Computer simulation metabolism. I. Model
of ischemic construction
rat heart
purine
MICHAEL C. KOHN AND DAVID GARFINKEL The Moore School of Electrical Engineering and Department of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19174 KOHN,MICHAELC., ANDDAVIDGARFINKEL. Computersimulation of ischemic rat heart purine metabolism. I. Model construction. Am. J. Physiol. 232(4): H386-H393, 1977 or Am. J. Physiol.: Heart Circ. Physiol. l(4): H386-H393, 1977. -A model is proposed for the partial depletion of the adenine nucleotide pool in the ischemic perfused rat heart which involves seven enzymes: adenylate cyclase, 3’,5’-cyclic AMP phosphodiesterase, 5’-nucleotidase, adenosine kinase, adenosine deaminase, purine nucleoside phosphorylase, and inorganic pyrophosphatase. The computer implementation of this model is in terms of rate laws, several of which were obtained by a systematic least-squares fitting procedure. Depletion of the adenine nucleotide pool is initiated by the release of endogenous noradrenaline into the interstitial fluid, which results from a fall in tissue PO,, and the subsequent activation of adenylate cyclase. In this model the substrate for V-nucleotidase is a membrane-bound AMP pool formed by hydrolysis of cyclic AMP. The adenosine thus produced is released into the extracellular fluid and functions as a vasodilator; excess adenosine is incorporated into the tissue by a “permease” with Michaelis-Menten kinetics and converted to AMP, inosine, and hypoxanthine. Alternative mechanisms, such as the deamination of AMP by adenylate deaminase and conversion of AMP to adenine by AMP pyrophosphorylase, were rejected primarily on qualitative biochemical grounds.
adenosine hypothesis; adenine nucleotide degradation; noradrenaline release; cyclic AMP; vasodilation
cardiac
tion. In this paper we report the construction of a model showing that the above nucleoside production may account for the depletion of adenine nucleotides in ischemia. The main features of the model are shown in the following scheme: MgATP (C) t adenylate cyclase cyclic AMP (C) + MgPPi (C) i cyclic AMP phosphodiesterase AMP (M) J 5’-nucleotidase adenosine (I) + Pi (I)
z
“nucleoside
permease” MgATP (0
adenosine i
inosine
(C, V)
MgADP (C)
adenosine kinase
) AMP (C)
adenosine deaminase
(C, V) + NH,+ (C, V)
Pi (W +$
purine nucleoside phosphorylase
hypoxanthine (V) + ribose l-phosphate (V) . MgPPi (C) + Mg’+ (C) > 2 MgPi CC> inorganic pyrophosphatase
THE TOTAL adenine nucleotide level in a working aerobic rat heart is constant with time (36), recent experiments with perfused rat and dog hearts have shown a progressive loss of adenine nucleotides under such pathological conditions as anoxia (44) and ischemia (13, 31). Berne (3) found decreased coronary vascular resistance accompanied by release of inosine and hypoxanthine into the coronary venous effluent in hypoxic but not aerobic cat and dog hearts. He attributed this to the production of adenosine and demonstrated its effectiveness as a vasodilator. Liu and Feinberg (24) found adenosine and inosine in the coronary venous blood of rabbits after, but not before, coronary occlusion. Tissue adenosine and inosine were also, found in ischemic dog (32) and rat (13) hearts; in the latter case-their production (plus hypoxanthine) equaled the depletion of adenine nucleotides. Gregg (14) explained his observed vasodilation in ischemic dog hearts by suggesting that the myocardium is marginally hypoxic and operating at a low PO,, which initiated adenosine release and subsequent vasodilaWHILE
The letters C, M, I, and V denote the cytosolic, membranous, interstitial, and vascular tissue compartments, respectively. This model relates the dynamically interdependent kinetics of molecular phenomena, notably enzyme-catalyzed reactions, and is implemented in terms of rate laws for the various processes occurring. Consequently, compartmentation of a metabolite (or enzyme) is indicated if its observed concentration is either too low or too high to reproduce the required flux when substituted into the appropriate rate law. Thus we are predicting compartmentation on the basis of enzyme kinetics rather than tracer kinetics as is usually done. In the course of this work we have abstracted much data from the literature and have made interpretations which are not to be ascribed to those who collected the data. Tissue contents or levels of metabolites (these words are used interchangeably) are given in nanomoles per gram dry weight (5 g wet wt equals 1 g dry wt (60)). The conversion factors for converting metabolite concentrations from micromoles per liter to nanomoles per gram dry weight are 1.8, 2.0, and 0.1 ml/g dry wt for the cardiac muscle cytoplasm, interstitial fluid (computed from the data of Williamson (60)), and vascular tissue compartments (see below), respectively.
N386
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PURINE
METABOLISM
MODEL
H387
CONSTRUCTION
Selection of a model. Three mechanisms have been proposed to explain the loss of adenine nucleotides. In the first, adenylic acid deaminase (EC 3.5.4.6) and 5’. nucleotidase (EC 3.1.3.5) convert AMP to inosine monophosphate and inosine. This fails to account for the adenosine in ischemic cardiac tissue (13, 32) or venous blood (24) and is contradicted by the finding that tissue IMP remains constant regardless of the depletion of adenine nucleotides (45). Furthermore, the K, for AMP in the adenylic acid deaminase rate law is about 1 mM (61). Because much AMP is mitochondrial (20), it is unlikely that cytosolic AMP will rise that high, and any tendency to do so would be resisted by rapid phosphorylation to ADP by myokinase (EC 2.7.4.3) (43). The second mechanism utilizes AMP pyrophosphorylase (EC 2.4.2.7) and purine nucleoside phosphorylase (EC 2.4.2.1) to reversibly convert AMP to adenine and adenosine. Liu and Feinberg (24) perfused ischemic rabbit hearts with [U-14C]adenosine and found no [14C]adenine indicating that this mechanism is not active. The most extensively investigated mechanism involves the production of adenosine from AMP by 5’nucleotidase, which has been shown to be present in sufficient amount (30) in dog and rat hearts. It has been localized in the sarcolemma, T tubules, and the sarcoplasmic reticulum by Rubio et al. (45) and others and in a “microsomal” cell fraction of heart muscle by Olsson et al. (34). Thus the enzyme could bind the intracellular substrate and release the products extracellularly, maximizing the effectiveness of adenosine as a vasodilator. The cytosolic concentrations of AMP, unchelated ADP, and unchelated ATP are much larger than their respective kinetic parameters (K, or Ki) as determined by Olsson et al. (34) for the 5’nucleotidase rate law. This suggests that 5’nucleotidase is always saturated with substrate and greatly inhibited. If the enzyme were exposed to the entire cytosolic pools of the adenine nucleotides, the inhibition would never decrease enough to permit 5”-nucleotidase to account for the observed depletion of adenine nucleotides during ischemia. If it were exposed only to a constant fraction of these pools, the calculated flux through the enzyme during ischemia would be greater, but the flux in the aerobic case would be too high. Olsson et al. (34) proposed a resolution for this dilemma by suggesting that the substrate for 5’.nucleotidase is a membranous pool of AMP derived from the hydrolysis of cyclic AMP. The small cyclic AMP content of the rat heart, 0.5-7.5 nmol/g dry wt (6,38,49), makes it likely that this membranal AMP level is much lower than the cytosolic AMP level. Adenylate cyclase (EC 4.6.1.1) has been localized in the membranes containing 5’nucleotidase (47), and a membrane-bound cyclic AMP phosphodiesterase (EC 3.1.4.17) was found by Thompson and Appleman (54) in rat brain. Das (6) found cyclic AMP phosphodiesterase in the 1,000 x g sediment of rat heart homogenates. A close association in the cell membranes of rat heart muscle of these three enzymes would render the product of one enzyme highly accessible as the substrate for the next. Thus, 5’.AMP from the hydrolysis of cyclic AMP, if it remains membrane-bound for a significant time, can serve as a local pool of 5’-AMP
which is the exclusive substrate for fi’nucleotidase, and would largely determine the reaction rate if the enzyme were exposed only to part of the cytosolic ADP and ATP (otherwise it would be completely inhibited). When adenylate cyclase activity is low (the usual aerobic case), this pool should be very small, and the total adenine nucleotide level should be stable. We propose that adenylate cyclase is stimulated during ischemia resulting in a significant rise in the level of membranal AMP and thus increased flux through 5’-nucleotidase. This is supported by the findings of Shahab et al. (49), who detected a rise in cyclic AMP in ischemic rat hearts and showed that it is probably the result of release of endogenous catecholamines, known activators of adenylate cyclase. It may be argued that this membranal AMP pool comes directly from cytoplasmic AMP, in which case a carrier would be needed to transport the cytosolic AMP to the site of 5’-nucleotidase. Since the tissue level of AMP continually rises during ischemia (13, 31, 44) whereas the rate of adenine nucleotide degradation decreases at longer times, translocation of cytosolic AMP would have to become greatly inhibited after prolonged ischemic perfusion. As an appropriate AMP-supplying mechanism can be constituted from components known to be present, it seems artificial as well as unnecessary to assume the presence of such a carrier. Three metabolic pathways for incorporation of the adenosine into the adenine nucleotide pool have been proposed. A pathway involving cleavage of the adenosine ribosyl linkage may be easily dismissed, because Liu and Feinberg (24) found no [14C]adenine in rabbit hearts perfused with [14C]adenosine, and Wiedmeier et al. (58) found evidence that adenosine is incorporated into the adenine nucleotides without cleavage of the purine-ribose linkage. It is conceivable that some of the inosine produced by deamination of adenosine is eventually incorporated into the adenine nucleotide pool according to the following scheme: inosine pi
nucleoside phosphorylase
ribose
l-phosphate
hypoxanthine phosphoribose nucleotide pyrophosphorylase
+
pyrophosphate
PPi
IMP
k
aspartate
adenylosuccinate synthetase
r-
adenylosuccinate
adenyl lyase
.osuccinate
fumarate
AMP
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II388
M. C. KOHN
Radioactive tracer experiments indicate that inosine is cleaved to hypoxanthine and ribose l-phosphate prior to incorporation into the adenine nucleotide pool (58), but the enzyme purine nucleoside phosphorylase is apparently localized in the pericytes and endothelial cells of the vascular tissue (46). Since the plasma membrane in muscle is generally considered impermeable to phosphorylated compounds, such a compartmentation of this enzyme makes the deamination pathway an unlikely candidate. Also, the adenine nucleotide pool was labeled much more when ischemic rabbit hearts are perfused with [ 14C]adenosine than when perfused with [ 14C]inosine (24). Th us it seems likely that adenosine kinase (EC 2.7.1.20) is the major mechanism of adenosine salvage (59). Maguire et al. (25) found a tissue capacity of adenosine kinase too low for this possibility, but they may have lost enough of this unstable enzyme in the course of removing interfering Mg2+-ATPase from their preparation to explain the discrepancies between the [14C]tracer studies and their work. Therefore, we have modeled adenosine salvage by the adenosine kinase pathway with deamination as a side reaction. Here we report the construction of a computer model corresponding to the first scheme above. The kinetic parameters for some of the rate laws composing the model were determined by a least-squares fit to the available kinetic data. The formal optimization techniques used in performing this fit have been reviewed elsewhere (12). TABLE
1. Kinetic parameters Enzyme
Adenylate
cyclase
Substrate
We have assumed that the tissue level of any enzyme is highly species dependent, but that the properties of the enzyme (in this case, K,‘s, K/s, Ki’s, specific activity, and molecular weight) are much less variable within a given mammalian tissue, so that an unmeasured parameter for a rat heart enzyme may be approximated by a value from another mammalian species. In some cases maximal velocities (V,,, = specific activity x molecular weight x enzyme concentration) for rat heart were determined from isolated enzymes rather than tissue homogenates or intact organs. Since the purification procedures used are likely to result in the loss of activity, we have used for these cases the somewhat higher values for V,,, reported for the dog heart enzyme. Since enzyme concentrations are expected to be greater in the rat heart than the dog heart, we believe this substitution is justified. The kinetic parameters used for the several enzymes in the model are listed in Table 1. Adenylate cyclase. Perkins (38) recently reviewed adenylate cyclase kinetics, identified the substrate as MgATP, and suggested that the enzyme is activated by Mg2+. Activity of the enzyme is apparently regulated by a protein phosphorylation-dephosphorylation mechanism (29). Hormones activate the enzymes by stimulating the phosphoprotein phosphatase (22). To estimate the degree of activation by this mechanism, we assume that Najjar’s membrane preparations (4, 22) contain 1% of the cyclase by weight (this is not critical, as the errors should cancel) and a linear model for the kinetics of the
for enzymes in model K,,
pM
Activator
K,, pM
MgATP, 187 Cyclic AMP, 3.88 MgPPi, 5.55
3’,5’-Cyclic AMP phosphodiesterase
Cyclic AMP, 1.50
SNucleotidase
AMP, 18.0 (9, 30, 34)
Nucleoside permease
Ado, 5.0 (16) Ino, 5.0
Hypoxanthine
Hx, 5.0
permease
AND D. GARFINKEL
Cyclic AMP, 2.15
Inhibitor
K,, pM
V max, pmol/g dry wt - min
MgPP,, 450 (48) ATP, 68.6 (7) ATPH, 665 (7)
3.62*
Mg2+, 123 (28)
5.5 (28)t
ADP, ADPH, 3.0 (34) ATP, ATPH, 11.0 (34)
11.15 (30)*
ATP, ATPH, 326 (35)
Kc%
65 mM (15)
0.09 (15)* 0.054*
1.0
0.0135*
1.0
Adenosine kinase
Ado, 0.909 (1) MgATP, 400 (26)
Adenosine deaminase
Ado, 43 (35)
6.0 (35)t (1.32, muscle) (4.68, vasculature)
Purine nucleoside phosphorylase
Ino, 58 (17, 37) Pi, 320 (17, 37) Hx, 23 (37) RIP, 500 (37)
4.68 (25)*
0.115 (35)t
Inorganic MgPP,, 16.6 (27) Mg2+, 16.0 (41) PP,, 7.88 (27) 4.228* pyrophosphatase References cited are in parentheses. Abbreviations Ado, adenosine; Ino, inosine; Hx, hypoxanthine; RlP, phate. * Literature or computed value for the rat heart enzyme. t Literature value for the dog heart enzyme
0.0185 (37)
ribose
l-phos-
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PURINE
METABOLISM
MODEL
H389
CONSTRUCTION
protein kinase and phosphatase: Eact + MgATP 2 Einact + MgADP E inact
SE
act
+
pi
Using Najar’s data (4,22) we estimate k, = 0.15 (nmol/g dry wt)+ min+ and k, = 318 min? The specific activity for dog skeletal muscle of 315 nmol/min mg (52), the maximal velocity for dog hearts of 93.4 nmol/g dry wt min (51) and a molecular weight of 1.5 x lo6 (23) yield a total enzyme concentration of 0.197 nmol/g dry wt. Substituting this enzyme level and several MgATP levels deduced for aerobic perfused rat hearts into the rate laws for the above processes yields an estimated basal activity for adenylate cyclase corresponding to lo13% of the enzyme in the active (dephospho) form. This compares favorably with the observation that the basal activity of guinea pig heart adenylate cyclase is about one eighth of the maximum activity obtained to date (8). As Severson et al. (48) observed, 7.13-fold sigmoidal activation of skeletal muscle adenylate cyclase by noradrenaline with half-activation at about 4 FM, we have modeled the effect of noradrenaline as increasing the rate constant for the protein phosphatase reaction above according to the sigmoidal equation: l
l
k 2 = 318[1 + 7.13(NA/q)3/(1
+ (NA/$31
NA is the interstitial level of noradren .aline, si.nce the hormone receptors are on the outer surface of the plasma membrane, and 7 is the concentration of noradrenaline required for half-maximal activation. The aerobic perfused rat heart was found to contain 20.65 nmol/g dry wt of endogenous noradrenaline and to lose the hormone at the rate of 0.059 nmol/g dry wt min (49). Assuming first-order kinetics for noradrenaline release, we compute an aerobic rate constant of 2.85 x 10m3 min- l. Taggart (53) suggested that a heart with a noradrenaline content of 1 pg/g tissue would be depleted of its noradrenaline after 15-30 min of ischemia. Assuming 95% depletion after 30 min low coronary flow perfusion, we compute a first-order rate constant for the release of noradrenaline into the interstitial fluid of 9.60 X 10e2 min-l. Since the ischemic myocardium may be expected to be hypoxic, we have modeled the transition between these two rates of noradrenaline release as sigmoidal in time: l
k = .00285 + .09315 (t/d3/[1
+ ( t/T>3]
where 7 is the half-time for the aerobic-hypoxic transition as measured by the fall in the respiration rate. A sigmoidal function is particularly desirable, because it permits aI smooth, contin .uous change from the i .nitial to the fina .l value an .d has a zero time derivative at both ends of the transition. The apparent Ka for Mg2+ activation of the guinea pig heart enzyme is reported as 2-3 mM (8). This value is much larger than the cytosolic unchelated Mg2+ level (57). We examined the authors’ published data (8) closely and found that the concentrations of Mg2+ and ATP were presented as totals uncorrected for chelation
equilibria. As a result, no two enzyme activity measurements were made on reaction mixtures differing only in the concentration of one chemical species, and no rigorous conclusions regarding the mechanism could be drawn. De Haen (7) modeled adenylate cyclase kinetics as a rapid equilibrium binding of the variously chelated ATP forms. He proposed that Mg2+ activates by reducing the concentrations of ATP4- and ATPH3-, which compete with the substrate MgATP for binding to the catalytic site. We have selected de Haen’s mechanism and the binding constants for the state that most closely approximates the fully activated cyclase system. The model also includes competitive inhibition by MgPPi as determined (48) for the skeletal muscle enzyme. We have applied our parameter estimation program (12) to Drummond’s data (8) and obtained an optimal Michaelis constant of 187 PM for MgATP. Substituting the value for the MgATP and MgPPi levels and the maximum rate of adenine nucleotide depletion deduced for the ischemic rat heart into the inferred adenylate cyclase rate law yields a required maximal velocity of 3.62 pmol/g dry wt min. We compute that 77% of the cyclase is activated at this point giving a turnover number of 23,950 min? The Michaelis constants for cyclic AMP and MgPPi are unknown. We approximated the K, for cyclic AMP as 3.88 PM its average value for 3’ ,5’-cyclic AMP phosphodiesterase in various mammalian tissues (2); and the K, for MgPPi as 5. 55 PM, somewhat below its concentration in the aerobic workin .g heart (see below) since its binding is reported as quite strong ( 23) . Substitution of these values and the normal tissue levels of the reactants into the adenylate cyclase rate law yields negligible reverse flux in agreement with others (15, 38). Thus these assumed K, values produce negligible error in our simulation. 3’,5’-Cyclic AMP phosphodiesterase. Thompson and Appleman (55) examined the kinetics of 3’ ,5’-cyclic -AMP phosphodiesterase in various rat tissues and generally found negative deviations from linearity in the double-reciprocal kinetic plots, which they interpreted as indicating negative allosteric cooperativity. Extrapolating these curves at low substrate concentrations for the heart and brain enzymes yielded apparent K,‘s of 3.85 and 0.51 PM, respectively. This extrapolation procedure is highly suspect. We used our formal optimization technique (12) to estimate the kinetic parameters for the brain enzyme, for which some velocity vs. concentration data are given (56), and found 10 rate laws that fit the experimental data within ca. 3%, yielding values for the K, in the range 0.04-20.4 PM. Thus, the information content of the data is insufficient to discriminate between rival mechanisms. We have modeled phosphodiesterase as substrate activated, a mechanism which produces velocity vs. concentration curves similar to those of negative cooperativity and, unlike cooperative mechanisms, is easily represented by a sequence of chemical reactions. J. R. Neely (personal communication) recently perfused a series of rat hearts under the same ischemic conditions as l
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H390
M.
previously published (31), and L. Wray (personal communication) analyzed them for cyclic AMP content. Although the results varied widely with an average value of 3.07 t 2.42 (SD) nmol/g dry wt, no apparent correlation with duration of ischemia was observed. The computed cyclic AMP level increases greatly during ischemia using Thompson and Appleman’s (55) K, for the rat heart enzyme. Appleman, Thompson, and Russell (2) report a Michael .is constant for the beef heart enzyme of 0.8 PM. We were able to reproduce the observed homeostasis with a compromise & of 1.50 PM and activation by two substrate molecules with a K, of 2.15 PM. Nair (28) obtained an activity for this enzyme of 5.5 bmol/g dry wt. min from dog heart homogenates, other literature values probably being low because of losses in extraction. Nair (28) also reported that Mg2+ is a required activator, and we obtained a K, for Mg2+ of 123 PM from his data with our parameter estimation program. Since aerobic hearts do not lose substantial amounts of adenine nucleotides ‘, the membranous AMP produced must be returned to the cytosol. bYpphosphodiesterase We have modeled the binding of AMP from this pool to the membrane as membranous
AMP + membrane* solic AMP
bound AMP -+ cyto-
which is equivalent to saturation kinetics. We represented these kinetics with a K, of 0.56 PM and a maximal velocity for release into the cytosol of 660 nmol/g dry wt emi .n, which is 50% greater than the flux through adenyl .ate cyclase a.t i ts basal activity level . The low K, resulted in a very small membrane AMP pool at low adenylate cyclase flux, which precluded significant flux through 5’nucleotidase under these conditions. 5’-NucZeotidase. The preparation of Olsson et al. (34) consisting of isolated membrane fragments probably more closely approximates the in vivo microenvironment of native 5’nucleotidase than a more highly purified sample. We have therefore selected their formulation of the kinetics. Following Sullivan and Alpers (51), we identified unchelated ADP and ATP as the inhibitors. We have previously suggested that the concentration of adenine nucleotides in the microenvironment of 5’nucleotidase differs from the bulk cytosolic concentration. There is a variety of evidence for this, including labeling experiments indicating a slow rate of exchange between this pool and the bulk adenine nucleotides (21). Shimizu and Okayama (50) prelabeled the adenine nucleotide pool in guinea pig brain slices with [14C]adenine and followed the appearance of the label in cyclic AMP with time. Fitting a straight line to their data yielded a value of approximately 5% for the fraction of the ATP pool available to the membrane-bound enzyme at zero time. Although the tissue content of adenine nucleotides is considerably greater for heart than brain, we expect this fraction to be similar in these tissues and therefore used this value to represent the fraction of the cytosolic nucleotides that serve as the inhibitors of 5’nucleotidase.
C.
KOHN
AND
D.
GARFINKEL
Nucleoside permease and diffusion of nucleosides into perfusate. It had been suggested that adenosine uptake is mediated by a membrane-bound adenosine kinase, but Hopkins and Goldie (16) and others presented evidence that adenosine kinase is located in the cytosol in the rat heart. Adenosine uptake follows simple Michaelis-Menten kinetics in the dog (35) and rat (16) heart. W e h ave modeled the translocation of nucleosides as mediated by a permease having MichaelisMenten kinetics. Kolassa et al. (19) observed that inosine was taken up 60% as rapidly and hypoxanthine only 15% as rapidly as adenosine from a perfusate equimolar in the two. As adenosine and inosine compete for the binding site (33), we have, in the absence of other information, assigned the K, determined for adenosine uptake (16) to all three nucleotides and set their maximal velocities of translocation in the ratio 100:60:15. While adenosine and inosine share a common carrier, a separate permease is included for hypoxanthine. Since purine nucleoside phosphorylase apparently is found exclusively in the pericytes and endothelial cells of the vascular tissue (46), we have reproduced these kinetics for a separate compartment representing this tissue. Recent studies with rabbit heart (10) indicate that the volume of this compartment is 3.6% of the total cardiac volume. When we correct for the volume of vascular lumen and interstitium, we estimate the volume of the vascular tissue as 5% of the cellular volume from which we derive the micromole per liter-to-nanomole per gram dry weight conversion factor cited previously. While we believe this to be a reasonable approxi-mation, it should be noted that it has little effect on the behavior of the entire model and determines only the intracellular level of the nucleosides, which is small in any event. Preliminary examination of the behavior of our model indicated that most of the extracellular purine derivative produced was adenosine, contrary to the observation (3, 32) that the venous effluent contains mostly inosine and hypoxanthine. Since the maximal velocity of the permease is less than that of adenosine deaminase or purine nucleoside phosphorylase in the vascular tissue compartment, the permease activity is rate limiting. Raising the maximal velocity of the permeases in this compartment by a factor of 20 increased the amount of adenosine degraded by increasing its rate of delivery to the site of the above two enzymes. The vascular tissue is so small a fraction of the total cardiac volume that such a discrepancy between the permease activity in this compartment and in the muscle tissue would only slightly perturb the computed purine content of the whole organ. Indeed, the only effects of this adjustment were to i .ncrease both the rate of equilibration of purines between this compartment and the interstitia 1 fluid and the adenosine degradation rate. In the 5’-deoxyadenosine countertransport studies of Olsson et al. (35), the appearance of the deoxynucleoside in the coronary effluent had a half-time of 56 s (which translates into a first-order rate constant of 0.742 min+) and was independent of the perfusate adenosine concentration. We interpret these results as indicating that Olsson was measuring the first-order kinetics of the
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PURINE
METABOLISM
MODEL
H391
CONSTRUCTION
diffusion of nucleoside between the interstitial fluid and the blood flowing through the capillaries, and we used the inferred rate constant to simulate the rate of diffusion of all small molecules between interstitial fluid and perfusate. We expect the bulk perfusate concentration to be a ieasonable approximation to the local concentration in the vasculature at high coronary flow rates. During ischemia the flow rate may fall to less than 10% of its control value (31), and the net rate of washout of purines from the interstitial fluid should decrease greatly. This is supported by a recent mathematical analysis of the appearance of metabolites in the capillary lumen (39), in which reducing the rate of blood flow decreases the rate of extracellular buildup of a metabolite. We have simulated this behavior by reducing the rate constant for diffusion between these two compartments by a factor proportional to the decrease in the coronary flow rate. Inorganic pyrophosphatase. Several mechanisms have been proposed to explain the kinetics of inorganic pyrophosphatase (EC 3.6.1.1); we have selected the simplified mechanism of Moe and Butler (27) and the&, for MgPPi and& for unchelated pyrophosphate which they determined by fitting the appropriate rate law to their kinetic data by nonlinear regression. We used the binding constant for Mg2+ determined by fluorescence measurements (41) and the pyrophosphate chelation equilibrium constants of Rapoport et al. (40). There are several reports quoting values of available or “metabolically active” pyrophosphate in liver ranging from 11.5 to 250 nmol/g dry wt. We have used nominal pyrophosphate levels of 25-50 nmol/g dry wt for the working rat heart in our model. A maximum fatty acid activation rate of 1.95 pmollg dry wt *min (and hence an equal rate of formation of MgPPi) has been deduced for a working rat heart from the data of Opie et al. (36). The pyrophosphatase rate law (27) requires a maximal velocity of 4.23 pmol/g dry wt. min to maintain a steady-state level of 50 nmol/g dry wt at normal Mg2+ levels. We compute a turnover number of 15,300 mine1 and a total enzyme level of 0.2765 nmol/g dry wt from the published molecular weight (42) and specific activity (5) for this enzyme. Degradation of adenosine. Literature values for the kinetic constants for adenosine kinase, adenosine deaminase (EC 3.5.4.4), and purine nucleoside phosphorylase were assembled (see Table l), and the last two enzymes were modeled following the kinetics of Olsson et al. (35) and of Parks and Agarwal (37), respectively. We have deduced from the data of Olsson et al. (35) that adenosine kinase is inhibited by unchelated ATP with a Ki (competitive against adenosine) of 326 PM and have modeled the enzyme accordingly. The first of these activities was assigned to the muscle tissue cytosol and the third to the vascular tissue; The low maximal velocity for adenosine uptake in cardiac muscle and the low K, for adenosine kinase prevents the accumulation of adenosine in the muscle tissue. If the bulk of the adenosine deaminase activity were located in this compartment, the relatively high K, for this enzyme would preclude the observed large production of inosine. Ac-
cordingly, we have assigned an adenosine deaminase activity equal to the purine nucleoside phosphorylase activity to the vascular tissue and the remainder to the muscle tissue. As a result, our model predicts that most of the adenosine produced is converted to inosine and hypoxanthine in the vasculature in agreement with the conclusions of Rubio et al. (46). Final modeZ. We combined the rate laws for the enzymes listed in Table 1, equations for the chelation and protonation equilibria of ADP, ATP, and pyrophosphate, and equations for the sigmoidal kinetics of noradrenaline release and its activation of phosphoprotein phosphatase into a single model. This model was written in our simulation language (11) (BIOSSIM, available through the SHARE Program Library Agency, catalog no. 360D.03.2.008) as a sequence of chemical reactions representing the mechanisms involved. This program derives the rate laws for the enzyme processes in the model and constructs the differential equations for the metabolite levels, which are then numerically integrated. The differential equations for the metabolite levels, which are then numerically integrated. The differential equations themselves are not normally isolated. The behavior of our model is reported in the companion paper which follows (18). The major thrust of this model is that degradation of adenine nucleotides in the ischemic rat heart is precipitated by a fall in tissue PO, resulting from the rate of oxygen utilization exceeding its rate of delivery. The subsequent release of noradrenaline into the interstitial fluid, coupled with its slow rate of washout due to the reduced coronary flow, causes a conversion of adenylate cyclase to its active form. The cyclic AMP produced is the precursor of a membrane-bound AMP pool which is converted to adenosine by 5’nucleotidase. The degree of depletion of adenine nucleoti .des then sh.ould be strongly dependen t on the coronary flow rate; the greater the restriction of the coronary flow, the greater and more rapid should be th .e loss of aden .ine n ucleo ltides. In the companion PaPer (1.8) we show that this beha vior is indeed obtained in quantitative agreement with experiment for a number of ischemic and normal-flow situations. ADDENDUM Our model predicts that beta cially continuous beta blockade) nucleotides and benefit ischemic lished in Acta Medica Scandinavica, reports that beta blockade limits coronary occlusion. These results they do not prove it, as this effect
blockade in ischemic heart (espeshould prevent the loss of adenine tissue. A recent symposium pubSupplementium 587 contains the area of necrosis following support our hypothesis, although may involve other causes.
We thank Ray A. Olsson of the Walter Reed Army Institute of Research for his helpful advice, suggestions, and criticisms during the course of this work. We also thank Linton Wray of the Walter Reed Army Institute of Research and James R. Neely of the Milton S. Hershey Medical Center of the Pennsylvania State University for making results of unpublished work available to us. This work was supported by National Institutes of Health Grants HL-15622 and RR-15.
Received
for publication
15 December
1975.
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H392
M. C. KOHN
AND D. GARFINKEL
REFERENCES 1. ALMA, M., AND H. FEINBERG. Purification and properties of cardiac muscle adenosine kinase (Abstract). Federation Proc. 30: 507, 1971. 2. APPLEMAN, M. M., W. J. THOMPSON, AND T, R. RUSSELL. Cyclic nucleotide phosphodiesterases. Aduan. Cyclic NucZeotide Res . 3: 65-98, 1973. 3. BERNE, R. M. Cardiac nucleotides in hypoxia: possible role in regulation of coronary blood flow. Am. J. Physiol. 204: 317-322,
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phys. Res. Commun. 53: 794-799, 1973. COOPERMAN, B. S., N. Y. CHIU, R. H. BRUCKMAN, G. J. BUNICK, AND G. P. MCKENNA. Yeast inorganic pyrophosphatase. I. New methods of purification. Biochemistry 12: 1665-1669, 1973. DAS, I. Effect of diabetes and insulin on the rat heart adenyl cyclase cyclic AMP phosphodiesterase and cyclic AMP. Horm. Metub. Res. 5: 330-335, 1973. DE HAYDN, C. Adenylate cyclase. A new kinetic analysis of the effects of hormones and fluoride ion. J. BioZ. Chem. 249: 27562762, 1974. DRUMMOND, G. I., AND L. DUNCAN. Adenyl cyclase in cardiac tissue. J. Biol. Chem. 245: 976-983, 1970. EDWARDS, M. J., AND M. H. MAGUIRE. Purification and properties of rat heart 5’-nucleotidase. Mol. PharmacoZ. 6: 641-648, 1970. FRANK, J. S., AND G. A. LANGER. The myocardial interstitium: its structure and its role in ionic exchange. J. CeZZ. BioZ. 60: 586601, 1974. GARFINKEL, D. A machine-independent language for the simulation of complex chemical and biochemical systems. Computers Biomed. Res. 2: 31-44, 1968. GARFINKEL, L., M. C. KOHN, AND D. GARFINKEL. Systems analysis in enzyme kinetics. Crit. Rev. Bioeng. In press. GERLACH, E., B. DEUTICKE, AND R. H. DREISBACH. Der Nucleoti-
dabbau im Herzmuskel bei Sauerstoffmangel lithe Bedeutung fur die Coronadurchblutung. schufien 14. GREGG,
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und seine mogNuturwissen-
1963.
D. E. Relationship between coronary flow and metabolic changes. Cardiology 56: 291-301, 1971/72. 15. HAYAISHI, O., P. GREENGARD, AND S. P. COLOWICK. On the equilibrium of the adenylate cyclase reaction. J. BioZ. Chem. 246: 5840-5843, 1971. 16. HOPKINS, S. V., AND R. G. GOLDIE. A species difference in the uptake of adenosine by heart. Biochem. PhurmucoZ. 20: 33593365, 1971. 17. KIM, B. K., S. CHA, AND R. E. PARKS, JR. Purine nucleoside
phosphorylase from human erythrocytes. I. Purification and properties. J. BioZ. Chem. 243: 1763-1770, 1968. 18. KOHN, M. C., AND D. GARFINKEL. Computer simulation of ischemic rat heart purine metabolism. II. Model behavior. Am. J. Physiol. 232: H394-H399, 19. KOLASSA, N., K. PFLEGER,
1977. AND W. RUMMEL.
sine uptake into the heart and inhibition
Specificity of adenoby dipyridamole. Euro-
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Feedback interactions in the control of citric acid cycle activity in rat heart mitochondria. J. BioZ. Chem., 247: 667-679, 1972. 21. LARAIA, P. J., AND W. J. REDDY. Hormonal regulation of myocardial adenosine 3’ ,5’-monophosphate. Biochim. Biophys. Actu 177: 189-195, 1969. 22. LAYNE, P., A. CONSTANTOPOULOS, J. F. X. JUDGE, R. RAUNER, AND V. A. NAJJAR. Occurrence of fluoride-stimulated membrane phosphoprotein phosphatase. Biochem. Biophys. Res. Commun. 53: 800-805, 1973. 23. LIPMANN, F., M. TAO, AND A. HUBERMAN. Bacterial adenyl cyclase, In: The Role of Adenyl Cycluse and Cyclic 3 ’ ,5’-AMP in Biological Systems, edited by T. W. Rall, M. Rodbell, and P.
Condliffe, p. 29-51.
Washington,
D.C.: U.S. Gov’t. Printing
Office, 1971,
Incorporation of adenosine-8-14C and inosine-8-14C into rabbit heart adenine nucleotides. Am. J.
24. LIU,
Physiol.
M.
S., AND H. FEINBERG. 220: 1242-1248,
1971.
M. H., M. C. LUKAS, AND J. F. RETTIE. Adenine nucleotide salvage synthesis in the rat heart: pathways of adenosine salvage. Biochim. Biophys. Actu 262: 108-115, 1972. 26. MEYSKENS, F. L., AND H. E. WILLIAMS. Adenosine metabolism in human erythrocytes. Biochim. Biophys. Actu 240: 170-179, 1971. 27. MOE, 0. A., AND L. G. BUTLER. Yeast inorganic pyrophosphatase. II. Kinetics of Mg2+ activation. J. BioZ. Chem. 247: 7308-
29.
30.
31. 32.
7314, 1972. NAIR, K. G. Purification
and properties of 3’,5’-nucleotide phosphodiesterase from dog heart. Biochemistry 5: 150-157, 1966. NAJJAR, V. A., AND A. CONSTANTOPOULOS. Activation of adenyl cyclase. I. Postulated mechanism for fluoride and hormone activation of adenylate cyclase. MOL. CeZZ. Biochem. 2: 87-93,1973. NAKATASU, K., AND G. I. DRUMMOND. Adenylate metabolism and adenosine formations in the heart. Am. J. Physiol. 223: 1119-1127, 1972. NEELY, J. R., M. J. ROVETTO, J. T. WHITMER, AND H. E. MORGAN. Effects of ischemia on function and metabolism of the isolated working rat heart. Am. J. Physiol. 225: 651-658,1973. OLSSON, R. A. Changes in content of purine nucleoside in canine myocardium during coronary occlusion. Circulation Res. 26: 301-
306, 1970. OLSSON, R. A., M. K. GENTRY, J. A. SNOW, G. P. FRICK, AND R. J. TOWNSEND. Steric requirements for binding of adenosine to a membrane carrier in canine heart. Biochim. Biophys. Actu 311: 242-250, 1973. 34. OLSSON, R. A., M. K. GENTRY, AND R. S. TOWNSEND. Adenosine 33.
metabolism:
Properties of dog heart microsomal5’nucleotidase.
Advun. Exptl. Med. BioZ. 39: 27-39, 1973. 35. OLSSON, R. A., J. A. SNOW, M. K. GENTRY, Adenosine uptake by canine heart. CircuZution 1972. 36. OPIE, L. H., K. R. L. MANSFORD, AND P.
AND G. P. FRICK. Res. 31: 767-778,
OWEN. Effects of increased heart work on glycolysis and adenine nucleotides in the perfused hearts of normal and diabetic rats. Biochem. J. 124:
37.
475-490, PARKS,
1971.
39.
l-64, 1973. POPESCU, A. I., AND
R. E., AND R. P. AGARWAL. Purine nucleoside phosphorylase. In: The Enzymes (3rd ed.), edited by P. D. Boyer. New York: Academic, 1972, p. 483-514. 38. PERKINS, J. P. Adenyl cyclase. Aduun. Cyclic NucZeotide Res. 3:
40.
A. A. POPESCU. A model of a physicochemical coupling of biological interest. BUZZ. Math. BioZ. 37: 5157, 1975. RAPOPORT, T. A., W. E. HOHNE, J. G. REICH, P. HEITMANN, AND S. M. RAPOPORT. A kinetic model for the action of inorganic
pyrophosphatase from baker’s yeast. The activating influence of magnesium ions. European J. Biochem. 26: 237-246, 1972. 41. RIDLINGTON, J. W., AND L. G. BUTLER. Yeast inorganic pyrophosphatase. I. Binding of pyrophosphate, metal ion, and metal ion-pyrophosphate complexes. J. BioZ. Chem. 247: 7303-7307, 42.
1972. RIDLINGTON,
J. W., Y. YANG, AND L. G. BUTLER. Yeast inorganic pyrophosphatase. IV. Purification, quaternary structure, and evidence for strongly bound Mg2+. Arch. Biochem. Biophys. 153: 714-725,
1972.
43. ROSE, I. A. The state of magnesium in cells as estimated from the adenylate kinase equilibrium. Biochemistry 61: 1079-1086, 1968. 44. ROVETTO, M. J., J. T. WHITMER, AND J. R. NEELY. Comparison of the effects of anoxia and whole heart ischemia on carbohydrate utilization in isolated working rat hearts. CircuZution Res. 32: 699-711, 1973. 45. RUBIO, R., R. M. BERNE,
sine production
AND J. G. DOBSON, JR. Sites of adenoin cardiac and skeletal muscle. Am. J. Physiol.
225: 938-953, 1973. 46. RUBIO, R., T. WIEDMEIER,
AND R. M. BERNE. Nucleoside phosphorylase: localization and role in the myocardial distribution of purines. Am. J. Physiol. 222: 550-560, 1972. 47. SCHULZE, W., E.-G. KRAUSE, AND A. WOLLENBERGER. Cytochemical demonstration and localization of adenyl cyclase in skeletal and cardiac muscle. Aduun. Cyclic NucZeotide Res. 1: 249-260, 1972. 48. SEVERSON,
D. L., G. I. DRUMMOND, AND P. V. SULAKHE. Adenylate cyclase in skeletal muscle. Kinetic properties and hormonal stimulation. J. BioZ. Chem. 247: 2949-2958, 1972.
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PURINE
METABOLISM
MODEL
L., A. WOLLENBERGER, Catecholamines and cyclic AMP
E.-G. KRAUSE, AND S. GENZ. levels. In: Effect of Acute Ischemia on Myocardial Function, edited by M. F. Oliver, D. G. Julian, and K. W. Donald. Baltimore: Williams & Wilkins, 1972, p. 99-107. SHIMIZU, H., AND H. OKAYAMA. ATP pool associated with adenyl cyclase of brain tissue. J. Neurochem. 20: 1279-1283, 1973. SULLIVAN, J. M., AND J. B. ALPERS. In vitro regulation of rat heart 5’-nucleotidase by adenine nucleotides and magnesium. J. Biol. Chem. 246: 3057-3063, 1971. SUTHERLAND, E. W., T. W. RALL, AND T. MENON. Adenyl cyclase. I. Distribution, preparation, and properties. J. BioZ. Chem. 237: 1220-1227, 1962. TAGGART, P. I. Catecholamines and cyclic AMP levels. [Discussion of Ref. 49.1 In: Effect of Acute Ischemicz on Myocardial Function, edited by M. F. ‘Oliver, D. G. Julian, and K. W. Donald. Baltimore: Williams & Wilkins, 1972, p. 108. THOMPSON, W. J., AND M. M. APPLEMAN. Cyclic nucleotide phosphodiesterase and cyclic AMP. Ann. N.Y. Acad. Sci. 185: 36-41, 1971. THOMPSON, W. J., AND M. M. APPLEMAN. Characterization of cyclic nucleotide phosphodiesterases of rat tissues. J. BioZ.
49. SHAHAB,
50. 51. 52.
53.
54.
55.
H393
CONSTRUCTION Chem. 246: 3145-3150, 1971. 56. VELOSO, D., R. W. GUYNN,
M. OSKARSSON, AND R. L. VEECH. Concentrations of free and bound magnesium in rat tissues. Relative constancy of free magnesium ion concentrations. J. BioZ. Chem. 248: 4811-4819, 1973. 57. VELOSO, D., R. W. GUYNN, M. OSKARSSON, AND R. L. VEECH. Concentrations of free and bound magnesium in rat tissues. Relative constancy of free magnesium ion concentrations. J. BioZ. Chem. 248: 4811-4819, 1973. 58. WIEDMEIER, V. T., R. RUBIO, AND R. M. BERNE. Inosine incorporation into myocardial nucleotides. J. MOL. CeZZ. Cardiol. 4: 445452, 1972. 59. WIEDMEIER,
V. T., R. RUBIO, AND R. M. BERNE. Incorporation and turnover of adenosine-U-14C in perfused guinea pig myocardium. Am. J. Physiol. 223: 51-54, 1972. 60. WILLIAMSON, J. R. Glycolytic control mechanisms. I. Inhibition of glycolysis by acetate and pyruvate in the isolated, perfused rat heart. J. BioZ. Chem. 240: 2308-2321, 1965. 61. ZIELKE, C. L., AND C. H. SUELTER. Purine, purine nucleoside, and purine nucleotide aminohydrolases. In: The Enzymes (3rd ed.), edited by P. D. Boyer. New York: Academic, 1971, p. 47-78.
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of ischemic construction
rat heart
purine
MICHAEL C. KOHN AND DAVID GARFINKEL The Moore School of Electrical Engineering and Department of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19174 KOHN,MICHAELC., ANDDAVIDGARFINKEL. Computersimulation of ischemic rat heart purine metabolism. I. Model construction. Am. J. Physiol. 232(4): H386-H393, 1977 or Am. J. Physiol.: Heart Circ. Physiol. l(4): H386-H393, 1977. -A model is proposed for the partial depletion of the adenine nucleotide pool in the ischemic perfused rat heart which involves seven enzymes: adenylate cyclase, 3’,5’-cyclic AMP phosphodiesterase, 5’-nucleotidase, adenosine kinase, adenosine deaminase, purine nucleoside phosphorylase, and inorganic pyrophosphatase. The computer implementation of this model is in terms of rate laws, several of which were obtained by a systematic least-squares fitting procedure. Depletion of the adenine nucleotide pool is initiated by the release of endogenous noradrenaline into the interstitial fluid, which results from a fall in tissue PO,, and the subsequent activation of adenylate cyclase. In this model the substrate for V-nucleotidase is a membrane-bound AMP pool formed by hydrolysis of cyclic AMP. The adenosine thus produced is released into the extracellular fluid and functions as a vasodilator; excess adenosine is incorporated into the tissue by a “permease” with Michaelis-Menten kinetics and converted to AMP, inosine, and hypoxanthine. Alternative mechanisms, such as the deamination of AMP by adenylate deaminase and conversion of AMP to adenine by AMP pyrophosphorylase, were rejected primarily on qualitative biochemical grounds.
adenosine hypothesis; adenine nucleotide degradation; noradrenaline release; cyclic AMP; vasodilation
cardiac
tion. In this paper we report the construction of a model showing that the above nucleoside production may account for the depletion of adenine nucleotides in ischemia. The main features of the model are shown in the following scheme: MgATP (C) t adenylate cyclase cyclic AMP (C) + MgPPi (C) i cyclic AMP phosphodiesterase AMP (M) J 5’-nucleotidase adenosine (I) + Pi (I)
z
“nucleoside
permease” MgATP (0
adenosine i
inosine
(C, V)
MgADP (C)
adenosine kinase
) AMP (C)
adenosine deaminase
(C, V) + NH,+ (C, V)
Pi (W +$
purine nucleoside phosphorylase
hypoxanthine (V) + ribose l-phosphate (V) . MgPPi (C) + Mg’+ (C) > 2 MgPi CC> inorganic pyrophosphatase
THE TOTAL adenine nucleotide level in a working aerobic rat heart is constant with time (36), recent experiments with perfused rat and dog hearts have shown a progressive loss of adenine nucleotides under such pathological conditions as anoxia (44) and ischemia (13, 31). Berne (3) found decreased coronary vascular resistance accompanied by release of inosine and hypoxanthine into the coronary venous effluent in hypoxic but not aerobic cat and dog hearts. He attributed this to the production of adenosine and demonstrated its effectiveness as a vasodilator. Liu and Feinberg (24) found adenosine and inosine in the coronary venous blood of rabbits after, but not before, coronary occlusion. Tissue adenosine and inosine were also, found in ischemic dog (32) and rat (13) hearts; in the latter case-their production (plus hypoxanthine) equaled the depletion of adenine nucleotides. Gregg (14) explained his observed vasodilation in ischemic dog hearts by suggesting that the myocardium is marginally hypoxic and operating at a low PO,, which initiated adenosine release and subsequent vasodilaWHILE
The letters C, M, I, and V denote the cytosolic, membranous, interstitial, and vascular tissue compartments, respectively. This model relates the dynamically interdependent kinetics of molecular phenomena, notably enzyme-catalyzed reactions, and is implemented in terms of rate laws for the various processes occurring. Consequently, compartmentation of a metabolite (or enzyme) is indicated if its observed concentration is either too low or too high to reproduce the required flux when substituted into the appropriate rate law. Thus we are predicting compartmentation on the basis of enzyme kinetics rather than tracer kinetics as is usually done. In the course of this work we have abstracted much data from the literature and have made interpretations which are not to be ascribed to those who collected the data. Tissue contents or levels of metabolites (these words are used interchangeably) are given in nanomoles per gram dry weight (5 g wet wt equals 1 g dry wt (60)). The conversion factors for converting metabolite concentrations from micromoles per liter to nanomoles per gram dry weight are 1.8, 2.0, and 0.1 ml/g dry wt for the cardiac muscle cytoplasm, interstitial fluid (computed from the data of Williamson (60)), and vascular tissue compartments (see below), respectively.
N386
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PURINE
METABOLISM
MODEL
H387
CONSTRUCTION
Selection of a model. Three mechanisms have been proposed to explain the loss of adenine nucleotides. In the first, adenylic acid deaminase (EC 3.5.4.6) and 5’. nucleotidase (EC 3.1.3.5) convert AMP to inosine monophosphate and inosine. This fails to account for the adenosine in ischemic cardiac tissue (13, 32) or venous blood (24) and is contradicted by the finding that tissue IMP remains constant regardless of the depletion of adenine nucleotides (45). Furthermore, the K, for AMP in the adenylic acid deaminase rate law is about 1 mM (61). Because much AMP is mitochondrial (20), it is unlikely that cytosolic AMP will rise that high, and any tendency to do so would be resisted by rapid phosphorylation to ADP by myokinase (EC 2.7.4.3) (43). The second mechanism utilizes AMP pyrophosphorylase (EC 2.4.2.7) and purine nucleoside phosphorylase (EC 2.4.2.1) to reversibly convert AMP to adenine and adenosine. Liu and Feinberg (24) perfused ischemic rabbit hearts with [U-14C]adenosine and found no [14C]adenine indicating that this mechanism is not active. The most extensively investigated mechanism involves the production of adenosine from AMP by 5’nucleotidase, which has been shown to be present in sufficient amount (30) in dog and rat hearts. It has been localized in the sarcolemma, T tubules, and the sarcoplasmic reticulum by Rubio et al. (45) and others and in a “microsomal” cell fraction of heart muscle by Olsson et al. (34). Thus the enzyme could bind the intracellular substrate and release the products extracellularly, maximizing the effectiveness of adenosine as a vasodilator. The cytosolic concentrations of AMP, unchelated ADP, and unchelated ATP are much larger than their respective kinetic parameters (K, or Ki) as determined by Olsson et al. (34) for the 5’nucleotidase rate law. This suggests that 5’nucleotidase is always saturated with substrate and greatly inhibited. If the enzyme were exposed to the entire cytosolic pools of the adenine nucleotides, the inhibition would never decrease enough to permit 5”-nucleotidase to account for the observed depletion of adenine nucleotides during ischemia. If it were exposed only to a constant fraction of these pools, the calculated flux through the enzyme during ischemia would be greater, but the flux in the aerobic case would be too high. Olsson et al. (34) proposed a resolution for this dilemma by suggesting that the substrate for 5’.nucleotidase is a membranous pool of AMP derived from the hydrolysis of cyclic AMP. The small cyclic AMP content of the rat heart, 0.5-7.5 nmol/g dry wt (6,38,49), makes it likely that this membranal AMP level is much lower than the cytosolic AMP level. Adenylate cyclase (EC 4.6.1.1) has been localized in the membranes containing 5’nucleotidase (47), and a membrane-bound cyclic AMP phosphodiesterase (EC 3.1.4.17) was found by Thompson and Appleman (54) in rat brain. Das (6) found cyclic AMP phosphodiesterase in the 1,000 x g sediment of rat heart homogenates. A close association in the cell membranes of rat heart muscle of these three enzymes would render the product of one enzyme highly accessible as the substrate for the next. Thus, 5’.AMP from the hydrolysis of cyclic AMP, if it remains membrane-bound for a significant time, can serve as a local pool of 5’-AMP
which is the exclusive substrate for fi’nucleotidase, and would largely determine the reaction rate if the enzyme were exposed only to part of the cytosolic ADP and ATP (otherwise it would be completely inhibited). When adenylate cyclase activity is low (the usual aerobic case), this pool should be very small, and the total adenine nucleotide level should be stable. We propose that adenylate cyclase is stimulated during ischemia resulting in a significant rise in the level of membranal AMP and thus increased flux through 5’-nucleotidase. This is supported by the findings of Shahab et al. (49), who detected a rise in cyclic AMP in ischemic rat hearts and showed that it is probably the result of release of endogenous catecholamines, known activators of adenylate cyclase. It may be argued that this membranal AMP pool comes directly from cytoplasmic AMP, in which case a carrier would be needed to transport the cytosolic AMP to the site of 5’-nucleotidase. Since the tissue level of AMP continually rises during ischemia (13, 31, 44) whereas the rate of adenine nucleotide degradation decreases at longer times, translocation of cytosolic AMP would have to become greatly inhibited after prolonged ischemic perfusion. As an appropriate AMP-supplying mechanism can be constituted from components known to be present, it seems artificial as well as unnecessary to assume the presence of such a carrier. Three metabolic pathways for incorporation of the adenosine into the adenine nucleotide pool have been proposed. A pathway involving cleavage of the adenosine ribosyl linkage may be easily dismissed, because Liu and Feinberg (24) found no [14C]adenine in rabbit hearts perfused with [14C]adenosine, and Wiedmeier et al. (58) found evidence that adenosine is incorporated into the adenine nucleotides without cleavage of the purine-ribose linkage. It is conceivable that some of the inosine produced by deamination of adenosine is eventually incorporated into the adenine nucleotide pool according to the following scheme: inosine pi
nucleoside phosphorylase
ribose
l-phosphate
hypoxanthine phosphoribose nucleotide pyrophosphorylase
+
pyrophosphate
PPi
IMP
k
aspartate
adenylosuccinate synthetase
r-
adenylosuccinate
adenyl lyase
.osuccinate
fumarate
AMP
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II388
M. C. KOHN
Radioactive tracer experiments indicate that inosine is cleaved to hypoxanthine and ribose l-phosphate prior to incorporation into the adenine nucleotide pool (58), but the enzyme purine nucleoside phosphorylase is apparently localized in the pericytes and endothelial cells of the vascular tissue (46). Since the plasma membrane in muscle is generally considered impermeable to phosphorylated compounds, such a compartmentation of this enzyme makes the deamination pathway an unlikely candidate. Also, the adenine nucleotide pool was labeled much more when ischemic rabbit hearts are perfused with [ 14C]adenosine than when perfused with [ 14C]inosine (24). Th us it seems likely that adenosine kinase (EC 2.7.1.20) is the major mechanism of adenosine salvage (59). Maguire et al. (25) found a tissue capacity of adenosine kinase too low for this possibility, but they may have lost enough of this unstable enzyme in the course of removing interfering Mg2+-ATPase from their preparation to explain the discrepancies between the [14C]tracer studies and their work. Therefore, we have modeled adenosine salvage by the adenosine kinase pathway with deamination as a side reaction. Here we report the construction of a computer model corresponding to the first scheme above. The kinetic parameters for some of the rate laws composing the model were determined by a least-squares fit to the available kinetic data. The formal optimization techniques used in performing this fit have been reviewed elsewhere (12). TABLE
1. Kinetic parameters Enzyme
Adenylate
cyclase
Substrate
We have assumed that the tissue level of any enzyme is highly species dependent, but that the properties of the enzyme (in this case, K,‘s, K/s, Ki’s, specific activity, and molecular weight) are much less variable within a given mammalian tissue, so that an unmeasured parameter for a rat heart enzyme may be approximated by a value from another mammalian species. In some cases maximal velocities (V,,, = specific activity x molecular weight x enzyme concentration) for rat heart were determined from isolated enzymes rather than tissue homogenates or intact organs. Since the purification procedures used are likely to result in the loss of activity, we have used for these cases the somewhat higher values for V,,, reported for the dog heart enzyme. Since enzyme concentrations are expected to be greater in the rat heart than the dog heart, we believe this substitution is justified. The kinetic parameters used for the several enzymes in the model are listed in Table 1. Adenylate cyclase. Perkins (38) recently reviewed adenylate cyclase kinetics, identified the substrate as MgATP, and suggested that the enzyme is activated by Mg2+. Activity of the enzyme is apparently regulated by a protein phosphorylation-dephosphorylation mechanism (29). Hormones activate the enzymes by stimulating the phosphoprotein phosphatase (22). To estimate the degree of activation by this mechanism, we assume that Najjar’s membrane preparations (4, 22) contain 1% of the cyclase by weight (this is not critical, as the errors should cancel) and a linear model for the kinetics of the
for enzymes in model K,,
pM
Activator
K,, pM
MgATP, 187 Cyclic AMP, 3.88 MgPPi, 5.55
3’,5’-Cyclic AMP phosphodiesterase
Cyclic AMP, 1.50
SNucleotidase
AMP, 18.0 (9, 30, 34)
Nucleoside permease
Ado, 5.0 (16) Ino, 5.0
Hypoxanthine
Hx, 5.0
permease
AND D. GARFINKEL
Cyclic AMP, 2.15
Inhibitor
K,, pM
V max, pmol/g dry wt - min
MgPP,, 450 (48) ATP, 68.6 (7) ATPH, 665 (7)
3.62*
Mg2+, 123 (28)
5.5 (28)t
ADP, ADPH, 3.0 (34) ATP, ATPH, 11.0 (34)
11.15 (30)*
ATP, ATPH, 326 (35)
Kc%
65 mM (15)
0.09 (15)* 0.054*
1.0
0.0135*
1.0
Adenosine kinase
Ado, 0.909 (1) MgATP, 400 (26)
Adenosine deaminase
Ado, 43 (35)
6.0 (35)t (1.32, muscle) (4.68, vasculature)
Purine nucleoside phosphorylase
Ino, 58 (17, 37) Pi, 320 (17, 37) Hx, 23 (37) RIP, 500 (37)
4.68 (25)*
0.115 (35)t
Inorganic MgPP,, 16.6 (27) Mg2+, 16.0 (41) PP,, 7.88 (27) 4.228* pyrophosphatase References cited are in parentheses. Abbreviations Ado, adenosine; Ino, inosine; Hx, hypoxanthine; RlP, phate. * Literature or computed value for the rat heart enzyme. t Literature value for the dog heart enzyme
0.0185 (37)
ribose
l-phos-
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PURINE
METABOLISM
MODEL
H389
CONSTRUCTION
protein kinase and phosphatase: Eact + MgATP 2 Einact + MgADP E inact
SE
act
+
pi
Using Najar’s data (4,22) we estimate k, = 0.15 (nmol/g dry wt)+ min+ and k, = 318 min? The specific activity for dog skeletal muscle of 315 nmol/min mg (52), the maximal velocity for dog hearts of 93.4 nmol/g dry wt min (51) and a molecular weight of 1.5 x lo6 (23) yield a total enzyme concentration of 0.197 nmol/g dry wt. Substituting this enzyme level and several MgATP levels deduced for aerobic perfused rat hearts into the rate laws for the above processes yields an estimated basal activity for adenylate cyclase corresponding to lo13% of the enzyme in the active (dephospho) form. This compares favorably with the observation that the basal activity of guinea pig heart adenylate cyclase is about one eighth of the maximum activity obtained to date (8). As Severson et al. (48) observed, 7.13-fold sigmoidal activation of skeletal muscle adenylate cyclase by noradrenaline with half-activation at about 4 FM, we have modeled the effect of noradrenaline as increasing the rate constant for the protein phosphatase reaction above according to the sigmoidal equation: l
l
k 2 = 318[1 + 7.13(NA/q)3/(1
+ (NA/$31
NA is the interstitial level of noradren .aline, si.nce the hormone receptors are on the outer surface of the plasma membrane, and 7 is the concentration of noradrenaline required for half-maximal activation. The aerobic perfused rat heart was found to contain 20.65 nmol/g dry wt of endogenous noradrenaline and to lose the hormone at the rate of 0.059 nmol/g dry wt min (49). Assuming first-order kinetics for noradrenaline release, we compute an aerobic rate constant of 2.85 x 10m3 min- l. Taggart (53) suggested that a heart with a noradrenaline content of 1 pg/g tissue would be depleted of its noradrenaline after 15-30 min of ischemia. Assuming 95% depletion after 30 min low coronary flow perfusion, we compute a first-order rate constant for the release of noradrenaline into the interstitial fluid of 9.60 X 10e2 min-l. Since the ischemic myocardium may be expected to be hypoxic, we have modeled the transition between these two rates of noradrenaline release as sigmoidal in time: l
k = .00285 + .09315 (t/d3/[1
+ ( t/T>3]
where 7 is the half-time for the aerobic-hypoxic transition as measured by the fall in the respiration rate. A sigmoidal function is particularly desirable, because it permits aI smooth, contin .uous change from the i .nitial to the fina .l value an .d has a zero time derivative at both ends of the transition. The apparent Ka for Mg2+ activation of the guinea pig heart enzyme is reported as 2-3 mM (8). This value is much larger than the cytosolic unchelated Mg2+ level (57). We examined the authors’ published data (8) closely and found that the concentrations of Mg2+ and ATP were presented as totals uncorrected for chelation
equilibria. As a result, no two enzyme activity measurements were made on reaction mixtures differing only in the concentration of one chemical species, and no rigorous conclusions regarding the mechanism could be drawn. De Haen (7) modeled adenylate cyclase kinetics as a rapid equilibrium binding of the variously chelated ATP forms. He proposed that Mg2+ activates by reducing the concentrations of ATP4- and ATPH3-, which compete with the substrate MgATP for binding to the catalytic site. We have selected de Haen’s mechanism and the binding constants for the state that most closely approximates the fully activated cyclase system. The model also includes competitive inhibition by MgPPi as determined (48) for the skeletal muscle enzyme. We have applied our parameter estimation program (12) to Drummond’s data (8) and obtained an optimal Michaelis constant of 187 PM for MgATP. Substituting the value for the MgATP and MgPPi levels and the maximum rate of adenine nucleotide depletion deduced for the ischemic rat heart into the inferred adenylate cyclase rate law yields a required maximal velocity of 3.62 pmol/g dry wt min. We compute that 77% of the cyclase is activated at this point giving a turnover number of 23,950 min? The Michaelis constants for cyclic AMP and MgPPi are unknown. We approximated the K, for cyclic AMP as 3.88 PM its average value for 3’ ,5’-cyclic AMP phosphodiesterase in various mammalian tissues (2); and the K, for MgPPi as 5. 55 PM, somewhat below its concentration in the aerobic workin .g heart (see below) since its binding is reported as quite strong ( 23) . Substitution of these values and the normal tissue levels of the reactants into the adenylate cyclase rate law yields negligible reverse flux in agreement with others (15, 38). Thus these assumed K, values produce negligible error in our simulation. 3’,5’-Cyclic AMP phosphodiesterase. Thompson and Appleman (55) examined the kinetics of 3’ ,5’-cyclic -AMP phosphodiesterase in various rat tissues and generally found negative deviations from linearity in the double-reciprocal kinetic plots, which they interpreted as indicating negative allosteric cooperativity. Extrapolating these curves at low substrate concentrations for the heart and brain enzymes yielded apparent K,‘s of 3.85 and 0.51 PM, respectively. This extrapolation procedure is highly suspect. We used our formal optimization technique (12) to estimate the kinetic parameters for the brain enzyme, for which some velocity vs. concentration data are given (56), and found 10 rate laws that fit the experimental data within ca. 3%, yielding values for the K, in the range 0.04-20.4 PM. Thus, the information content of the data is insufficient to discriminate between rival mechanisms. We have modeled phosphodiesterase as substrate activated, a mechanism which produces velocity vs. concentration curves similar to those of negative cooperativity and, unlike cooperative mechanisms, is easily represented by a sequence of chemical reactions. J. R. Neely (personal communication) recently perfused a series of rat hearts under the same ischemic conditions as l
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H390
M.
previously published (31), and L. Wray (personal communication) analyzed them for cyclic AMP content. Although the results varied widely with an average value of 3.07 t 2.42 (SD) nmol/g dry wt, no apparent correlation with duration of ischemia was observed. The computed cyclic AMP level increases greatly during ischemia using Thompson and Appleman’s (55) K, for the rat heart enzyme. Appleman, Thompson, and Russell (2) report a Michael .is constant for the beef heart enzyme of 0.8 PM. We were able to reproduce the observed homeostasis with a compromise & of 1.50 PM and activation by two substrate molecules with a K, of 2.15 PM. Nair (28) obtained an activity for this enzyme of 5.5 bmol/g dry wt. min from dog heart homogenates, other literature values probably being low because of losses in extraction. Nair (28) also reported that Mg2+ is a required activator, and we obtained a K, for Mg2+ of 123 PM from his data with our parameter estimation program. Since aerobic hearts do not lose substantial amounts of adenine nucleotides ‘, the membranous AMP produced must be returned to the cytosol. bYpphosphodiesterase We have modeled the binding of AMP from this pool to the membrane as membranous
AMP + membrane* solic AMP
bound AMP -+ cyto-
which is equivalent to saturation kinetics. We represented these kinetics with a K, of 0.56 PM and a maximal velocity for release into the cytosol of 660 nmol/g dry wt emi .n, which is 50% greater than the flux through adenyl .ate cyclase a.t i ts basal activity level . The low K, resulted in a very small membrane AMP pool at low adenylate cyclase flux, which precluded significant flux through 5’nucleotidase under these conditions. 5’-NucZeotidase. The preparation of Olsson et al. (34) consisting of isolated membrane fragments probably more closely approximates the in vivo microenvironment of native 5’nucleotidase than a more highly purified sample. We have therefore selected their formulation of the kinetics. Following Sullivan and Alpers (51), we identified unchelated ADP and ATP as the inhibitors. We have previously suggested that the concentration of adenine nucleotides in the microenvironment of 5’nucleotidase differs from the bulk cytosolic concentration. There is a variety of evidence for this, including labeling experiments indicating a slow rate of exchange between this pool and the bulk adenine nucleotides (21). Shimizu and Okayama (50) prelabeled the adenine nucleotide pool in guinea pig brain slices with [14C]adenine and followed the appearance of the label in cyclic AMP with time. Fitting a straight line to their data yielded a value of approximately 5% for the fraction of the ATP pool available to the membrane-bound enzyme at zero time. Although the tissue content of adenine nucleotides is considerably greater for heart than brain, we expect this fraction to be similar in these tissues and therefore used this value to represent the fraction of the cytosolic nucleotides that serve as the inhibitors of 5’nucleotidase.
C.
KOHN
AND
D.
GARFINKEL
Nucleoside permease and diffusion of nucleosides into perfusate. It had been suggested that adenosine uptake is mediated by a membrane-bound adenosine kinase, but Hopkins and Goldie (16) and others presented evidence that adenosine kinase is located in the cytosol in the rat heart. Adenosine uptake follows simple Michaelis-Menten kinetics in the dog (35) and rat (16) heart. W e h ave modeled the translocation of nucleosides as mediated by a permease having MichaelisMenten kinetics. Kolassa et al. (19) observed that inosine was taken up 60% as rapidly and hypoxanthine only 15% as rapidly as adenosine from a perfusate equimolar in the two. As adenosine and inosine compete for the binding site (33), we have, in the absence of other information, assigned the K, determined for adenosine uptake (16) to all three nucleotides and set their maximal velocities of translocation in the ratio 100:60:15. While adenosine and inosine share a common carrier, a separate permease is included for hypoxanthine. Since purine nucleoside phosphorylase apparently is found exclusively in the pericytes and endothelial cells of the vascular tissue (46), we have reproduced these kinetics for a separate compartment representing this tissue. Recent studies with rabbit heart (10) indicate that the volume of this compartment is 3.6% of the total cardiac volume. When we correct for the volume of vascular lumen and interstitium, we estimate the volume of the vascular tissue as 5% of the cellular volume from which we derive the micromole per liter-to-nanomole per gram dry weight conversion factor cited previously. While we believe this to be a reasonable approxi-mation, it should be noted that it has little effect on the behavior of the entire model and determines only the intracellular level of the nucleosides, which is small in any event. Preliminary examination of the behavior of our model indicated that most of the extracellular purine derivative produced was adenosine, contrary to the observation (3, 32) that the venous effluent contains mostly inosine and hypoxanthine. Since the maximal velocity of the permease is less than that of adenosine deaminase or purine nucleoside phosphorylase in the vascular tissue compartment, the permease activity is rate limiting. Raising the maximal velocity of the permeases in this compartment by a factor of 20 increased the amount of adenosine degraded by increasing its rate of delivery to the site of the above two enzymes. The vascular tissue is so small a fraction of the total cardiac volume that such a discrepancy between the permease activity in this compartment and in the muscle tissue would only slightly perturb the computed purine content of the whole organ. Indeed, the only effects of this adjustment were to i .ncrease both the rate of equilibration of purines between this compartment and the interstitia 1 fluid and the adenosine degradation rate. In the 5’-deoxyadenosine countertransport studies of Olsson et al. (35), the appearance of the deoxynucleoside in the coronary effluent had a half-time of 56 s (which translates into a first-order rate constant of 0.742 min+) and was independent of the perfusate adenosine concentration. We interpret these results as indicating that Olsson was measuring the first-order kinetics of the
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PURINE
METABOLISM
MODEL
H391
CONSTRUCTION
diffusion of nucleoside between the interstitial fluid and the blood flowing through the capillaries, and we used the inferred rate constant to simulate the rate of diffusion of all small molecules between interstitial fluid and perfusate. We expect the bulk perfusate concentration to be a ieasonable approximation to the local concentration in the vasculature at high coronary flow rates. During ischemia the flow rate may fall to less than 10% of its control value (31), and the net rate of washout of purines from the interstitial fluid should decrease greatly. This is supported by a recent mathematical analysis of the appearance of metabolites in the capillary lumen (39), in which reducing the rate of blood flow decreases the rate of extracellular buildup of a metabolite. We have simulated this behavior by reducing the rate constant for diffusion between these two compartments by a factor proportional to the decrease in the coronary flow rate. Inorganic pyrophosphatase. Several mechanisms have been proposed to explain the kinetics of inorganic pyrophosphatase (EC 3.6.1.1); we have selected the simplified mechanism of Moe and Butler (27) and the&, for MgPPi and& for unchelated pyrophosphate which they determined by fitting the appropriate rate law to their kinetic data by nonlinear regression. We used the binding constant for Mg2+ determined by fluorescence measurements (41) and the pyrophosphate chelation equilibrium constants of Rapoport et al. (40). There are several reports quoting values of available or “metabolically active” pyrophosphate in liver ranging from 11.5 to 250 nmol/g dry wt. We have used nominal pyrophosphate levels of 25-50 nmol/g dry wt for the working rat heart in our model. A maximum fatty acid activation rate of 1.95 pmollg dry wt *min (and hence an equal rate of formation of MgPPi) has been deduced for a working rat heart from the data of Opie et al. (36). The pyrophosphatase rate law (27) requires a maximal velocity of 4.23 pmol/g dry wt. min to maintain a steady-state level of 50 nmol/g dry wt at normal Mg2+ levels. We compute a turnover number of 15,300 mine1 and a total enzyme level of 0.2765 nmol/g dry wt from the published molecular weight (42) and specific activity (5) for this enzyme. Degradation of adenosine. Literature values for the kinetic constants for adenosine kinase, adenosine deaminase (EC 3.5.4.4), and purine nucleoside phosphorylase were assembled (see Table l), and the last two enzymes were modeled following the kinetics of Olsson et al. (35) and of Parks and Agarwal (37), respectively. We have deduced from the data of Olsson et al. (35) that adenosine kinase is inhibited by unchelated ATP with a Ki (competitive against adenosine) of 326 PM and have modeled the enzyme accordingly. The first of these activities was assigned to the muscle tissue cytosol and the third to the vascular tissue; The low maximal velocity for adenosine uptake in cardiac muscle and the low K, for adenosine kinase prevents the accumulation of adenosine in the muscle tissue. If the bulk of the adenosine deaminase activity were located in this compartment, the relatively high K, for this enzyme would preclude the observed large production of inosine. Ac-
cordingly, we have assigned an adenosine deaminase activity equal to the purine nucleoside phosphorylase activity to the vascular tissue and the remainder to the muscle tissue. As a result, our model predicts that most of the adenosine produced is converted to inosine and hypoxanthine in the vasculature in agreement with the conclusions of Rubio et al. (46). Final modeZ. We combined the rate laws for the enzymes listed in Table 1, equations for the chelation and protonation equilibria of ADP, ATP, and pyrophosphate, and equations for the sigmoidal kinetics of noradrenaline release and its activation of phosphoprotein phosphatase into a single model. This model was written in our simulation language (11) (BIOSSIM, available through the SHARE Program Library Agency, catalog no. 360D.03.2.008) as a sequence of chemical reactions representing the mechanisms involved. This program derives the rate laws for the enzyme processes in the model and constructs the differential equations for the metabolite levels, which are then numerically integrated. The differential equations for the metabolite levels, which are then numerically integrated. The differential equations themselves are not normally isolated. The behavior of our model is reported in the companion paper which follows (18). The major thrust of this model is that degradation of adenine nucleotides in the ischemic rat heart is precipitated by a fall in tissue PO, resulting from the rate of oxygen utilization exceeding its rate of delivery. The subsequent release of noradrenaline into the interstitial fluid, coupled with its slow rate of washout due to the reduced coronary flow, causes a conversion of adenylate cyclase to its active form. The cyclic AMP produced is the precursor of a membrane-bound AMP pool which is converted to adenosine by 5’nucleotidase. The degree of depletion of adenine nucleoti .des then sh.ould be strongly dependen t on the coronary flow rate; the greater the restriction of the coronary flow, the greater and more rapid should be th .e loss of aden .ine n ucleo ltides. In the companion PaPer (1.8) we show that this beha vior is indeed obtained in quantitative agreement with experiment for a number of ischemic and normal-flow situations. ADDENDUM Our model predicts that beta cially continuous beta blockade) nucleotides and benefit ischemic lished in Acta Medica Scandinavica, reports that beta blockade limits coronary occlusion. These results they do not prove it, as this effect
blockade in ischemic heart (espeshould prevent the loss of adenine tissue. A recent symposium pubSupplementium 587 contains the area of necrosis following support our hypothesis, although may involve other causes.
We thank Ray A. Olsson of the Walter Reed Army Institute of Research for his helpful advice, suggestions, and criticisms during the course of this work. We also thank Linton Wray of the Walter Reed Army Institute of Research and James R. Neely of the Milton S. Hershey Medical Center of the Pennsylvania State University for making results of unpublished work available to us. This work was supported by National Institutes of Health Grants HL-15622 and RR-15.
Received
for publication
15 December
1975.
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H392
M. C. KOHN
AND D. GARFINKEL
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