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Home , Biochemistry

Energy and Raul K. Suarez*1

ABSTRACT Although firmly grounded in metabolic , the study of energy metabolism has gone well beyond this discipline and become integrative and comparative as well as ecological and evolutionary in scope. At the cellular level, ATP is hydrolyzed by energy-expending processes and resynthesized by pathways in . A significant development in the study of bioenergetics is the realization that fluxes through pathways as well as metabolic rates in cells, tissues, organs, and whole are “system properties.” Therefore, studies of energy metabolism have become, increasingly, in systems . A significant challenge continues to be the integration of phenomena over multiple levels of organization. Body mass and temperature are said to account for most of the variation in metabolic rates found in . A mechanistic foundation for the understanding of these patterns is outlined. It is emphasized that , leading to to diverse lifestyles and environments, has resulted in a tremendous amount of deviation from popularly accepted scaling “rules.” This is especially so in the deep sea which constitutes most of the biosphere. C 2012 American Physiological Society. Compr Physiol 2:2527- 2540, 2012.

Introduction The study of the biology of energy expenditure has become part of the research agenda of comparative (112). Cells expend energy mainly in the synthesis of large The most noble aim of the , , active transport across membranes, and the per- often discussed when inebriate, seldom when sober, formance of mechanical work. These are made possible by is to relate the in vitro to the in vivo group transfer and reactions involving ATP. Under Chantler (20). steady-state conditions, ATP concentrations remain relatively stable because rates of synthesis are matched to rates of hy- Energy metabolism has been the subject of much research drolysis. As cells change the rates at which they engage in for over a century. The intricate details of the reactions in- , active transport, or mechanical work, regulatory volved as well as the structures and properties of the mechanisms ensure that rates of ATP synthesis are dynami- that catalyze them now fill multiple chapters in undergradu- cally matched to rates of ATP hydrolysis. ATP turnover is the ate textbooks. So much is known about the subject that it is central process of cellular energy metabolism (2). often regarded by nonspecialists as a static collection of facts. Given the complex, multicellular nature of , purely However, new discoveries and advances in the understand- biochemical, reductionist approaches to the study of bioener- ing of biochemical processes underlying energy metabolism getics provide a very incomplete picture of the process. The continue to be made. While many continue to metabolism of an consisting of multiple and focus primarily on questions concerning mechanisms, oth- types, supplied with metabolic fuels and O2 by a circulatory ers have joined with physiologists, expanding the scope of system and displaying a rate of physiological that is investigations to address functional significance. Thus, the regulated according to the needs of the whole cannot study of energy metabolism in animals has evolved to be- be explained solely on the basis of biochemical phenomena come much broader, more integrative and, therefore, physio- occurring within individual cells. It is the animal, consisting logical. Studies of energy metabolism address a wide range of multiple (metabolizing) organs, that displays a whole-body of questions concerning how the enzymes and pathways of metabolic rate that changes with the animal’s behavior and re- bioenergetics operate in vivo, how metabolism is integrated sponds to changes in its environment (Fig. 1). Thus, to address over multiple levels of biological organization and regulated a wide range of questions, metabolic rates are measured at over time courses ranging from seconds to years. Evolution- rest, or as time-averaged values in the field, as values elevated ary processes have made animals structurally and function- ally diverse as well as adapted to a wide range of environ- *Correspondence to [email protected] mental conditions. Therefore, in addition to asking whether 1Department of , Evolution and , University of metabolic rates adapt physiologically within the lifetimes of California, Santa Barbara, California individual animals, researchers ask whether adaptation occurs Published online, October 2012 (comprehensivephysiology.com) across generations, whether evolution gives rise to qualitative DOI: 10.1002/cphy.c110009 or quantitative variation in pathways, enzymes, and fluxes. Copyright C American Physiological Society

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found in most, if not all, animal species. Biochemists have been profoundly impressed by what they consider to be the highly conserved nature of organisms at the molecular level, that is, the unity of . Upon further investigation, compara- tive physiologists and biochemists came to realize that there is considerable diversity within this apparent unity (67). Cell types within an as well as homologous cells across species vary in terms of the kinds or amounts of enzymes that they express; such variation commonly leads to variation in the extent to which fuels and pathways are used for energy metabolism. In-depth coverage of adaptive variation in kinds of enzymes (e.g. in relation to temperature, hydrostatic pres- sure, and solute microenvironment) is beyond the scope of this article; excellent introductory accounts have been published and updated over the past decades (65 and 66). With respect to concentrations, there is a well-developed concep- tual framework (83, 84, 110) for the use of maximal enzyme activities, i.e., Vmax values, measured in vitro, as measures of the maximum capacities for flux through these pathways in vivo. In this context Figure 1 The transport of fuels and O2 to cells at various rates of energy expenditure [from Weibel (134), with permission]. The illustra- = × , tion emphasizes how, at basal metabolic rate (BMR), ATP hydrolysis Vmax [E] kcat by processes such as biosynthesis and transport mainly determine the rate of whole-body energy metabolism. Physical activity results in where [E] is enzyme concentration and k is catalytic effi- increasing contribution to ATP hydrolysis by muscle work such that, at cat maximum metabolic rate (MMR or V˙O2max), 90% or more of whole- ciency or turnover number. In general, the kcat values of or- body metabolic rate is due to the respiration of muscle mitochondria. thologous enzymes purified from animals with similar body It is proposed that, at BMR, energy expenditure dominates the control temperatures are remarkably similar (66, 67). Thus, interspe- of whole-body V˙O2 while, at MMR, processes involved in the delivery of fuels and/or O2 to cells contribute to the control of V˙O2max (34). cific or inter-tissue variation in Vmax is due to variation in [E]. It is possible to compare maximum capacities for flux, estimated using this approach, with physiological rates of flux during exercise, digestion, lactation, thermogenesis, osmoreg- in vivo. This approach has been used, for example, to deter- ulation or depressed during hibernation, anoxia, dessication, mine the main substrates and pathways used by the locomo- or estivation. The importance of a fundamental understanding tory muscles of many species of and invertebrates of the mechanisms underlying temporal, mass-dependent, on- (27-29, 123, 149). togenetic, intrapopulation, or interspecific variation in rates of energy metabolism has become recognized across biological disciplines. However, the scope of the subject is so enor- Understanding metabolic regulation mous that an introduction to it is necessarily incomplete and Critical to the study of energy metabolism is a basic un- idiosyncratic. This one is intended for readers with a basic derstanding of metabolic biochemistry. The qualitative and background in physiology and biochemistry. It serves as a quantitative variation observed in bioenergetic pathways can gateway to some key concepts that have emerged, as well as be understood in light of these basic principles, but gain bio- the literature pertinent to them. logical meaning in the context of ecology and evolution. Enzyme-catalyzed reactions in multistep pathways dif- Biochemical Underpinnings fer in their thermodynamic and kinetic properties. In the glycolytic pathway, for example, certain reactions (glyco- Anything that is true of E. coli must be true for elephants, gen , , and ) are except more so held far from equilibrium in vivo; that is, the ratios of [prod- (in a discussion in 1954). uct]/[] of these reactions in vivo are much less than

The complete combustion of compounds to CO2 + their respective equilibrium constants, measured in vitro.As H2O leads to the production of heat. However, in biolog- a result, their Gibbs free energy changes, G, are large and ical systems, the operation of pathways for the oxidation negative, given of , , and amino acids leads to both heat production—Kleiber’s “Fire of Life” (73), as well as the step- G = Go − RT ln[]/[substrate], wise, regulated capture of some of the energy contained in these compounds through the synthesis of ATP (2). Glycol- where, Go is the standard Gibbs free energy change (es- ysis, the Krebs cycle, and oxidation are pathways timated in vitro), R is the gas constant, and T is absolute

2528 Volume 2, October 2012 Comprehensive Physiology Energy and Metabolism temperature. These reactions are considered to be thermo- single rate-limiting step has fallen into disfavor (49). Flux is dynamically irreversible in the cell. The Vmax values of en- considered a system property and its control tends to be shared zymes catalyzing such reactions are commonly measured to by multiple steps, including enzyme-catalyzed reactions and estimate upper limits to flux at nonequilibrium steps in path- . The degree to which the control of flux ways (83,84). In contrast, other reactions are maintained close is shared by multiple steps can be empirically determined by to equilibrium in vivo; that is, [product]/[substrate] ratios of estimation of flux control coefficients, Ci, which represent the these reactions in the cell are close to their respective equilib- degree to which various steps, i, contribute to the regulation of rium constants. These reactions are reversible in vivo and the flux, J. Ci is expressed, for any step, as the fractional change rate of net flux is the difference between forward and reverse in flux (δJ/J) that occurs in response to a fractional change in fluxes. Both the rate and direction of net flux can change in enzyme activity (δei/ei): response to changes in [product]/[substrate] in the cell. The = δ / / δ / . nature of such steps in pathways is such that their Vmax values Ci ( J J) ( ei ei ) are typically much greater than the rate of pathway flux. In It is possible to experimentally determine C values for , for example, enzyme Vmax values 2 to 3 orders i of magnitude greater than flux are not unusual. It is a rather various enzyme-catalyzed steps or transport processes in path- common notion that pathways have “excess enzyme” in the ways such as glycolysis (71), fatty acid oxidation (42) and sense that there is more enzyme than is needed to sustain mitochondrial respiration (10) using a variety of approaches pathway flux. However, this is an oversimplification of the including genetic manipulation, inhibitor , bottom-up, or top-down control analysis. It is also possible to quantify situation in vivo. For example, the Vmax of phosphoglucose (PGI) in honeybee flight muscles is about 30-fold the extent to which ATP-utilizing processes contribute to the greater than the rate of glycolytic flux during flight. Model- rate of cellular energy metabolism relative to the contribution ing the reaction according to the Haldane relationship (58) made by ATP-synthesizing pathways (16). Ci values of dif- ferent steps in a pathway or of different processes in a cell reveals that this is the Vmax required for net flux to occur at the rate required during flight while the enzyme maintains can dramatically change, depending on physiological circum- stances (Fig. 2). Fell (49) provides an excellent and accessible near-equilibrium (109). Thus, in this example, the Vmax for PGI is, in Diamond’s words, “enough but not too much” (38). introduction to the theory and practice of metabolic control While the rules of “solution biochemistry” might be sup- analysis as applied to the analysis of the control of flux at the ported by much empirical data (e.g. references 25, 71, and biochemical level. 129), it is necessary to consider alternative possibilities. It is An issue that often arises in comparative physiological possible, perhaps likely, that metabolism does not happen in studies of metabolic design, fuel use, and flux concerns the a homogeneous “soup” (137, 143). For example, it has been “rate-limiting step.” It was previously thought that if the rate- suggested that the Krebs cycle enzymes operate in the mito- limiting step of a pathway could be identified, then measure- chondrial matrix under conditions so crowded that the rules ment of the Vmax of the enzyme catalyzing this step would of solution biochemistry may not apply (107, 108). Instead, make possible the prediction of the maximum physiological the Krebs cycle enzymes may operate as part of a multien- flux rate in vivo (83,84). Metabolic control analysis, of course, zyme complex, the “” (93), wherein Krebs cycle has made this a nonissue. In addition, it is now realized that intermediates are handed directly from one enzyme to the next in a process called “metabolic channeling” (124). When 1.0 glycolytic enzymes are genetically modified such that they no longer localize at specific parts of myofibrils in Drosophila 0.8 flight muscles, the flies can no longer fly (148). The hexok- inase isoform that binds to porin on the outer mitochondrial 0.6 membrane preferentially uses ATP obtained from the translocase to phosphorylate over ATP in 0.4 bulk solution (146). There is evidence of metabolic channel- ing in other processes and pathways, but whether “structured metabolism” and channeling occur in all cell types is not 0.2 clear. It is also unclear whether some, most, or all of the

flux in metabolism occurs via channeling or whether the de- respiration Flux-control coefficient over 0204060 80 100 gree of channeling might change under various circumstances Respiration rate (% of state 3) (111, 137). Figure 2 Flux control coefficients of ATP turnover (solid line), sub- strate oxidation (thick dashed line), and leak (thin dashed line). Flux is a system property Results from top-down control analysis show how contributions to con- trol change as the system approaches 100% of state 3 respiration rate. With the development of metabolic control theory and its Adapted, with permission, from Suarez and Darveau (114); redrawn, application as metabolic control analysis, the concept of the with permission, from Brand et al. (10).

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whether the maximum rate of flux of a pathway in vivo ever tative anaerobes that use O2 for mitochondrial ATP synthesis matches the Vmax values of any of the enzymes catalyzing when it is available, but switch to pathways similar to those nonequilibrium reactions is an empirical question. Because in helminths when anaerobic. Under anoxic or hypoxic con- of the need to regulate flux through pathways, it has been ditions and, in some cases, during exercise, many species of argued that metabolic enzymes should not operate at Vmax in marine mollusks also produce a variety of anaerobic end prod- vivo (2). Even in the case of glycolysis, which displays some ucts including octopine (51), alanopine, or strombine (52). of the highest metabolic flux rates known, enzymes typically The production of these compounds is catalyzed by opine do not operate at Vmax (122). Nevertheless, it is important to dehydrogenases in reactions considered to be functionally add that enzyme Vmax values can be used to address various equivalent to that catalyzed by lactate dehydrogenase (LDH). types of questions (110), including those asked in metabolic Whereas vertebrates use only creatine as their control analysis (e.g. references 71 and 75). muscle phosphagen compound, across invertebrate species, With such heavy emphasis on biochemistry must come a there is great variation in phosphagens as well as in the phos- reminder that many species of animals transport O2 from the phagen that catalyze their synthesis and breakdown external environment to mitochondria in various cell types, (43, 44). tissues, and organs via diffusive and convective steps through Figure 3 is a simplified diagram of the main pathways respiratory and cardiovascular systems. It seems clear that used in and fatty acid oxidation in cardiac, fast basal metabolic rate (BMR) values in mammals, for example, and slow oxidative muscles of animals. Figure 4 are determined by rates of energy expenditure by internal or- shows carbohydrate oxidation in insect flight muscles. These gans (34,115,116,132), rather than by delivery rates through are used for comparison to illustrate the paradox of unity and a distribution system. At the maximum aerobic metabolic diversity in cellular bioenergetics. The examples have in com- rates achieved during exercise (Vúo2max), when 90% or more mon glycolysis, the Krebs cycle and, although not shown, the of whole-body metabolic rate is accounted for by muscle mitochondrial pathways and mechanisms for electron trans- mitochondria, control is shared by multiple steps in the O2- port, proton pumping, and ATP synthesis. Despite these simi- transport pathway (36,37,70,131) (Fig. 1). Clearly, elephants larities, carbohydrate oxidation in vertebrate and insect flight must differ from Escherichia coli in terms of the control of muscles differ with respect to the mechanisms used to main- metabolic rate and approaches that transcend the study of tain the high cytoplasmic [NAD+]/[NADH] ratios required cellular biochemistry must be adopted to gain a more com- for high glycolytic flux. Two shuttles that transfer reducing plete understanding of energy metabolism and its regulation equivalents from the cytoplasmic to mitochondrial compart- in animals. ment are known. These operate through the enzyme-catalyzed reduction of a in the cytoplasm; this leads to oxida- tion of cytoplasmic NADH to NAD+. The reduced compound Variations on Common Themes is then transported into the matrix, where it is oxidized. The oxidation reaction is accompanied by the reduction of NAD+ Enzyme Vmax data (27-29, 83) as well as other lines of to NADH or FAD to FADH2 in the mitochondrial matrix. evidence, for example, from studies of mitochondrial The net effect is the transfer of reducing equivalents from substrate preferences in vitro (80, 113, 117), make possible the cytoplasm to the mitochondrial matrix. Operation of both the construction of metabolic maps showing the major malate-aspartate (Fig. 3) and 3-phosphate shuttles routes of carbon flow through catabolic pathways in energy can be demonstrated in mitochondria isolated from vertebrate metabolism. Such studies have revealed that pathways muscles (7). In contrast, insect flight muscles that rely heav- of energy metabolism are most highly conserved among ily or exclusively on carbohydrate oxidation (e.g. bees) use vertebrate animals. However, despite such conservatism, the glycerol 3-phosphate shuttle (Fig. 4) and are completely levels of expression of elements of the metabolic machinery incapable of using fatty acids to fuel metabolism during flight for ATP synthesis can vary tremendously, reflecting lifestyles (98). Vertebrate muscles typically express high activities of and environments. Mitochondria occupy less than 5% of LDH and, under certain circumstances (e.g. when glycolysis muscle cell volume in some species but as high as 35% in serves as the main source of ATP during burst exercise), accu- hummingbirds (119) and 51% in some Antarctic fish (69). mulate lactate as an anaerobic end product. In contrast, energy The Vmax values of orthologous glycolytic and Krebs cycle metabolism during flight in insects functions as an obligately enzymes can vary by as much as a 1000-fold when comparing aerobic, O2-dependent, process (65). the muscles of sluggish, deep-sea species (21, 41) with those Such examples of variation on the common themes of of high-speed predators such as tunas (56, 57). energy metabolism are seen in enzymatic capacities for fuel Given their long evolutionary histories and degrees of use. For example, among vertebrates as well as in insects, evolutionary divergence, it is not surprising that greater vari- muscles that rely more on exogenous (blood or haemolymph) ation on the common themes of energy metabolism would be glucose to fuel energy metabolism display higher hexokinase found among invertebrate taxa. Parasitic helminth worms are Vmax values (28, 117, 123, 149) than muscles that rely more obligately anaerobic and make lactate, acetate, and propionate on endogenous stores of . Those that rely more on as end products (78). Marine intertidal invertebrates are facul- glycogen and less on exogenous glucose as the carbon source

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GLUCOSE HK Glu Glu Oxa

GLYCOGEN G6P FATTY ACID Asp Asp 2- KGA NADH

NAD 2-KGA Oxa Fatty acylCoA

GAP Mal Mal CPT NAD NADH Fatty acylcarnitine Fatty acylcarnitine NADH NAD CT carnitine carnitine 1,3DPG CPT

Pyruvate Pyruvate Fatty acylCoA

AcetyCoA

Oxaloacetate Citrate

KREBS CYCLE

CYTOPLASM MITOCHONDRION CYTOPLASM

Figure 3 Pathways of glucose (left) and fatty acid oxidation (right) in vertebrate muscles, highly simplified, and redrawn, with permission, from Suarez et al. (120). Readers are encouraged to consult a biochemistry textbook for details. Diagram shows the role played by the malate-aspartate shuttle in maintaining high cytoplasmic [NAD+]/[NADH] during the oxidation of glucose. Abbreviations: HK, hexokinase; G6P, glucose 6-phosphate; GAP, glyceraldehyde 3-phosphate; 1,3 DPG, 1,3-diphosphoglycerate; NAD+, nicotinamide adenine dinucleotide (oxidized); NADH, nicotinamide adenine dinucleotide (reduced); Oxa, oxaloacetate; Mal, malate; 2-KGA, 2-ketoglutarate; Glu, glutamate; Asp, aspartate; CPT, carnitine palmitoyltransferase; CT, carnitine acyl- translocase.

for pyruvate production display higher glycogen phospho- to increase to ATP yield beyond what can be derived from rylase Vmax values (28, 57, 117, 123, 149). Oxidative verte- glycolysis alone (64,66). This, along with the storage of large brate muscles typically possess the capacity to fuel exercise quantities of glycogen and the depression of metabolic (ATP metabolism using both carbohydrate or fatty acids and switch turnover) rates, eliminates the need for O2 in the case of back and forth between these, depending upon factors such as parasitic helmith worms and enables many marine intertidal prandial state (139, 140) or exercise intensity (11, 133). Bee species to survive anoxia for prolonged periods. Higher ATP flight muscles do not express fatty acid oxidizing enzymes and yields are obtained in aerobic energy metabolism and Brand are incapable of using fatty acids to fuel flight (29, 117). In (9) provides the most recent estimates of the maximum pos- contrast with bees, other insect species, for example, locusts sible ATP yields of carbohydrate and long-chain fatty acid (6,18), and moths (85,86), also switch between carbohydrate oxidation (Table 1). The calculations on which these are and fatty acid oxidation when fueling flight. based are not as straightforward as might be imagined be- cause, in addition to substrate-level in the catabolic pathways, the stoichiometry of H+ pumping by el- ements of the and diffusion back in ATP yield through ATP must be considered. Thus, while gly- The physiological purpose of pathways of energy metabolism colysis alone results in a net yield of 2 moles of ATP per mole is the production of ATP; therefore, it is relevant to consider of glucose metabolized, glucose oxidation, when the malate- how much ATP can be obtained from them. In the absence aspartate shuttle is used for redox balance results in 28.9 moles of O2, obligate as well as facultative invertebrate anaerobes ATP per mole of glucose with a maximum P/O ratio (ADP use pathways that couple the use glycogen and amino acids phosphorylated to ATP per O consumed) of 2.41. The

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FLIGHT MUSCLE HEMOLYMPH BODY

GLYCOGEN TREHALOSE TREHALOSE TREHALOSE Pi

G6P glucose glucose ATP F6P ATP ADP FDP H PROL PROL G3P DHAP GAP

PYR CYTO MITO G3P DHAP PYR H HCO3

ACETYL-CoA PROL CIT OXA -KG glut

Figure 4 Carbohydrate oxidation in bee flight muscles, also highly simplified, from Suarez et al. (117). Readers are encouraged to consult a biochemistry textbook for details. Diagram highlights the roles played by fat body, hemolymph, cytoplasmic, and mitochondrial reactions and shows the main routes of carbon flow, the role played by the glycerol 3-phosphate (G3P) shuttle in maintaining high cytoplas- mic [NAD+]/[NADH] during the oxidation of glucose, and anaplerotic (pyruvate carboxylase and proline oxidation) reactions. Abbreviations: Pi, inorganic phosphate; G6P, glucose 6-phosphate; F6P, 6-phosphate; FDP, fructose 1,6-diphosphate; DHAP, dihydroxyacetone phosphate; GAP, glyceraldehyde 3-phosphate; pyr, pyruvate; G3P, glycerol 3-phosphate; H, ; OXA, oxaloacetate; CIT, citrate; αKG, alpha-ketoglutarate; glut, glutamate; PROL, proline; CYTO, cytoplasmic compartment; MITO, mitochondrial matrix.

oxidation of a mole of palmitate yields 96.46 moles of ATP at direct or respirometry, that is, measurement of O2 a maximum P/O ratio of 2.097. While the stoichiometries of consumption (Vúo2) and CO2 (VúCO2) production rates (50). glucose and palmitate oxidation to CO2 + H2O are fixed, the ATP yields and P/O ratios allow realistic calculation of cel- ATP yields and P/O ratios are not predetermined and result lular ATP turnover rates. Under certain circumstances, such from evolved properties of bioenergetic pathways (2, 9). calculations can be performed using respirometric data ob- The balanced equations are useful for the determination of tained from whole animals. For example, in animals engaged substrate oxidation rates under steady-state conditions by in- in aerobic, steady-state hovering, the flight muscles account for more than 90% of whole-body metabolic rate. In bees and hummingbirds, these muscles consist of a single fiber type. Thus, it is possible to use data obtained with respirometry Table 1 Stoichiometries, Respiratory Quotients (RQ), ATP Yields, and to determine which fuel(s) are oxidized, to estimate the flux Maximum P/O Ratios from Carbohydrate and Long-Chain Fatty Acid through the relevant pathways, and to estimate the rate of Oxidation, Taken from Brand (9) ATP turnover (118). For example, the rate of ATP hydrolysis required to hold a hummingbird aloft during hovering should Total ATP Maximum Pathway RQ yield P/O be independent of the nature of the fuel(s) oxidized. There- fore, given the 15% higher P/O ratio when carbohydrate is oxidized compared with the oxidation of fatty acid (9), the Glucose + 12[O] → 6CO2 + 6H2O Malate-aspartate shuttle 1.0 28.9 2.41 Vúo2 would be expected, and is observed, to decline by about Glycerol 3-phosphate shuttle 1.0 27.5 2.29 this much when fasted hummingbirds that oxidize fatty acids + → + Palmitate 46[O] 16CO2 16H2O 0.7 96.5 2.10 switch to carbohydrate oxidation as they feed on (138). Total ATP yields, when glycogen substitutes for glucose, increase by The lower requirement for O2 when oxidizing carbohydrate 1.0. may facilitate hover feeding at high altitude.

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Mechanisms Underlying Variation in necessarily lead to changes in flux in glycolysis, the Krebs cy- cle or in mitochondrial respiration. It is possible that change Metabolic Rate in [E] results in no change in flux, as in a classic Variation in rates of energy metabolism in the same organ or involving (100). It is possible that an observed change in animal over time, among individuals in a population, or across flux is the result of metabolic regulation and not hierarchical species can result from two general types of mechanisms. regulation. Or, it could be the result of both. The first, called metabolic regulation, can be the outcome of Hans Westerhoff’s group developed hierarchical regula- allosteric mechanisms, covalent modification, or mass-action tion analysis (15, 95, 127, 128) to address the problem of dis- effects on flux. For example, within seconds, glycolytic flux tinguishing between metabolic and hierarchical regulation. can be activated by several-hundred-fold when muscles go The hierarchical regulation coefficient, ρh, which measures from rest to intense exercise (31); this change in flux does the contribution of [E], and the metabolic regulation coeffi- not require the synthesis of new , that is, it does not cient, ρm, which measures the contribution of mechanisms require the of transcription and translation. The regulating a constant concentration of enzyme, to variation in second category of mechanism that causes variation in flux, flux, are related as called hierarchical regulation (127), involves changes in [E] = ρ + ρ . and are detectable by measurement of Vmax values. The term 1 h m “hierarchical” comes from the idea that the change in flux, in this case, is the consequence of changes in [E] that result At any enzyme-catalyzed step i, ρh is a function of the from changes somewhere in the hierarchy from to relative change in rate, ∂vi , divided by the relative change in transcriptome to proteome. enzyme concentration, ∂ei , times the ratio of change in ei to Techniques with which to examine changes in mRNA the change in flux J. Since ∂ ln vi /∂ ln ei equals 1 (127), then levels (e.g. northern blots, real-time quantitative polymerase ∂ v chain reaction, and microarrays) are now widely used in ln i d ln ei d ln ei ρh = · = . comparative physiology. Some investigators use these tech- ∂ ln ei d ln J d ln J niques to specifically address questions concerning energy metabolism. In other cases, the screening of the expression Similarly, at any step i, metabolic regulation results from a of large numbers of in response to some kind of envi- change in an enzyme-catalyzed rate divided by the change in ronmental or physiological perturbation yields results indicat- concentration of its substrate, product, or , ing changes in mRNA levels of enzymes involved in energy X, times the ratio of change in X to change in J, resulting in metabolism. It is not uncommon to hear at scientific confer-  ∂ ln v ∂ ln X ences, or to read in scientific papers, statements to the effect ρ = i · . m ∂ ln X ∂ ln J that because mRNA levels of metabolic enzymes change, then X i metabolism must have changed in response to the perturba- tion. This is not necessarily so. For example, Feder and Walser One approach to obtaining ρh is to estimate the slope of (48) examined the results reported in 21 papers concerning ln Vmax versus ln J. The other value is obtained by subtrac- responses and found that changes in protein levels can tion as ρm = 1–ρh. This particular approach is illustrated be predicted by changes in mRNA levels less than 50% of in pioneering work by ter Kuile and Westerhoff using proto- the time. However, belief that mRNA and protein levels (or zoa (127). Change in flux can be entirely due at certain steps metabolic rates) are closely related is strong among some re- to hierarchical regulation (when ρh = 1) and, at other steps, searchers (55). This is inspired by positive results obtained, due entirely to metabolic regulation (when ρh = 0). In cer- for example, in model organisms such as yeast (82) as well as tain cases, both mechanisms contribute to the change in flux the finding that more than 80% of the variation in metabolic (when ρh > 0but< 1). Hierarchical regulation analysis has rates of isolated cardiac ventricles is explained by variation been applied to yeast metabolism and has been extended to in mRNA coding for metabolic enzymes in Fundulus (30). consider time-dependent changes in the relative contributions These issues are addressed and a brief summary of mech- of hierarchical and metabolic regulation (15, 128). anisms that often lead to lack of correspondence between Approaches such as hierarchical regulation analysis have mRNA and protein levels is provided in reference 121. the potential to allow comparative physiology to take the next Two-dimensional polyacrylamide gel has major step in studies of the mechanisms underlying tempo- been used in combination with MALDI-TOF mass spectrom- ral variation in flux within animals as well as variation in etry as the favored approach in , taking molecular flux across species. In Panamanian orchid bees, for example, data a step closer to physiological function. However, as pre- there is allometric variation in flux rates through pathways viously discussed, flux is a system property, and typically not of carbohydrate oxidation in muscle during hovering (32). the consequence of the activity of a single, rate-limiting step Plots of enzyme Vmax values against ln J allowed estimation within the pathway. If the control of flux is shared by multiple of regulation coefficients. It was found that the interspecific steps, changes in [E], for example, at the phosphofructoki- variation in J at all steps examined are likely due to metabolic nase or citrate synthase or cytochrome c oxidase steps, do not regulation, except for the hexokinase reaction where ρh = 1.

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The interspecific variation in flux at the hexokinase step in of materials to cells by branching or fractal-like distribution orchid bees is accounted for by interspecific variation in [E], systems (3-5,142). According to this view, as animals become even after taking phylogenetic relationships among species larger, their delivery systems become less able to provide fuels into account (116). and/or O2 to cells and, therefore, energy metabolism in cows, elephants, and whales is more supply limited than in mice and shrews. There seems little doubt that capacities for de- Size and Temperature Effects livery should scale allometrically, but whether physiological rates of delivery actually limit metabolic rates and mecha- That body size (measured as mass) and temperature have nistically explain the allometric scaling of metabolism under profound effects on rates of energy metabolism has been basal, field, or maximal conditions, and whether b = 0.75 are well known to biochemists and physiologists for decades empirical questions. (17, 65, 72, 73, 101). Among mammalian species, for exam- Animals consist of multiple cell types arranged as tissues ple, body mass varies by several orders of magnitude; this and organs. (74) was perhaps the first to show drives the allometry in basal (144, 145), field (81) and maxi- that metabolic rates of tissues from animals of differing mass mal metabolic rates (135, 136). On the other hand, the mech- could be measured in vitro and summed to explain whole- anistic underpinnings of temperature effects on the rates of body metabolic rates and how they scale. A similar approach chemical reactions date back to the work of Boltzmann and proved successful when applied to fish (87). Recently, organ Arrhenius in the 1800s. Consideration of both mass and tem- metabolic rates in vivo, combined with information concern- perature effects on metabolism has led to new approaches and ing the scaling of organ masses, allowed the estimation of b = insights into theoretical modeling and empirical investiga- 0.76 in mammals (132). So, at least in the case of vertebrates, tions of ecological phenomena at the population, , larger animals have proportionately less of certain internal and ecosystem levels (13). organs than smaller animals. In addition, the mass-specific metabolic rates of these organs decline with increasing mass (Table 2). Body mass and energy metabolism This leads to the question, what determines the mass- Why a kg of mouse displays a BMR about 10-fold greater than specific metabolic rates of internal organs? Top-down a kg of cow has captured the interest of physiologists for more metabolic control analysis (8) of the respiration of mitochon- than half a century. Various theories to explain the allometric dria in vitro reveals that the Ci values for ATP turnover, sub- relationship between metabolic rate and body mass have been strate oxidation and proton leak change as the rate approaches proposed since the pattern was first described (reviewed in state 3, the maximum rate of ADP-stimulated respiration. references 1, 14, 17, and 101). This section is not intended When the mitochondria are actively engaged in ATP synthe- to discuss all these theories or the many controversies sur- sis (as they would be in vivo), respiration is controlled mainly rounding them (see, for example, references 1,115, and 141). by ATP turnover and secondarily by substrate oxidation and Instead, the focus shall be on aspects of energy metabolism proton leak (10) (Fig. 2). Control analysis of respiration in and its regulation that are relevant to the mechanistic under- isolated cells, for example, yields Ci = 0.29 for the pro- standing of the size dependence of metabolic rates. cesses that generate the proton electrochemical gradient, 0.49 When metabolic rate, y, plotted against body mass, M,on for the processes involved in ATPturnover, and 0.22 for proton logarithmic axes, yields a slope, b < 1, the relationship is said leak (12). In the case of the heart, 85% of cardiac metabolic to be allometric. In contrast, isometric scaling yields b = 1. rate is due to the combined energetic costs of mechanical The equation describing this relationship can be expressed as work and ion pumping (94) and control analysis of cardiac a power function in the form respiration yields a Ci value of 0.9 for ATP hydrolysis (39, 40). Although Ci values for the control of kidney respiration y = aMb, do not appear to be available, the value for ATP hydrolysis would be expected to be high as rates O2 consumption are where a is a normalization constant. Whether b, the allomet- directly related, in linear fashion, to rates of Na+ pumping 3 ric exponent, is 4 (99) when all organisms, or all animals, (76). Clearly, the rates of energy expenditure (ATP hydrol- all mammals, or only select taxa are considered is a matter ysis) of internal organs play large roles in determining their of dispute. On the surface, such debate may appear trivial. O2 consumption rates. In vivo, rates of energy expenditure However, quantitative, mechanistic theories have been pro- of internal organs are regulated, according to physiological 3 posed that predict a 4 exponent. In contrast, empirical data conditions, to suit the needs of the whole animal. Allometric from various taxa yield exponents that deviate significantly scaling of BMR is observed in euthermic rodents; however, 3 from 4 (114,115). Thus, the mechanistic assumptions under- the allometry is lost and BMR scales isometrically (Fig. 5) lying proposed theories should be considered in relation to (103) when rates of energy expenditure are actively down- the empirical data collected by comparative physiologists. regulated (61, 62) during hibernation. The role of a supply It has been proposed that the metabolic scaling exponents system that physiologically constrains BMR and, in doing so, close to 0.75 result from physical limits to the rates of delivery determines how it scales is not apparent in mammals.

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Table 2 Scaling of Organ Masses and Metabolic Rates in Mammals, Taken from Wang et al. (132)

Organ Specific metabolic Organ mass × specific Organ mass = rate = metabolic rate =

Liver 0.033M0.87 2861M−0.27 94.4M0.60 Brain 0.011M0.76 1868M−0.14 20.5M0.62 Kidneys 0.007M0.85 2887M−0.08 20.2M0.77 Heart 0.006M0.98 3725M−0.12 22.4M0.86 Remainder 0.939M1.01 125M−0.17 117.4M0.84

M is body mass in kg; specific metabolic rates are in kJ kg−1 day−1. Organ masses and specific metabolic rates decline with increasing body mass.

Given the observed decline in organ mass-specific system, there is abundant evidence to support the idea that al- metabolic rates with increasing body mass, it is relevant to lometric scaling patterns in animals at rest are driven mainly consider allometric scaling in the structures and functional by rates of energy expenditure (34, 114, 115). capacities of the machinery involved in cellular bioenerget- Animals are capable of increasing metabolic rates to var- ics. Vmax values for citrate synthase, the Krebs cycle enzyme ious degrees. Among mammals, maximal aerobic metabolic often used as an indicator of mitochondrial content (79), de- rates (Vúo2max values) are, on average, about 10-fold higher cline with increasing body mass in the locomotory muscles than BMR (126) while in insects, the difference between of mammals (47, 63) and pelagic fishes (23, 106). In var- metabolic rates at rest and in flight can be as high as 100-fold + + ious mammalian organs, Vmax values for Na -K -ATPase (98). During the transition from rest to high-intensity aerobic (26) and Ca2+-ATPase (59), as well as mitochondrial con- exercise, animals undergo a dramatic physiological transfor- tent (45, 46, 68, 77) decline with increasing mass. Thus, bio- mation. Whereas resting values are determined mainly by the chemical capacities for ATP hydrolysis as well as for the metabolic rates of internal organs (132), Vúo2max and values aerobic synthesis of ATP decline with increasing body mass, close to it are determined mainly by mitochondrial respira- along with physiological rates of energy metabolism. In con- tion rates in exercising muscles (125) (Fig. 1). At the level trast with the absence of data indicating that basal or resting of muscle fibers, actomyosin ATPase is responsible for about metabolic rates in animals are physiologically limited by the half of the control of mitochondrial respiration; the rest of supply of materials by a branching or fractal-like distribution the Ci values are shared by the adenine nucleotide translocase and the electron transport chain (147). It is when whole-body metabolic rates approach or reach Vúo2max that supply lim- 50 itations imposed by a branching or fractal-like distribution system might be expected. Control analyses of mammalian Vúo2max during exercise reveal that control is distributed among

) 40

–1 the multiple convective and diffusive steps in the pathway for O from the external environment to muscle mitochondria 30 2 × min (36,70,130,131). Under these conditions, b = 0.87 (136) and –1 significantly higher than 0.75, as would be predicted by mod- 20 × kg

2 els based on supply limitation. In addition, the mitochondrial respiration rate in muscles during exercise at Vúo2max is mass 10 independent and lies within the narrow range of 3 to 5 mL 3

MR (mL O O2/cm of mitochondria per minute (126). These results do 0 not indicate that muscle mitochondria in larger mammals are more limited by the supply of O2 or substrates than in smaller ú 0.01 0.1 110 mammals during exercise at Vo2max. In honeybees, the tra- Body mass (kg) cheal system appears to possess substantial excess capacity for O2 flux (60). A detailed interspecific study of orchid bees

Figure 5 Metabolic rate (V˙O2) as a function of body mass in ro- revealed that the of flight provides a sufficient dents, denoted by various symbols (left to right: hazel mouse, edible explanation for the allometry of Vúo2 during hovering. In these dormouse, ground squirrel, European hamster, European hedgehog, and alpine marmot). Solid line shows that basal metabolic rate (BMR) insects, the interspecific variation in wing-loading (mass per scales allometrically during euthermia while dashed line shows how, unit area) accounts for the interspecific variation in wing-beat during hibernation, metabolic rate scales isometrically. Euthermic and frequency, such that higher wing loading results in higher fre- hibernating metabolic rates differ due to changes in the rates of energy expenditure in internal organs. Adapted, with permission, from Suarez quency. Wing-beat frequency, a major determinant of mus- and Darveau (114); redrawn, with permission, from Singer et al. (103). cle power output during steady-state flight (90), determines

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hovering Vúo2, so interspecific variation in frequency accounts alyze metabolic reactions undergo conformational changes, for the interspecific variation in Vúo2values (33). The biochem- bind substrates, and release products by reversible formation ical machinery for aerobic ATP synthesis is mainly subject to and breakage of weak bonds. Weak bonds and, therefore, metabolic regulation; hierarchical regulation (ρm = 1) is ob- higher order protein structure as well as -binding affini- served only at the hexokinase reaction when phylogeny is ties are perturbed by changes in temperature. The Michaelis taken into account (116). constant, km, is temperature dependent and, among metabolic enzymes, typically increases with temperature (65 and 66). An important mechanism in thermal adaptation involves the Temperature and energy metabolism evolution of differential sensitivities to temperature; that is, km The thermal biology of animals, thermal adaptation, mech- values of orthologous enzymes for their substrates are found anisms of thermogenesis and thermoregulation constitute a to be similar when measured at their respective biologically large and well-developed area of scientific inquiry (66, 67). relevant body temperatures (65 and 66). The second is that Awareness of the importance of a fundamental, mechanistic “energy metabolism” concerns ATP turnover: the hydrolysis understanding of temperature effects on energy metabolism of ATP by energy-utilizing processes in cells and its con- has grown at least partly as a result of climate change effects comitant resynthesis by pathways in bioenergetics. Thus, a on species distribution and abundance (91, 92). Gilooly et al. mechanistic explanation for temperature effects on rates of (54) express the combined effects of mass and temperature on energy metabolism must provide a mechanistic explanation the mass-corrected rate of energy metabolism, I, in a single for its effects on rates of enzyme-catalyzed processes involv- equation as ing ATP hydrolysis as well as its effects on enzyme-catalyzed rates of ATP synthesis (24). Because ATP hydrolysis and syn- 3/4 −E/kT I = io M e , thesis are kinetically and stoichiometrically coupled (2), the question of temperature effects on metabolism concerns its −E/kT where io is a normalization constant, M is mass, e is effects on metabolic regulation and goes well beyond the ide- the Boltzmann factor wherein k is the Boltzmann constant, alized behavior of molecules in a population, as described by E is the , and T is the absolute temperature. the statistical mechanics of the 1800s. The mechanisms un- This equation serves as the basis for the “metabolic theory derlying temperature effects on energy metabolism continue of ecology” (13). Using empirical data from the literature to be the subject of research in comparative and ecological and plotting ln I against 1/kT yields straight lines for vari- physiology. Because flux is a system property, temperature ous taxa, with negative slopes corresponding to organismal effects on flux must be studied in terms of its effects on activation energies, E, between 0.41 and 0.74 eV (mean = system properties. Therefore, a promising approach involves 0.62 eV). Upon mass-correcting and temperature-correcting the application of metabolic control analysis to this problem organismal metabolic rates, it is observed that unicells, (16, 19). and animals differ in their specific metabolic rates by only 20- fold, at most; the rest of the variation in nature is explainable 3 Energy metabolism in the deep ocean in terms of the Boltzmann factor and mass-dependent 4 power scaling. A point of controversy is whether the metabolic the- Most of the Earth’s surface is covered by ocean and most ory of ecology is mechanistic. For example, it is proposed of it is deep (35). Given the great diversity and ancient lin- that because the lower metabolic rates of hibernators can be eages of marine animal species, it is not surprising that many explained in terms of their lower body temperatures, there is possess mechanisms and pathways for ATP production that no need to invoke other mechanisms to explain the reduction differ markedly from those well studied in vertebrate animals. in metabolic rate (54). Having previously dealt with the mech- For example, certain species of sea slugs that feed on algae anistic determinants of and mass effects on metabolic rates, incorporate chloroplasts into their own cells and photosyn- brief consideration of temperature effects is appropriate. thesize (96,97). Deep-dwelling species such as hydrothermal Based on the foundations laid by Arrhenius and Boltz- vent tubeworms engage in chemoautotrophy with the aid of mann, it is understood that at a given temperature, only a symbiotic , taking up sulfide from the en- small fraction of molecules in a large population possesses vironment and oxidizing it as a source of energy for CO2 sufficient energy (“activation energy”) to undergo an uncat- fixation (53). Since many marine invertebrate species harbor alyzed . Increased temperature causes an bacterial symbionts and engage in chemoautotrophy (22), it is increase in the fraction of molecules with sufficient activa- only from a nonbiological, excessively anthropocentric per- tion energy; this causes the increase in the reaction rate. The spective that such processes would be considered unusual, utility of direct application of the Arrhenius/Boltzmann ap- given that most of the biosphere consists of deep ocean. proach to rates of energy metabolism in organisms is limited In the deep sea, high hydrostatic pressures perturb bio- by at least two factors. The first is that biochemical reactions chemical processes such as ligand binding, protein folding, are enzyme-catalyzed; metabolic enzymes typically operate at conformational changes, polymerization and depolymeriza- low, subsaturating substrate concentrations, so in vivo rates of tion, affecting enzyme-catalyzed rates, and biochemical equi- enzyme are substrate limited. The enzymes that cat- libria in bioenergetic (and other) pathways. The perturbation

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is thought to result from effects of pressure on the volume specific variation in metabolic rates than body mass (102). changes accompanying these processes (66). The thermody- Thus, namics of these processes is usually considered in terms of ... · the Gibbs free energy change, G, “a deep-living vampire squid weighing just 1 g has the same mass-specific metabolic rate as an elephant...while an epipelagic squid weighing 10·kg has the same mass-specific G = H − T S, metabolic rate as a mouse” (102). Decreases in metabolic rates with increasing depth are where H is the enthalpy change, T is temperature, and S also seen in pelagic crustaceans and fishes (21). These data is the change in entropy. This expression ignores a third term raise the intriguing possibility that the “metabolic theory of that, at high pressure, becomes significant. The more complete ecology” (13) does not apply to most of the biosphere. equation that applies to deep-sea environments that comprise most of the biosphere is Concluding Remarks G = H − T S + PV, Energy metabolism is a many-splendored thing. Much mech- anistic, experimental biology as well as analyses of patterns where P is pressure and V is the change in volume associ- and processes have yielded insights into the nature of and ated with the biochemical process (104). Pressure effects on mechanisms underlying metabolic variation among animals. biochemical processes are thought to have led to the evolution The unity and diversity observed in energy metabolism among of reduced volume changes associated with ligand binding, animals exemplifies the tension between yin and yang famil- conformational changes, polymerization, and depolymeriza- iar to practitioners of comparative biochemistry and physiol- tion in deep-sea organisms. Reduction of volume changes ogy (67, 105). It can be reasonably argued that knowledge of would result in minimization of the perturbing effects of high the metabolic similarities and differences among animals and hydrostatic pressure on protein structure, , their underlying causes may contribute to the understanding and regulation (66, 104). of metabolic afflicting humans (88, 89) as well as The diversity of life is the outcome of evolutionary pro- responses and adaptation to climate change (91, 92). cesses. Animal species have evolved to exploit innumerable niches, evolving body masses spanning several orders of mag- nitude as well as extremely diverse lifestyles and environ- ments. Although biological systems certainly obey physical Acknowledgements laws, evolutionary processes have produced emergent out- The author is grateful to C. D. Moyes and to an anonymous comes, that is, patterns and processes that could not have reviewer for critical comments. His research has been funded been predicted simply on the basis of physical laws. It is by the US National Foundation (IOB 0517694). because of evolution and adaptation that many taxa display metabolic scaling exponents that deviate significantly (115) from the b value of 0.75 predicted by supply-limitation models (3, 141). Energy expenditure plays a significant role in deter- References whole-body metabolic rates and the manner in which 1. Agutter PS, Wheatley DN. Metabolic scaling: Consensus or contro- these scale under basal, field, and maximal exercise conditions versy? Theor Biol Med Model 2004: 1-13, 2004. 2. Atkinson DE. Cellular Energy Metabolism and Its Regulation.New (114,115). As deep ocean comprises most of the biosphere, an York: Academic Press, 1977. interesting and important issue concerns the factors that deter- 3. Banavar JR, Damuth J, Maritan A, Rinaldo A. Supply-demand balance and metabolic scaling. Proc Natl Acad Sci U S A 99: 10506-10509, mine the metabolic rates of deep-sea animals (21). Although 2002. metabolism scales with respect to body mass in allometric 4. Banavar JR, Maritan A, Rinaldo A. Size and form in efficient trans- portation networks. Nature 399: 130-131, 1999. fashion and changes in response to temperature as expected, 5. Banavar JR, Moses ME, Brown JH, Damuth J, Rinaldo A, Sibly RM, considerable research on pelagic species reveals that mass- Maritan A. A general basis for quarter-power scaling in animals. Proc Natl Acad Sci U S A 107: 15816-15820, 2010. specific metabolic rates decline with increasing depth of dis- 6. Beenakkers AMT, VanDer Horst DJ, VanMarrewijk WJA. Metabolism tribution in the column. Associated with these lower during locust flight. Comp Biochem Physiol 69B: 315-321, 1981. 7. Bookelman H, Trubels JMF, Sengers RCA, Janssen AJM, Veerkamp metabolic rates are reduced locomotory activity and lower JH, Stadhouders AM. Reconstitution of malate-aspartate and alpha- enzyme Vmax values (21). Pelagic, deep-sea animals live in a glycerophosphate shuttle activity in rat mitochondria. Int J Biochem 10: 411-414, 1979. perpetually dark environment. Therefore, it has been hypoth- 8. Brand MD. Top down metabolic control analysis. J Theor Biol 182: esized that relaxation of the selective forces associated with 351-360, 1996. 9. Brand MD. The efficiency and plasticity of mitochondrial energy trans- visual predation (e.g. pursuit of prey and predator avoidance) duction. Biochem Soc Trans 33: 897-904, 2005. explains the decline in enzyme activities and metabolic rates 10. Brand MD, Chien L-F, Rolfe DFS. Regulation of oxidative phospho- rylation. Biochem Soc Trans 21: 757-762, 1993. with increasing depth. For example, among cephalo- 11. Brooks GA. Mammalian fuel utilization during sustained exercise. pod mollusks, habitat depth accounts for more of the inter- Comp Biochem Physiol 120B: 89-107, 1998.

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