 1B, and that translates to the following system of equations (for detailed justification, see Supporting Text sections 1 and 2, Table 1, and, Figs. 4 and 5, all of which are published as supporting information on the PNAS web site):
with
To characterize the performance of a system, we must first identify the requirements that must be met by its state variables, namely concentrations and fluxes. In
Fig. 2, we outline the rationale for identifying the aspects of performance that mediate natural selection for the wild-type values of biochemical parameters. The physiological description and quantitative definition of 14 such requirements relevant for the system represented in
Fig. 1B are given in the Supporting Text section 3. These descriptions and definitions are an expanded version of those used in ref.
16 for the characterization of normal G6PD activity. To compare the activities of GSR and G6PD under a common set of requirements, we also reexamined the selection of G6PD activity in light of the additional requirements. The methods of analysis have been described in ref.
16.
Fig. 2.
Rationale for identifying the aspects of performance that mediate selection for the wild-type values of biochemical parameters. We consider a two-tiered effect of parameters on fitness. Tier 1 (lower part of the diagram) refers to the effect of the parameters on the various aspects of performance (P1, …, P4), whereas tier 2 (upper part of the diagram) refers to the effect of each aspect of performance on fitness. Any aspect of performance that mediates natural selection for the wild-type values of a parameter must satisfy the following two conditions with respect to variations of the parameter about its wild-type range: (i) it must be sensitive to that variation (thick lines in tier 1), and (ii) it must influence the organism’s fitness (thick lines in tier 2). Here, these conditions are satisfied by P2 for parameter 1 and by P3 for parameter 2.
Aspects of Performance Incapable of Mediating Selection for High GSR Activity
The buffering of NADPH concentration against changes in oxidative load was identified as the main functional requirement driving natural selection for high G6PD activities ( 16), and our reexamination did not change this conclusion ( Fig. 3A and C). Could the same functional requirement drive natural selection for high GSR activities? Clearly not, because the buffering of NADPH concentration against changes in oxidative load [low values of LNADPH (see Fig. 3 for definitions)] is not influenced by GSR activities down to ≈2% of normal ( Fig. 3B). Of the other 12 aspects of performance with potential for mediating selection of high values for G6PD and GSR activity, our analysis shows that 7 aspects have a flat characteristic about their normal values (Fig. 6, which is published as supporting information on the PNAS web site). These aspects of performance cannot propagate the effect of selection across tier 1 in Fig. 2 and are thus irrelevant for the evolutionary tuning of these enzyme activities. Here we present the results of our analysis for another 6 aspects that are also incapable of mediating selection but for reasons that are less intuitively obvious.
Fig. 3.
Dependence of metabolic performance on the activities of G6PD (A and C) and GSR (B and D) in human erythrocytes. For definitions and rationale for the performance indices, see Supporting Text section 3. Activities and performance indices are normalized with respect to their respective values in the wild type. (A and B) Log gain in NADPH concentration with respect to changes in oxidative load (LNADPH = ∂ log NADPH∕∂ log kox, black), and time for half-maximal response of NADPH supply to changes in oxidative load (t1/2,v1, cyan). (C and D) Steady-state concentration of GSSG (black), log gain in GSH concentration with respect to changes in oxidative load (LGSH = ∂ log GSH∕∂ log kox, red, overlapped by the black curve in both panels), and time for half-maximal response of GSH supply to changes in oxidative load (t1/2,v2, cyan, overlapped by the black curve in both panels). A value of LX = z means that X changes by z% when kox changes by 1%. Thus, low values of LX indicate good buffering of X with respect to the oxidative load. The indices t1/2,v2 and t1/2,v1 are obtained by calculating numerically the time for half-maximal response of NADPH supply (t1/2,v1) and of GSH supply (t1/2,v2) to a 2-fold increase in kox. Low values of t1/2 indicate fast responses. Thus, performance improves with decreasing values of the indices shown in this figure. Other potentially relevant aspects of performance are not influenced by changes in G6PD or GSR about their normal values (see Fig. 6).
The requirement for a fast response of the NADPH supply (low values for the time required to reach one-half the maximal response, t1/2,v1, Supporting Text section 3) also may help drive natural selection for high G6PD activity when this activity is insufficient to avoid large NADPH depletion ( 16). Given that t1/2,v1 decreases sharply with GSR activity near its normal values ( Fig. 3B), one might think that the requirement for low t1/2,v1 could drive natural selection for high GSR activities. However, within the context of the integrated system, analysis shows that higher GSR activities are, if anything, slightly disadvantageous. **
The above analysis suggests that different functional requirements mediate natural selection for high activities of G6PD and GSR. Nevertheless, the parallel roles of GSR and G6PD with regard to GSH and NADPH, respectively, might suggest that the functional requirements mediating natural selection for high GSR activity (regarding GSH) are cognate to those mediating natural selection for high G6PD activity (regarding NADPH). Namely, buffering of the GSH concentration with respect to changes in oxidative load (low values of LGSH), as a primary requirement, and a fast response of the GSH supply (low values of t1/2,v2), as a secondary requirement. Both LGSH and t1/2,v2 do indeed decrease with increasing GSR activity near its normal range. However, contrary to what happens with NADP+, even moderately elevated GSSG concentrations are deleterious (see Requirement for Low GSSG Concentrations Is Capable of Mediating Selection for High GSR Activity). For this reason, the requirement to maintain the concentration of GSSG low is much more relevant in mediating natural selection for high GSR activities. Before examining the relevance of GSSG concentrations for design, however, we will show why LGSH, t1/2,v2, and several other aspects of performance contribute negligibly to the selection for normal GSR activity.
Under basal load, the ratio 2GSSG∕GSH is very low, which results in LGSH being very small (≈10−4), and LGSSG being ≈1.0. Therefore, on the time scale relevant for this analysis, significant GSH depletion can occur only under heavy oxidative load, with a large accumulation of GSSG. On longer time scales, even moderate oxidative loads can significantly deplete GSH but only as a consequence of GSSG accumulation. As GSH depletion is significant only for long and∕or pronounced oxidative stresses, the normal responsiveness of GSH supply (t1/2,v2 = 0.94 s) also has little functional relevance. For near normal GSR activities and moderate oxidative loads, t1/2,v2 is representative of the temporal responsiveness of the GSSG concentration as well, because the rate of GSH regeneration is then proportional to the GSSG concentration and nearly independent of NADPH concentration. Nevertheless, t1/2,v2 also has little relevance for the time-average concentration of GSSG, because a lower t1/2,v2 will accelerate to the same extent both the accumulation of GSSG during a pulse of oxidative load and the restoration of the GSSG concentration after the pulse. A lower t1/2,v2 is even slightly disadvantageous by allowing higher GSSG concentrations to be reached during short pulses of oxidative load.
Although another two aspects of performance [robustness of NADPH supply (Iv1, Supporting Text section 3) and robustness of GSH supply (Iv2, Supporting Text section 3), where a small value for Iz means that none of the structural parameters have a strong effect on z] are strongly influenced by GSR activity in its normal range (blue curves in Fig. 6 D and H), they have little influence on fitness of the wild type because they are both too weak (Iv1,ref = 2.0 × 10−4 and Iv2,ref = 1.0 × 10−4) to cause significant variation of these rates over the physiologically plausible range of the structural parameters, even under moderate GSR deficiency. In summary, the aspects of performance discussed in this paragraph and the previous paragraph cannot propagate the effect of selection across tier 2 in Fig. 2.
The results in this section show that natural selection against mild deficiencies of G6PD and GSR cannot be mediated by the same or cognate functional requirements. However, we must still assess the hypothesis that the final aspect of performance, the requirement for keeping the GSSG concentration low, mediates selection against mild GSR deficiency.
Requirement for Low GSSG Concentrations Is Capable of Mediating Selection for High GSR Activity
GSR deficiency is a rare mutation, and therefore, epidemiological data about this condition are scant. However, the available biochemical data support the notion that elevated GSSG concentrations decrease fitness significantly. Increased GSSG concentrations are deleterious for two main reasons. First, they exacerbate the active efflux of GSSG, which is the main process depleting the erythrocytic glutathione pool. A pseudo-first-order rate constant of ≈0.02 s−1 for this process is estimated from the turnover time of the glutathione pool ( 28) and from the observation that the GSSG-stimulated ATPases have Kms ( 29) in >500-fold excess of the estimated basal concentration of GSSG (0.16 μM). Because in erythrocytes the glutathione pool can be replenished only very slowly through ATP-dependent de novo GSH synthesis ( 28) (which is independent of GSR), an increased efflux is energy wasteful. If sustained, this efflux also causes prolonged GSH depletion, thus compromising GSH-dependent processes that prevent and repair oxidative damage to cellular components and that eliminate toxic agents ( 30). The fact that erythrocytes actively excrete GSSG, despite the deleterious consequences of depleting the glutathione pool, strongly suggests that intracellular GSSG has other deleterious effects. Indeed, the data below support this conjecture.
Second, GSSG glutathionylates hemoglobin with a pseudo-first-order rate constant of ≈0.1 s−1 (with respect to GSSG) ( 31). In vivo, hemoglobin glutathionylation is probably substantially faster owing to catalysis by glutaredoxin ( 32). †† Thus, under moderate GSR deficiency, GSSG consumption by hemoglobin glutathionylation may outcompete GSR-catalyzed reduction, which has a pseudo-first-order rate constant of 0.75 s−1 at normal GSR activity. Furthermore, glutathionyl-hemoglobin has a long half-life: ≈15 min, as estimated from the concentration of glutaredoxin (≈1 μM) ( 34) and from kinetic data about this enzyme ( 32). In healthy individuals, 1.2–16% of total hemoglobin ( 35 ⇓– 37) is glutathionylated (although these high estimates have been challenged by ref. 38), and various situations that cause oxidative stress exacerbate glutathionylation ( 36 ⇓– 38). The glutathionyl-hemoglobin adduct has lower cooperativity at half-saturation and has a 4- to 10-fold higher oxygen affinity than hemoglobin A ( 39), making for poorer oxygen delivery to tissues. As physical performance of an individual is proportional to hemoglobin concentration in blood ( 40), a partial inactivation of the hemoglobin pool resulting from GSR deficiency should reduce physical performance. Glutathionylation through thiol–disulfide exchange with GSSG inhibits various glycolytic enzymes as well ( 41) (Supporting Text section 4).
The Michaelis–Menten kinetics of GSR dictate that the (quasi)steady-state concentration of GSSG must increase near linearly with oxidative load (LGSSG ≈ 1) if the ratio 2GSSG∕GSH is to remain small (Supporting Text section 5). Occasional accumulation of GSSG is thus unavoidable as erythrocytes are exposed to pulses of heightened oxidative load as a result of various physiological and pathological processes such as circulation through pulmonary capillaries, contact with phagocytes (at inflammatory sites or during immune clearance), and some modalities of physical exercise ( 42 ⇓– 44).
The wild-type values of the structural parameters of this system are consistent with its being designed for maintenance of low GSSG concentration. Indeed, all but two of the parameters have a considerable range around their wild-type value over which the steady-state concentration of GSSG is nearly minimum (Fig. 7, which is published as supporting information on the PNAS web site). The values for the remaining two parameters, kox and KM,GSSG, are also consistent in the following sense: As noted in the previous paragraph, the buffering of GSSG concentrations with respect to changes in kox (LGSSG ≈ 1) is very nearly as good as it can be for this system if the ratio 2GSSG∕GSH is to remain small. The near-linear dependence of GSSG concentration on KM,GSSG is a necessary consequence of the system exhibiting a near maximum response of the GSH supply in response to an increased oxidative load [Lv2 ≈ 1 (Supporting Text section 5)].
Discussion
Any effective approach to analyzing evolutionary adaptations must avoid the pitfalls highlighted by Gould and Lewontin ( 45) in their critique of the adaptationist program. We have addressed these pitfalls as follows: We avoid atomization into “traits” by (i) considering an integrated system (earlier sections and Supporting Text sections 1 and 2) and (ii) explaining in detail (Supporting Text sections 1.1, 1.4, and 2) how known or plausible interactions with metabolic components external to the system might affect the conclusions. We avoid overlooking constraints by considering only variations in design that are consistent with known physicochemical constraints of the analyzed system. Many of these constraints are embodied in the mathematical model as explained in Supporting Text sections 1.2 and 1.3. When many physicochemical constraints are imposed on a system, the freedom to speculate about purported adaptations (or accidental occurrences) is severely restricted. To avoid overlooking alternative explanations for the design, we consider an extensive list of potential explanations, including nonadaptive ones. Indeed, our analysis identifies nonadaptive features of the system as well as adaptive ones. Our analysis makes falsifiable predictions, which can be tested against biochemical, genetic, epidemiological, and clinical data. Finally, our aim is not to address the historical evolution of the present design but to identify the functional constraints that, at present, contribute to its maintenance. Our analysis is thus incapable of confusing the present utility of a trait with the reasons for its historical evolution.
Although one might expect two sequential steps in a physiological process to experience similar selective pressures, our results demonstrate that the G6PD–GSR pathway contradicts this expectation. The normal activity of G6PD is under selective pressure by virtue of its ability to diminish the depletion of NADPH after an increase in oxidative load, whereas the normal activity of GSR has no effect on this response ( Fig. 3 A and B). Conversely, the normal activity of GSR is under selective pressure by virtue of its ability to minimize the accumulation of GSSG, whereas the normal activity of G6PD has no effect on this response ( Fig. 3 C and D).
The nature and time scale of the physiological processes mediating selection for high activities of each enzyme also differ. Only pronounced oxidative stresses cause a large enough NADPH depletion ( 16) to mediate natural selection for normal G6PD activities. Erythrocytes are only briefly exposed to such heavy oxidative loads, which occur when interacting with activated phagocytes ( 43, 46). A different situation holds for GSR. The most deleterious consequences of increased GSSG concentrations (depletion of GSH, of the overall glutathione pool, and of hemoglobin glutathionylation) occur on a slower time scale than the pulses of oxidative load caused by interaction with phagocytes. However, the Michaelis–Menten kinetics of GSR dictate that the (quasi)steady-state concentration of GSSG must increase nearly linearly with oxidative load (Supporting Text section 5). Therefore, oxidative stresses (such as those elicited by physical exercise or by diet) that are too modest to cause significant NADPH depletion may nevertheless cause significantly increased GSSG concentrations and excretion. Such sustained oxidative stresses are more relevant for natural selection of high GSR activities than those caused by intense but short pulses of oxidative load.
Our results clarify why flux capacities (e.g., enzyme activities) of adjacent components of a serial process ( 4) can not only greatly exceed the flux capacity of the process but also be strongly mismatched ( 15); such excess and mismatched capacities may be a side effect of distinct components having each evolved to meet qualitatively different functional demands. Selection for one aspect of performance can lead, as side effects, to large safety factors ( 14) for other aspects of performance (e.g., enzyme activities much greater than the flux capacity of the pathway). In contrast, the functional advantages of safety factors that greatly exceed the normal variability of the loads are too weak to mediate the selection for further investment in a component. Therefore, comparisons of safety factors measured in terms of the wrong reference may lead to misinterpretation in studies of quantitative evolutionary design. This assertion is true when it is assumed that the same criteria apply to all of the components and that all capacities are referred to these same criteria, when in fact different criteria apply to each of the distinct components. Our work suggests a more meaningful comparison of safety factors by insisting that these factors be measured separately for each component and in reference to the actual criteria that are influencing their individual design.
Our results also show that modulating the levels of the different enzymes that catalyze the sequential steps of a pathway can affect different aspects of performance, even when the steady-state flux remains virtually unchanged. In contrast, several approaches ( 7 ⇓– 9) attempting to relate enzyme activities to cellular performance rely on the assumption that this relationship is mediated by the effect of the activities on steady-state fluxes. These approaches are thus prone to two types of errors. First, they underestimate the functional consequences of modulating gene expression, especially for the many enzymes ( 19, 47) whose normal activities have little influence on the steady-state flux of the embedding pathways. ‡‡ Second, they incorrectly predict that similar functional consequences ensue when changes in any two enzymes of the same metabolic branch yield the same change in flux.
Although one might consider the same network topology from the engineering perspective of an analogous electrical circuit, it is unreliable to derive functional consequences from network topology alone. Unlike electronic circuits, whose nodes represent undifferentiated current summation points, in biochemical networks each node represents a metabolite with distinctive chemical properties. These distinctive properties are relevant for design. For instance, the topological “homology” between GSR and G6PD with respect to the GSH and NADPH redox cycles, respectively, suggests increased susceptibility to GSH depletion as the primary functional consequence of moderate GSR deficiency. However, because GSSG, in contrast to NADP+, has a significant nonspecific reactivity, the increased GSSG concentration is far more relevant.
The notion that different performance requirements may mediate natural selection for high activities of different enzymes in a pathway and the realization of the importance of the intrinsic chemical properties of metabolic intermediates help to elucidate a puzzling but recurrent finding in evolutionary physiology. Namely, adaptation to conditions that require higher glycolytic flux in muscle cells is accompanied by a large increase in the concentrations of the enzymes that catalyze steps near equilibrium, but a modest increase in the enzymes that catalyze reactions far from equilibrium ( 17 ⇓– 19). Furthermore, among the latter enzymes, only those downstream in the pathway (enolase and∕or pyruvate kinase) are significantly up-regulated ( 18, 19). For example, this pattern is found in fish populations adapting to different water temperatures ( 18), across fish species ( 17), and in comparisons between slow-twitch and fast-twitch myotomal muscles in fishes ( 19). Attempts to understand these observations in terms of flux control ( 18, 19) leave important questions unresolved: The same increase in flux could be achieved more economically through a modest up-regulation of one of the enzymes that has a large influence on flux and that is present at low concentrations. Why then is a strong up-regulation of the near-equilibrium enzymes that are already in high concentration necessary? And why, among the nonequilibrium enzymes, only the downstream ones are significantly up-regulated? Well supported answers to these questions would require a detailed analysis of the glycolytic pathway, which lies beyond the aims of the present work. Nevertheless, the following considerations seem illuminating.
Should the increase in flux be achieved through up-regulation of an upstream enzyme, the concentrations of glycolytic intermediates would markedly increase. Some intermediates, such as fructose 6-phosphate and glyceraldehyde 3-phosphate, are powerful protein glycation agents ( 48). Because glycation irreversibly inactivates proteins, the levels of these reactive intermediates should be kept low and should be robust to changes in the kinetic parameters. Additionally, accumulation of intermediates would undesirably slow the response of pathway flux to abrupt changes in energetic demand. Analytical calculations for a simple unbranched pathway (A.S. and M.A.S., unpublished data) and numerical results for a simple model pathway that was parameterized to resemble glycolysis ( 49) indicate that up-regulation of the equilibrium and downstream nonequilibrium enzymes achieves increased flux without the previous disadvantages. In metabolic engineering, it has also been found that large increases in some enzyme activities intended to increase flux over a pathway actually lead to growth inhibition owing to accumulation of toxic metabolic intermediates ( 50). The problem is overcome by overexpressing an enzyme that catalyzes the consumption of the toxic intermediate through an alternative pathway ( 50).
We have shown that the activities of enzymes in a two-step pathway are evolutionarily tuned to fulfill different functional requirements. The same can happen in pathways of any length. Moreover, our approach can in principle be used to investigate the quantitative evolutionary design of virtually any biochemical parameter in networks of arbitrary topology. Enough information must be available, however, for (i) quantitative mathematical modeling to show the effect of the parameters on the pertinent performance indices and (ii) demonstrating the relevance of these performance indices for organism fitness. Finally, our approach is relevant to detecting natural selection ( 51). The presently available methods, based on genetic and sequence analysis, pinpoint genetic loci that are subject to selection but tell little about the factors that mediated selection at those loci. Furthermore, the application of these tests to human populations is riddled with uncertainties, as pointed out in a recent review ( 51) that concludes:
The only current safeguard against gross misinterpretation of test results vis-à-vis selection vs. historical demography is to have an a priori hypothesis about the type and direction of selection that are expected for the locus under investigation.
Our approach can generate such a priori hypotheses and indicate which aspects of performance mediate selection at the identified loci.
Supplementary Material
Supporting Information[pnas_0510776103_index.html][pnas_0510776103_4.pdf][pnas_0510776103_5.pdf][pnas_0510776103_1.pdf][pnas_0510776103_2.pdf][pnas_0510776103_3.pdf][pnas_0510776103_10776Fig4.jpg][pnas_0510776103_Image120.gif][pnas_0510776103_Image121.gif][pnas_0510776103_Image122.gif][pnas_0510776103_Image123.gif][pnas_0510776103_Image124.gif][pnas_0510776103_Image125.gif][pnas_0510776103_Image126.gif][pnas_0510776103_Image127.gif][pnas_0510776103_Image128.gif][pnas_0510776103_Image129.gif][pnas_0510776103_Image130.gif][pnas_0510776103_Image131.gif][pnas_0510776103_Image132.gif][pnas_0510776103_Image133.gif][pnas_0510776103_Image134.gif][pnas_0510776103_Image135.gif][pnas_0510776103_Image136.gif][pnas_0510776103_Image137.gif][pnas_0510776103_Image138.gif][pnas_0510776103_Image139.gif][pnas_0510776103_Image140.gif][pnas_0510776103_Image141.gif][pnas_0510776103_Image142.gif][pnas_0510776103_Image143.gif][pnas_0510776103_Image144.gif][pnas_0510776103_Image145.gif]
Acknowledgments
We thank Dr. Rui Alves (Faculty of Basic Medical Sciences, University of Lleida, Spain) for a critical review of the manuscript and Dr. Winchil Vaz (Chemistry Department, University of Coimbra, Portugal) for support. This work was supported in part by U.S. Public Health Service Grant R01-GM30054 (to M.A.S.) and fellowships from the Portuguese Fundação para a Ciência e a Tecnologia (SFRH∕BPD∕9457∕2002) and Pfizer (to A.S.).
Footnotes
- ↵¶To whom correspondence should be addressed. E-mail: masavageau{at}ucdavis.edu
Author contributions: A.S. and M.A.S. designed research; A.S. and M.A.S. performed research; A.S. contributed new reagents/analytic tools; A.S. and M.A.S. analyzed data; and A.S. and M.A.S. wrote the paper.
Conflict of interest statement: No conflicts declared.
↵∥ “Quantitative evolutionary design” has been defined as “the quantitative relationship of biological capacities to each other and to the peak natural loads on them”( 10). However, comparisons between capacities with respect to a single functional requirement fail to yield insight on the evolutionary tuning of physiological parameters when different functional requirements mediate the tuning of distinct parameters. Our results suggest that the latter should often be the case, thus prompting us to redefine the problem of quantitative evolutionary design in the more general sense used in this paper. Namely, we use the term to mean the problem of identifying the qualitative and quantitative functional requirements that mediate the evolutionary tuning of biological parameters and evaluating the extent to which the parameters are matched to those functional requirements.
↵** This result follows because the normal G6PD activity is sufficient to avoid large NADPH depletion ( 16). Furthermore, if significant depletion were to occur, an increased GSR activity can lower the response time t1/2,v1 only by making the demand for NADPH increase rapidly (i.e., by lowering the response time t1/2,v2) as well, with the net effect of accelerating NADPH depletion.
↵†† The evolutionary maintenance of a glutaredoxin activity, despite the apparent functional disadvantage of accelerating thiol exchange between GSSG and hemoglobin, may be explained by two functional advantages. First, the coupling of GSSG reduction to NADPH oxidation, by means of GSR, drives the glutaredoxin reaction in the protein deglutathionylation direction in most circumstances. This activity is important because GSH can also glutathionylate proteins without mediation by GSSG, though at a lower rate ( 33). Second, glutaredoxin-catalyzed thiol exchange between GSSG and proteins permits temporarily using the protein-thiol pool to regenerate GSH under strong NADPH depletion.
↵‡‡ If, as seems likely, the glycolytic pathway represents the typical situation, most enzymes are excess-activity enzymes, and these are usually also the most abundantly expressed enzymes in each pathway ( 19, 47). Much, if not most, of the cellular protein with enzymatic activity may thus be fulfilling functional requirements other than flux capacity.
- Abbreviations:
- G6PD,
- glucose-6-phosphate dehydrogenase;
- GSH,
- reduced glutathione;
- GSSG,
- oxidized glutathione;
- GSR,
- glutathione reductase.
- Received January 10, 2005.
- © 2006 by The National Academy of Sciences of the USA
References
Evolution of enzymes in a series is driven by dissimilar functional demands
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Image courtesy of Sean Peterson (photographer).
QnAs with NAS member and plant biologist Sheng Yang He
Image courtesy of Sheng Yang He.