Editorial Commentary
Equilibrium Enzymes in Regulatory Systems
A Problem in Scalar-Vector Transition
Patrick F. Dillon
See related article, p 68–73
T
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he work by Karamat et al1 contains evidence that creatine
kinase (CK) mRNA in vascular smooth muscle has a direct
correlation with blood pressure. This result is both interesting
and problematic: there is no previous evidence from in vitro
experiments that smooth muscle CK is a regulatory enzyme,
and there is considerable evidence that the enzyme is at equilibrium inside cells. As the data indicate a regulatory role for
the equilibrium enzyme CK in control of blood pressure, the
general problem of investigating the role of an equilibrium
enzyme in a regulatory system is inherently intriguing.
Cytosolic CK has been always considered an equilibrium
enzyme, whether in striated or smooth muscle. This assumption was used to calculate the free concentration of ADP in
cells, in which the concentrations of ATP, PCr, and creatine
could be determined. Phosphate NMR was used to measure
the relative free concentrations of ATP, PCr, and Pi, and from
the chemical shifts of Pi and β-ATP, the pH and free Mg++
of the cell could also be determined. Coupled with chemical
measurements of creatine, and using in vitro measurements of
the CK equilibrium constant, the free concentration of ADP
(and thus the free energy of the cell) could be calculated.
Measurements of free ADP cannot be made from chemical
analyses because ADP liberated from f-actin compromises
these measurements.2 ADP could not be seen as a peak in striated muscle phosphate NMR because of both its low concentration and chemical shift similarity to the ATP resonances.
The lower concentration of Mg++ in smooth muscle meant
that β-ADP had a different chemical shift from γ-ATP, and
ADP peaks could be seen under anoxic conditions in vascular smooth muscle.3 Using the relative concentrations of ADP
from these experiments, it was shown that smooth muscle CK
is both at equilibrium, and has an equilibrium constant inside
cells consistent with its in vitro determination. Given this, the
results presented herein are unexpected.
All living biological systems have to exist at free energy
levels greater than that of the local ambient energy. Systems
can only exist at a steady state in this elevated energy state
with the constant input of energy exactly balancing the
increase in entropy of the system over time. Maintenance of a
living system requires that the system be in a nonequilibrium
state. However, this requirement does not mean that every part
of the system must always be in a nonequilibrium state. In
the glycolytic pathway for instance, hexokinase, phosphofructokinase, and pyruvate kinase all have free energies that
indicate nonequilibrium states, while all of the other enzymes
are at equilibrium.4 Furthermore, PFK is a regulatory enzyme,
exhibiting rate changes produced by nonsubstrate molecules
as well as crossover conditions in which the rate can be shown
to increase even when the substrate concentration decreases.5
CK has never been shown to have these properties. Thus, an
increase in energy flux tied to CK concentrations can only
occur if the flux is rate limited by CK, which therefore would
not be at equilibrium.
CK has been implicated in the creatine shuttle hypothesis,
in which the sites of ATP production (mitochondria) and consumption (actomyosin ATPase) are physically separated. The
hypothesis has the phosphate flux borne by PCr, rather than
ATP, based on the smaller size and more rapid diffusion of
PCr compared with ATP, and creatine compared with ADP.
The creatine shuttle can only work when diffusion is the ratelimiting aspect of energy use, a condition that can only exist
when the diffusion distances are large, and the energy consumption is large.4 These conditions are unlikely to occur in
smooth muscle cells, in which the diffusion distance from the
mitochondria to the actin-myosin filaments would be much
smaller than in striated muscle, and even more dramatically
the ATPase rate is much smaller. The rate of ATP usage is so
low that it is most likely that CK would always be at equilibrium in smooth muscle, as shown previously.
Having CK be at equilibrium and still be part of a regulatory
pathway are not impossible, however, noting the multiple glycolytic equilibrium enzymes cited above. Determination that
enzyme clusters that exchange metabolites directly between
enzymes without releasing the metabolites into the cytosol,
shown for example in glycolytic clusters,6 glycolytic-Na-KATPase activity,7 and PK-CK complexes,8 makes the concept
of metabolite concentration a difficult problem. If diffusional
limitations on CK function are unlikely to produce a reasonable creatine shuttle model, what would be the characteristics
of a regulatory system that could include CK?
One of the distinguishing features of biological, as opposed
to biochemical, systems, is the conversion of scalar biochemical activity into vector biological function. If all the components of actomyosin ATPase, actin, myosin, ATP, Mg++, the
right pH and ionic strength were placed in a test tube the
reaction would proceed, ATP hydrolyzed and heat produced,
but the test tube would not move. The reaction would have
The opinions expressed in this article are not necessarily those of the
editors or of the American Heart Association.
From the Department of Physiology, Michigan State University, East
Lansing, MI.
Correspondence to Patrick F. Dillon, Department of Physiology, 2178
Biomedical and Physical Sciences, 567 Wilson Rd, Michigan State
University, East Lansing, MI 48823. E-mail [email protected]
(Hypertension. 2014;63:27-28.)
© 2013 American Heart Association, Inc.
Hypertension is available at http://hyper.ahajournals.org
DOI: 10.1161/HYPERTENSIONAHA.113.02251
27
28 Hypertension January 2014
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Figure. Equilibrium enzymes in scalar and vector systems. Left,
For an equilibrium enzyme (yellow, with a red catalytic site) free
in solution, the enzyme has rotational and translation motion
in all directions. The substrates (green and blue dots) will be
distributed uniformly in the solution and will have a kinetic rate
K through the enzyme until they reach equilibrium. This system
is a scalar: it has magnitude but no direction. Right, Equilibrium
enzymes imbedded in enzyme clusters in which there are
nonequilibrium enzymes either before or after the equilibrium
enzyme (top) or in which the equilibrium enzyme is active in 2
regions structurally separated from one another (bottom) will
be part of a vector system in which there is both magnitude and
direction. In the lower case, the enzyme kinetic rate K must be
significantly faster than the diffusion rate through the enzymes
for the system to be a vector. If the diffusion rate were faster than
the kinetic rate, there would not be a functional separation of the
enzymes and the system would be a scalar.
magnitude but no direction. Inside muscle cells, the reversal
of polarity of the filaments at the Z-line and the m-line results
in ATP hydrolysis, but also force and shortening, that is, there
is both magnitude and direction. Similar logic works for ion
ATPase and the creation of ion gradients across membranes.
Vector biological systems evolve from scalar biochemical systems because of the structures in the systems: the polarity of
the filaments and the phase separation of the membrane. It
should be noted that biological systems convert living systems
to nonliving systems by compromising membrane integrity
using T cells and the complement system. The presence of
equilibrium enzymes in scalar and vector systems is shown
in the Figure.
The diffusion gradient present in the creatine shuttle
hypothesis is also a vector system, having both PCr (mitochondria to filament) and Cr (filament to mitochondria)
concentration magnitude and direction. If this system does
exist under some conditions in smooth muscle because the
low ATPase rate is known to exist, the diffusion coefficient
for the creatine compounds would have to be much lower
than those measured in vitro, and the diffusion coefficients
of ATP and ADP would have to be lower still. Should these
conditions not exist, there could still be structural limitations on CK activity. CK has been shown to associate with
muscle filaments and with ion ATPases, as noted in Karamat
et al.1 It could be that this association plays a role altering
CK-actomyosin activity or CK-ion pump activity in a way
that makes force generation, and thus blood pressure, CK
dependent. In any case, a system in which the equilibrium
enzyme CK is part of a regulatory, vectorial system must
have a structural component. If the equilibrium enzyme is
in series with a nonequilibrium enzyme, the system as a
whole will be a vector. Also, if the structural arrangement
of the enzyme limits the access of its substrates to the extent
that flux through the enzyme is less than that of the energy
consuming enzymes, increases in the concentration of CK
could increase the overall flux of the system. In this case,
there is a functional diffusional limitation at the molecular
level. Future experiments testing such structural localization
of vascular smooth muscle contractile control may reveal
regulatory processes not predicted by in vitro biochemical
properties alone.
Disclosures
None.
References
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van Montfrans GA, Brewster LM. Resistance artery creatine kinase
mRNA and blood pressure in humans. Hypertension. 2014;63:68–73.
2. Hozumi T. Structural aspects of skeletal muscle F-actin as studied by tryptic digestion: evidence for a second nucleotide interacting site. J Biochem.
1988;104:285–288.
3. Fisher MJ, Dillon PF. Direct determination of ADP in hypoxic porcine
carotid artery using 31P NMR. NMR Biomed. 1988;1:121–126.
4.Dillon PF. Biophysics: A Physiological Approach. Cambridge, UK:
Cambridge University Press; 2012.
5. Newsholme EA, Start C. Regulation in Metabolism. Chichester, UK: John
Wiley & Sons; 1973.
6. Maughan DW, Henkin JA, Vigoreaux JO. Concentrations of glycolytic
enzymes and other cytosolic proteins in the diffusible fraction of a vertebrate muscle proteome. Mol Cell Proteomics. 2005;4:1541–1549.
7.Paul RJ, Bauer M, Pease W. Vascular smooth muscle: aerobic glycolysis linked to sodium and potassium transport processes. Science.
1979;206:1414–1416.
8. Dillon PF, Clark JF. The theory of diazymes and functional coupling of
pyruvate kinase and creatine kinase. J Theor Biol. 1990;143:275–284.
Equilibrium Enzymes in Regulatory Systems: A Problem in Scalar-Vector Transition
Patrick F. Dillon
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Hypertension. 2014;63:27-28; originally published online October 14, 2013;
doi: 10.1161/HYPERTENSIONAHA.113.02251
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