Multi-level regulation and metabolic scaling
1 Department of Ecology, Evolution and Marine Biology, University of
California, Santa Barbara, CA 93106-9610, USA
2 Department of Zoology, University of British Columbia, Vancouver, BC,
Canada V6T 1Z4
* Author for correspondence (e-mail: suarez{at}lifesci.ucsb.edu)
Accepted 18 January 2005
Summary
Metabolic control analysis has revealed that flux through pathways is the
consequence of system properties, i.e. shared control by multiple steps, as
well as the kinetic effects of various pathways and processes over each other.
This implies that the allometric scaling of flux rates must be understood in
terms of properties that pertain to the regulation of flux rates. In contrast,
proponents of models considering the scaling of branching or fractal-like
systems suggest that supply rates determine metabolic rates. Therefore, the
allometric scaling of supply alone provides a sufficient explanation for the
allometric scaling of metabolism. Examination of empirical data from the
literature of comparative physiology reveals that basal metabolic rates (BMR)
are driven by rates of energy expenditure within internal organs and that the
allometric scaling of BMR can be understood in terms of the scaling of the
masses and metabolic rates of internal organs. Organ metabolic rates represent
the sum of tissue metabolic rates while, within tissues, cellular metabolic
rates are the outcome of shared regulation by multiple processes. Maximal
metabolic rates (MMR, measured as maximum rates of O2 consumption,
O2max) during
exercise also scale allometrically, are also subject to control by multiple
processes, but are due mainly to O2 consumption by locomotory
muscles. Thus, analyses of the scaling of MMR must consider the scaling of
both muscle mass and muscle energy expenditure. Consistent with the principle
of symmorphosis, allometry in capacities for supply (the outcome of physical
design constraints) is observed to be roughly matched by allometry in
capacities for demand (i.e. for energy expenditure). However, physiological
rates most often fall far below maximum capacities and are subject to
multi-step regulation. Thus, mechanistic explanations for the scaling of BMR
and MMR must consider the manner in which capacities are matched and how rates
are regulated at multiple levels of biological organization.
Key words: metabolic regulation, respiration, mitochondria, BMR, O2max, allometry
Introduction
Metabolic rates scale allometrically, such that a unit mass of elephant has
a metabolic rate much less than that of a unit mass of mouse. To empiricists,
the question `what causes the allometric scaling of metabolic rates?'
is one that is inextricably linked to the question `what determines
metabolic rates?' This is because whatever phenomena determine metabolic rates
should presumably play major roles in driving their allometric scaling. The
fundamental importance of both questions has been recognized by biologists for
a century, and studies addressing them have had long and illustrious
histories. Introductions to the phenomenon of metabolic scaling and accounts
of the historical development of ideas and studies devoted to the subject can
be found in excellent books (Calder,
1984; Schmidt-Nielsen,
1984
) and reviews (Calder,
1981
; Hoppeler et al.,
1980
; Porter,
2001
; Taylor,
1987
; Weibel,
1987
) and are beyond the scope of this article. Here, we discuss
some empirical data from the literature of comparative physiology to address
the issue of what determines metabolic rates in animals. We relate this
information to the allometric scaling of metabolic rates and comment on
recently proposed models for metabolic scaling.
Animals as the sum of their parts
When data for basal metabolic rate, BMR, are plotted against body mass,
Mb, on logarithmic coordinates, the slope of the linear
relationship, referred to as the allometric exponent, b, in the
equation:
![]() | (1) |
is significantly less than 1.0, where a is the vertical intercept
(Schmidt-Nielsen, 1984).
Whether b is closer to 3/4
(Savage et al., 2004
) or to
2/3 (Dodds et al., 2001
;
White and Seymour, 2003
) is
still hotly debated. The issue continues to be worthy of debate, at least
partly because of the mechanistic implications of what the allometric
exponents happen to be (Suarez et al.,
2004
). Schmidt-Nielsen
(1984
) pointed out that
regression lines and allometric equations are simply quantitative descriptions
of data. It is, therefore, reasonable to expect that explanations for the
scaling of metabolic rates, i.e. why the points lie where they do and why the
slopes are as they are, should be consistent with what is known about how
metabolic rates are regulated in animals.
Attempts to account for the allometry in BMR scaling by considering the sum
of organ metabolic rates go at least as far back as the work of Krebs
(1950). The rather simple idea
behind this is that by considering the scaling of organ masses as well as
organ metabolic rates, one should be able to explain the scaling of whole-body
BMR. While the work of Krebs was limited by the use of in vitro
metabolic rates, more recently Wang et al.
(2001
) used more
physiologically relevant data obtained in vivo. Among mammals, the
masses and metabolic rates of internal organs (liver, brain, kidneys and
heart) account for a large fraction of BMR. Wang et al.
(2001
) found that with
increasing body mass, this fraction declines, from 68% of BMR in a mammal
weighing 100 g to 34% in one weighing 1000 kg. In their analysis, the rest of
BMR is accounted for by `remaining tissues', a category that includes skeletal
muscles. The internal organs show variable mass-scaling exponents (from 0.76
for brains to 0.98 for hearts) and metabolic rate scaling exponents (-0.08 for
kidneys to -0.27 for livers; Table
1). When the metabolic rates of these organs and the remaining
tissues are summed, the outcome is a value for b of 0.76, which is
remarkably close to the much-quoted exponent obtained by Kleiber
(1932
). The actual value of
b, of course, is a subject of dispute and, given the relatively
narrow body mass range considered by Wang et al.
(2001
), their findings serve
mainly to illustrate that the allometric scaling of BMR can be accounted for
by the scaling of organ masses and organ metabolic rates.
|
Does supply determine organ metabolic rates?
Given the allometric scaling of the metabolic rates of internal organs and
their contributions to the scaling of BMR, it is relevant to consider what is
currently known concerning what determines organ metabolic rates.
Fig. 1 shows how mass-specific
resting metabolic rates decline with increasing body mass in several species
of small mammals (from Singer et al.,
1995). Recently, it has been suggested that metabolic rates are
determined by the rates of resource supply to cells via branching
(Banavar et al., 2002
) or
fractal-like (West et al.,
1997
,
1999
,
2002
) structures. It is
well-known to physiologists that blood flow is acutely adjusted to
physiological needs such that internal organs in resting animals typically do
not experience a limiting supply of O2 or metabolic substrates. In
addition, whole-body metabolic rates among mammals increase, on average, by
about tenfold as they go from BMR to MMR (maximum aerobic metabolic rates,
expressed as the maximum rate of O2 consumption,
O2max) during
exercise (Weibel, 2000
). More
athletic species display even higher metabolic scopes
(Jones and Lindstedt, 1993
;
Weibel, 2000
). The presence of
large excess capacities in the cardio-respiratory systems of mammals, by
itself, should cast doubt upon the idea that the supply of materials through
the circulation should limit rates of organ metabolism at rest. The data
presented in Fig. 1 were
obtained from hibernators. In the same species, the transition from the
euthermic to hibernating state results in dramatic declines in (and, resulting
isometry of) whole-body metabolic rates. This is not simply a passive effect
of cooling, but the result of active downregulation of rates of energy
expenditure within internal organs
(Heldmaier and Elvert, 2004
;
Heldmaier and Ruf, 1992
). It
can be inferred from all these, as well as the lack of supply limitations,
that the energy expenditure in internal organs determines their metabolic
rates and contributions to whole-body BMR.
|
Cellular energy metabolism: lessons from control analysis
Organs consist of multiple tissues that, in turn, consist of specific cell types. The control of metabolism in hepatocytes, neurons, tubule cells, and cardiomyocytes therefore becomes a central issue to consider when determining what controls the rate of metabolism in livers, brains, kidneys, hearts and, ultimately, whole animals.
Early in the development of metabolic biochemistry as a discipline,
break-through discoveries of individual enzyme-catalyzed reactions and the
pathways they constitute were followed by measurements of flux rates and
studies of their regulation. Monod's concept of allosterie, of such
great importance that he referred to it as the `second secret of life' (see
Perutz, 1990), led to much
research effort to identify rate-limiting steps and to elucidate how the
activities of allosteric enzymes are altered in response to changes in the
concentrations of modulators. After many years of such research, the concept
of the rate-limiting step became problematic. For example, in the case of
glycolysis, perhaps the best-studied of all pathways, multiple steps were
found to be displaced from equilibrium and potentially rate-limiting, and
several enzymes were discovered to be subject to various forms of regulation.
Is there really just one rate-limiting step? Over the past three decades, much
progress has been made towards a more sophisticated, quantitative
understanding of the control of metabolism. A major factor contributing to
this was the development of metabolic control theory and the application of
metabolic control analysis to studies of the control of flux (Fell,
1992
,
1997
). Metabolic control
theory considers the flux through a pathway as a system property that is
subject to shared control by multiple steps. The degree of control at each
step can be quantified by estimation of its flux control coefficient,
Ci, which represents the degree to which a step,
i, contributes to the regulation of flux, J, through a
pathway. Ci for any step is expressed in terms of the
fractional change in pathway flux (
J/J) that occurs
in response to an infinitesimal fractional change in the rate of enzyme
activity (
ei/ei):
![]() | (2) |
There are now many examples of the application of metabolic control
analysis to studies of the control of flux through various pathways
(Fell, 1997). The prediction,
based on theoretical considerations, that control should be shared by multiple
steps, is now supported by a large body of empirical evidence. For example,
arguments concerning what is rate-limiting in glycolysis are now informed by
quantitative data. Using a bottom-up approach that involves estimating
Ci values from the elasticities (i.e. enzyme kinetic
responses to variation in substrate concentration) at each of the steps,
Kashiwaya et al. (1994
) found
not only distribution of control among multiple steps, but also changes in
Ci values as hearts were perfused with or without insulin
and with single or multiple substrates. Thus, the control of flux is shared by
multiple steps whose relative contributions can change in response to changes
in physiological conditions.
Under steady-state, aerobic conditions, most of the total cellular
O2 consumption is due to mitochondrial respiration (for the present
discussion, we shall ignore the small fraction due to non-mitochondrial
processes). Because energy metabolism is inherently complex, addressing the
question of what controls mitochondrial O2 consumption in intact
cells is potentially more difficult than determining Ci
values for individual steps in linear pathways. To a large extent, the
difficulties have been surmounted by the use of top-down metabolic control
analysis. This is a simplifying approach, developed by Brand and colleagues
(Brand, 1996), which involves
conceptually subdividing metabolism into blocks consisting of entire pathways,
networks of pathways or groups of reactions. Individual blocks are considered
to be linked to each other via a common intermediate, and the
strength of control of blocks over each other is estimated empirically. In
isolated liver mitochondria, Hafner et al.
(1990
) designated the group of
reactions involving substrate oxidation that create the proton-motive force,
p, as one such block. Two other blocks were designated as
those involved in dissipating
p, i.e. proton leak and the
phosphorylation system (i.e. ATP synthesis). The kinetic responses of these
blocks, measured as O2 consumption, to changes in their common
intermediate,
p, were determined.
Fig. 2 plots the
Ci values of substrate oxidation, proton leak and
phosphorylation systems on mitochondrial respiration as a function of percent
of the state 3 rate (maximum rate of O2 consumption coupled to ATP
synthesis). It is seen that non-phosphorylating mitochondria (state 4) respire
at between 10-20% of the maximum rate. Under these conditions, substrate
oxidation accounts for a small fraction and proton leak accounts for most of
the control of respiration, while ATP synthesis has no influence. As
mitochondria approach 100% of their state 3 respiration rate, control by
proton leak declines while control by ATP synthesis increases. Control of
substrate oxidation increases more gradually until it shares, along with ATP
synthesis, most of control, while proton leak has minimal influence over
respiration at 100% of state 3.
|
In contrast with isolated mitochondria, both ATP synthesis and hydrolysis
occur simultaneously and might be expected to regulate each other in intact
cells. Applying the top-down approach to the control of respiration in
isolated rat hepatocytes, Brown et al.
(1990) estimated
Ci values of 0.29 for the processes that generate
p, 0.49 for the processes that synthesize, transport and use
ATP, and 0.22 for the proton leak. In isolated perfused rat livers in the
`resting' state, i.e. when no substrates for gluconeogenesis or ureagenesis
are provided, Soboll et al.
(1998
) found that
mitochondrial respiration is controlled by `maintenance' ATP-hydrolyzing
reactions, while mitochondrial reactions involved in ATP synthesis have no
influence. However, when livers are made to synthesize glucose and urea at
high rates, mitochondrial ATP synthesis exerts strong control over its own
rate as well as on both gluconeogenesis and ureagenesis. In addition, both
gluconeogenesis and ureagenesis exert negative control over each other's
rates, presumably by competing for ATP. In such active livers, maintenance
ATP-hydrolyzing reactions are unaffected by rates of mitochondrial ATP supply
and demand by other processes, but exert control over all other pathways. It
is likely that in vivo, when livers are actually performing their
physiological functions, control of mitochondrial O2 consumption is
shared by ATP-requiring biosynthetic and maintenance reactions with processes
involved in ATP synthesis and proton leak
(Rolfe et al., 1999
).
Mammalian kidneys are estimated to have `basal' rates of O2
consumption that are between 3-18% of the normal physiological rates expressed
when active ion transport is occurring. Experiments involving manipulation of
rates of Na+ transport yield a positive, linear relationship
between transport and O2 consumption rates, and such results have
been used to calculate the ATP cost of Na+ pumping by
Na+-K+-ATPase
(Mandel and Balaban, 1981).
Although control analysis has not been conducted on perfused kidneys or kidney
tubules in vitro, it is apparent that the metabolic rates of kidneys
are controlled by rates of energy expenditure, i.e. ATP hydrolysis, driven
primarily by active ion transport.
Arrested hearts consume O2 at only 15% of the rates seen in
normal, working hearts. Therefore, about 85% of cardiac metabolic rate
represents the energetic cost of performing mechanical work plus the cost of
excitation-contraction coupling (Rolfe and
Brown, 1997). Cardiac
O2 increases
linearly with work rate, and intracellular free Ca2+ may be
involved in the concerted regulation of both
O2 as well as
work rate (Balaban and Heineman,
1989
; Territo et al.,
2001
). In recent work involving top-down control analysis of
cardiac energy metabolism, Diolez et al.
(2000
,
2002
) designated
ATP-synthesizing and hydrolyzing reactions as two separate blocks, linked by
their common intermediate, ATP. Using perfused rat hearts, they found that ATP
hydrolysis accounts for about 90% of the control of respiration, while the
remainder is accounted for by ATP synthesis. Energy metabolism in cardiac
tissue is not limited by the supply of O2 or substrates
(Mootha et al., 1997
;
Zhang et al., 1999
). These
findings, as well as the results of Diolez et al.
(2002
), provide quantitative
support for the widely held view that energy expenditure (i.e. work rate),
rather than the rate of material supply, sets the pace for cardiac energy
metabolism.
The control of O2max
The relative contributions of various organs to whole body
O2 change
dramatically as animals go from their basal to maximal, aerobic metabolic
rates, expressed as
O2max
(Weibel, 2002
). Here, we
consider
O2max
achieved during exercise (although some animals are known to achieve
O2max in other
circumstances, e.g. pythons during digestion of food;
Secor and Diamond, 1995
).
Under these conditions, cardiac output increases to values several-fold higher
than at rest and most of the increase in blood flow is directed to locomotory
muscles. At
O2max during
exercise, skeletal muscle mitochondria are responsible for 90% or more of
whole body O2 consumption rate
(Taylor, 1987
).
Control analysis, performed using isolated muscle mitochondria, yields
results similar to those shown in Fig.
2 (Brand et al.,
1993). A more `complete' system, consisting of skinned muscle
fibers, has also been used wherein actomyosin-ATPase activities and
mitochondrial oxidative phosphorylation can be varied by manipulation of free
Ca2+ concentration. Control analysis, applied to such preparations,
reveals that about half of the control of respiration resides in
actomyosin-ATPase, while the balance is accounted for by the mitochondrial
adenine nucleotide translocase and mitochondrial reactions involved in
electron transport (Wisniewski et al.,
1995
).
Control analysis has been applied by Brown
(1994) to the control by organs
of the concentrations and flux rates of metabolites in the blood. This
approach is of heuristic value and was applied by Brown
(1994
) to analyze ketone body
metabolism. However, simplifying assumptions made concerning the route of
blood flow and the (quite understandable) lack of incorporation of
cardio-respiratory parameters precludes the application of this particular
approach to the analysis of the control of
O2max.
Nevertheless, over the years, a number of forms of control analysis have been
adopted in studies of the respiratory physiology of exercise. These studies
reveal that, during exercise at
O2max, the rate
of transport of materials by branching or fractal-like structures does play a
role in limiting whole body metabolic rate. Using an approach that is most
closely analogous to the control analysis performed by metabolic biochemists,
Jones (1998
) estimated control
coefficients for
O2max in
thoroughbred racehorses of 0.309, 0.308, 0.263 and 0.120 for ventilation rate,
pulmonary O2 diffusing capacity, cardiac output, and muscle
O2 diffusing capacity, respectively. Although differing in
methodological details and in the species used, these findings are consistent
with those obtained by others (e.g. di
Prampero, 1985
; Wagner,
1993
,
1996
); i.e. control analysis
of whole animal
O2max reveals
that control is shared among the convective and diffusive steps in the
transport of O2 from the external environment, through the lungs
and circulation, to the muscle mitochondria.
Causation in metabolic scaling
In recent years, the publication and popularization of proposed
explanations (Banavar et al.,
2002; West et al.,
1997
,
1999
,
2002
) for metabolic scaling
have stimulated renewed interest in the subject. The model of West et al.
(1997
), in particular, serves
as the basis for what is now referred to as a mechanistic `metabolic theory of
ecology'. Metabolic rate as mass to the 3/4 power (and a correction factor for
temperature) might be good enough for the purposes of ecosystem ecologists,
regardless of what the underlying mechanism(s) that drive the relationships
might be. However, are such models truly mechanistic in the sense that they
reflect the causal relationships that bring about metabolic rates and their
scaling?
An inherent problem with the models proposed by both Banavar et al.
(2002) and West et al.
(1997
) is that both are based
on the assumption that metabolic rates are supply-limited. Thus, according to
their logic, a model for the scaling of supply rates serves as the explanation
for the scaling of metabolic rates. West et al.
(2002
) state this explicitly:
`A quantitative theoretical model
(West et al.,
1997
) has been developed that accounts for quarter-power
scaling on the basis of the assumption that metabolic rates are constrained by
the rate of resource supply.' Similar reasoning led Banavar et al.
(2002
) to argue that
`intracellular processes and properties - including the rates of chemical
reactions in organelles, the function and concentration of enzymes, and the
strength of chemical bonds - are most unlikely to exhibit necessary changes in
direct response to the overall size of the organism.' They add that
`The correspondence between the scaling exponent for the capacity of the
circulatory system and that observed for overall metabolism' leads to the
conclusion that `the rates of intracellular metabolic-related processes
conform roughly to the scaling of the supply network and exert little, if any,
net effect on the scaling of overall metabolism.'
If supply rates do not regulate BMR, then models describing the scaling of
supply rates alone cannot provide adequate explanations for the scaling of BMR
(Suarez et al., 2004). In
their paper describing the scaling of BMR on the basis of the organ mass and
metabolic rate scaling, Wang et al.
(2001
) appropriately pointed
out the importance of determining the mechanisms that drive the allometric
scaling of organ metabolic rates.
It turns out that, contrary to the assertions of proponents of supply-based
models of metabolic scaling, the metabolic rates of cells isolated from
mammals (Porter, 2001), birds
(Else et al., 2004
), reptiles
and archosaurs (Hulbert et al.,
2002
) decline with increasing body mass. There is, in fact, much
work directed towards investigation of the biochemical bases for the
allometric scaling of cellular metabolism (reviewed by
Suarez et al., 2004
). Because
rates of cellular energy expenditure scale allometrically, we developed a
`multiple-cause' explanation as an alternative to `single-cause' supply-based
explanations for metabolic scaling
(Darveau et al., 2002
;
Hochachka et al., 2003
). In
essence, the idea is that metabolic scaling is the consequence of the
contributions of various processes involved in both the supply of materials
and energy expenditure to the control of
O2. Although
formal presentation of this concept (called the `allometric cascade') is
beyond the scope of the present paper, in light of the preceding sections, it
should be apparent, if supply does not limit BMR, that multiple contributors
to, and the relative strengths of their control over, whole body metabolic
rates must be considered to account for BMR. The allometric cascade has been
challenged (Banavar et al.,
2003
; West et al.,
2003
) on the basis of mathematical flaws; these and other
limitations have been acknowledged by us
(Darveau et al., 2003
).
Nevertheless, the physiological and biochemical bases are valid, and the
concept itself remains unchallenged.
In principle, the same arguments should apply to the allometric scaling of
O2max, a
condition wherein the supply of materials via branching or
fractal-like networks plays an increased role in limiting whole-body metabolic
rate. It is interesting that despite this,
O2max in mammals
scales with an exponent of about 0.86
(Taylor et al., 1989
;
Weibel et al., 2004
), a value
significantly higher than the exponent of 0.75 predicted by models that assume
supply limitation. Mitochondrial respiration rates in exercising muscles are
mass-independent, at about 5 ml O2 cm-3 mitochondria
min-1 (Hoppeler and Lindstedt,
1985
; Taylor et al.,
1989
; Weibel et al.,
2004
). The isometry of mitochondrial respiration rates in
vivo at
O2max has been
interpreted to mean that the delivery of O2 is adjusted
via adaptations in structure and function such that, on average,
muscle mitochondria in large species are as well supplied with O2
as those in small species. Large animals, therefore, are not disadvantaged
relative to small animals with respect to their abilities to supply the
requirements of their mitochondria under basal or maximal aerobic rates of
metabolism. Rather, supply matches demand, and demand is set by the rate of
energy expenditure. We are led to conclude that the scaling of muscle mass and
the processes involved in muscle energy expenditure must be considered in
addition to the scaling of supply rates to explain the allometric scaling of
O2max
(Suarez et al., 2004
). Such a
shift from considering only the scaling of supply rates to consideration of
the scaling of energy expenditure provides an explanation for deviations from
3/4 power scaling exponents commonly observed in intra- and interspecific
studies. Much of the deviation is the outcome of evolutionary adaptation to
lifestyles and environments (Childress and
Somero, 1990
; Suarez et al.,
2004
).
Capacities vs rates
In the present context, flux rates are viewed as being acutely regulated to
satisfy physiological requirements. Capacities, on the other hand, represent
the upper limits to flux rates (Suarez et
al., 1997). Although rates and capacities are different, focus on
the allometric scaling of rates has resulted in relative neglect of the
scaling of capacities and the significance of this. At the level of each
enzyme-catalyzed step in pathways, the maximum capacity for flux,
Vmax, is a function of enzyme concentration, [E],
and catalytic efficiency, kcat, such that
Vmax=[E]xkcat.
Regardless of the degree of displacement from equilibrium of the reactions
they catalyze, most metabolic enzymes operate far below their maximal
capacities in vivo (Suarez et
al., 1997
). Their operation at low fractional saturation of
substrate binding sites makes possible regulation by substrate (and product)
concentrations, as well as by alterations in binding affinities via
allosteric mechanisms or covalent modification. This also enables metabolic
enzymes to regulate, within very narrow ranges, the concentrations of
metabolic intermediates in pathways
(Atkinson, 1977
;
Fell, 1997
).
Species with similar body temperatures possess enzyme orthologues with
similar kcat values
(Hochachka and Somero, 2002),
so among such animals, the intra- and interspecific variation in
Vmax values at any particular step in metabolism is mainly
the result of variation in [E]. Allometric variation in flux
capacities is widespread. In various organs, capacities for membrane ion
pumping, i.e. Vmax values for
Na+-K+-ATPase
(Couture and Hulbert, 1995
)
and Ca2+-ATPase (Hamilton and
Ianuzzo, 1991
) decline with increasing mass. Allometry in
Vmax values for citrate synthase, a Krebs cycle enzyme
that serves as an index of oxidative capacity, is observed in the skeletal
muscles of mammals (Emmett and Hochachka,
1981
) and fishes (Childress
and Somero, 1990
; Somero and
Childress, 1990
). Consistent with these patterns is the decline in
mitochondrial content observed in skeletal muscle, heart, liver, kidney and
brain with increasing mass (Else and Hulbert,
1985a
,b
;
Hoppeler et al., 1984
;
Mathieu et al., 1981
). Because
enzymes and mitochondria usually do not operate at their maximum capacities,
allometry in flux capacities provides only a partial explanation for allometry
in cellular O2 consumption rates. Further insights can be derived
from the work of Porter (2001
)
and Else et al. (2004
), who
found decreasing rates of proton leak and ATP turnover (i.e. hydrolysis by
ATPases matched by rates of mitochondrial oxidative phosphorylation) in
mammalian and avian hepatocytes as a function of increasing body mass. Thus,
biochemical capacities (the outcome of both ontogeny and phylogeny)
as well as the actual rates of ATP hydrolysis and oxidative
phosphorylation (`system properties', controlled by multiple steps) decline
with increasing body mass.
Why do the rates decline? Pioneering studies of the regulatory mechanisms
that drive these allometric relationships in mammalian hearts have been
conducted by Dobson and colleagues
(Dobson, 2003;
Dobson and Headrick, 1995
;
Dobson and Himmelreich, 2002
).
Cardiac work rates and, therefore, rates of ATP hydrolysis per unit mass of
cardiac tissue, decline with increasing body mass. The allometric scaling of
cardiac energy expenditure is reflected in the scaling of bioenergetic
parameters that are thought to be involved in regulating mitochondrial ATP
synthesis. Cytosolic free ADP concentrations in cardiac ventricles increase
with body mass, such that 1/[ADP] scales as
Mb-0.23 and the cytosolic phosphorylation
potential, [ATP]/[ADP][Pi], scales as
Mb-0.28. Dobson et al. suggest that, in smaller
animals, the higher phosphorylation potential results in a higher Gibbs free
energy of ATP hydrolysis as well as a higher `kinetic gain', wherein small
fractional changes in [ADP] result in greater fractional changes in cardiac
VO2 relative to larger animals.
It is reasonable to expect, given the diversity of animals and their
adaptations to lifestyles and environments, that there should be many reasons
for the allometric scaling of rates and capacities at multiple levels of
organization (Suarez et al.,
2004). Although physical laws may dictate that capacities for the
supply of materials to cells via branching or fractal-like structures
must decline with increasing body mass, the lack of control of whole body BMR
by the supply of materials, as well as its only partial control over
VO2max, require a re-examination of the
consequences of allometry in capacities for delivery.
Metabolic scaling and symmorphosis
More than two decades ago, Taylor and Weibel
(1981) proposed symmorphosis,
a concept that says animals are designed economically such that structures and
functional capacities satisfy, but do not exceed, maximum physiological
requirements or `loads'. The proposal that capacities should match maximum
loads is, at least implicitly, an optimality hypothesis that says natural
selection eliminates excess capacities. It also predicts that capacities in
multi-step processes or pathways should be matched to each other. It is
important to digress by pointing out that symmorphosis has provoked
considerable controversy, mainly because of its evolutionary implications.
Favourable views include (and here is a caricature), `Symmorphosis is so
obviously correct that there is no need for the term and no need to study the
phenomenon; it is like saying that animals that need big feet
have big feet'. Another, consistent with the use of optimality
theory in evolutionary biology (Parker and
Maynard Smith, 1990
), is that symmorphosis is a good starting
hypothesis and deviation from its predictions is informative
(Diamond, 1992
). On the other
hand, critics state that the concept is naïve because optimal matches
between capacities and maximum physiological requirements are, in principle,
unlikely to result from natural selection and are, in reality, not observed
(Dudley and Gans, 1991
;
Garland and Huey, 1987
). This
is the position often taken by evolutionary physiologists, some of whom
suggest that `adequacy' or `sufficiency'
(Gans, 1993
) is a better way
of looking at animal design than optimality. Attempts to rigorously test
symmorphosis as a hypothesis have yielded a broad spectrum of outcomes, and
Garland (1998
) has presented
ideas concerning how proper interspecific tests of symmorphosis should be
conducted. In the cardio-respiratory system, Weibel et al.
(1991
) report that there is
excess capacity for O2 flux in mammalian lungs, unlike other steps
where there are close matches between physiological requirements at
O2max and
capacities for O2 transport. This interpretation has been
challenged by Garland and Huey
(1987
). In a survey of
available information from many different physiological systems, Diamond
(1998
) found excess
capacities, i.e. `safety factors', virtually everywhere in the vertebrate body
and at all levels of biological organization.
Debates concerning symmorphosis have subsided and the concept has come to
be regarded by some as a useful design principle, rather than a hypothesis
with precise and rigid criteria for acceptance or rejection. In this spirit,
the data available to comparative physiologists and biochemists (summarized in
Suarez et al., 2004) can be
seen as consistent with the idea that allometry, in capacities for the supply
of oxidative fuels and O2 to cells by branching or fractal-like
networks, has been matched, through evolution, by allometry in capacities for
substrate oxidation, aerobic ATP synthesis and ATP utilization. There are many
mechanistic reasons for why elephants should not consist of cells with the
same biochemical capacities as the cells in mice, and vice versa.
However, just as homeostatic mechanisms have evolved to ensure that rates of
ATP hydrolysis are matched by the rates of ATP synthesis in cells, at higher
levels of organization, regulatory mechanisms have also evolved to ensure that
delivery and utilization rates are matched to each other at rest as well as
during steady state, aerobic exercise. It is, perhaps, for this reason (among
others) that natural selection has not produced exact matches among functional
capacities at various steps in oxygen transport.
Supply and demand systems are better viewed as having coevolved with each
other, as having developed as interacting systems during ontogeny, and as
exerting acute regulatory influences upon each other in living animals.
Metabolic scaling is such a wonderful, many-splendoured thing that models
based on supply limitation alone fail to do it justice. Progress towards a
deeper understanding of the multiple causes of the allometric scaling of
metabolism depends upon further advances in our understanding of the nature of
structural and functional integration in animals, i.e. our ability to put
Humpty Dumpty together again (Schultz,
1996).
Acknowledgments
We are most grateful to Brad Seibel, Jim Childress and Ewald Weibel for helpful discussions. Supported by NSF grant IBN 0075817 to R.K.S. and predoctoral fellowships from NSERC and FCAR to C.A.D.
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