Equilibrium Enzymes in Regulatory Systems
A Problem in Scalar-Vector Transition
See related article, p 68–73
The 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 rate-limiting 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-K-ATPase 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 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.
The opinions expressed in this article are not necessarily those of the editors or of the American Heart Association.
- © 2013 American Heart Association, Inc.
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