Roles of hierarchical and metabolic regulation in the allometric scaling of metabolism in Panamanian orchid bees
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
3 Smithsonian Tropical Research Institute, Barro Colorado Island, Republic
of Panama
* Author for correspondence (e-mail: suarez{at}lifesci.ucsb.edu)
Accepted 6 July 2005
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Summary |
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Key words: allometry, metabolism, glycolysis, hovering flight, metabolic scaling, orchid bee
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Introduction |
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Within an individual bee, >90% of the whole body metabolic rate during
hovering flight is due to O2 consumption by flight muscle
mitochondria (Rothe and Nachtigall,
1989; Suarez,
2000
). Therefore, rates of whole-body CO2 production
(
CO2) or
O2 consumption
(
O2) can be used
to estimate flux rates through catabolic pathways
(Suarez et al., 1996
) or
through mitochondrial respiratory chain enzymes (Suarez et al.,
1999
,
2000
). These fluxes represent
steady-state rates whose control can be analyzed quantitatively, at least in
principle, through metabolic control analysis
(Fell, 1997
). On the other
hand, interspecific variation in flux can be considered within the framework
proposed (but, originally, in an intraspecific context) by ter Kuile and
Westerhoff (2001
). At any step
in metabolism, such variation in flux may be due to `hierarchical regulation',
i.e. variation in enzyme concentration, [E], across species. An alternative is
that [E] at a given step is constant across species and variation in flux at
this step is due to variation in the concentrations of substrates, products or
allosteric effectors, i.e. `metabolic regulation'. A third possibility is that
variation in flux may result from a combination of hierarchical and metabolic
regulation.
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Materials and methods |
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The hierarchical regulation coefficient h, which is a
measure of the contribution of enzyme concentration [E], and the metabolic
regulation coefficient
m, which is a measure of the
contribution of mechanisms that result in the modulation of the activity of a
constant concentration of enzyme, to variation in flux, are related as:
![]() | (1) |
At any enzyme-catalyzed step i, h is a function of
the relative change in rate,
vi, divided by the
relative change in enzyme concentration,
ei, times
the ratio of change in ei to the change in flux
J. Assuming that
lnvi/
lnei equals 1
(ter Kuile and Westerhoff,
2001
),
![]() | (2) |
Similarly, at any step i, metabolic regulation results from a
change in an enzyme-catalyzed rate divided by the change in concentration of
its substrate, product or allosteric modulator (X), times the ratio
of change in X to change in J, such that:
![]() | (3) |
Orthologous enzymes from organisms of similar body temperature display
similar catalytic efficiencies (kcat values)
(Hochachka and Somero, 2002).
Because
![]() | (4) |
it follows that interspecific variation in Vmax
measures variation in ei. From Eq. 1, the slope of
lnVmax plotted against lnJ yields the
hierarchical regulation coefficient h. It follows that
1-
h yields the metabolic regulation coefficient
m.
We note here that this approach was not devised for interspecific
comparisons; ter Kuile and Westerhoff
(2001) applied it to the
analysis of variation in glycolytic rates in protozoa resulting from
experimental manipulation. However, the mechanistic bases for and the
quantitative relationships that describe intraspecific variation in flux among
protozoa apply equally well to interspecific variation in flux among orchid
bees. In a given steady-state situation (in this case, high rates of
carbohydrate oxidation during hovering flight), the interspecific variation in
flux can be accounted for either by interspecific variation in [E] or by
interspecific variation in substrate, product or modulator concentrations.
However, the interspecific variation in flux may also be due to variation in
other morphological, physiological and biochemical traits besides these. Thus,
in the work described herein, the value of slope of lnVmax
plotted against lnJ is potentially influenced by other traits that
covary with the biochemical parameters that we measured.
We address the above problem with the use of Felsenstein's method of
phylogenetically independent contrasts (PIC analysis;
Felsenstein, 1985;
Garland et al., 1992
).
Briefly, in conventional statistical analyses of interspecific data, it is
assumed that species are equally related to each other. In reality, they are
related to each other by their phylogenetic relationships. Because closely
related species tend to display greater similarity than more distantly related
ones, estimates of
h from slopes of linear regressions may be
biased by phylogenetic relationships and correlated traits other than those
hypothesized to account for interspecific variation in, as in the present
study, flux rates. PIC analysis provides a statistical approach that allows
for phylogenetic non-independence and makes possible the application of the
approach described by ter Kuile and Westerhoff
(2001
) to the analysis of
interspecific data. In the present work, PIC analysis was conducted using the
PDAP (Midford et al., 2003
)
module in Mesquite (Maddison and Maddison,
2004
). The analyses were performed using both gradual and
speciational models of character evolution, with branch-lengths obtained from
genetic distances inferred from cytochrome b partial sequences
(Darveau et al., 2005a
) or with
branch lengths set to 1.
Sources of data
Glycolytic flux rates were estimated from
CO2 during
flight (Darveau et al., 2005a
).
Enzyme Vmax values are from Darveau et al.
(2005b
). Hypothetical
phylogenies used in PIC analysis were generated on the bases of partial
sequences for the mitochondrial cytochrome b gene
(Darveau et al., 2005a
).
Calculations
Mathematical modeling of the phosphoglucoisomerase reaction was performed
using Mathcad Professional, version 8 (MathSoft, Inc., Cambridge, MA, USA).
Model assumptions, equations and parameters are provided in the text.
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Results and discussion |
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Our results are similar to those obtained by ter Kuile and Westerhoff
(2001) in the sense that most
of the variation in glycolytic flux in their intraspecific study of protozoa
was due to metabolic regulation, and complete or partial hierarchical control
contributed to the regulation of only a few steps in energy metabolism. It is
important to point out that
h and
m values are
not flux control coefficients; i.e. they are not measures of the contributions
of individual enzyme-catalyzed steps to the control of flux relative to other
steps in a pathway. Rather, they allow quantitative determination of the
relative contributions of two alternative mechanisms (i.e. hierarchical or
metabolic regulation) in explaining pathway flux changes at individual
steps.
Although allometric variation in biochemical flux capacities is widespread
among animals (Suarez et al.,
2004), the regulatory mechanisms underlying allometry in [E]
remain largely unexplored. Two quite noteworthy exceptions to this are
intraspecific studies on fish by Yang and Somero
(1996
) and Burness et al.
(1999
). In both studies are
found examples wherein [E] does not correlate directly with the tissue content
of the corresponding mRNA. This indicates that translation rates and/or rates
of enzyme degradation may play important roles in the allometric variation in
[E]. It would be worthwhile to determine whether HK mRNA content is
size-dependent in orchid bees. However, given the preponderance of metabolic
regulation revealed by our results, how such mechanisms lead to the allometric
scaling of metabolism in orchid bees also merits further consideration.
Metabolic regulation at the PGI step
In previous work using honeybees Apis mellifera, we combined
empirical and modeling approaches to try to understand the relations between
flux capacities and flux rates at the PGI step, a near-equilibrium,
reversible, glycolytic reaction at which glucose 6-phosphate, G6P, is
converted to fructose 6-phosphate, F6P
(Staples and Suarez, 1997). At
such a near-equilibrium step, the enzyme catalyzes reactions in both
directions, and net glycolytic flux equals the forward rate minus the reverse
rate. Using Haldane's equations (Haldane,
1930
) in a similar manner as Veech et al.
(1969
), we showed that the
high Vmax at this step could be rationalized on the bases
of the enzyme's dual roles, i.e. to maintain a net forward flux, equal to the
overall rate of glycolysis, and to maintain the reaction close to equilibrium.
We now consider how substrate and product concentrations in vivo
would have to change to account for the range of net flux rates observed
interspecifically among orchid bees. The Haldane
(1930
) equation applied to PGI
is:
![]() | (5) |
where J is the net flux, [G6P] and [F6P] are glucose 6-phosphate
and fructose 6-phosphate concentrations, respectively, Kf
and Kr are Michaelis constants for the forward (G6P is
substrate) and reverse (F6P is substrate) reactions, respectively. We used
Kf=1.07 mmol l-1 and
Kr=0.117 mmol l-1, obtained under
simulated intracellular conditions using purified honeybee PGI
(Staples and Suarez, 1997). It
is assumed that both Kf and Kr are
mass-independent and conserved across orchid bee species.
Keq is the equilibrium constant obtained in
vitro, equal to 0.3 (Staples and
Suarez, 1997
). Vr represents the
Vmax value in the direction of F6P conversion to G6P.
These scale isometrically in orchid bees and average 345.6 µmol
g-1 min-1 (Darveau et
al., 2005b
). Vf is the
Vmax in the glycolytic direction, estimated from the
Haldane (1930
) equation for
Keq,
![]() | (6) |
as 948.2 µmol g-1 min-1. This is close to the
Vf value measured empirically in honeybee flight muscles
(Staples and Suarez, 1997).
Eq. 5 is used to solve for the mass action ratios, i.e. the ratios of
[F6P]/[G6P] in the flight muscles, required to account for the range of
estimated flux rates. The decline in mass action ratio
(Fig. 2A) is extremely small, a
result that can also be demonstrated by holding [F6P] constant to 0.1 mmol
l-1, a value within the range measured in vivo
(Staples and Suarez, 1997
),
and solving for the range in [G6P] required to obtain the range of observed
net forward flux rates (Fig.
2B). The model predicts that a change of about 0.02 mmol
l-1 in [G6P] is enough to account for the entire range of variation
in flux across orchid bee species. A highly amplified response to a small
change in substrate concentration, as seen here, is a characteristic of
near-equilibrium reactions (Newsholme and
Crabtree, 1976
). Given this result, it seems unlikely that the
expected range of variation in [F6P]/[G6P] in orchid bee flight muscles would
be detectable in a comparative, interspecific study. At many other steps in
metabolism, this problem is exacerbated by even lower steady-state
concentrations of substrate and product (e.g.
Kashiwaya et al., 1994
). Thus,
a modeling approach such as the one described here may be the only way to
address the issue of metabolic regulation at such steps.
|
Further insights into the role played by metabolic regulation can be
derived from work concerning bioenergetic scaling in mammalian hearts.
Top-down control analysis has revealed that work rate (therefore ATP
hydrolysis rate) dominates the control of oxidative metabolism in the heart
(Diolez et al., 2002). Using
31P-NMR spectroscopy, Dobson and Headrick
(1995
) and Dobson and
Himmelreich (2002
) found that
cytosolic free [ADP] declines as body mass increases in hearts, such that
1/[ADP] and the cytosolic phosphorylation potential [ATP]/[ADP][Pi]
both scale allometrically with exponents close to -0.25. Dobson and colleagues
propose that these result in higher `kinetic gain' such that small changes in
[ADP] result in greater fractional changes in metabolic rate in the hearts of
small mammals compared with larger ones. This scheme provides a plausible
control mechanism by which allometry in work rate drives allometry in
metabolic rates. That this applies to orchid bee flight muscles is a testable
hypothesis.
Conclusion
The relative importance of the roles played by hierarchical regulation,
resulting from variation in [E], and metabolic regulation in accounting for
interspecific variation in metabolic rates is not well understood. Among
orchid bees, the allometry in metabolic rates during hovering flight involves
the hierarchical regulation of flux at the HK step and metabolic regulation at
all other enzyme-catalyzed reactions that we examined. Thus, although
techniques for the study of gene expression can be brought to bear on the
problem of metabolic scaling, the predominance of metabolic regulation in
accounting for interspecific variation in flux rates also warrants the
application of a systems approach to the control of flux
(Fell, 1997) and the manner in
which it scales (Darveau et al.,
2002
; Suarez et al.,
2004
).
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Acknowledgments |
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Footnotes |
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