P.W. Hochachka, "The metabolic implications of intracellular circulation", Proc. Natl. Acad. Sci. USA 96 , 12233

P.W. Hochachka, "The metabolic implications of intracellular circulation", Proc. Natl. Acad. Sci. USA 96 , 12233
The metabolic implications of intracellular circulation
P. W. Hochachka*
Departments of Zoology, Radiology, and Sports Medicine Division, University of British Columbia, Vancouver, BC Canada V6T 1Z4
Communicated by Ewald R. Weibel, University of Bern, Herrenschwanden, Switzerland, August 16, 1999 (received for review May 17, 1999)
metabolic regulation 兩 oxygen delivery 兩 oxygen regulation 兩 intracellular
perfusion 兩 intracellular diffusion
Two Models and Research Approaches in Cell Metabolism and
t is a rule of thumb in biology that many physiological and
molecular functions are the sum of individual processes linked in
sequence; in isolation, many such individual processes have no clear
functions at all. How such systems are designed and regulated have
presented perplexing problems to both biochemists and physiologists. Integrated function is often evaluated by comparing changes
in flux through the pathway per se with changes in concentrations
of substrates and products of individual enzyme reactions within the
pathway. Two guiding paradigms or frameworks (for convenience
we will term them model I and model II) have guided these
evaluations. Although rarely stated, the implicit assumptions in
model I studies are that simple ‘‘solution chemistry’’ rules apply to
the cell兾tissue as a whole, that changes in rates of enzyme–substrate
or protein–ligand interactions are generally diffusion dominated,
and that cell behavior can thus be considered to be similar to that
expected for a watery bag of organic materials. For model II studies,
the starting point is structure—the microanatomy of the inside of
the cell. These studies recognize that cells are filled with organelles,
membranous networks, microfilaments, microtubules, channels,
pumps, and motors, and that movements (not dead-still solutions as
in formal model I assumptions) dominate processes inside of cells.
In short, model II approaches explicitly assume that threedimensional order and structure constrain metabolite behavior and
that metabolic regulation theory has to incorporate this information to realistically describe in vivo processes. This polarization can
be illustrated by considering a major, so far unsolved problem and
paradox in the current literature; namely, that essentially all metabolite concentrations are remarkably stable (homeostatic) over
large changes in pathway fluxes (1).
Phosphate Metabolite Homeostasis in Human Skeletal and
Cardiac Muscles
One of our own recent noninvasive 31P magnetic resonance spectroscopy (MRS) studies (2) clearly illustrates the situation. In
gastrocnemius muscle, during exercise requiring up to 40-fold
changes in ATP turnover rates, the concentrations of ATP are
stable throughout the rest–work experimental protocols. The concentrations of phosphocreatine (PCr) and Pi change as linear
functions of work, but these changes are still much smaller than the
change in work (about 3-fold compared with the 40-fold increase in
ATP turnover rate). Interrogated simultaneously in soleus muscle,
these changes in [PCr] and [Pi] are found to be less than in
gastrocnemius, whereas [ATP] and [ADP] are again stable in all
states examined (2). Similar MRS studies of human (3) and dog (3)
heart indicate a metabolism so well regulated that change in cardiac
work is achieved with even less perturbation of MRS ‘‘visible’’
phosphate metabolites than in skeletal muscles.
Metabolite Homeostasis Is a General Rule
A key point is that the results for human muscles are in no way
unusual. Similar data for the adenylates, phosphagen, Pi, and H⫹
arise from studies of a wide assortment of animals (4–13) as well
as other human studies (6). These include invertebrates (7),
fishes and other ectothermic vertebrates (8–10), mammals, and
birds (see ref. 5). What is more, some of these studies have also
analyzed many of the intermediates in specific ATP supply
pathways, such as glycolysis (8–12), the Krebs cycle (13), amino
acid metabolism, and the ␤-oxidation pathway of free fatty acid
catabolism (see ref. 10 and references therein); here too, changes
in pathway intermediates are modest (0.5- to 3-fold) despite
large (from severalfold, up to and over 100-fold) changes in
pathway fluxes that are simultaneously sustained by the working
The implications emerging from such studies are (i) that ATP is
almost perfectly homeostatic under most conditions (except under
very extreme fatigue conditions) and (ii) that other intermediates
in pathways of ATP supply or ATP demand are stabilized within
Abbreviations: MRS, magnetic resonance spectroscopy; PCr, phosphocreatine; CPK, creatine phosphokinase; Mb, myoglobin.
*E-mail: [email protected]
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PNAS 兩 October 26, 1999 兩 vol. 96 兩 no. 22 兩 12233–12239
Two views currently dominate research into cell function and regulation. Model I assumes that cell behavior is quite similar to that
expected for a watery bag of enzymes and ligands. Model II assumes
that three-dimensional order and structure constrain and determine
metabolite behavior. A major problem in cell metabolism is determining why essentially all metabolite concentrations are remarkably
stable (are homeostatic) over large changes in pathway fluxes—for
convenience, this is termed the [s] stability paradox. For muscle cells,
ATP and O2 are the most perfectly homeostatic, even though O2
delivery and metabolic rate correlate in a 1:1 fashion. In total, more
than 60 metabolites are known to be remarkably homeostatic in
differing metabolic states. Several explanations of [s] stability are
usually given by traditional model I studies—none of which apply to
all enzymes in a pathway, and all of which require diffusion as the
means for changing enzyme–substrate encounter rates. In contrast,
recent developments in our understanding of intracellular myosin,
kinesin, and dyenin motors running on actin and tubulin tracks or
cables supply a mechanistic basis for regulated intracellular circulation
systems with cytoplasmic streaming rates varying over an approximately 80-fold range (from 1 to >80 ␮m ⴛ secⴚ1). These new studies
raise a model II hypothesis of intracellular perfusion or convection as
a primary means for bringing enzymes and substrates together under
variable metabolic conditions. In this view, change in intracellular
perfusion rates cause change in enzyme–substrate encounter rates
and thus change in pathway fluxes with no requirement for large
simultaneous changes in substrate concentrations. The ease with
which this hypothesis explains the [s] stability paradox is one of its
most compelling features.
less rigorously controlled concentration ranges. In one of our earlier
analyses (14), the latter condition was described as ‘‘relatively’’
homeostatic because the percent changes in concentrations of
intermediates are far less than the percent changes in metabolic
rates with which they correlate. For convenience, we shall refer to
the homeostasis of substrate concentration, [s], in the face of large
changes in cell work and cell metabolism, as the [s] stability paradox,
for which there are several explanations already advanced.
Traditional or Model I Explanations of the [s] Stability Paradox
A cursory examination of the literature indicates that currently
advanced explanations for metabolite homeostasis at any given step
in metabolism depend on the kind of enzyme involved. For simple
enzymes obeying Michaelis–Menten kinetics, in vivo operation is
assumed to be under near-equilibrium conditions with very high
catalytic capacities assuring sensitive ‘‘high gain’’ responses to small
changes in [substrate]兾[product] ratios (see refs. 1, 15, and 16 for
literature in this area). Such near-equilibrium function of creatine
phosphokinase (CPK) is the accepted explanation for the especially
precise regulation of ATP during rate transitions—the traditional
ATP ‘‘buffering’’ role of CPK (2). For allosteric enzymes, usually
functioning far from equilibrium under in vivo conditions, large
changes in rate can often be sustained with relatively modest change
in key modulators. A quintessential example that fits this pattern is
phosphofructokinase (PFK) regulation by several modulators that
operate mainly through effects on enzyme–substrate affinity, rather
than through changes in maximum reaction velocity. Substrate and
product concentrations, however, would be expected to change
drastically during large-scale allosteric activation of PFK, because
comparable in vitro catalytic rates require the enzyme to approach
saturation with its substrates (see ref. 10). In liver and other tissues,
where the difference between rest and maximally activated metabolism is modest, a widely accepted model used to explain stable
concentrations of adenylates (and other intermediates) at varying
ATP turnover rates assumes coordinate control by Ca2⫹ of both
ATP supply and ATP demand pathways (see ref. 17 and literature
therein). These mechanisms, formally similar to other allosteric
regulations, apply only to Ca2⫹-sensitive steps, which represent only
a small fraction of all the enzyme-catalyzed reactions in ATP
demand and supply pathways. For muscle and heart, these Ca2⫹mediated mechanisms in any event seem inadequate to account for
the large rate changes observed, and the same may apply for the
kidney, which can sustain a very high metabolic scope between
ischemic, low-flow states and maximally activated, high-flow states
(4, 10). In a third category are enzymes that are regulated by
phosphorylation–dephosphorylation or other covalent modifications; when coupled with signal amplification (18), large changes at
these specific loci in metabolism can be achieved with modest
change in substrate兾product concentrations, but again these processes apply to only a modest subset of enzymes in the complex web
of pathways that contribute to ATP turnover during cell work. In
cases involving covalent modification, the ratio of catalytically
active to inactive enzyme is the main parameter being modulated;
this is the main reason why change in reaction rate can occur with
minimal change in substrate concentrations. We generalized this
concept and reasoned (5, 19) that the simplest model to account for
widespread metabolite homeostasis assumes regulation of the
concentrations of catalytically active enzymes in pathways of both
ATP demand and ATP supply (eo regulation). This would achieve
changes in ATP turnover rates proportional to the kcat of the
enzymes involved with no required change in substrates or products. Such regulation could be achieved by protein–protein based
‘‘on–off’’ switching between active and inactive forms of enzymes,
as in actomyosin ATPase (5), by redox-based ‘‘on–off’’ switching,
as in V-type ATPases (20), or by translocation from an inactive to
an active intracellular location (essentially isolating enzymes from
their target substrates), as in glucose transporters (21).
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In short, to explain metabolite homeostasis in varying metabolic
states with simultaneous precision and integration of linked sequences of enzyme function, several regulatory models are currently being evaluated by workers in this field (1, 4, 6, 22–29). These
include: (i) simple feedback and mass action controls (for so-called
equilibrium enzymes), (ii) allosteric controls (for regulatory enzymes such as phosphofructokinase), (iii) models involving the
regulation of eo (the concentration of functional catalytic sites by
means of alteration in protein interactions, by change in phosphorylation state, by change in redox state, or by translocation from
inactive to an active intracellular location), and additionally, (iv)
various versions of metabolic control analysis originally introduced
over a decade ago (see ref. 30).
Such studies are admittedly, if variably, successful in explaining
metabolite homeostasis during changes in work rate [some, like
metabolic control analysis, are empirical mathematical models that
do not directly address the issue of mechanisms of metabolite
homeostasis and, in fact, recognized this as an issue only after our
papers began to appear in the literature (31)]. Despite some
admitted success of these earlier analyses, for models assuming key
regulatory roles for pathway intermediates, the striking homeostasis of most metabolites consistently presents a thorny problem that
has not really been acceptably explained: namely, the percent
change in putative regulatory intermediate is always less than the
percent change in flux required to match the change in ATP
turnover rate. Put another way, the kinetic order is usually ⬍1, too
low for change in [s] to be ‘‘driving’’ the observed flux or metabolic
rate changes. Given that this is observed for all categories of
enzymes discussed above, it would be a statistical miracle to observe
similar [s] stability for all of them. Yet a cursory count for pathways
of glucose, fat, and amino acid metabolism (5, 10) shows that the
percent changes in concentrations of more than 60 substrates and
intermediates quantified to date are far less than the percent
changes in pathway and enzyme flux rates with which they correlate.
The only metabolite that seems to be an exception is oxygen. Even
this turns out not to be a real exception, but the research here is so
instructive that it is useful to reason our way through the empirical
Oxygen Delivery Is Fundamental to Metabolic Regulation
A huge literature has developed on how O2 functions both as a
substrate and as a potential regulator of tissue metabolism over
varying times of exposure (32–40), and I shall not review this
comprehensively at this time. Suffice it to emphasize that over and
over again numerous studies have found essentially 1:1 relationships
between O2 delivery and muscle work, in some cases somewhat
offset by changes in O2 extraction. For example, in recent studies
using a dog gastrocnemius preparation (26, 33), we found such a
relationship between O2 delivery and work over an 18-fold change
in ATP turnover rate. Later, Hogan et al. (27) used the same
preparation to analyze subtle submaximal work changes. These
transitions were sustained with immeasurable change in [PCr], [Pi],
and [ATP]; presumably, therefore, the concentrations of other
metabolites in participating metabolic pathways were also stable, as
in other systems (4, 5, 11). Yet, through these transitions, a 1:1
relationship between change in work and change in O2 delivery was
maintained. Because these kinds of results are qualitatively similar
to those found in many other studies, we and many others in the
field accept that O2 plays a key role in regulating change in ATP
turnover (5). But how is the O2 signal transduced within the cell?
Oxygen Signal Transduction in Working Muscle
Unfortunately, the answer to this question remains unclear, and the
only mechanisms proposed by traditional studies in this area assume
the Krogh cylinder and calculate smooth diffusion gradients within
the cell ending in mitochondrial O2 sinks. So far, this approach has
been less than satisfactory because, to unravel the puzzle of how O2
delivery translates into effects on metabolism within the cell, we
aerobic maximum work rate [representing huge ATP turnover
rates, equivalent to about 50–80 ␮mol of ATP ⫻ g⫺1 ⫻ min⫺1 (5)],
percent MbO2 (65–70%) did not change significantly, in agreement
with earlier studies (37), whereas at the maximum work rate, a
further modest desaturation to about 50% MbO2 occurred, which
is not in full agreement with earlier data (37). Because of the mixed
fiber and recruitment problems, we are not surprised by these
modestly different results, and, at least tentatively, we consider that
the small discrepancies probably arise from artifacts caused by
differing metabolic states in different fiber types. Thus, they do not
strongly influence our main conclusion that [O2] is largely homeostatic.
In fact, even if most workers probably would accept that Mb
should function to buffer intracellular [O2], the significance of this
has not been fully appreciated. As Carl Honig explained to the
author in a discussion in 1987, this may be because of a too
enthusiastic acceptance of traditional diffusion models assuming
smooth gradients across the capillary–muscle cell threshold all the
way to the mitochondrial sinks. Such models (see ref. 39 for an
example), which assume complete homogeneity and necessarily
ignore the issues of fiber type and recruitment heterogeneity, are
not accepted by the Honig group (40). According to Honig et al.,
the structure of the capillary–muscle system develops steep gradients (and localized high O2 fluxes) only at the capillary–muscle
interface, but very shallow gradients within the muscle cell per se,
as indeed found by the above later MRS data on percent MbO2 in
vivo (36–38). That is why, in one of our earlier reviews (14), we
already accepted the MRS data on percent MbO2 at face value and
emphasized that, under normoxic conditions, O2 is perfectly homeostatic in the sense that its concentration is stable even while its
flux to cytochrome oxidase can change by two or more orders of
magnitude. In the examples given (1, 37, 39), the concentration of
O2 ranged between 2 and 4 ␮M during pathway flux changes from
about 1 to ⬎80 ␮mol of ATP ⫻ g⫺1 ⫻ min⫺1 [these high mass
specific metabolic rates are attainable because most of the cardiac
output during these protocols is available for supporting the work
of relatively small muscle masses (see ref. 5)].
To recapitulate, the situation arising from these new studies of O2
and metabolic regulation can be summarized as follows: First,
because of the buffering role of Mb, O2 concentrations are low (in
the P50 or Kd range of about 3 ␮M), and intracellular [O2] gradients
must be quite shallow. The latter point is more fully discussed by the
Rochester group (24, 40); one of the most important insights
emphasized by these researchers is that the capillary–muscle contact surface area is only a fraction of the surface area of inner
mitochondrial membranes and cristae; at steady state, of course, the
same net O2 transfers are occurring at both sites. That is why the
highest gradients and highest O2 fluxes must be at the smaller
contact zones (i.e., at capillary–muscle cell interfaces) and why O2
gradients are necessarily much shallower in the cytosol. Second, the
low intracellular [O2] is powerfully ‘‘buffered’’ by Mb and remains
essentially stable throughout large changes in work and metabolic
rates. Thus the [s] stability paradox (constant [s] when flux and
hence enzyme–substrate encounter and catalysis rates are increasing) applies to O2 as well as to other metabolites. Nevertheless, O2
consumption and O2 delivery are closely related, suggesting a key
role for oxygen in metabolic regulation.
Given that it is O2 delivery, not intracellular [O2], that correlates
with work rate, the problem we are left with is the issue of how the
O2 signal is transmitted to the machinery of cell metabolism. At this
time, we admit that there is no widely accepted answer. When we
first recognized this puzzling situation, we proposed a model that
postulates an O2 sensing system presumably located in the cell
membrane (or even more distally) and signal transduction pathways
or mechanisms for ‘‘telling’’ the cell metabolic machinery when and
how potently to respond to changing availability of O2 (5). However,
the nature and even existence of such sensing and signal transducing
systems remain to be elucidated. In any event, this and all of the
PNAS 兩 October 26, 1999 兩 vol. 96 兩 no. 22 兩 12235
require hard data on intracellular O2 concentration. The problem
is that for most tissues this key parameter remains elusive and
unknown. The situation in muscle is more favorable, however. In
this tissue, myoglobin (Mb) supplies a direct intracellular detector
of [O2]. Mb is a relatively small, monomeric respiratory pigment
occurring in heart and mitochondria-rich skeletal muscles at concentrations of ⬍0.5 mM; in muscles of marine mammals such as
seals, Mb concentrations reach into the 4–5 mM range. Gene
knockout experiments (34, 35) show that mice can survive without
Mb (34) but that they can do so only by activating compensating
mechanisms such as increasing capillary densities and blood O2
carrying capacity (35). It is therefore usually assumed that Mb is
functionally important under usual physiological conditions. At
37°C, O2 solubility in physiological solutions is about 1 ␮M兾torr (1
torr ⫽ 133 Pa). Because the reaction Mb ⫹ O2 º MbO2 is always
in equilibrium, with a P50 of 3 torr (Kd of about 3 ␮M), whenever
[O2] is less than saturating for Mb, measures of percent MbO2
directly estimate intracellular [O2]. Earlier attempts at such measurements with working muscle preparations relied almost exclusively on near infrared spectroscopy (see ref. 36 and references
therein). More recently, MRS is being used to take advantage of a
histidine-H being 1H MRS ‘‘visible’’ in deoxyMb but being MRS
‘‘invisible’’ in oxyMb. This new technology supplies workers in the
field with a noninvasive window on the oxygenation state of muscles
in different work and metabolic states, at least for muscles with a
high enough Mb to be 1H MRS ‘‘visible.’’ When this method was
applied to both working human skeletal muscles (37) and to heart
(38), the same striking results were reported: essentially stable
percent MbO2 through large changes in work rate. In such tests, as
soon as a work load is imposed [even very low intensity exercise,
such as unloaded pedaling (37)], percent MbO2 quickly establishes
a new steady state, usually between 40% and 70% saturation, both
as a function of time (36) and as a function of tissue work intensity
(37, 38). Along with gold-labeling studies showing a random Mb
distribution in rat heart and skeletal muscles (S. Shinn and P.W.H.,
unpublished data), the MRS data imply that percent MbO2 and
intracellular [O2] both remain relatively constant up to the maximum sustainable aerobic metabolic rate of the tissue (37, 38). As
CPK serves to ‘‘buffer’’ ATP concentrations during changes in
muscle work, so Mb apparently serves to ‘‘buffer’’ intracellular
oxygen concentrations in different metabolic states. Parenthetically, it should be acknowledged that the region of interest in these
kinds of MRS studies is large, and the MRS data necessarily are
averages of large numbers of fibers. Human muscles, like muscles
in other mammals, are formed from mixtures of fiber types, and as
work intensity rises for a given muscle mass, there may be changes
in recruitment and in the percent contribution of different fiber
types. This problem does not arise in studies of heart muscle, which
is biochemically rather homogenous (38). Whereas Richardson et
al. (37) apparently avoided this artifact, this does not seem to be the
case in a recent study (39) on an unknown mix of fibers in human
calf muscle. Evidence of the problem initially arises from the 31P
MRS data, which showed an expected linear decrease in [PCr] as
work increased; at maximum aerobic work, [PCr] changed by
maximally about 3-fold (39). Because the same [PCr] change occurs
when gastrocnemius work rate reaches only 40% of sustained
aerobic maximum, but much smaller changes in [PCr] occur in (the
mainly slow fibers of) soleus during the same work transition (2), it
is probable that the regions of interest in the Mole et al. (39) study
may have overlapped into muscles rich in slow-twitch fibers, where
the change in [PCr] is less for a given level of work than in fast-twitch
fibers (2). Otherwise, it would be difficult to understand why their
preparation had to be pushed to its maximum work level to achieve
the same percent [phosphagen] shifts that we observed at only 40%
of aerobic maximum (2). For these reasons, the percent MbO2
values recorded at different work intensities almost certainly represent different combinations of fiber types. Nevertheless, these
studies (39) reported that at about 50% and 80% of sustained
other above attempts to explain the [s] stability paradox are based
on diffusion control of change in enzyme–substrate encounter
rates. Model II questions this assumption. It takes an entirely
different tack and postulates that intracellular circulation, not
diffusion, is the main means for bringing ligands and their binding
sites together during upwards or downwards transitions in metabolic and tissue work rates.
Model II: Explaining the [s] Stability Paradox with Intracellular
Structure and Intracellular Perfusion Systems
Conceptually, the major difference between the above traditional
approach to metabolic regulation and model II is the emphasis
placed on intracellular order and structure. The point of departure
for the latter view is that the cell is not a bag of enzymes; instead,
it assumes that most metabolic systems operate within an ordered
milieu and that important functional consequences arise. Time and
space will not allow a detailed review of the evidence for this
position. Suffice it to emphasize that it arises from a variety of
approaches and that the overall hypothesis is constructed from
several different lines of evidence favoring intracellular perfusion
and lines of argument not favoring diffusion as the main means for
changing the rates at which enzymes and their substrates are
brought together. First and most fundamental is the structural
argument: ultrastructural, histochemical, and cytochemical studies
do not indicate the cell as a static bag of enzymes, but rather a
three-dimensional membrane-bound microcosm housing an internal milieu filled with complex organelles, motors, membranes,
cables, trabecullae, pumps, and channels. Rather than a static,
dead-still solution [as would be required for formal application of
laws of diffusion (41)], the internal media of cells are very much
‘‘alive’’ in the sense that movement is the rule of thumb, movement
of organelles, of particles, and of cytosol. In large cells, so-called
cytoplasmic streaming occurs at rates from ⬍1 to about 80 ␮m兾sec
(42, 43). The process is metabolically controlled (44), varies with
metabolic state (42), is based on ATP-dependent and ATP-utilizing
myosin motors [so-called unconventional myosin isoforms (45)]
that can be activated to run on actin filaments (45, 46), and behaves
for practical purposes like an intracellular circulation system. What
is more, because of the conservative nature of macromolecular
structures and functions, we have good reasons for thinking that
this, and comparable systems based on kinesin and dynein motors
running on microtubules, are widespread and probably characteristic of all cells (46). Additionally, in contrast to what might be
expected of a bag of enzymes, over a half-century of research has
clearly concluded that many metabolic pathways and their component enzymes are restricted to specific cell compartments, and
numerous so-called soluble enzymes (see ref. 47 for a recent study
of aldolases) show intracellular binding to specific intracellular sites
(48, 49). Order, structure, and circulation are thus the key players
in the game, as far as the literature on cell ultrastructure is
concerned, and it is not a diffusion-dominated game. Take away the
order and the system behavior falls apart; sometimes function is lost
completely. A good recent example of this comes from genetic
studies of Drosophila flight muscle metabolism. Whereas earlier
studies had shown that aldolase, glyceraldehyde-3-phosphate dehydrogenase, and ␣-glycerophosphate dehydrogenase colocalize
mainly at Z-discs, Wojtas et al. (50) used clever genetic manipulations (that influenced binding but not overall catalytic activities) to
show that mislocating these enzyme activities in the cytosol rather
than correctly bound to Z-discs would render Drosophila flightless.
This is a compelling demonstration that enzyme–substrate encounter by simple diffusion mechanisms is inadequate to maintain
function, even if all three enzymes are expressed at adequate
activities; their three-dimensional organization is part and parcel of
in vivo regulated function of the pathway.
Second is the argument on macromolecular diffusional constraints. As we might expect from the above (and indeed find), the
intracellular mobilities of enzymes and of carrier proteins such as
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Mb are not equivalent to those in simple aqueous solutions. For
example, intracellular diffusibility estimates for Mb in the cytosol
range from as low as 1兾10 that found in simple solutions (51) to
values of about 1兾2 (52). Interestingly, the latter MRS study
estimated rotational diffusion, whereas Juergens et al. (51) estimated translational diffusion and these may change independently
(53). Be that as it may, even so-called soluble cytosolic enzymes and
other proteins are also apparently highly restricted in their intracellular mobility (51); again, this picture is not easily compatible
with the concept of the cell as a bag of easily diffusible enzymes.
Order and structure seem to be constraining the intracellular
behavior of macromolecules, and their restricted mobilities would
not facilitate the kind of enzyme–substrate encounters required for
simple solution models of cell function. In contrast, an intracellular
perfusion system could easily circumvent these kinds of limitations
on bringing enzymes and substrates together.
Third is the argument on metabolite mobility. Because of the
complexity of the internal milieu, the translational mobility even of
simple molecules may be restricted compared with simple solutions
(53), and this is especially true in the mitochondrial matrix (54). A
recent study dissected different contributions to limiting mobility of
intracellular metabolites. Compared with water, hindrance to translational diffusion in cytoplasm could be attributed to three independent factors—viscosity, binding, and interference from cell
solids: (i) fluid-phase cytoplasmic viscosity in the fibroblasts used in
the study was nearly 30% greater than water; (ii) nonspecific,
transient binding of small solutes (such as the fluorescent probe
used in the study) by intracellular components of low mobility
decreased metabolite mobility by about 20%; and (iii) translational
diffusion of small solutes was hindered 2.5-fold by collisions with
cell solids comprising about 15% of isosmotic cell volume. Together, these three factors could account for translational diffusion
in cytosol that was decreased to only 27% that observed in water
(53). Interestingly, these studies also demonstrated that, during
osmotic stress (cell volume increasing to 2 times isosmotic volume,
during which the cells sustained a proportional increase in metabolism as part of osmoregulatory costs), the relative translational
diffusion coefficient increased by about 6-fold, while the rotational
diffusion constant remained constant. Similar insights arise from
recent studies of the phosphagen system in vertebrate muscles.
Recall that two fundamental assumptions underlie traditional
dogma on CPK function in phosphagen-containing cells: (i) CPK
always operates near equilibrium, and (ii) CPK has access to, and
reacts with, the total pool (tCr) of PCr and creatine (Cr). Recently,
we tested the latter assumption in fish fast-twitch muscle by
introducing [14C]Cr into the muscle pool in vivo (55). Current model
I theory would predict that at steady state, after [14C]Cr administration, the specific activities of PCr and Cr should be the same
under essentially all conditions. In contrast, we found that the
specific activity of PCr greatly exceeded that of Cr in various
metabolic states between rest and recovery from exercise. The data
imply that a significant fraction of Cr is not free to rapidly exchange
with exogenously added [14C]Cr; releasing of this unlabeled or
‘‘missing’’ Cr on acid extraction accounts for lowered specific
activities. Because Cr dominates tCr only in fatigue states, the
reduced mobilities implied by these studies correlate with states of
lowered metabolic rate. In a follow-up study, 1H MRS was used to
further evaluate the in vivo behavior of (the methyl triplet of) tCr
in human gastrocnemius muscle. We found (56)† that the T2 values
for tCr decrease on transition from rest (through a volitional
exercise protocol) to ischemic fatigue. In ischemic fatigue, the ATP
turnover rate of human calf muscle is severely depressed (5).†
Because Cr forms the bulk of tCr in ischemic fatigue, its MRS
behavior (especially the reduced molecular mobility implied by the
M. E., Allen, P. S., Gheorghiu, D., Hanstock, C. C. & Hochachka, P. W., Proceedings
of the International Society of Magnetic Resonance Meeting, 1997, Vancouver, p. 1337.
it easily explains the [s] stability paradox of pathway substrates and
intermediates, including O2. As in the perfusion of tissues such as
muscle mentioned above, the rate of intracellular metabolism by
this model is a product of intracellular perfusion rate: the greater
the intracellular perfusion rate the greater the metabolic rate with
no concomitant change in substrate concentrations required—a
coarse control principle, long and well appreciated by physiologists
as the Fick principle. To be sure, this need not rule out other control
mechanisms, the kinds that have so far absorbed much of metabolic
research; it merely puts them into a different physiological context.
For O2 transport, this view places Mb function into an entirely
different perspective as well, where the fundamental purpose of an
intracellular Mb may be to equalize [O2] everywhere in the cytosol.
Functionally, this would ensure that intracellular convection would
always be delivering similar amounts of O2 per unit volume of
cytosol to cytochrome oxidases. This model would predict that Mb
knockout mice would either be seriously disturbed [as indeed
frequently noted (34)], or through ontogeny would develop compensatory mechanisms [as indeed is also observed in those mice
that survive Mb gene deletion (35)]. However, from this new point
of view, the ‘‘buffering’’ function of Mb, the main function of a half
O2 saturated, randomly distributed Mb, is to ensure a similar [O2]
everywhere in the cytosol (and simultaneously to minimize or even
destroy intracellular [O2] gradients). While this model is consistent
with the minimal intracellular [O2] gradients in muscle cells proposed by the Honig, Connett, and Gayeski work (40), it takes on
quite a different meaning. Finally, the concept of an intracellular
perfusion system supplies purpose and meaning to intracellular
movements (motor-driven or otherwise induced cytoplasmic
streaming), which, until this point in time, have been pretty well
ignored by traditional metabolic studies.
Diffusion of course is a limited solution to limited problems.
Earlier (5), I pointed out that, in the up-regulation of metabolic
capacities of skeletal and heart muscles [for example, in organisms
such as the hummingbird (67)], the higher the O2 fluxes required,
the shorter the diffusion distances and the less and less dependent
on diffusion muscle metabolic organization seems to become. Of
course, these same adaptations mean that the higher the fluxes
required, the shorter the intracellular perfusion distances. The
flight muscles of insects might represent these phenomena close to
their limit, with tracheal-supplied mitochondria and myofilaments
being packed so tightly together that there is hardly any room left
for (and hardly any need for) any intracellular perfusion systems
(see refs. 5 and 67 and references therein). Adaptations in the same
direction seem to be evident in recent Mb gene knockout studies,
which show that some Mb-free mice survive the deletion, apparently because of compensatory mechanisms such as increased
capillary densities (35). Although heart muscle cell diameters were
not recorded (35), in similar CPK knockout protocols, ontogenetic
adjustments led to smaller muscle cells (see ref. 5). Functionally,
these adjustments would mean minimizing diffusion and perfusion
distances, as in hummingbird and insect flight muscles. To this
point, physiologists have generally agreed that organisms get
around diffusion limitation problems of O2 transport by relying on
convection systems: ventilation at the lungs and circulation to the
tissues, interspersed with diffusion-based steps along the way. The
concept of intracellular convection modifies our overall view to
include an intracellular component to the chain of convective and
diffusive steps in the overall path of O2 from air to mitochondria
In considering the concept of intracellular convection, early
pioneers in this field may be prone to over-enthusiastic pressing of
their case; this is understandable because it seems to explain so
much previously puzzling data so easily (41, 58). Nevertheless, there
clearly remain critical functions that are largely or solely diffusionbased, so the understandable over-enthusiasm with which model II
proponents minimize the importance of diffusion in energy metabolism puts them at risk of casting away a very useful concept. To
PNAS 兩 October 26, 1999 兩 vol. 96 兩 no. 22 兩 12237
reduced T2 values) is consistent with the earlier 14C results and may
explain the mystery of ‘‘missing’’ creatine in the 14C study. The key
point is that, just as in the Kao et al. fibroblast study (53), the
solution behavior of metabolite-sized molecules such as Cr seems
to be a function of the metabolic state of the tissue—high molecular
mobilities (caused in part by high intracellular circulation rates?)
correlating with high metabolic rates. In all of these kinds of studies,
order and structure seem to dominate the intracellular behavior of
micromolecules such as metabolite intermediates, and serious
constraints on diffusion would again not readily facilitate largescale increases or decreases in enzyme–substrate encounters as
required for simple solution models of cells functioning in widely
varying activity and metabolic states. Again, these limitations could
be easily circumvented with intracellular circulation systems.
Given that enzymes are structurally localized and not free to
readily diffuse about and that substrates are also relatively restricted
compared with simple solutions, workers in this area (41, 57, 58)
consider diffusion by itself to be an inadequate, inefficient, and
minimally regulatable means of delivering carbon substrates and O2
to appropriate enzyme targets in the cell under the variable
conditions and rates that are required in vivo. Instead, an intracellular circulation or convection system is proposed as an elegantly
simple ‘‘assist’’ mechanism providing for the efficient bringing
together of substrates (including O2) and enzymes under varying
metabolic conditions. The main evidence for this concept is indirect
and comes from studies showing cytoplasmic steaming at velocities
far exceeding those to be reasonably expected from diffusion alone,
especially in the absence of steep [metabolite] and [O2] gradients.
As mentioned above, such intracellular movement is known to be
[possibly Ca2⫹ (44)] regulated and to be based on two kinds of
molecular motors: myosin motors traveling on actin filaments and
kinesin or dynein motors traveling on tubulin tracks (59, 60). Even
organelles such as mitochondria display metabolically regulated
movement in cells; actin and tubulins can both be used as tracks for
moving mitochondria, but questions of where and how such motors
interact with (and are localized on) the outer mitochondrial membrane are not yet fully resolved (61). Nevertheless, mitochondrialbound myosins are clearly required for directional movements of
mitochondria (62), and a recent study showed that depolymerization of F-actin causes a large (5-fold!) decrease in the velocity of
mitochondrial movement (63), presumably coincident with a large
drop in O2 consumption caused by the same kind of manipulation
(64). Except for a few recent analyses (41, 57, 58), the metabolic
implications of such intracellular convection systems have been
completely overlooked (or ignored). However, the idea of intracellular convection as a means for increasing enzyme–substrate
encounter rates with increasing tissue work is quite compelling. Not
only is the rate of cytoplasmic streaming variable [over at least an
80-fold or more range (42, 43) as would be required in vivo], in
several cell systems (43, 65) there is evidence for a direct relationship between cell work and cytoplasmic streaming rates; and, in a
plant cell model, a linear relationship exists between the myosin
motor velocity and the force against which it must operate (66). The
1H MRS studies mentioned above (56)† show that low metabolic
rate states (such as ischemic fatigue) correlate with low molecular
mobilities of key metabolites such as Cr (consistent with times of
low intracellular circulation rates). Using fibroblasts and osmotic
stress, the studies of Kao et al. (53) similarily show that increasing
metabolic rate correlates with increasing molecular translational
mobilities (which, again, could be consistent with increased intracellular circulation rates). Thus, we already have some good reasons
for anticipating that changes in intracellular convection correlate
with changes in cell metabolic rate, although more studies along
these lines are clearly desirable.
From the point of view of the current paper, the key advantage
of this model is that it easily explains how enzymes and substrates
can be brought together and how reaction rates can occur at widely
varying rates with minimal change in substrate concentrations; i.e.,
finally assemble a model that can realistically explain a realistic
working range of metabolic systems, what seems to be required for
the future is an opening up of channels of communication between
the above two very differing views of metabolic regulation.
dominated by intracellular perfusion or convection systems. Current evidence suggests that cytoplasmic streaming (at surprisingly
high maximum rates) is controlled by means of controlling molecular motors on actin filaments or on microtubules. Our analysis of
the metabolic implications of an intracellular circulation system
leads to the concept of intracellular convection as an added and
critical means for regulating rates of enzyme–substrate encounter.
Increasing enzyme–substrate encounter rates with increasing perfusion rates easily explains changes in pathway fluxes with minimal
changes in substrate concentrations. This mechanism for accelerating reaction rates would work equally well at all steps in complex
metabolic pathways, no matter what the catalytic and regulatory
properties of enzymes might be at these loci in metabolism. Indeed,
the ease with which the model II (intracellular convection) model
explains the [s] stability paradox is one of its most appealing
Finally, it may be worth emphasizing that developments in the
above two research approaches have been progressing for the last
three to four decades, along surprisingly independent trajectories,
with minimal communication between the two fields. The usual
lack of dialogue between the two research approaches is all the
more peculiar when it is pointed out that some of us sometimes
work within one paradigm, while at other times we work within the
other’s constraints. I include myself in this situation; for example,
the study by Allen et al. (2) illustrates model I approaches, while
Hochachka and Mossey (55) clearly illustrate a model II preference.
Because both paradigms cannot be right, we consider that it may be
time to treat the schizophrenia in these two fields, a process that for
certain would require opening up communication channels between them. Whether or not this turns out to be possible remains
to be seen; nevertheless, the present paper is part of our ongoing
attempt to facilitate this process.
Acute responses to increases in cell work (to increases in ATP
demand) invariably require the activation of ATP supply pathways.
The requirements for cell homeostasis would also require that these
transitions occur with minimal perturbation of metabolite concentrations, whereas most metabolic regulation models would predict
major changes in concentrations of pathway intermediates. Empirically, it is observed that the demands of cell homeostasis prevail;
i.e., that during transition from low to high work rates, the concentrations of most substrates in ATP demand and ATP supply
pathways are remarkably stable. I term this the [s] stability paradox
in this paper. Researchers have tried to resolve this paradox while
working within two guiding paradigms. The first, model I, looks on
the cell as a watery bag of enzymes. Within this framework, several
explanations have been advanced to explain the apparent homeostasis of pathway metabolites during small- and large-scale
changes in pathway fluxes. While admittedly successful, different
mechanisms have to be postulated to account for different kinds of
enzymes, and thus different mechanisms have to be postulated for
specific loci in metabolic pathways. On balance, we consider it
unlikely that all of these different mechanisms would summate to
similar [s] stabilities observed for more than 60 metabolites at
different loci in different metabolic pathways. So, within model I
approaches, we consider that the [s] paradox remains unresolved.
Model II approaches to metabolic regulation recognize cell
structure to be an inherent part of cell function. A subset of these
studies places especial emphasis on the fact that the intracellular
milieu is not a still, watery solution in which bulk transfer of
metabolites occurs mainly by diffusion; instead, it is a threedimensional structured system in which transport of materials is
These studies were supported by the Natural Sciences and Engineering
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