Computer simulation of energy metabolism in anoxic perfused rat heart MURRAY J. ACHS AND DAVID GARFINKEL Moore School of Electrical Engineering, William Pepper Laboratory, Department of Pathology, and Departments of Medicine and Biophysics, University of Pennsylvania, Philadelphia, Pennsylvania 19174

ACHS, MURRAY J., AND DAVID GARFINKEL. Computer simdation of energy metabolism. in anoxic perfused rat heart. Am. J. Physiol. 232(5): R164-Rl74, 1977 or Am. J. Physiol.: Regulatory Integrative Comp. Physiol. l(3): R164-Rl74, 1977. -We have modeled the energy metabolism of the perfused rat heart in order to elucidate the interaction of physiological and biochemical control mechanisms. This model which includes glycolysis, the Krebs cycle, and related metabolism, contains 68 submodels of individual enzymes and transport mechanisms including both cytosolic and mitochondrial reactions. The method of model construction, which relies heavily on fitting observed in situ behavior to known algebraic rate laws for isolated enzymes, and its data requirements and necessary assumptions are described. Simulation of a COinduced anoxic preparation is described in detail. Here glycolysis increases sharply, due to both increased glucose uptake and phosphorylase activation (there is rapid interconversion between a and b forms, both of which are active here); this causes a damped glycolytic oscillation originating with the glycogen-handling enzymes rather than phosphofructokinase. The behavior and physiological consequences of ATPase activity and of a lactate permease which exports lactate to the perf’usate are discussed.

physiological integration; sis; lactate permease

regulation;

glycolysis;

glycogenoly-

WE REPORT HERE a computer simulation of the energy metabolism of the perfused rat heart, including glycolysis, the Krebs cycle, their interaction, and related metabolism. We have attempted to integrate into a meaningful physiological system the considerable volume of relevant biochemical information, and examine its regulatory and adaptive properties. With this model, it is possible to trace physiological effects back to their underlying biochemical causes. It is difficult to do this otherwise, since so many variables are involved. Furthermore, a cause is often remote from its effect, either in time or in location. This area of metabolism was investigated because its regulation has considerable physiological importance, and breakdown of this regulation has great pathological importance. Although the amount of quantitative data available for the entire system is large it is nevertheless insufficient to completely determine its properties. We have therefore used the more abundant information about the individual subunits, enzymes, and membrane

transport mechanisms, which comprise this metabolic system. The procedures used in this work (1, 8, 13) permit evaluating the behavior of the known subunits and the concepts of their regulation, and verifying their consistency with each other. The model reported here features a number of controllers not considered in our previous simulations of this metabolic area (9). These include intracellular Mg’+ and pH, and their effects on individual enzymes and transport mechanisms under physiological conditions. It has not yet been feasible to include other controllers of this type, such as Ca2+. The aim of this research was to gain knowledge about myocardial metabolism by extracting all the information inherent in the available experiments with perfused rat hearts. It is based on experiments with three individual perfused heart preparations run under different conditions (22, 23, 26, 32), which yielded primarily whole tissue metabolite levels as a function of time. We describe here the construction of the model and its application to the most nearly complete sets of available data: those of Williamson (32) and Safer and Williamson (26). Simulating the observed behavior requires reproducing with differential equations or the equivalent the observed metabolite concentrations and enzyme fluxes as a function of time as well as satisfying algebraic rate equations for the individual enzymes at a given time point. Simulating an experiment involves the following steps, whose interrelationship is shown in scheme I. a) Assemble data base including data on perfused heart and the individual components (transport mechanisms are treated like enzymes here). b) Distribute adenine nucleotides between cytosol and mitochondria as described in the preceding paper (13)

c)’ Distribute enzymes between cytosol and mitochondria, on the basis of the literature information about this distribution. d) At selected time intervals, including those where there are measured data, determine the flux through the individual enzymes and transport mechanisms, initially by appropriately adding together the concentration changes due to the flow of material through them. e) From these fluxes and the known tissue capacities and rate laws of the enzymes involved, obtain estimates

R164

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METABOLISM

c

PERFUSED RAT HEART DATA Tissue contents vs. t fme

ISOLATED ENZYME DATA Kinetic and equilibrium constants T 4

ENZYME TISSUE CAPACITIES AND SUBCELLUWIR DISTRIBUTIONS

4-

ENZYME EiATE EQUATIONS

I1,

ENZOIE SUBMODELS 7

I

COMPUTE FLUXES THROUGH ENZYMES and ESTIMATE UNKNOWN OR TIME-DEPENDENT CONCENTRATIONS at individual time points. This is an iterative operation, as each of these computations may affect the other.

I

EXlT

INTEGRATE DIFFERENTIAL EQUATIONS starting from the results of the time-point-by-time-point process

COMPARE INTECIIATED RESULTS AGAINST THE r DATA SCHEME

of unmeasured concentrations, including distribution between cytosol and mitochondria and of time-dependent input to the differential equations (fl>. f) Integrate the differential equations representing the complete model (or a substantial submodel -it is not necessary to do everything all at once) over the entire experimental interval. It may be necessary to use timedependent input data in this process, determined in steps d and e, to represent external intervention or illdefined situations, or to keep the model size within reasonable bounds. As we are trying to build a biologically meaningful model, we have kept outright “curvefitting” and time-dependent inputs to a minimum. This is a heuristic procedure so.that many iterations must be repeated to obtain a satisfactory fit to the data. Perhaps 50 such interations of the model here described have been performed thus far, of which three involved really major revisions. Although the resulting computed chemical concentrations are not unique, because there are insufficient direct measurements to rigidly define so complicated a system, they are required to be consistent with a very large volume of known information, e.g., the calculated value of a concentration is expected to be within the observed concentration range for that chemical reported

DOES NOT FIT DATA

3

I I

REVISE ONE OR ) MORE SUBMODELS

1.

in the literature. They are therefore likely to be a reasonable approximation to biological reality. Furthermore, it is difficult to estimate, by inspection of the data or by a simple mathematical treatment, the unobserved chemical concentrations (including H+ or pH) which are calculated with the model; some of these concentrations are not presently measurable, The same considerations apply to the rates of processes in the model. The work reported here is part of a process of constructing a broadly applicable model of cardiac metabolism. This is intended to permit extracting from an experiment in this subject area all the information inherent in it, rather than that part obtainable by inspection. It would also permit explaining some of the physiological and pathological consequences of metabolism and its derangements, and hopefully suggest clinically useful manipulations. The overall construction process involves simulating an experimental preparation, validating the results by using them to represent other preparations, comparing them against the known properties of the heart, and seeking testable predictions. In our experience these predictions have usually held up well. Such predictions may be confirmed in the literature, either by subsequent publications or by preexisting ones not considered in model construction, or in

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experiments done in response to the model. When a prediction fails or a model conflicts with a known fact, it must be modified, often by modifying the constituent submodels. Computations were performed with the PDP-10 computer of the Medical School Computer Facility and the 360/65 computer of the Physics Department, University of Pennsylvania. Although the model is reported in the biochemical simulation language’ of Garfinkel (71, most of the computation was done with equivalent handcoded programs. Other details of the computer procedures and software have been (8) or will be described elsewhere. The construction of individual enzyme models, based heavily on nonlinear regression methods, which may be applied to in vitro or in situ data, has been reviewed elsewhere (11). DESCRIPTION

OF EXPERIMENTAL

PREPARATIONS

In the several experiments on which this model is based, rat hearts, usually several per time point, were perfused with Krebs-Henseleit bicarbonate buffer equilibrated with 95% O,-5% CO, at 3%37”C, with possible additives such as Ca’+, and with glucose (if added at all) in concentrations of 5-20 mM. At the end of the experiment, the hearts were freeze-clamped, extracted with perchloric acid, and chemical concentrations determined by standard assays. Work output and 0, saturation of the eMuent perfusate were usually measured. There were differences in experimental detail, e.g., whether perfusate was recirculated or not, whether insulin was added or not, or what the nutritional state of the animals was. In the experiments (32) considered in this paper, hearts from what appear to be starved rats were switched from 95% 0.)~5% CO, to 95% CO-5% CO, as the equilibrated gas at time zero (CO yields a deeper anoxia than NZ, which is often used for this purpose). The perfusate level of glucose in these experiments was 20 mM, and there was no insulin in the perfusate. The initial glycogen levels used in the simulation came from a similar experimental preparation by the same author (30)

J. ACHS

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GARFINKEL

values for the constituent enzymes and transport mechanisms has been deposited as an auxiliary document.” Complete information about tissue concentrations of metabolites has never been available. Thus far, fortunately, only some is needed for the method of model construction used. To analyze glycolysis one must know the inputs (glucose uptake and glycogen consumption), the outputs (lactate and pyruvate), and a measure of pyruvate oxidation if it, occurs. For aerobic glycoZysis, respiration rates are mandatory, and concentrations of at least one glycolytic intermediate, preferably two, one on either side of phosphofructokinase. These values should be obtained for each time point studied. The high-energy intermediates such as ATP are of course necessary here, but are normally reported. More than this should be obtained for at least one time point: preferably all the significant glycolytic intermediates at the initial steady state. Values obtained for the same time point should, if possible, come from the same experiment. Often the value of data is limited by lack of precise definition of exactly what was measured. Every additional measured quantity available beyond the above minimum eliminates one estimate and thus increases the reliability of the entire model somewhat. In this type of analysis there is no such thing as a number which is reliable but insignificant. In this and the following paper the model is applied to the data of Williamson (32), and Safer and Williamson (261, The technical characteristics of these data sets are sufficiently different to considerably test both the model and the model-building method. One set (32) has continuously changing derivatives for all measured concentrations, and considerable oscillatory character, whereas the other (26) is a smooth and apparently simple transition to a new steady state. Also, one has mostly measurements of glycolytic intermediates (32) whereas the other (26) has mostly measurements of Krebs cycle intermediates. CONVENTIONS

AND

ASSUMPTIONS

In engineering terms, the metabolic system we are analyzing is a “gray box”: something whose external behavior is observable, but whose internal behavior is only partially known. In particular, we assume the relevant part of the internal structure is adequately approximated by the major known routes of metabolism. A good accounting of what materials go into the cell and what comes out is required, as well as all available information on internal structure, in this case tissue capacities and reaction mechanisms for enzymes and transport mechanisms. Our assembly of numerical

Tissue levels of molecular species are usually reported in nmol or pmollg dry wt. One gram dry weight is equivalent to 5 g fresh wt, which contains 4 ml of water, of which 2 are intracellular; 0.2 ml of this intracellular water is in the mitochondrial matrix and 1.8 in the cytosol. These compartments are considered internally homogeneous, and no further compartmentation is assumed. These conventions are based on the work of Williamson (31) and allow for the edema observed in perfused rat hearts. Time is given in minutes. Kinetic constants are adjusted to the above dimensions. AK,,, of 1 mM becomes, 1,800 and 200 nmol/g dry wt for the cytosolic and mitochondrial compartments, respectively. Molarity-based rate constants can be converted to these units by dividing by (1.8 x 10” nmol/g dry wt per MY1 for a cytosolic reaction and by (2 x 10” nmol/g

’ This language has recently been named BIOSSIM and is distributed through the SHARE Program Library Agency (catalog no. 360D. 03.2.008), and through the Argonne Code Center.

’ For auxiliary data, order fiche Publications, P.0. Box York, N. Y. 10017.

l

DATA

REQUIREMENTS

AND

DATA

3ASE

NAPS 3513,

Document 02998 from Grand Central Station,

MicroNew

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METABOLISM

R167

dry wt per MY-’ for a mitochondrial reaction, where n is the order of the reaction. Inhibition constants (K,) usually equal the inhibitor concentration which reduces the uninhibited velocity by half. It is assumed that measured metabolite levels reflect intraceEZuZar concentrations, or are corrected for extracellular fluid content, which is valid for the data sets considered here. The following sums are constant throughout (leakage, synthesis, or degradation of these substances is slow enough to be neglected in these short-term experiments): ATP + AMP + ADP in each compartment; NAD + NADH and NADP + NADPH in each compartment; creatine + creatine phosphate; CoA + acetyl CoA + succinyl CoA. (The model does not now include fatty acyl CoA.) The mitochondrial membrane is impermeable to oxaloacetate and to pyridine nucleotides; the sum of the adenine nucleotides in the mitochondria is normally constant, according to the concepts prevailing in the mitochondrial literature. (This assumption may break down where the integrity of the mitochondrial membrane is compromised, as in ischemia (131, but there is no reason to believe this is happening for the preparations described here.) As a result of this membrane impermeability, the ratios of NAD and NADH in each compartment are only indirectly related to each other. The several enzymes and transport mechanisms constituting the model obey rate laws kinetically reflecting the current free substrate and effector levels. As considerable fractions of some of these substances (e.g., NADH and NAD) may be protein-bound, this does not necessarily reflect total tissue contents. For those glycolytic enzymes showing preference for a specific anomeric form of a substrate, extensive trials indicate that the rate of interconversion is fast enough not to be limiting.

the Krebs cycle, transaminases, membrane transports, and other enzymes connecting these. The enzymes in each of the following two groups were combined because of insufficient data: diphosphoglycerate mutase, phosphoglycerate mutase, and enolase; succinate dehydrogenase, fumarase, and succinate thiokinase. Creatine kinase, adenylate kinase, and phosphofructokinase have been discussed in the preceding paper (13). The composite statement of the complete model including the detailed mechanisms of these enzymes, the literature data on which they are based, as well as additional figures illustrating the behavior of the model or its fit to the data, are deposited in an auxiliary document.’ A filled-in example of our internal working diagram of this system is given in Fig. 8 of the following paper (5). Only the most noteworthy information of individual enzymes can be mentioned here. One group of enzymes that has been represented, rather crudely considering their complexity, is that interconverting glycogen and glucose phosphates. While there are many complex controls here, many of the enzymes are interconvertible among more than one form, and glycogen itself is a quite complex macromolecule. The present model does permit simulation of the available data, but a more detailed study of the glycogenhandling enzymes appears desirable. A number of other enzymes require comment. One is pyruvate kinase, which is one of the three glycolytic enzymes catalyzing substantially irreversible reactions. Its importance for control of glycolysis relative to the other enzymes does not appear to be intuitively obvious; it exerts considerable control by “backing up” intermediates, but we have not yet worked out the details. There is considerable mediation of this control by free Mg2+ since the actual substrates of this enzyme are the Mg2+ complexes of the adenine nucleotides, while the inhibitors are the uncomplexed forms. Pyruvate dehydrogenase, the enzyme linking glycolysis and the Krebs cycle, is actually an enzyme complex whose activity is determined by its phosphorylation state; this is mediated by a specific kinase and phosphatase, which are affected by free (intramitochondrial) MgL’. The enzyme activity is further modified by acetyl CoA and NADH, which are also ordinary product inhibitors. We have approximated this situation by making mitochondrial Mg”+ the controller of this enzyme complex in the model, but have encountered particular situations where each of the two products may be the exclusive controller. Mechanisms for transport across membranes, particularly the mitochondrial and cell membranes are included in the model to represent the interaction of membranes and enzymes. EMux of pyruvate and lactate to the perfusate across the cell membrane is not first order with respect to their intracellular concentrations, but appears to be affected by changes in permeability or transport characteristics of the cell membrane. We have represented this by cell membrane permeases for lactate and pyruvate. These are probably reversible, as the heart uses lactate and pyruvate as fuels. Such behavior has also been encountered by others in heart (14,17,29),

SIMULATION

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SUBMODELS

As far as possible, individual submodels were based on literature data for the isolated in vitro species. The submodels were formulated in the simplest terms that explained their in situ behavior. Nonlinear regression techniques were used to determine numerical parameters in the submodels. When literature data were inadequate to define a submodel because of incompleteness or apparent error, such submodels had to be determined primarily from data for the intact system. Sometimes the literature data appears to be incorrect or contradictory. It has been pointed out by Cumme et al. (6) that equilibrium constantsas reported may be in error by a factor of up to three, and varying them by this amount has usually been the first expedient tried in this situation. STRUCTURE

OF

THE

MODEL

The model contains 68 submodels of individual enzymes, membrane transport mechanisms, and equivalent structures, plus additional FORTRAN coding to modify their behavior as required to respond to physiological events. These include the enzymes of glycolysis,

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and has been most thoroughly Spencer and Lehninger (28) MITOCHONDRIAL

studied

AND

D. GARFINKEL

in ascites cells by

OXIDATION

It has been shown (15, 24) that the mitochondrial membrane is impermeable to NADH arising from glycolysis; reducing equivalents enter the mitochondria indirectly. In the heart this occurs primarily by the malate-asparate shuttle (26), and secondarily by the cyglycerophosphate shuttle (33). The former shuttle effectively moves reducing equivalents into the mitochondria in malate molecules, bringing the carbon skeletons back out as aspartate molecules, and maintaining nitrogen balance by exchanging a-ketoglutarate for glutamate. This is carried out by glutamate-oxaloacetate transaminase and malate dehydrogenase in both compartments, and by antiport mechanisms which exchange malate for a-ketoglutarate and glutamate for aspartate across the mitochondrial membrane. The representation of this shuttle in this model keeps the motochondria reduced relative to the cytoplasm, even though there is no irreversible step, contrary to the expectation of Newsholme and Start (21) that one is necessary. This expectation may be based on an intuitive evaluation of the equilibrium behavior, although the system is not at equilibrium and its behavior requires calculation. The fact that the model was constructed using this shuttle in this way confirms the conclusion that this shuttle is predominant (26, 33). However, some modification of the quantitative behavior of the shuttle or related reactions may be required by circumstances. In the CO-anoxia preparation, at-glycerophosphate accumulates, with an effect on the cytoplasmic NADH level. As a result, the pyruvate which is not reduced to lactate cannot be oxidized and must instead be transaminated to alanine; the model predicts a pileup of this substance. The amino groups are ultimately supplied by glutamine, and their actual transfer, via glutamate, takes place in the mitochondria. A similar situation may prevail in cardiac ischemia. RESULTS

J. ACHS

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SIMULATION

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PREPARATION

Williamson (32) notes that about 5 s were required for CO to permeate through the heart after its administration. We compute that mitochondrial NAD starts to go reduced at this time (Fig. 1) and mitochondrial oxidation effectively collapses about 0.2 min after this. A little mitochondrial activity does continue, e.g., the malate-cu-ketoglutarate antiport retains l/lo its original velocity around I min. GLYCOGENOLYSIS

AND

GLUCOSE

TRANSPORT

Most of the metabolism in these hearts is cytosolic. The rate of glycolysis during this transition to anoxia is biphasic. This is shown by the curve giving tissue levels of lactate as a function of time (Fig. 7). We had a choice of assuming either a switch from one source of glycolytic feedstock to another with a transient interruption in supply, or a single source with some kind of interruption in supply. More specifically, in view of the known biol-

1 0

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TiME-MIN FIG. 1. Calculated free NADH/NAD and cytoplasm (- 4 in CO anoxia.

ratios

for mitochondria

(-1

ogy, the choice is between initially using primarily glycogen and then switching toward perfusate glucose, or simultaneously using glycogen and glucose, with a decrease in utilization whose cause is at the physiological level, since we do not know of any chemical reason for such an interruption. We chose a switch in carbohydrate source, since it is reasonable to expect glycogen and glucose, which are distinct biochemically, to be metabolized differently. In a somewhat comparable study of ischemia in dog heart, Wollenberger and Krause (35) found rapid activation of phosphorylase, which supports the first alternative. Accordingly a model was constructed that is consistent both with the present experimental data and with the known properties of the enzymes, substrates, and effectors involved. The calculated rate of supply of glucose equivalents by glycogenolysis and membrane transport from the perfusate is shown in Fig. 2. The increase of glucose transport resembles that observed under other conditions, but is not accompanied by the same changes in other metabolites. Several aspects of the calculated behavior shown in this figure are at least somewhat unexpected, in view of prevailing or recent past beliefs about what is represented. 1) Most of the time most of the calculated phosphorylase activity here is in the b form: at 0.5 min 97% of the activity is in the b form; at 2 min 98%. Most of the time control is then being exercised by AMP, ATP, glucose 6phosphate, and the other effecters of the b form. (This situation was recognized by Wollenberger et al. (36J.j This is the primary basis for calculating the phosphorylase forms, since 3’5’cyclic AMP, which is involved in converting the b form to the a form, was not measured here. Initially glycogenolysis is very low because most (99.3%) of the phosphorylase is in the b form and there is insufficient AMP to activate it. 2) The calculated shift between a and b forms is extremely fast: we go from 97% activity in the b form to 76% ofactivity in thea form in 0.4 min. It takes about 9 s to go from 3O:l b:a to 1:l b:a. 3) A steady state is finally reached where the speed of the debranching enzymes is limiting, rather than that of phosphorylase.

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Phosphorylases

(minutes)

2. Degradation of glycogen by phosphorylase (a, b, and total) and by gIycogen debranching enzymes, and glucose transport into the cells, as a function of time after CO anoxia. FIG.

4) Glycogenolysis and membrane glucose transport should be regulated differently; in particular, insulin suppresses the former and stimulates the latter. Here the two are fairly closely coordinated- to the point where the total phosphorylase activity curve is close to being proportional to the derivative of the membrane glucose transport curve used. Glucose uptake, initially at 4.6 pmol/g dry wt per min, starts to rise at 0.4 min in a sigmoidal curve which levels out at 18.6 pmol/g dry wt per min, with some accumulation of intracellular glucose after 0.8 min, so that the majority of the glycolytic input is almost always coming from glycogen after 0.4 min. 5) Both glycogenolysis and glucose transport generally start to rise about when the level of glucose 6phosphate, owing to phosphofructokinase activation, reaches a minimum (Fig. 3). It is not intuitively expected here that phosphofructokinase is being activated when its substrate is lowest. This portion of the model under these conditions was derived from the following considerations. Glucose uptake rates for rat hearts under conditions workably close to those at the start of the experiment have been assembled from the literature (J. Phifer and D. Garfinkel; Computer fitting of kinetic constants of glucose transport; submitted for publication). Glucose uptake rates in deep anoxia have been measured. As an initial aDDroximation to the final steady-

state glucose uptake rate which appears to fit the other facts of this situation well, we took the highest such reported value (25) and added 25% to it. We can partition phosphorylase activity between a and b forms because there is information on glucose 6phosphate and on cytoplasmic V-AMP and ATP (calculated as described in the preceding paper (13)) which permits determining b form activity. The a form activity is then what is left after this calculation. This implies a time profile for cyclic AMP, which catalyzes conversion of the b to the a form, roughly similar to the phosphorylase a profile, with possible effects of compartmentation and binding. It is then necessary to determine the shape of the transition curves between these two steady states. The time of initiation of the transition around 0.4 min, is established as the time when the increased lactate production is no longer accounted for by the decreases in glycolytic intermediates. At the final steady state, when mitochondrial oxidation has ceased, there is a steady state such that the rate of formation of lactate + pyruvate + alanine + glycolytic intermediates equals glucose uptake + plus rate of release of glucose skeletons from glycogen. During glycogenolysis glucose phosphate is released by phosphorylase and glucose by the glycogen debranching enzymes. These latter enzymes are operating at their known rates for rat hearts which are adjusted for the shielding of branch points by the outer branches of glycogen. The glucose transport rate will both take some time to begin rising (0.4 min) and to reach its maximum (glycolytic flux does not reach its maximum till nearly I min). We have assumed that the shape of this rate as a function of time is sigmoid, both as the mathematically IUUO

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glucose fructose mental

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3. Concentrations, as a function of time after CO anoxia, of 6-phosphate (G6P), o; fructose diphosphate, (FDP), q ; and 6-phosphate (F6P), o (lines are calculated; points are experimeasurements).

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simplest curve meeting these specifications, and as a curve that is often observed in such situations. The details of this curve shape will not greatly affect glycogenolysis curves since glycogenolysis is larger than glucose uptake. The activities of the debranching enzymes and of phosphorylase b are calculated from the composition of the remaining glycogen (with allowance for time delay in the relief of inhibition due to the outer-branch glycogen forms) and from the effects of phosphorylase b as mentioned above. The phosphorylase a activity is again determined by difference. The reasonableness of the curve obtained is established by the experiments of Wollenberger and Krause (35), who suddenly induced acute ischemia in the dog heart, took serial samples, and assayed phosphorylase a as a function of time. The time course they obtained is quite similar to that calculated here, except that it went faster. Also, in an earlier study of this type (36), these authors observed phosphorylase b to CI;to b conversion, with a curve for phosphorylase a shaped similarly to that shown in Fig. 2, although with quantitative differences. The actual numerical models of the phosphorylase forms, debranching, etc. were obtained by fitting to experimental data (12, 18, 25) submodels organized according to the literature. Glycogen synthase activity is low throughout the process because of the absence of insulin. All of the above would of course be more firmly determined by appropriate additional measurements of which the glucose uptake rate would be the easiest. Some other factors known to be involved to some extent, such as Ca)+, are not included in the model. GLYCOLYTIC

PATHWAY

As seen in Figs. 3-5 showing, respectively, the hexose phosphates, triose phosphates, and adenine nucleotides, glycolysis responds on the same time scale, and does so in an undulating fashion - many intermediates fall and then rise. (The fit of the model to the experimental data is primarily illustrated by Figs. 3, 5, 7, 8, and a number of figures which have been deposited.‘) The changes with time of some of the chelations forms of ATP and ADP are shown in Fig. 6, partly to illustrate how difficult they are to predict intuitively. Tissue lactate rises by a factor of 6, the real increase beginning at 20 s, and export of lactate increases even more, on a comparable time scale (Fig. 7). These curves differ enough to indicate that the linkage is other than passive diffusion, so that there is a lactate permease involved, as noted above. Although the behavior of the giycolytic intermediates appears somewhat confused, examination of the activities of the glycolytic enzymes as a function of time (Fig. 8) shows a clear pattern: there is a damped oscillation of the fluxes through the glycolytic enzymes in which the hexose-metabolizing enzymes lead those farther down the chain when glycolytic flux is increasing, whereas the reverse is true when glycolytic flux is decreasing. The degree of difference in the time course of the glycolytic enzyme activities shown in Fig. 8 is the largest we have encountered for any physiological situation; it can

J.

l4

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1.2

TIMEFIG. 4. Concentrations, 3-phosphoglyceric acid pyruvate (PYR), o.

ACHS

2.0

MIN

as a function of time after (3PGA), n; phosphenolpyruvate

CO anoxia, of (PEP), O; and

be decreased by slight modification of the model. Usually the time profiles for most glycolytic enzymes are nearly identical to within the error in drawing the curves. This oscillation originates with the glycogenhandling enzymes (Fig. 2). Phosphorylase a and b are both clearly active and oscillating, and the total debranching enzyme activity also co&ributes to the oscillating character. To some extent this oscillation is a function of pH, which falls with time, as one would expect: the local minimum in glycolytic flux at 1.1 min coincides with a transient drop of pH below 6.5 (Fig. 9). Similar pH effects, determined by other methods, have been noted in other anoxic preparations (20). The fall in pH considerably affects the behavior of the NADH/NAD ratio (Fig. 1) and things related to it, such as lactate/ pyruvate ratio, because NAD-linked enzymes release one H+ for each NADH they form. In this instance the cytoplasm goes only moderately reduced, because it goes acid, whereas the mitochondria go considerably more reduced more rapidly. It should be noted that acidification of the cytoplasm within limits protects against excessive reduction by driving the (NADH) (H+)/(NAD) equilibria toward NAD. Excessive reduction may inhibit such enzymes as glyceraldehyde phosphate dehydrogenase, or drive too much material to a-glycerophosphate (where it is rather unavailable) or lactate. It might also completely deplete the mitochondrial NAD pool. Phosphofructokinase is activated as part of the general increase in glycolytic enzyme activity, but the activation is due to concerted action of many of its positive effecters, (ADP, AMP, fructose 1,6-diphosphate, and inorganic phosphate) which collectively manage to overcome the increase in the principal inactivator, HATP.

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these intermediate levels fall together; as the hexose monophosphates are included, the cause must precede phosphofructokinase. As often happens, pyruvate (Fig. 4) does not have the same shape as the preceding glycolytic intermediates; but it is 180” out of phase with NADH/NAD, as might be expected. The slowness of response of the substances having “high-energy phosphate” bonds (ATP, Fig. 5) and creatine phosphate, which hold fairly constant somewhat past the mitochondrial metabolism collapse, indicates a sharp early drop in ATPase activity. When ATP does finally fall, most of the decrease is in MgATP (Fig. 6),

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METABOLISM

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of adenine (cyto) and ATP, ADP,

nucleotide forms in CO anmitochondrial (mite) with and AMP, as a function of 0

.L

The time profile of total hexokinase activity closely follows the perfusate glucose uptake and is totally unlike that of the other glycolytic enzymes. A slow shift between membrane-bound and soluble forms may be occurring (10). Control here must involve both fast and slow phenomena. The glycolytic intermediate time profiles do bear a moderate resemblance to each other, in that most of them have a peak at about 1 min, but the shape of this peak varies. These time profiles differ sufficiently from those of the enzyme activities that factors other than substrate regulation are significant; this situation differs from others we have studied. For glucose 6-phosphate and fructose 6-phosphate (Fig. 3), which are depleted by the activation of phosphofructokinase, and which do not rise very high owing to absence of insulin, there is a sharp drop at 0.4 min. This drop propagates down the line, but is quantitatively weaker. These substances then rise again, at about 1 min, but later than substances that follow them, such as fructose 1,6-diphosphate (Fig. 3) indicating a large influence of phosphofructokinase on curve shape at this time. Then all

FIG.

function

6. Some of time

1.2

.0 TIME

important chelation after CO anoxia.

\

\ \

1.6

20

(minutes)

\ -I

forms

of ADP

LACTATE PERMEASE , -\ --w / -w-k / 0

and

/ /

ATP

/

,’

as a

/

0 0

.4

.I9

1.2

I.6

2.0

TIME-MIN

7. Tissue lactate (right scale), lactate export to perfusate (Zeft scale), and lactate permease (in arbitrary units) as a function of time after CO anoxia; a, observed tissue lactate levels. FIG.

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M. w-3----

A

PHOSPHOHEXOSEISOMERASE GLYCERALDEHYOE PHOSPHATE DEHYDROGENASE LACTATE DEHYDROGENASE

/ 0, M 0

f

I

1

1

.4

.B

I.2

1.6

TIME-

0 2.0

MIN

8. Fluxes through phovphohexoseisomerase ( A$ scale) (phosphofructokinase is nearly identical); glyceraldehyde phosphate dehydrogenase, and lactate dehydrogenase (right scale) as a function of time after CO anoxia; a, observed rate of lactate production (flux through lactate dehydrogenase) for comparison. FIG.

0 0

I .4

I .8

I 1.2

I ! -6

2.0°1

TIME-MIN FIG.

puted

9. Cytoplasmic pH as a funct ion of time by creatine kinase submodel.

in CO anoxia,

com-

rather than unchelated ATP, which is not intuitively obvious. ATPase activity, effectively calculated as the difference between ATP utilization and production, resembles in its time profile such concentrations as pyruvate and glucose 6-phosphate (Figs. 3 and 4). We have not yet found any definable chemical signal which triggers the drop in ATPase activity. A fall in pH would be expected to diminish ATPase activity because H+ competes with Ca+ for binding to troponin (34) but the fall in pH here (Fig. 9) is much later than the fall in ATPase activity. DISCUSSION

Williamson (32) based his analysis of these data almost entirely on the behavior of phosphofructokinase, which he noted to be activated by 20 s, maximally

J. ACHS

AND

Il.

GARFINKEL

activated at 40-60 s, and decreasing in activity from 6080 s, with AMP, ADP, and inorganic phosphate as allosteric controllers. He did suggest an acidification on the basis of the creatine kinase equilibrium. However, he failed to notice the existence of a glycolytic oscillation or its origin at the level of glycogenolysis and glucose transport into the cell rather than at phosphofructokinase, where most glycolytic oscillations originate, and devoted only a half-sentence to possible stimulation of glycogenolysis. He concluded that there was “a complex sequence of interactions between the various control sites in the glycolytic pathway” the causes of which could not be ascertained with certainty on the basis of his data. A failure of the crossover-theorem analysis used by Williamson for this analysis is illustrated by his conclusion that glycolytic flux falls due to phosphofructokinase inhibition when the hexose monophosphates simultaneously fall even more; this is because glycogen cannot be included in such an analysis. Examination of these experiments raises more questions than it answers. The most important ones concern the supply of glycolytic feedstock (glucose and glycogen) and the disposition of the product (lactate). As has been noted piecemeal at various points above, the following sequence of events takes place following administration of CO: the rate at which the cell membrane exports lactate starts to rise at about 0.15 min; mitochondrial metabolism collapses (ca 0.3 min); ATPase activity is greatly decreased (ca 0.3-0.8 min and again at 1 min); glycogenolysis accelerates (0.3 min) with a coordinated increase in membrane glucose transport and in glycolysis; glycogenolysis falls off at about 1 min. It is quite obvious why mitochondrial metabolism collapses, but less obvious why most of the other events happen. The decrease in glycogenolysis at 1 min may be due to the chemical nature of glycogen and of the collection of enzymes which metabolize it. Effectively, glycogenolysis is rapid when straight-chain segments are readily available to phosphorylase, it slows down when primarily branched-chain segments are left (Le., the polysaccharide approaches a limit dextran structure), as these require rearrangement to the linear structure by the slower-acting debranching enzymes before glycogenolysis can proceed. It has been noted above that a lactate permease was important in lactate efflux from the heart. It is also quite possible that the permease transports lactate into the cell when the heart is burning it rather than exporting it. This entity is not well known in isolation. An important literature description for heart (17) is concerned with steady state isotopic exchange, which is quite different from the conditions we have considered. However, Kiibler (14) has characterized this as a reversible facilitated transport in heart and has obtained an indication of the affinities and capacities, but not of the control properties. The lactate concentration and lactate output curves for this preparation are shown in Fig. 7. It is obvious that they do not have the same shape, as would be expected for passive diffusion out of the cell. The activity profile for lactate permease (Fig. 7), computed by

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SIMULATION

OF

ANOXIC

PERFUSED

RAT

HEART

R173

METABOLISM

dividing lactate export by lactate concentration, looks much like that of the typical glycolytic enzyme, displaced forward in time about 12 s, so that activity begins to increase at about 8 s. Nearly the only other things th .at happen in so short a time are th e co11apse of mitochondrial metabolism, and changes in myokinase and ATPase. On summing up the information for all the experiments we have examined, some indication of the lactate permease control mechanism is possible. Roughly

physiological condition and the behavior of the permease may be a reasonable adaptation to it. Since ischemia is a pathological condition, no adaptation to it has taken place. It is quite possible that the presence of the permease may offer a fertile opportunity for pharmaceutical intervention to diminish the accumulation of lactate in isch .emia by activating the per mease, (e.g., increasing & in the preceding equation). This simulation, which is based on biochemical evidence, permits making a physiological prediction: these hearts will stop beating shortly after 2-min, since their lactate permease activity ATP production would fall below the level at which the d(lactate) + C d(H+) --c :z heart goes quiescent, 70 pmol/g dry wt min (19), and -~ + c, 1 dt dt they would be capable of performing only “housekeeping” functions. It can be seen from the data of Williamwhere Cl, C”, and C:, are empirical constants, and where son (32) that both rate and force of contraction are C:, describes the later time-course (steady-state) portion linearly approaching zero at 2 min. of the lactate permease curves. Spencer and Lehninger It is also worth explicitly ndting that the behavior of (28) did show a relationship between lactate permease this system under this anaerobic condition is quite simiactivity and ApH across the cell membrane in ascites lar to what would be expected from the aerobic situacells. C, is generally much higher in anoxia than in any tions we have examined. The fact that mitochondrial aerobic situation we have examined, and has not thus metabolism is blocked does not appear to change the far been found to respond to any other steady-state way in which glycolytic enzymes perform in situ. condition. The permease seems to respond quite rapidly As discussed in more detail in the following paper, to stresses which threaten to raise the lactate level, or to this model assists in the understanding of cardiac merates of changes of pH or metabolites related to lactate, tabolism (in addition to quantitatively explaining the and its activity often closely follows that of lactate dehyobserved data) through relating physiological events to drogenase. C:, is quite low (near zero) in ischemia, (with underlying quantitative causes at the biochemical level, some dependence on whether the perfusate contains which are otherwise difficult to follow, as well as oxygen or not), and lactate then piles up greatly (20). through making testable predictions and aiding in the There is some evidence that liver behaves in the same design of experiments. way: Sies et al. (27) found that liver export of lactate transiently increases when CO, pressure is suddenly The technical assistance of John Phifer and Lucy Whit.ley is increased, and transiently decreases when CO, pressure gratefully acknowledged. is suddenly decreased. This study was supported by National Institutes of Health A possible explanation for this is the finding (16) that Grants GM-16501, HL-15622, and RR-K the observed tissue partial pressure of 0, in the heart may indeed fall to approximately zero under physiological conditions, so that transient anoxia may be a normal Received for publication 15 July 1976.

REFERENCES ,I.

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ACHS, M. J., AND D. GARFINKEL. Simulation of the detailed reguIation of glycolytic oscillation in a heart supernatant preparation. Computers Biomed. Res. 2: 92-110, 1968. ACHS, M. J., AND D. GARFINKEL. Detailed simulation of energy metabolism in the perfused rat heart (Abstract). Federation Proc. 30: 491, 1971. ACHS, M. J., AND, D. GARFINKEL. Regulation of energy metabolism transients in perfused rat hearts (Abstract). Federation Pm=. 31: 859, 1972. ACHS, M. J., AND D. GARFINKEL. Computer simulation of ischemia in dog heart and its metabolic consequences (Abstract). Federation Proc. 34: 447, 1975. ACHS, M. J., AND D. GARFINKEL. Computer simuIation of rat heart metabolism after adding glucose to the perfusate. Am. J. Physiul. 232: Rl75-R184, 1977. CUMME, G. A., A. HORN, AND W. ACHILLES. Metal complex formation and its importance for enzyme regulation. Acta Biol. Med. Ger. 31: 349-64, 1973. GARFINKEL, D. A machine-independent language for the simulation of complex chemical and biochemical systems. Computers Biomed. Res. 2: 31-44, 1968. GARFINKEL, D., M. J. ACHS, M. C. KOHN, J. PHIFER, AND G.-C. ROMAN. Construction of more reliable metabolic models without repeated solution of the differential equations composing them. Proc. Summer Computer Simulation Conf., 1976, 493-9.

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