Distribution of adenine nucleotides in the perfused rat heart MICHAEL C. KOHN, MURRAY J. ACHS, AND DAVID GARFINKEL Moore School of Electrical Engineering and Department of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19174 ACHS, ANDDAVIDGARFINimportant step in the construction of our computer nucleottdes in the perfused rat model of the isolated perfused rat heart (1). It is applicaheart. Am. J. Physiol. 232(5): R158-R163, 1977 or Am. J. ble to any physiological state of the heart provided that Physiol.: Regulatory Integrative Camp. Physiol. l(3): R158the necessary data are available. R163, 1977. -A computer technique for determination of the distribution of adenine nucleotides among compartmented, AND ASSUMPTIONS protonated, and metal-chelated species has been developed for CONVENTIONS the perfused rat heart.. This procedure requires knowledge of In constructing our model we assumed that only the tissue levels of creatine, creatine phosphate, ATP, ADP, and metabolism in the cytosol and mitochondria is relevant AMP and the glycolytic and respiration rates. The method is to the processes being simulated and that that these applicable to any physiological state of the organ and has been compartments are maintained internally homogeneous applied to transient behavior in aerobic, anoxic, and ischemic hearts. The results suggest that ADP uptake and ATP export by cardiac contraction and are not subcompartmented. We considered protonation and Mg”+ and K+ chelation by mitochondria are normally linked and equal in rate during aerobic metabolism or short-term anoxia but become separate to be the only important chelation equilibria. In the and unequal during ischemia, so that mitochondrial adenine discussion which follows mitochondrial species are denucleotides, primarily AMP, accumulate. noted by an asterisk (*) following the chemical symbol. KOHN,MICHAELC., KEL. Llistrihrhm
MURRAYJ.
of adenine
energy metabolism; simulation; cardiac ischemia; AMP compartmentation; chelation; cytoplasmic pH determination; cytoplasmic Mg?+ determination
THIS AND THE TWO FOLLOWING papers we report the construction of a computer model of energy metabolism in the perfused rat heart. Adenine nucleotides perform key functions in this metabolism. Due to compartmentation of these nucleotides, primarily between cytosol and mitochondria, only a portion of a given nucleotide is accessible to a particular enzyme. The metabolically available ADP pool is reduced by binding to F-actin. Also, Helmreich and Cori (6) have noted that, if tissue AMP were entirely cytosolic, its activation of phosphorylase b would result in excessively high rates of glycogenolysis in resting muscle. Furthermore, an enzyme usually preferentially binds a specific chelated, protonated ? or uncomplex form of a nucleotide. For these reasons it is essential to distribute the adenine nucleotides among their various compartmented and complexed forms-before a physiologic&y realistic model involving them can be constructed. We report here the development of a method for computing the distribution of adenine nucleotides in the perfused heart which will satisfy all the biochemical constraints upon them. As Mgz+ and H+ are important ligands of ad&ine nucleotides, the techniques involved also required computation of cytosolic unchelated Mgzf concen6ation and cytosolic pH, quantities that are difflcult to measure accurately. This method constitutes an IN
Unless otherwise noted, metabolite levels are given in nmol/g dry wt, and fluxes are in nmol/g dry wt min? These units may be converted to PM (or pM/min) by dividing by 1.8 or 0.2 ml/g dry wt for the cytosolic and mitochondrial compartments respectively (36). Enzymatic rate laws were derived from reaction mechanisms by the method of King and Altman (9). Mechanistic details and kinetic constants for the various enzyme rate laws used have been deposited as supplementary material to the following paper (1). l
BIOCHEMICAL DISTRIBUTION
CONSTRAINTS
ON
THE
NUCLEOTIDE
To define the nucleotide distribution we must find the total amount of each nucleotide in each compartment, the fraction of cytosolic ADP bound to actin, the cytosolic Mg’+ concentration, and the cytosolic pH. Nine constraints are required to evaluate these nine unknowns. The tissue levels of each nucleotide, the creatine kinase and phosphofructokinase rate laws, the adenylate kinase equilibrium, a model of ADP binding to actin, and the empirical ADP*-respiration rate relationship quoted below provide eight constraints. The total amount of adenine nucleotides in the mitochondria (CANP*) has been treated as a parameter and serves as the ninth constraint. We have observed that this quantity is required to lie in a fairly narrow range to preclude the computation of negative concentrations or physiologically unrealistic pH values. All these constraints must be simultaneously satisfied, but it is not possible to solve for them sequentially, because the
R158
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CARDIAC
NUCLEOTIDE
R159
DISTRIBUTION
variables are not separable. Furthermore, the resulting so the complete system is equations are nonlinear, mathematically intractable and must be solved iteratively with a computer. Mitochondrial ATP and ADP. LaNoue et al. (14) found that AMP* varied greatly with the respiration state in isolated rat heart mitochondria. However, their data suggest that the ADP*/ATP* ratio is proportional to the respiration rate. If CANP*, the cytosolic AMP level, and the respiration rate were known for a particular physiological state, we could compute the amount of each nucleotide in the mitochondrial compartment using the following empirical relationship deduced from LaNoue’s data ADp*
=
9.95 x lo-‘; R(.ANP* - AMP*) 1 + 9.95 x lo-“R
R is the respiration rate in nmol/g dry wt 4min- I, and AMP* is the difference between the tissue and cytosolic AMP levels. The concentration of ATP* is calculated as the difference between XANP* and the sum of the concentrations of ADP* and AMP*. The above treatment of mitochondrial adenine nucleotides is an expedient designed to avoid detailed modeling of the complex kinetics of the mitochondrial membrane nucleotide translocases and oxidative phosphorylation. Most of what is known on this subject was obtained with complex in vitro preparations (isolated mitochondria and submitochondrial particles), whereas we are concerned primarily with events in intact tissue. This does not introduce large errors into the mitochondrial metabolism part of our model, the citric acid cycle and the malate-aspartate shuttle, because these processes do not depend primarily on adenine nucleotides. Thus our crude method of compartmentation is adequate. Furthermore, the bulk of the adenine nucleotide content is cytosolic, so reasonable errors in the estimated mitochondrial levels do not produce significant errors in the computed cytosolic levels. Compartmenthun of AMP. Adenylate kinase catalvzes the reaction AMP”-
+ MgATP”-
e ADP:j-
+ MgADP-
Substitution of a range of physiologically realistic concentrations for these chemical species into the rapid random equilibrium rate law for this enzyme (22) indicate that this system is always near equilibrium in the rat heart because of the high tissue capacity of the enzyme (31). Clearly, the position of this equilibrium will depend on the position of the nucleotide chelation and protonation equilibria in the cytosol. We have included KS chelation in our model and set the nominal cytosolic ionic strength to 0.1 M, considering this to be equal to the K+ concentration. We used the MgZ+ and K+ chelation and protonation stability constants of Nihei et al. (21). The literature values for K,lIgA1)l’ invariably predicted cytosolic AMP levels which are too low to exert any control on phosphorylase b in the presence of physiological levels of glucose 6-phosphate and ATP (6, 17). Since the stability constant for MgADP is not accurately known (341, we have treated this constant as a
parameter whose value was adjusted to reproduce a neutral pH for the aerobic, steady-state rat heart (see below). The optimal value of 686 M-l is just slightly smaller than that obtained experimentally by Smith and Alberty (30). Rose (23) cites a Mg’+-free, pH-indepedent, apparent equilibrium constant at an ionic strength of 0.1 M of 0,37 for the enzyme-catalyzed reaction K’
=
(ATP=j-)( AMP”-) ~--~ (ADP:‘-)’
= o 37 -
Combining the above constants we can compute the true adenylate kinase equilibrium constant as (MgADP-)(
ADP”-)
K .htgaA1)l'= o 026 -
Kw = (MgATP"-- )(AMP2- ) = &lW'l'
from which we can compute the cytosolic uncomplexed AMP level. The cytosolic AMP’- levels obtained by this method for situations when cyclic AMP is low, and glycogen is being depleted (L. Opie, personal communication), are great enough to activate phosphorylase b. After computing the HAMPand MgAMP levels, the AMP* level is found from tissue AMP by difference. Cytosolic pH. Creatine kinase catalyzes the reaction creatine
+ MgATP’-
*
creatineP-
+ MgADP-
+ H+
If the reactant levels and the rate of change of creatine phosphate (or creatine) are known, we can compute that H+ concentration which will reproduce the observed flux through the enzyme when substituted into the creatine kinase rapid random equilibrium rate law (34). Rose (23) previously suggested that the position of the creatine kinase equilibrium could be used to compute the cytosolic pH, and this method was employed by Siesjii et al. (29) to compute the pH in brain tissue in steady-state situations. Applicability of this method for computation of the pH in muscle, where ADP binding to actin is important, is supported by the recent observation (25) of a linear relationship between the logarithm of the apparent equilibrium constant for this reaction and the tissue pH in human quadriceps muscle. Binding of ADP to actin. The ADP which is bound to F-actin becomes accessible to creatine kinase at a very slow rate (32). This can be interpreted to indicate either that the bound ADP can, with difficulty, serve as a substrate for creatine kinase or that the binding of ADP is reversible. In a recent review (35) it was stated that the nucleotide is bound to G-actin as ATP and is hydrolyzed to ADP during polymerization to F-actin. This would suggest that the bound ADP pool is nearly constant. During ischemia, the tissue ADP of rat hearts nearly doubles while ATP falls (19). Our model would predict alkaline pH values during this period, in contradiction to the acidic pH values obtained by direct measurements (ZO), if the newly produced ADP were not allowed to bind to actin. Furthermore, Williamson (37) observed a fall in ADP and lactate and a rise in creatine phosphate tissue levels upon reoxygenation of anoxic rat hearts. According to our model, the pH would have to rise while ADP is falling. This can only occur if the level of unbound ADP rises. For these reasons we treat
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R160
KOHN,
binding of ADP to actin as a slowly non and use the simplified model
reversible
ACHS,
AND
GARFINKEL
phenome-
program which solves the differential equations for the ADP-actin binding system. We have written another computer program (5), which algebraically solves an enzyme rate law for the ADP + actin 1‘l ADP-actin complex h2 instantaneous concentration of one substrate (or modiThe rate constant for the release of bound ADP (12, = 5 fier) which reproduces the known flux through the enzyme given the concentrations of all other substrates min? was chosen to approximate the rate of formation and modifiers. Because this program does not integrate of ATP from bound ADP observed by Szent-Gyijrgi and the differential equations defined by the rate laws, each Prior (32). We used an ADP-binding rate constant (k,) enzyme behaves (instantaneously) independently of all of 4.11 x lO-:j (nmol/g dry wt)+ min-’ with an actin the others, and we therefore named this mode of model content in heart muscle of 2,870 nmol/g dry wt (32). This “decomposition.” For each time point exmodel predicts that 70.2% of the cytosolic ADP will be construction amined the computed a&in-bound and unbound ADP bound to actin at equilibrium. This model was then checked against other data. Seraydarian et al. (28) levels along with other metabolite levels are input into program. In the course of iterafound an average of 65.9% of the tissue ADP bound in our “decomposition” tively solving for the Mg’+ concentration which will resting frog skeletal muscle. The enzyme phosphoglycreproduce the observed (or deduced) flux through phoserate kinase, which binds MgADPas a substrate and phofructokinase, this program computes a new estimate an inhibitor (27) is one element of our rat heart model of the cytosolic AMP level from the adenylate kinase (1). The act’ in- b’in d ing model results in MgADPlevels equilibrium. The input to the a&in-binding integrating which enable us to reproduce the observed 1,3-diphosprogram is modified according to the new cytosolic AMP phoglycerate and 3-phosphoglycerate levels in Kiibler’s profile, and the procedure is repeated until this profile (12) ischemic heart preparation. does not change between successive computation cycles. Cytosolic Mg”. We have been able to deduce the flux One to four cycles are normally sufficient for converthrough phosphofructokinase for each physiological gence of the distribution procedure. In the course of state we have examined. This enzyme shows marked determining the optimal MgS+ concentration, the “dechanges in catalytic capacity with pH (13). We modeled composition” program automatically computes the cytothis behavior as a pH-dependent interconversion beof mitochondrial and tween an active and an inactive conformation. The ob- solic pH and the concentrations from the creatine kiserved catalytic capacity is adequately reproduced by a complexed cytosolic nucleotides nase rate law, the ADP*-respiration rate relationship, level of the active conformation given by the equation and the chelation equilibria, respectively. PFK;l,.ti,., = Our perfused rat heart model has been implemented 5.2345 exp I- (7.3009-pH)‘/O. 3448]nmol/g dry wt as a simulation program following the conventions of Garfinkel’s (4) simulation language (BIOSSIM, availawhich was determined by nonlinear regression analysis and is valid over the pH range 6.0-7.3. Since this en- ble from SHARE Program Library Agency, catalog no. 360D.03.2.008). The optimal AMP* and MgZ+ profiles zyme binds MgATP”as a substrate and MgATP’+, determined as above are input into the simulation proHATPI-, MgADP-, and AMP”(as well as orthophosgram as tables of their graphically determined time phate, citrate, and cyclic AMP) as effecters (15, 331, its derivatives vs. time. During integration of the full activity under various physiological conditions is highly is computed directly dependent on the nucleotide chelation equilibria at a model the nucleotide distribution and equilibrium expressions given given p-fructose 6-phosphate level. Our h&art model (1) from the kinetic above. The observation that the distribution computed includes a fairly sophisticated representation of the klis the same as that generated by the netics of phosphofructokinase based on the model of during simulation “decomposition” program for the corresponding time Garfinkel (3). Because it has not been possible to meapoint is a verification of the adequacy of our methods. sure the concentration of cytosolic, uncomplexed Mg’+ deduced by this proions, we have treated this quantity as a parameter and The cytosolic Mg”+ concentrations found that value which generates-a distribution of che- cedure (typical values appear in Tables 1-3) are in good agreement with the value of 0.2 mM (360 nmol/g dry wt) lated and unchelated nucleotide species which reprocalculated by Williamson et al. (38). The cytosolic AMP duces th .e observed flux through the enzyme when subprofile generated by our procedure predicts phosphorylstituted into the phosphofructok inase rate la .W. ase b activities which enable us to reproduce the observed temporal profiles for tissue glycogen during peDISTRIBUTION METHODOLOGY riods when the cyclic AMP level is too low to cause Since we are concerned in our modeling efforts with conversion of the enzyme to the more active a form (L. physiological transitions rather than steady states, we Opie, personal communication). This result serves as first assume a temporal profile for ZANP*. This is very the final validation of this method. quickly optimized as the biochemical constraints on the It is difkult to estimate confidence limits for the system force modifications in the profile. We select metabolite levels computed by this procedure, since enough time points to adequately describe the temporal there are many sources of errors, partly because the profiles of the tissue nucleotide levels, ZANP*, respirainformation comes from many sources. However, we tion rate, tissue AMP, and an estimate of the cytosolic believe that uncertainties in the measured metabolite AMP level. These arrays serve as input to a computer tissue contents which are required by our techniques l
l
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CARDIAC
NUCLEOTIDE
R161
DISTRIBUTION
are the major potential sources of error. Our experience indicates that the calculated metabolite levels usually agree adequately with subsequent experiment. It has not yet been feasible to perform a rigorous error analysis. RESULTS
We have applied the above techniques to an aerobic, an anoxic, and an ischemic perfused rat heart preparation. The aerobic Langendorff preparation undergoes a transition from perfusion with buffered solution in the absence of exogenous substrate to perfusion with a buffered solution containing glucose and insulin (24). The adenine nucleotide distribution at several points during the transition are given in Table 1. As the respiration rate increases, tissue ATP rises while ADP and AMP fall, i.e., the metabolism functions at a higher energy state. LaNoue et al. (14) found a total adenine nucleotide content in isolated rat heart mitochondria of 1,200 nmol/g dry wt when the AMP* level was low (loo200 nmol/g dry wt). We were able to maintain the computed ZANP* constant at that value for this preparation, suggesting that antiport translocation of ADP and ATP across the mitochondrial membrane is unimpaired. The very low cytosolic AMP levels are consistent with nearly inactive phosphorylase b and net synthesis of glycugen as required by the data of Safer and Williamson (24). The adenine nucleotide distribution at several points during the transient induced in a Langendorff prepara-
2. Adenine nucleotide distribution during anoxia TABLE
0 min
ATP+ HATP”KATP:‘MgATP’MgHATPTotal cytosolic ATP ATP* ADP”HADP” KADP”MgADPMgHADP Actin-bound ADP Total cytosolic ADP ADP* AMP”HAMPMgAMP Total cytosolic AMP AMP*
0 min
ATPIHATP”KATP” MgATP’MgHATPTotal cytosolic ATP ATP* ADP:+ HADP2KADP” MgADP MgHADP Actin-bound ADP Total cytosolic ADP ADP* AMP’HAMPMgAMP Total cytosolic AMP AMP* PH Mg”+ PFK flux 0, consumption rate
818 1,085 1,372 19,598 218 23,091
1 min
during
3 min
-
T
12 min
1,216 1,002 2,041 19,011 126 23,396
1,101 804 1,850 19,707 116 23,578
1,184 840 1,987 19,464 112 23,587
809
774
767
763
200 168 178 36.7 6.3 1,403 1,992
194 101 172 23.2 2.8 1,203 1,696
180 82.9 160 24.6 2.5 1,068 1,518
181 81.2 161 22.8 3.0 1,061 1,510
198
224
227
230
18.2 7.6 0.5 26.3
11.5 3.0 0.2 14.7
10.9 2.5 0.2 13.6
9.9 2.2 0.2 12.3
194
205
206
207
6.778 442 200 24,600
6.992 314 4,655 29,100
7.036 348 4,905 29,700
7.049 330 4,925 30,300
1 min
2 min
663 995 1,162 17,322 167 20,309
480 1,176 809 13,443 270 16,178
464 1,002 782 13,464 239 15,951
1,255
1,187
1,372
1,389
299 125 266 35.5 2.5 1,720 2,448
257 244 230 51.4 9.6 1,775 2,567
528 815 471 113 35 4,405 6,367
753 552 493 122 32 4,605 6,557
312
284 37.1 17.6 1.1 55.8
3.4
3.3
215 166 6.7 388
244 166 7.9 418
162
259
355
338
7.078 311 4,540 25,000
6.723 523 5,100 23,950
6.511 560 40,640 250
6.566 581 36,260 240
.
tlon oy cnanglng from perfusion with oxygenated buffer to perfusion with buffer gassed with 95% CO-5% COm, (37) is given in Table 2. After 0.3 min, by which time thi residual oxygen in the tissue has been consumed, the ATP falls, while ADP and AMP rise, indicating a rapid transition to a lower energy state. The greatly increased glycolytic flux coupled with the large rise in cytosolic AMP indicate that a significant portion of glycolysis is due to activation of phosphorylase b (I>. Koch and LaNoue (10) found CANP* to be constant in isolated mitochondria unless irreversible damage is incurred. Since these anoxic hearts return to their normal functioning upon reoxygenation, we have held BANP* constant at 1,730 nmol/g dry wt during the course of this experiment to provide room for the increase in AMP*. This suggests that short-term anoxia does not compromise either the adenine nucleotide translocases or the integrity - - of the mitochondrial membrane. In the third experiment we have modeled (191, ischemia was induced in a working rat heart by placing a one-way ball valve in the aortic cannula, thus restricting retrograde perfusion of the coronary arteries during diastole. The computed nucleotide distributions are given in Table 3. We see a transition to a lower energy state similar to that determined for anoxia, but the process is much slower. In this case the computed value of XANP* is not constant; it rises from 1,200 to 3,900 nmol/g dry wt in 30 min. Most of the mitochondrial nucleotide pool is AMP*, which accumulates while ATP* and ADP* fall. A possible mechanism for this increase is suggested by the 1
TABLE 1. Adenine nucleotide distribution the no substrate-glucose transition
0.3 min
1,076 714 1,806 16,748 86 20,403
30.7 6.5 0.5 37.7
PH Mg2+ PFK flux 0, consumption rate
/
l
1
1
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R162
KOHN,
TABLE 3. Adenine nucleotide distribution during ischemia 0 min
-~ ATP4 HATP:+ KATP:’ MgATP MgHATPTotal ATP ATP*
cytosolic
ADP”HADP;! KADP2 MgADPMgHADP Actin-bound Total cytosol ADP ADP*
ADP ic
T
30 min
960 768 1,612 15,186 99 18,625
505 795 852 14,600 188 16,940
492 1,319 831 8,585 189 11,416
475
860
584
388 196 346 47.0 6.0 2,320 3,303
466 463 417 103 22 3,341 4,812
551 932 493 73.4 25 4,883 6,957
193 565 174 29.2 17 2,318 3,296
188
43.6
3.7
196
AMP” HAMP MgAMP Total cytosolic AMP AMP* PH Mg2+ PFK flux 0, consumption rate
12 min
58.5 14.8 1.0 74.3
160 79.7 5.2 245 155
6.997 316 6,300 41,500
6.703 578 17,440 22,000
229 194
4.4 427
176 817 299 3,484 132 4,908
+ GTP Q ADP
GARFINKEL
DISCUSSION
-
92.4
78.8 115 1.7 196
2,573
3,804
6.472 348 5,500 7,500
6.234 395 2,620 4,000
observations of Martin and LaNoue (16), who found evidence that mitochondrial fatty acyl CoA inhibits ATP* export from isolated rat heart mitochondria, when respiration is inhibited by arsenite. They observed an accumulation of AMP* at the expense of ATP* and ADP* under these conditions and interpreted this as indicating that nucleosidetriphosphate:adenylate phosphotransferase, which catalyzes the reaction AMP
AND
nine nucleotides may indicate another factor contributing to irreversible damage in the ischemic heart.
--~
2 min
ACHS,
+ GDP
is limited by lack of GTP. Neely (18) found that fatty acyl CoA does accumulate during ischemia and that nearly all of it is mitochondrial. Our results are consistent with these observations and suggest that the nucleotide translocation mechanism, whereby ADP enters the mitochondria and equimolar ATP emerges, is altered during ischemia, so- that ADP uptake is unimpeded relative to respiration requirements, while ATP* export by the mitochondrial membrane translocases is- inhibited, accounting for the rise in-XANP*. The dramatic changes in the computed levels of mitochondrial ade-
While the adenine nucleotide translocases do not appear explicitly in our model, their activities are implicit in the imposition of a XANP* profile. It has been suggested (8, 26) that the high-energy phosphate produced by oxidative phosphorylation may emerge from the mitochondria as creatine phosphate rather than ATP or that phosphoryl transfer from ATP* to creatine is the principal mode of translocation. However, the maximal velocity of creatine kinase in rat heart is about 1,000 pmol/g dry wt min- ’ (3l), of which approximately 30% is mitochondrial (26). Since the highest oxygen consumption rate reported for the rat heart (7) corresponds to a translocation rate of 600 pmollg dry wt gmin-’ under conditions where creatine kinase is near equilibrium, we are forced to conclude that creatine phosphate is not the principal medium of translocation of the mitochondrial high-energy phosphate. Even for the lower respiration rates in the preparations we have modeled, substitution of the observed or deduced creatine, creatine-F-, MgATP+, and MgADPlevels into the creatine kinase rate law predicts too low a flux to accommodate the required translocation of high-energy phosphate. Our distribution technique results in the prediction of very low pH values during the final states of respiratory failure in ischemia. In a previous version of this model (11) the distribution method yielded a pH of 5.92 after 30 min of ischemia. We found that a reduction of the rate constant for binding of ADP to actin was required to maintain a pH near the physiologically more realistic value of 6.4. While the pH predicted by the present model is an improvement, our results still suggest that reduced afinity of actin for ADP after 12 min of ischemia in this preparation may be a real phenomenon. A similar situation has been observed in muscles worked to exhaustion where the fraction of ADP bound to actin decreased from 65.9% in resting muscle to 29.2% of the tissue content (28). We believe that this phenomenon may reflect significant changes in the conformation or state of polymerization of the contractile proteins, in agreement with Bing (2). l
We thank Center of the This work HL-15622 and Received
Kathryn F. LaNoue of the Milton S. Hershey Pennsylvania State University for her helpful was supported by National Institutes of Health RR-15.
for publication
15 July
Medical advice. Grants
1976.
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5. GARFINKEL,
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CARDIAC
NUCLEOTIDE
R163
DISTRIBUTION
cent Advan.
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37.
38.
actions in perfused rat heart. Role of coupled transamination in repletion of citric acid cycle intermediates. J. Biol. Chem. 248: 2570-2579, 1973. SAHLIN, K., R. C. NORRIS, AND E. HULTMAN. Creatine kinase equilibrium and lactate content compared with muscle pH in tissue samples obtained after isometric exercise. B&hem. J. 152: 173-180, 1975. SAKS, V. A., G. B. CHERNOUSOVA, D. E. GUKOVSKY, V. N. SMIRNOV, AND E. I. C~kzov. Studies of high energy transport in heart cells. European J. Biochem. 57: 273-290, 1975. SCOPES, R. K. 3-Phosphoglycerate kinase. In: The Enzymes (3rd ed.!, edited by P. D. Boyer. New York: Academic, 1973, p. 335351. SERAYDARIAN, K., W. F. H. M. MOMMAERTS, AND A. WALLNER. The amount and compartmentation of adenosine diphosphate in muscle. Biochim. Biophys. Acta 65: 443-460, 1962. STESJ~, B. K., J. FOLBERGROV& AND V. MACMILLAN. The effect of hypercapnia upon intracellular pH in the brain, evaluated by the bicarbonate-carbonic acid method and from the creatine phosphokinase equilibrium. J. Neuroch,em. 19: 2483-2495, 1972. SMITH, R. H,, AND R. A. ALBERTY. The apparent stability constants of ionic complexes of various adenosine phosphates with divalent cations. J. Am. Chem. Sot. 78: 2376-2380, 1956. STAUDTE, H. W., AND D. PETTE. Correlation between enzymes of energy-supplying metabolism as a basic pattern of organization in muscle. Comp. Biochem. Ph.ysioZ. 41B: 533-540, 1972. SZENT-GY~RGYI, A. G. AND G. PRIOR. Exchange of adenosine diphosphate bound to actin in superprecipitated actomyosin and contracted myofibrils. J. MoZ. Biol. 15: 515-538, 1966. UJ, M. Multiple inhibitor sites for ATP on muscle phosphofructokinase as influenced by a change of pH: a computer analysis of “non-linear” kinetic data. Biochim. Biophys. Acta 159: 50-63, 1968. WATTS, D. C. Creatine kinase. In: The Enzymes (3rd ed.), edited by P. D. Boyer. New York: Academic, 1973, p. 383-455. WEBER, A., AND J. M. MURRAY. Molecular control mechanisms in muscle contraction. Physiol. Rev. 53: 612-673, 1973. WILLIAMSON, J. R. Glycolytic control mechanisms. I. Inhibition of glycolysis by acetate and pyruvate in the isolated, perfused rat he&t. J. Biot, Chem. 240: 2308-2321, 1965. WILLIAMSON, J, R. GIycolytic control mechanisms. II. Kinetics of intermediate changes during the aerobic-anoxic transition in perfused rat heart. J. Biol. Chem. 241: 5026-5036, 1966. WILLIAMSON, J. R., C. M. SMITH, K. F. LANOUE, AND J. BRYLA. Feedback control of the citric acid cycle. In: Energy Metabolism and the Regulation of Metabolic Processes in the Mitochondria, edited by M. A. Mehlman and R. W. Hanson. New York: Acader?ic, 1972, p. 185-210.
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MURRAYJ.
of adenine
energy metabolism; simulation; cardiac ischemia; AMP compartmentation; chelation; cytoplasmic pH determination; cytoplasmic Mg?+ determination
THIS AND THE TWO FOLLOWING papers we report the construction of a computer model of energy metabolism in the perfused rat heart. Adenine nucleotides perform key functions in this metabolism. Due to compartmentation of these nucleotides, primarily between cytosol and mitochondria, only a portion of a given nucleotide is accessible to a particular enzyme. The metabolically available ADP pool is reduced by binding to F-actin. Also, Helmreich and Cori (6) have noted that, if tissue AMP were entirely cytosolic, its activation of phosphorylase b would result in excessively high rates of glycogenolysis in resting muscle. Furthermore, an enzyme usually preferentially binds a specific chelated, protonated ? or uncomplex form of a nucleotide. For these reasons it is essential to distribute the adenine nucleotides among their various compartmented and complexed forms-before a physiologic&y realistic model involving them can be constructed. We report here the development of a method for computing the distribution of adenine nucleotides in the perfused heart which will satisfy all the biochemical constraints upon them. As Mgz+ and H+ are important ligands of ad&ine nucleotides, the techniques involved also required computation of cytosolic unchelated Mgzf concen6ation and cytosolic pH, quantities that are difflcult to measure accurately. This method constitutes an IN
Unless otherwise noted, metabolite levels are given in nmol/g dry wt, and fluxes are in nmol/g dry wt min? These units may be converted to PM (or pM/min) by dividing by 1.8 or 0.2 ml/g dry wt for the cytosolic and mitochondrial compartments respectively (36). Enzymatic rate laws were derived from reaction mechanisms by the method of King and Altman (9). Mechanistic details and kinetic constants for the various enzyme rate laws used have been deposited as supplementary material to the following paper (1). l
BIOCHEMICAL DISTRIBUTION
CONSTRAINTS
ON
THE
NUCLEOTIDE
To define the nucleotide distribution we must find the total amount of each nucleotide in each compartment, the fraction of cytosolic ADP bound to actin, the cytosolic Mg’+ concentration, and the cytosolic pH. Nine constraints are required to evaluate these nine unknowns. The tissue levels of each nucleotide, the creatine kinase and phosphofructokinase rate laws, the adenylate kinase equilibrium, a model of ADP binding to actin, and the empirical ADP*-respiration rate relationship quoted below provide eight constraints. The total amount of adenine nucleotides in the mitochondria (CANP*) has been treated as a parameter and serves as the ninth constraint. We have observed that this quantity is required to lie in a fairly narrow range to preclude the computation of negative concentrations or physiologically unrealistic pH values. All these constraints must be simultaneously satisfied, but it is not possible to solve for them sequentially, because the
R158
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CARDIAC
NUCLEOTIDE
R159
DISTRIBUTION
variables are not separable. Furthermore, the resulting so the complete system is equations are nonlinear, mathematically intractable and must be solved iteratively with a computer. Mitochondrial ATP and ADP. LaNoue et al. (14) found that AMP* varied greatly with the respiration state in isolated rat heart mitochondria. However, their data suggest that the ADP*/ATP* ratio is proportional to the respiration rate. If CANP*, the cytosolic AMP level, and the respiration rate were known for a particular physiological state, we could compute the amount of each nucleotide in the mitochondrial compartment using the following empirical relationship deduced from LaNoue’s data ADp*
=
9.95 x lo-‘; R(.ANP* - AMP*) 1 + 9.95 x lo-“R
R is the respiration rate in nmol/g dry wt 4min- I, and AMP* is the difference between the tissue and cytosolic AMP levels. The concentration of ATP* is calculated as the difference between XANP* and the sum of the concentrations of ADP* and AMP*. The above treatment of mitochondrial adenine nucleotides is an expedient designed to avoid detailed modeling of the complex kinetics of the mitochondrial membrane nucleotide translocases and oxidative phosphorylation. Most of what is known on this subject was obtained with complex in vitro preparations (isolated mitochondria and submitochondrial particles), whereas we are concerned primarily with events in intact tissue. This does not introduce large errors into the mitochondrial metabolism part of our model, the citric acid cycle and the malate-aspartate shuttle, because these processes do not depend primarily on adenine nucleotides. Thus our crude method of compartmentation is adequate. Furthermore, the bulk of the adenine nucleotide content is cytosolic, so reasonable errors in the estimated mitochondrial levels do not produce significant errors in the computed cytosolic levels. Compartmenthun of AMP. Adenylate kinase catalvzes the reaction AMP”-
+ MgATP”-
e ADP:j-
+ MgADP-
Substitution of a range of physiologically realistic concentrations for these chemical species into the rapid random equilibrium rate law for this enzyme (22) indicate that this system is always near equilibrium in the rat heart because of the high tissue capacity of the enzyme (31). Clearly, the position of this equilibrium will depend on the position of the nucleotide chelation and protonation equilibria in the cytosol. We have included KS chelation in our model and set the nominal cytosolic ionic strength to 0.1 M, considering this to be equal to the K+ concentration. We used the MgZ+ and K+ chelation and protonation stability constants of Nihei et al. (21). The literature values for K,lIgA1)l’ invariably predicted cytosolic AMP levels which are too low to exert any control on phosphorylase b in the presence of physiological levels of glucose 6-phosphate and ATP (6, 17). Since the stability constant for MgADP is not accurately known (341, we have treated this constant as a
parameter whose value was adjusted to reproduce a neutral pH for the aerobic, steady-state rat heart (see below). The optimal value of 686 M-l is just slightly smaller than that obtained experimentally by Smith and Alberty (30). Rose (23) cites a Mg’+-free, pH-indepedent, apparent equilibrium constant at an ionic strength of 0.1 M of 0,37 for the enzyme-catalyzed reaction K’
=
(ATP=j-)( AMP”-) ~--~ (ADP:‘-)’
= o 37 -
Combining the above constants we can compute the true adenylate kinase equilibrium constant as (MgADP-)(
ADP”-)
K .htgaA1)l'= o 026 -
Kw = (MgATP"-- )(AMP2- ) = &lW'l'
from which we can compute the cytosolic uncomplexed AMP level. The cytosolic AMP’- levels obtained by this method for situations when cyclic AMP is low, and glycogen is being depleted (L. Opie, personal communication), are great enough to activate phosphorylase b. After computing the HAMPand MgAMP levels, the AMP* level is found from tissue AMP by difference. Cytosolic pH. Creatine kinase catalyzes the reaction creatine
+ MgATP’-
*
creatineP-
+ MgADP-
+ H+
If the reactant levels and the rate of change of creatine phosphate (or creatine) are known, we can compute that H+ concentration which will reproduce the observed flux through the enzyme when substituted into the creatine kinase rapid random equilibrium rate law (34). Rose (23) previously suggested that the position of the creatine kinase equilibrium could be used to compute the cytosolic pH, and this method was employed by Siesjii et al. (29) to compute the pH in brain tissue in steady-state situations. Applicability of this method for computation of the pH in muscle, where ADP binding to actin is important, is supported by the recent observation (25) of a linear relationship between the logarithm of the apparent equilibrium constant for this reaction and the tissue pH in human quadriceps muscle. Binding of ADP to actin. The ADP which is bound to F-actin becomes accessible to creatine kinase at a very slow rate (32). This can be interpreted to indicate either that the bound ADP can, with difficulty, serve as a substrate for creatine kinase or that the binding of ADP is reversible. In a recent review (35) it was stated that the nucleotide is bound to G-actin as ATP and is hydrolyzed to ADP during polymerization to F-actin. This would suggest that the bound ADP pool is nearly constant. During ischemia, the tissue ADP of rat hearts nearly doubles while ATP falls (19). Our model would predict alkaline pH values during this period, in contradiction to the acidic pH values obtained by direct measurements (ZO), if the newly produced ADP were not allowed to bind to actin. Furthermore, Williamson (37) observed a fall in ADP and lactate and a rise in creatine phosphate tissue levels upon reoxygenation of anoxic rat hearts. According to our model, the pH would have to rise while ADP is falling. This can only occur if the level of unbound ADP rises. For these reasons we treat
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R160
KOHN,
binding of ADP to actin as a slowly non and use the simplified model
reversible
ACHS,
AND
GARFINKEL
phenome-
program which solves the differential equations for the ADP-actin binding system. We have written another computer program (5), which algebraically solves an enzyme rate law for the ADP + actin 1‘l ADP-actin complex h2 instantaneous concentration of one substrate (or modiThe rate constant for the release of bound ADP (12, = 5 fier) which reproduces the known flux through the enzyme given the concentrations of all other substrates min? was chosen to approximate the rate of formation and modifiers. Because this program does not integrate of ATP from bound ADP observed by Szent-Gyijrgi and the differential equations defined by the rate laws, each Prior (32). We used an ADP-binding rate constant (k,) enzyme behaves (instantaneously) independently of all of 4.11 x lO-:j (nmol/g dry wt)+ min-’ with an actin the others, and we therefore named this mode of model content in heart muscle of 2,870 nmol/g dry wt (32). This “decomposition.” For each time point exmodel predicts that 70.2% of the cytosolic ADP will be construction amined the computed a&in-bound and unbound ADP bound to actin at equilibrium. This model was then checked against other data. Seraydarian et al. (28) levels along with other metabolite levels are input into program. In the course of iterafound an average of 65.9% of the tissue ADP bound in our “decomposition” tively solving for the Mg’+ concentration which will resting frog skeletal muscle. The enzyme phosphoglycreproduce the observed (or deduced) flux through phoserate kinase, which binds MgADPas a substrate and phofructokinase, this program computes a new estimate an inhibitor (27) is one element of our rat heart model of the cytosolic AMP level from the adenylate kinase (1). The act’ in- b’in d ing model results in MgADPlevels equilibrium. The input to the a&in-binding integrating which enable us to reproduce the observed 1,3-diphosprogram is modified according to the new cytosolic AMP phoglycerate and 3-phosphoglycerate levels in Kiibler’s profile, and the procedure is repeated until this profile (12) ischemic heart preparation. does not change between successive computation cycles. Cytosolic Mg”. We have been able to deduce the flux One to four cycles are normally sufficient for converthrough phosphofructokinase for each physiological gence of the distribution procedure. In the course of state we have examined. This enzyme shows marked determining the optimal MgS+ concentration, the “dechanges in catalytic capacity with pH (13). We modeled composition” program automatically computes the cytothis behavior as a pH-dependent interconversion beof mitochondrial and tween an active and an inactive conformation. The ob- solic pH and the concentrations from the creatine kiserved catalytic capacity is adequately reproduced by a complexed cytosolic nucleotides nase rate law, the ADP*-respiration rate relationship, level of the active conformation given by the equation and the chelation equilibria, respectively. PFK;l,.ti,., = Our perfused rat heart model has been implemented 5.2345 exp I- (7.3009-pH)‘/O. 3448]nmol/g dry wt as a simulation program following the conventions of Garfinkel’s (4) simulation language (BIOSSIM, availawhich was determined by nonlinear regression analysis and is valid over the pH range 6.0-7.3. Since this en- ble from SHARE Program Library Agency, catalog no. 360D.03.2.008). The optimal AMP* and MgZ+ profiles zyme binds MgATP”as a substrate and MgATP’+, determined as above are input into the simulation proHATPI-, MgADP-, and AMP”(as well as orthophosgram as tables of their graphically determined time phate, citrate, and cyclic AMP) as effecters (15, 331, its derivatives vs. time. During integration of the full activity under various physiological conditions is highly is computed directly dependent on the nucleotide chelation equilibria at a model the nucleotide distribution and equilibrium expressions given given p-fructose 6-phosphate level. Our h&art model (1) from the kinetic above. The observation that the distribution computed includes a fairly sophisticated representation of the klis the same as that generated by the netics of phosphofructokinase based on the model of during simulation “decomposition” program for the corresponding time Garfinkel (3). Because it has not been possible to meapoint is a verification of the adequacy of our methods. sure the concentration of cytosolic, uncomplexed Mg’+ deduced by this proions, we have treated this quantity as a parameter and The cytosolic Mg”+ concentrations found that value which generates-a distribution of che- cedure (typical values appear in Tables 1-3) are in good agreement with the value of 0.2 mM (360 nmol/g dry wt) lated and unchelated nucleotide species which reprocalculated by Williamson et al. (38). The cytosolic AMP duces th .e observed flux through the enzyme when subprofile generated by our procedure predicts phosphorylstituted into the phosphofructok inase rate la .W. ase b activities which enable us to reproduce the observed temporal profiles for tissue glycogen during peDISTRIBUTION METHODOLOGY riods when the cyclic AMP level is too low to cause Since we are concerned in our modeling efforts with conversion of the enzyme to the more active a form (L. physiological transitions rather than steady states, we Opie, personal communication). This result serves as first assume a temporal profile for ZANP*. This is very the final validation of this method. quickly optimized as the biochemical constraints on the It is difkult to estimate confidence limits for the system force modifications in the profile. We select metabolite levels computed by this procedure, since enough time points to adequately describe the temporal there are many sources of errors, partly because the profiles of the tissue nucleotide levels, ZANP*, respirainformation comes from many sources. However, we tion rate, tissue AMP, and an estimate of the cytosolic believe that uncertainties in the measured metabolite AMP level. These arrays serve as input to a computer tissue contents which are required by our techniques l
l
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CARDIAC
NUCLEOTIDE
R161
DISTRIBUTION
are the major potential sources of error. Our experience indicates that the calculated metabolite levels usually agree adequately with subsequent experiment. It has not yet been feasible to perform a rigorous error analysis. RESULTS
We have applied the above techniques to an aerobic, an anoxic, and an ischemic perfused rat heart preparation. The aerobic Langendorff preparation undergoes a transition from perfusion with buffered solution in the absence of exogenous substrate to perfusion with a buffered solution containing glucose and insulin (24). The adenine nucleotide distribution at several points during the transition are given in Table 1. As the respiration rate increases, tissue ATP rises while ADP and AMP fall, i.e., the metabolism functions at a higher energy state. LaNoue et al. (14) found a total adenine nucleotide content in isolated rat heart mitochondria of 1,200 nmol/g dry wt when the AMP* level was low (loo200 nmol/g dry wt). We were able to maintain the computed ZANP* constant at that value for this preparation, suggesting that antiport translocation of ADP and ATP across the mitochondrial membrane is unimpaired. The very low cytosolic AMP levels are consistent with nearly inactive phosphorylase b and net synthesis of glycugen as required by the data of Safer and Williamson (24). The adenine nucleotide distribution at several points during the transient induced in a Langendorff prepara-
2. Adenine nucleotide distribution during anoxia TABLE
0 min
ATP+ HATP”KATP:‘MgATP’MgHATPTotal cytosolic ATP ATP* ADP”HADP” KADP”MgADPMgHADP Actin-bound ADP Total cytosolic ADP ADP* AMP”HAMPMgAMP Total cytosolic AMP AMP*
0 min
ATPIHATP”KATP” MgATP’MgHATPTotal cytosolic ATP ATP* ADP:+ HADP2KADP” MgADP MgHADP Actin-bound ADP Total cytosolic ADP ADP* AMP’HAMPMgAMP Total cytosolic AMP AMP* PH Mg”+ PFK flux 0, consumption rate
818 1,085 1,372 19,598 218 23,091
1 min
during
3 min
-
T
12 min
1,216 1,002 2,041 19,011 126 23,396
1,101 804 1,850 19,707 116 23,578
1,184 840 1,987 19,464 112 23,587
809
774
767
763
200 168 178 36.7 6.3 1,403 1,992
194 101 172 23.2 2.8 1,203 1,696
180 82.9 160 24.6 2.5 1,068 1,518
181 81.2 161 22.8 3.0 1,061 1,510
198
224
227
230
18.2 7.6 0.5 26.3
11.5 3.0 0.2 14.7
10.9 2.5 0.2 13.6
9.9 2.2 0.2 12.3
194
205
206
207
6.778 442 200 24,600
6.992 314 4,655 29,100
7.036 348 4,905 29,700
7.049 330 4,925 30,300
1 min
2 min
663 995 1,162 17,322 167 20,309
480 1,176 809 13,443 270 16,178
464 1,002 782 13,464 239 15,951
1,255
1,187
1,372
1,389
299 125 266 35.5 2.5 1,720 2,448
257 244 230 51.4 9.6 1,775 2,567
528 815 471 113 35 4,405 6,367
753 552 493 122 32 4,605 6,557
312
284 37.1 17.6 1.1 55.8
3.4
3.3
215 166 6.7 388
244 166 7.9 418
162
259
355
338
7.078 311 4,540 25,000
6.723 523 5,100 23,950
6.511 560 40,640 250
6.566 581 36,260 240
.
tlon oy cnanglng from perfusion with oxygenated buffer to perfusion with buffer gassed with 95% CO-5% COm, (37) is given in Table 2. After 0.3 min, by which time thi residual oxygen in the tissue has been consumed, the ATP falls, while ADP and AMP rise, indicating a rapid transition to a lower energy state. The greatly increased glycolytic flux coupled with the large rise in cytosolic AMP indicate that a significant portion of glycolysis is due to activation of phosphorylase b (I>. Koch and LaNoue (10) found CANP* to be constant in isolated mitochondria unless irreversible damage is incurred. Since these anoxic hearts return to their normal functioning upon reoxygenation, we have held BANP* constant at 1,730 nmol/g dry wt during the course of this experiment to provide room for the increase in AMP*. This suggests that short-term anoxia does not compromise either the adenine nucleotide translocases or the integrity - - of the mitochondrial membrane. In the third experiment we have modeled (191, ischemia was induced in a working rat heart by placing a one-way ball valve in the aortic cannula, thus restricting retrograde perfusion of the coronary arteries during diastole. The computed nucleotide distributions are given in Table 3. We see a transition to a lower energy state similar to that determined for anoxia, but the process is much slower. In this case the computed value of XANP* is not constant; it rises from 1,200 to 3,900 nmol/g dry wt in 30 min. Most of the mitochondrial nucleotide pool is AMP*, which accumulates while ATP* and ADP* fall. A possible mechanism for this increase is suggested by the 1
TABLE 1. Adenine nucleotide distribution the no substrate-glucose transition
0.3 min
1,076 714 1,806 16,748 86 20,403
30.7 6.5 0.5 37.7
PH Mg2+ PFK flux 0, consumption rate
/
l
1
1
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R162
KOHN,
TABLE 3. Adenine nucleotide distribution during ischemia 0 min
-~ ATP4 HATP:+ KATP:’ MgATP MgHATPTotal ATP ATP*
cytosolic
ADP”HADP;! KADP2 MgADPMgHADP Actin-bound Total cytosol ADP ADP*
ADP ic
T
30 min
960 768 1,612 15,186 99 18,625
505 795 852 14,600 188 16,940
492 1,319 831 8,585 189 11,416
475
860
584
388 196 346 47.0 6.0 2,320 3,303
466 463 417 103 22 3,341 4,812
551 932 493 73.4 25 4,883 6,957
193 565 174 29.2 17 2,318 3,296
188
43.6
3.7
196
AMP” HAMP MgAMP Total cytosolic AMP AMP* PH Mg2+ PFK flux 0, consumption rate
12 min
58.5 14.8 1.0 74.3
160 79.7 5.2 245 155
6.997 316 6,300 41,500
6.703 578 17,440 22,000
229 194
4.4 427
176 817 299 3,484 132 4,908
+ GTP Q ADP
GARFINKEL
DISCUSSION
-
92.4
78.8 115 1.7 196
2,573
3,804
6.472 348 5,500 7,500
6.234 395 2,620 4,000
observations of Martin and LaNoue (16), who found evidence that mitochondrial fatty acyl CoA inhibits ATP* export from isolated rat heart mitochondria, when respiration is inhibited by arsenite. They observed an accumulation of AMP* at the expense of ATP* and ADP* under these conditions and interpreted this as indicating that nucleosidetriphosphate:adenylate phosphotransferase, which catalyzes the reaction AMP
AND
nine nucleotides may indicate another factor contributing to irreversible damage in the ischemic heart.
--~
2 min
ACHS,
+ GDP
is limited by lack of GTP. Neely (18) found that fatty acyl CoA does accumulate during ischemia and that nearly all of it is mitochondrial. Our results are consistent with these observations and suggest that the nucleotide translocation mechanism, whereby ADP enters the mitochondria and equimolar ATP emerges, is altered during ischemia, so- that ADP uptake is unimpeded relative to respiration requirements, while ATP* export by the mitochondrial membrane translocases is- inhibited, accounting for the rise in-XANP*. The dramatic changes in the computed levels of mitochondrial ade-
While the adenine nucleotide translocases do not appear explicitly in our model, their activities are implicit in the imposition of a XANP* profile. It has been suggested (8, 26) that the high-energy phosphate produced by oxidative phosphorylation may emerge from the mitochondria as creatine phosphate rather than ATP or that phosphoryl transfer from ATP* to creatine is the principal mode of translocation. However, the maximal velocity of creatine kinase in rat heart is about 1,000 pmol/g dry wt min- ’ (3l), of which approximately 30% is mitochondrial (26). Since the highest oxygen consumption rate reported for the rat heart (7) corresponds to a translocation rate of 600 pmollg dry wt gmin-’ under conditions where creatine kinase is near equilibrium, we are forced to conclude that creatine phosphate is not the principal medium of translocation of the mitochondrial high-energy phosphate. Even for the lower respiration rates in the preparations we have modeled, substitution of the observed or deduced creatine, creatine-F-, MgATP+, and MgADPlevels into the creatine kinase rate law predicts too low a flux to accommodate the required translocation of high-energy phosphate. Our distribution technique results in the prediction of very low pH values during the final states of respiratory failure in ischemia. In a previous version of this model (11) the distribution method yielded a pH of 5.92 after 30 min of ischemia. We found that a reduction of the rate constant for binding of ADP to actin was required to maintain a pH near the physiologically more realistic value of 6.4. While the pH predicted by the present model is an improvement, our results still suggest that reduced afinity of actin for ADP after 12 min of ischemia in this preparation may be a real phenomenon. A similar situation has been observed in muscles worked to exhaustion where the fraction of ADP bound to actin decreased from 65.9% in resting muscle to 29.2% of the tissue content (28). We believe that this phenomenon may reflect significant changes in the conformation or state of polymerization of the contractile proteins, in agreement with Bing (2). l
We thank Center of the This work HL-15622 and Received
Kathryn F. LaNoue of the Milton S. Hershey Pennsylvania State University for her helpful was supported by National Institutes of Health RR-15.
for publication
15 July
Medical advice. Grants
1976.
REFERENCES 1. ACHS, M. J., AND D. GARFINKEL. Computer simulation of energy metabolism in anoxic perfused rat heart. Am. J. Pbysiol, 232: Rl64-R174, 1977. 2. BINC, R. J. Cardiac metabolism. Physiol. Rev. 45: 171-213, 1965. 3. GARFINKEL, D. A simulation study of mammalian phosphofructokinase. J. Biol. Chem. 241: 286-294, 1966. 4. GARFINKEL, D. A machine-independent language for the simulation of complex chemical and biochemical systems. Computers Biomed. Res. 2: 31-44, 1968.
5. GARFINKEL,
D., M. J. ACHS, M. C. KOHN, J. PHIFER, AND G.-C. Construction of more reliable metabolic models without repeated solution of the differential equations composing them. Proc. Summer Computer Simulation Conf. 493-499, 1976. 6. HELMREICH, E., AND C. F. CORI. The role of adenylic acid in the activation of phosphorylase. Proc. N&Z. Acad. Sci., US 51: 13L 138, 1964. 7. ILLINCSWORTH, J. A., W. C. L. FORD, K. KOBAYASHI, AND J. R. WILLIAMSON. Regulation of myocardial energy metabolism. ReROMAN.
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CARDIAC
NUCLEOTIDE
R163
DISTRIBUTION
cent Advan.
8. 9.
10.
11.
12.
13.
14.
15.
16.
17.
18. 19.
20.
21.
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