Quantitative Analysis of the Change of Metabolite Fluxes along the Pentose Phosphate and Glycolytic Pathways in Tetrahymena in Response to Carbohydrates*

A metabolic scheme of glycolysis and the pentose phos- phate pathway has been constructed, assuming that the reactions occur in a single compartment. From this scheme, equations are written for a system in metabolic and isotopic steady state. These allow computation of the specific activity of every carbon atom of all the intermediates of the glycolytic and pentose phosphate pathways and conse-quently of the flux of carbon along each step of these pathways. large number of well distributed of incorporation of radioactive from different positions of several substrates into intermediates all the fluxes. This is done by choosing a set of metabolic fluxes, calculating incorporation with the aid of a computer, and then manipulating the flux rates until the computed incorporations match the data. The model is this to analyze the metabolism of the protozoan Z’etruhymena pyriformis. The scheme of the model is consistent with all available information on the enzyme complement of this ciliate. inoculated a of

A metabolic scheme of glycolysis and the pentose phosphate pathway has been constructed, assuming that the reactions occur in a single compartment.
From this scheme, equations are written for a system in metabolic and isotopic steady state. These allow computation of the specific activity of every carbon atom of all the intermediates of the glycolytic and pentose phosphate pathways and consequently of the flux of carbon along each step of these pathways.
A sufficiently large number of well distributed measurements of incorporation of radioactive label from different positions of several substrates into intermediates or products must be made to determine all the fluxes. This is done by choosing a set of metabolic fluxes, calculating incorporation with the aid of a computer, and then manipulating the flux rates until the computed incorporations match the data. The model is used in this paper to analyze the metabolism of the protozoan Z'etruhymena pyriformis.
The metabolic scheme of the model is consistent with all available information on the enzyme complement of this ciliate. Cells grown to transition phase in proteoselpeptone medium were inoculated into a mixture of glucose (6 mu), fructose (6 mu), ribose (3 mu), and glycerol (3 mu) and incubated for 1 h. In each of these experiments, one of the following labeled substrates was present: [l-, 2-, 6-, or CT-"Clglucose; [I-or UJ4Clfructose; [l-or U-"Clribose; [l(3)or 2J4Clglycerol. The incorporation of label from these substrates into CO,, lipid, glycogen, and RNA was measured.
In contrast to earlier studies on the metabolism of 2-and 3-carbon substrates by Tetruhymena, the rate of incorporation of label from some substrates into some products (e.g. from [l-'*Clglucose into COZ) changed during the incubation. To treat these time-dependent data within the framework of the steady state model, the l-h incubation was divided into three 20-min intervals; within each of these, the rates of incorporation were approximately constant, as required for a steady state system. Measurements of the pool sizes of glucose-6-P and fructose-6-P showed that only slow changes in pool sizes occurred after the first 5 min of incubation and indicated that the system was effectively in a metabolic and isotopic steady state throughout most of the * This investigation was supported by Grant 5ROl HD01269 from the National Institutes of Health. $ Supported by a James B. Duke Fellowship.
incubation. The finding that a low concentration of cycloheximide prevented the acceleration of 'CO, production from labeled glucose suggests a role for protein synthesis in the slow adaptation to carbohydrate addition and supports the quasi-steady state treatment of this system.
The expected incorporation into each product was computed for trial sets of 18 independent flux rates. A set of flux values was found which yielded a good fit to the 29 measurements made for each interval. These flux values therefore constitute a quantitative description of temporal changes in carbon flow along the glycolytic and pentose phosphate pathways during the 1st h of adaptation to the carbohydrate mixture.
The rates of utilization of glucose, fructose, glycerol, and ribose were in the ratio of about 5:1:0.25:0.1. Ribose utilization increased a-fold during the hour, most of it being used for RNA synthesis. Over 80% of the carbon utilized is accounted for by the high, constant rate of glycogen synthesis. There is a progressive increase in glycolytic flux, most probably resulting from an increasing flux through phosphofructokinase and to a lesser extent from increasing glucose uptake or phosphorylation or both. Fatty acid synthesis shuts off early in the incubation.
Fluxes through hexose-P isomerase, glycerol-P dehydrogenase, and transaldolase increase about 3-fold during the incubation.
The triose phosphates, but not the hexose phosphates, are at isotopic equilibrium. There is an appreciable bidirectional flux through the nonoxidative portions of the pentose cycle, and, as expected from in vitro enzyme measurements, a very small flux through the oxidative portion.
A futile cycle between fructose-6-P and fructose 1,6-diphosphate amounting to -70% of the forward carbon flux occurs throughout the incubation. The operation of this futile cycle is the only path for incorporation of label from [6-14Clglucose into carbon 1 of the glucose moiety of glycogen; measurement of the amount of label so incorporated matched the predictions of the model, thereby independently corroborating the values obtained for the metabolic fluxes, and in particular the value of the futile cycle. Late in the incubation, ATP expenditure in this futile cycle comprises up to 9% of the total ATP consumption of the cells. During the first 40 min of adaptation the cells utilize more ATP than is derived from catabolism of the carbohydrate mixture. Thereafter they are in positive net energy balance Analysis of Pentose Phosphate and Glycolytic Pathways even without utilization of other components of the medium.
Although a large number of well distributed measurements is required to determine all the in uiuo fluxes, we have developed methods for estimating, from limited data, fluxes through hexose phosphate isomerase, triose phosphate isomerase, glycerol-P dehydrogenase and through the exchange reactions of transaldolase and transketolase. Most previous models have required one or more assumptions about these reactions as well as the assumption that a futile cycle at phosphofructokinase and fructose-l$-diphosphatase is absent. Since this model requires none of these assumptions, it can be used to test earlier models and to investigate the validity of their predictions when any of the assumptions are not justified. These considerations, including an analysis of extant data on rat mammary tissue, are presented in miniprint as Appendix I of this paper.
Much work has been done to characterize the in uiuo behavior of many enzymes of intermediary metabolism with respect to substrates and modulators with the ultimate aim being to understand the in uivo operation and control of metabolism. Extrapolation from in vitro to in vivo behavior is hazardous, however, and studies of metabolism in living cells are of increasing importance. A method of quantitatively studying whole cell metabolism, developed in this laboratory, has previously been used to analyze acetyl-CoA metabolism in the ciliated protozoan, Tetruhymenu pyriformis (see references in 1). Raugi et al. (1) constructed a model consistent with all known information on Tetruhymena's enzyme complement and compartmental structure, specifying in detail acetyl-CoA metabolism in the Krebs cycle, the glyoxylate bypass, p oxidation, and related pathways. The model enabled computation of the specific activity of each carbon of any metabolic intermediate and hence computation of the mass fluxes along the pathways considered. In this earlier work, the segment of metabolism connecting the hexose and triose phosphates was greatly simplified to facilitate the analysis; there was assumed to be a direct exchange of label between phosphoenolpyruvate and the glycosyl moieties of glycogen.
The present work is an expanded treatment of the in viuo carbohydrate metabolism of Tetruhymena, complementing the previous studies of Raugi et al. (2).
Although there have been numerous theoretical and experimental studies aimed at quantitating fluxes through glycolysis and the pentose phosphate pathway, the complexity of these pathways necessitated models based on simplifying assumptions which, while allowing reasonable estimates of flux through the oxidative steps of the pen&e phosphate pathway, did not permit assessment of the fluxes through each reaction of both pathways. These methods were, in any case of limited applicability for studying the role of this pathway in the metabolism of Tetruhymena since the available evidence indicated that little if any glucose-6-P dehydrogenase or 6-phosphogluconate dehydrogenase was present in this organism, although the enzymes of the nonoxidative portion of the pentose cycle were found (2-4).
Absence of the oxidative steps of the pentose-phosphate pathway in Tetruhymenu raises many questions about the role of the nonoxidative reactions in this organism, making it of interest to assess the direction and magnitude of carbon flux in this pathway. Earlier work with Tetruhymenu (5) had shown that the ratio of '%O, produced from L6-'4C]glucose to that from [1-Ylglucose was between 1.2 and 1.5, which was interpreted as implying a role for transaldolase in glucose metabolism. In addition, the finding that reserpine reduced this ratio to nearly 1.0' suggested that studies of the pentose phosphate pathway in Tetruhymenu might contribute to our understanding of the evolution of the regulation of carbohydrate metabolism in eukaryotes.
With these and other related questions in mind, a model of Tetruhymenu metabolism was developed. Some general properties of this model and its application to other systems are described in detail in Appendix I, in miniprint format.g The model, relatively free of simplifying assumptions, accounts for the metabolism of the substrates glucose, fructose, ribose, and glycerol, in an expanded scheme of glycolysis, glycogen synthesis, the pentose phosphate pathway, and an abbreviated tricarboxylic acid cycle. The structure of the model is consistent with the known facts of Tetruhymenu metabolism with the exception that the fate of acetyl-CoA is greatly simplified. The equations that have been derived permit computation of the incorporation of radioactivity from any carbon atom of the substrates into a variety of products. By making experimental measurements of the rates of llC incorporation into products" (CO,, lipid, glycogen, and RNA) and comparing these to the predictions of the model, the actual fluxes through the major metabolic pathways in the cell can be ascertained.

Analysis
of Pentose Phosphate and Glycolytic Pathways nucleic acid synthesis (V,,). V,, Vll, V,,, and the steps allowing for the utilization of pyruvate (V,,;, V,,, V,,, and VJ were considered as irreversible, and, although phosphorylase is present in Tetruhyntena (9), it was assumed that no glycogen degradation occurred under conditions where glycogen deposition from glucose was occurring at a very high rate. Fructose is shown as entering metabolism only via hexokinase (Vv) since fructokinase was looked for but not found in this cell (111. All other steps of the glycolytic and pentose phosphate pathways were considered to be reversible. Of the 22 independent parameters in this scheme, 4 were set equal to zero (V',;, V,,, V,., and V,); justification for this is discussed in detail below.

Choice of Substrates and Experimental
Design-Since a large number of measurements is needed in order to determine the 18 independent flux rates with a minimum of ambiguity, it was decided to use a total of 10 labeled substrates in the standard mixture of glucose (6 mM), fructose (6 mM), ribose (3 mM), and glycerol (3 mM). A series of initial experiments was performed on cells that were grown to transition phase and then briefly centrifuged and resuspended in an inorganic medium, but the data obtained from these experiments were too variable to allow determination of the flux values to the precision we desired. These experiments did, however, indicate that the utilization of glucose and ribose becomes independent of concentration in the range from 3 to 6 mM. Since glucose was utilized at a much faster rate than ribose, we chose 6 mM glucose and 3 mM ribose as the concentrations in our standard substrate mix. The concentration of fructose, which is consumed more slowly than glucose, was also chosen as 6 mM. The rate of glycerol utilization increased with concentration up to the highest concentration tested. It was convenient to use it at 3 mM. At these concentrations, less than 2% of the ribose, glycerol, and fructose, and less than 10% of the glucose was consumed during the course of a l-h incubation, so that the concentration of each of the four substrates remained essentially constant during the course of these experiments. Since centrifuging the cells and suspending them in an inorganic medium caused an unacceptably large variance in the data, the experiments reported in this paper were performed by adding cells in their growth medium to the standard mixture of the four substrates, as described in detail under "Materials and Methods" (see Appendix II).
Applicability of the Model under Non-Steady State Conditions-In the derivation of the model (see Appendix I for details) the assumption is made that the system is in a metabolic steady state i.e. that no net accumulation or destruction of any intermediate occurs.
If the observed incorporations of label from substrates into products are linear with time, this constitutes presumptive evidence that the pool sizes of intermediates are not changing. Although incorporation of label into glycogen from all substrates was linear with time, the rate of incorporation of several substrates into the other products was not constant. Examples of this are given in Fig. 2 applicability of a steady state model under these experimental conditions.
From considerations presented in detail in Appendix II, it was concluded that an approximate steady state is achieved within the first few minutes after substrate addition and that the system remains in a quasi-steady state thereafter.
Treatment of Data-In previous experiments with substrates where label incorporation into product was linear with time, we established the linearity and the duration of the lag period, if any, with a few time course experiments (1). We then computed the average rate of label incorporation by making repeated measurements at a single time (usually 60 min). In an analogous manner, in the present investigation we used a few experiments to establish the "shape" of the curve of incorporation from each labeled substrate into each product. Details of this procedure are presented in Appendix II. The equations used to calculate the experimental data at 20, 40, and 60 min after the addition of the carbohydrate substrates are listed in Table II of Appendix II. The resulting data are listed with their estimated standard errors in Table III. A total of 29 measurements was made at each of the three time intervals. Since the data have been adjusted for the incorporation of label into fatty acids during the first 20 min and there was practically no label incorporated into fatty acids at later times, VI, in Fig. 1 has been set to zero. V17, the rate of lactate production, has also been set to zero since in previous experiments," we have been unable to detect any lactate production. V,,, which represents the input of P-enolpyruvate from the Krebs and glyoxylate cycles, was set to zero since the gluconeogenic flux in the presence of large amounts of glucose, fructose, glycerol, and ribose and the absence of added acetate or pyruvate is likely to be very small. It was found that when V,, = 0, the choice of V', was entirely arbitrary so that it, too, was set to zero. Thus the 29 incorporation measurements made at each time point provide considerable redundancy for determining the 18 independent parameters. These measurements, plus others to be described below, thus enable the model to be subjected to a stringent test.

Analysis of Pentose Phosphate and Glycolytic Pathways 1593
Choice of Solutions which Best Fit Data at Each Time -As discussed in detail earlier (11, a trial and error procedure was necessary to find an acceptable solution and then refine it to achieve the best fit. Because many of the flux values were clearly changing during the course of the incubation, an assumption of minimal complexity was made so that, where possible, the same rate was chosen for all three times. The numbers next to each arrow in Fig. 1 show the flux values, in nanomoles/h/lO" cells, which gave the best fit to the data. The numbers are arranged vertically, the topmost of each set being the average flux during the 0 to 20-min interval, the next being that during the 20 to 40-min interval, and the bottom number that during the 40 to 60-min interval. The expected incorporation from each labeled substrate into each product at 20,40, and 60 min, computed from these flux values (which are also listed in Table IV) is shown in Table III immediately below each measurement.
With a few exceptions which are discussed below, the overall fit to the data is good, and the flux configurations shown in Fig. 1 therefore can be considered an accurate representation of the temporal pattern of metabolite flow in these pathways. It should be pointed out that the measurements of the incorporation of [1-'Qfructose into lipids were not used in obtaining the fits. The closeness with which these values are predicted constitutes further evidence that the values in Fig. 1 reflect the in vivo carbon flows throughout the l-h period.

Assessment of Flux Values and Probable
Limits of Confidence -In spite of the large excess of measurements, not all of the 29 measurements are independent so that some flux values are more tightly determined than others. To establish the permissible range of variation for each parameter, the procedure employed was to vary a single parameter until the fit to the data worsened significantly and then attempt to re-establish a fit through variation of other parameters. No significant improvement on the best fits shown in Fig. 1 could be obtained in this way, in agreement with the definition of these values as the best fit values. Table IV presents the flux value for the best fit in each interval. (Some of these numbers were rounded off in Fig. 1 for convenience in presentation.) The numbers in parentheses show the acceptable range of variation, i.e. that within which a good fit was still attainable. Table IV shows the maximal in vitro rates reported in the literature for many of the reactions of Fig. 1. Clearly, most of the in vivo flux values computed here are consistent with the in vitro assays.
When the parameters directly associated with substrate utilization or product formation (V,,, V,, VoL, V,, V,2, V,4, and V,,) were varied the fit to the data failed rapidly and could not be restored by variation of any other parameter even with deviations of as little as 3 to 5% from the best fit values. Thus these values are fairly precisely determined.
It is clear that the preferred substrate is glucose; it is used at about 5 times the rate of fructose and nearly 50 times that of ribose. That glucose should be utilized more rapidly than fructose when the concentration of each is 6 mM is expected, since the hexokinase of Tetrahymena has the same V,,,,, for these two hexoses but the K,,, for glucose is about 4 x lo-" M while that for fructose is about 7 x lo-" M (11). The much lower rate of utilization of ribose accords well with the lower amount of ribokinase reported compared to hexokinase (Table IV). It can also be seen that while fructose and glycerol are metabolized at essentially constant rates during the entire hour of incubation, the rates of ribose and, to a lesser extent, glucose utilization increased with time.
The bulk of the carbon utilized under these conditions winds up in glycogen, with V,, accounting for about 85 to 90% of all products formed (given by V,, + V,, + V,, + V,). It should be noted that there was practically no change in the rate of glycogen synthesis throughout the l-h incubation. The other  Table II. The  computed at 20,40, and 60 min. In the case of incorporation into lipid lower part of each pair of numbers represents the value for incorpoglycerol, the values for total lipid, generated from Table II, were ration in nanomoles/lOfi cells, computed from the best iit flux paramcorrected for fatty acid incorporation as described in the text. These eters presented in Table IV     principle pathway of hexose utilization i.e. glycolysis with subsequent oxidation in the Krebs cycle, increases 3-fold, accounting for about 6% of substrate utilization at early times and increasing up to 17% by the end of the hour. The rates of production of lipid glycerol (V,,) and RNA (V,,) represent a much smaller fraction of the total. Lipid glycerol synthesis remains nearly constant, but the incorporation of ribose into RNA rises almost 3-fold during the hour. Since ribose utilization (V,) increases at about the same rate as V,4r the amount of ribose entering the remainder of the metabolic pathway remains constant.
The flux through hexose phosphate isomerase (V, and V'J was fixed to within about 20% during the first 20-min interval and to within about 40% thereafter. The value of Vz is not large, relative to Vo, and the specific activities of glucose-6-P and fructose-6-P calculated by the model for the best fit values are not equal (data not shown), as expected since there is an upper limit to the acceptable values of V,. V2 increased during the l-h incubation, although the exact pattern of this increase is not clear because of the range of uncertainty in this parameter. In contrast to this, the flux through triose phosphate isomerase (V, and V',) could be made as large as one desired without disturbing the goodness of fit, and even at their lowest permissible levels was sufficiently large to ensure that dihydroxyacetone-P and glyceraldehyde-3-P were close to isotopic equilibrium throughout the incubation. Although the net flux through glycerol-P dehydrogenase (Vo, -V,,) remains constant at about 40 nmol/lO" cells/h in the direction of glycerol-P oxidation, both V,, and V,,, increased significantly during the hour. In so far as we are aware this constitutes the first description of a seemingly pointless bidirectional flux of reducing equivalents (in excess of the net flux of reducing equivalents) at this step.
One of the principle purposes of this investigation was to provide a quantitative estimate of the metabolic flux through the reactions of the pentose phosphate pathway. As noted earlier, most investigations (2-4) have reported the near absence of glucose-6-P and 6-phosphogluconate dehydrogenases from Tetruhymena.
We therefore attempted to fit the data with V, (which represents both these reactions) set to zero. This was possible in the 20 to 40-and 40 to 60-min intervals, but for the first 20-min interval, a good fit could not be obtained unless some flux through V, was allowed. We have therefore chosen to set V, = 8 nmol/lO" cells/h and to keep it constant throughout the incubation. It should be noted that this value of V, is well within the reported range of activities in the in vitro assays and at the lower limit of the sensitivity of those assays in which no activity was found.
Although there is at most a very small flux of metabolites through the oxidative steps of the pentose cycle, there is clearly an appreciable flux through all the nonoxidative steps. Despite the large number of measurements, the data are not sufficient to estimate all these fluxes with precision. In particular, varying any of the fluxes, V, (ribulose-P epimerase), V, (ribose-P isomerase), or V',, and V',, (transketolase), had qualitatively similar effects. Since the effects of raising any of these parameters could largely be compensated by lowering another, they were free to vary over a wide range. To determine the permissible ranges, V, and V, were varied as a pair, as were V', and V', , . As shown in Table IV, V, and V8 had no upper bound, but if they were taken to be large, V'!, and V',, had to be lowered to their minimum value of about 10 nmol/lO" cells/h. If V', and V',, were kept at their best fit values (20 nmol/lO" cells/h), then V, and Vs had an upper limit of about 300 nmol/lO" cells/h. Similarly, there was an obligatory association between the minimal acceptable values for V, and V, and the upper limits of V', and V',,. For the best fit, an intermediate value of 20 nmol/lO" cells/h was chosen for V', and V', , and this was found to be associated with values for V, and V, of 150. Although, as just discussed, this combination is not unique, several important conclusions may be drawn nevertheless. V, and V, must be at least 40 nmol/lO" cells/h during the first part of the incubation and flux through these steps must be at least twice this at later times. Similarly, the flux through transketolase does not exceed 50 nmol/lO' cells/h and is probably less than that. Furthermore, the fluxes V', and vr,l, which represent the "backward" reactions of the pentose cycle, must be at least as large as the net flux through these reactions at all times, no matter what values are chosen for V, and V,.
In contrast to the relative indeterminancy in the magnitude of flow through these reactions, the flux through the remaining nonoxidative reaction, catalyzed by transaldolase (V,,, and V',,,), could be determined fairly precisely. Flux through transaldolase was of the same magnitude as that through the other nonoxidative steps of the pentose phosphate pathway, but unlike the other reactions, the data required that flux through transaldolase increase about 3-fold during the hour. (From the range of acceptable values for V,,, it would seem that a smaller increase is possible than was chosen. This would, however, necessitate having certain calculated values for incorporation fall at one extreme of the data at one time point and at the opposite extreme at the next point. Thus although the increase in V,,, may not be quite as linear as depicted in Fig. 1, it is unlikely that the flux through transaldolase differs markedly from this.) It should also be noted that the bidirectional flux through transaldolase, like that through the other nonoxidative reactions, is large relative to the net flux.
Unlike methods based on the use of tritium-labeled substrates which are subject to error because of uncertainty in the extent of tritium exchange in viuo (25), the present method provides a relatively unambiguous estimate of the extent of futile cycling at the phosphofructokinase (V,,)/fructose-1,6-diphosphatase (V'J couple. Table IV shows that VR increases about 7-fold during the course of the l-h incubation, and that this is accompanied by a comparable increase in V':,. At each time interval, V', is at least two-thirds of V:,, so that futile cycling represents an appreciable portion of the total flux through phosphofructokinase. It should also be stressed that there is a large increase in net flux in the direction of glycolysis through this pair of steps, going from -15 nmolil6" cells/h at the beginning of the l-h incubation to about 100 at the end. Precise determination of the limits to V':, is complicated by the fact that manipulation of V, and V', has the same qualitative effect on the fit of the data as does manipulation of V':?. For the best fit we assumed V4 to be constant at 500 nmol/lO" cells/h. For higher values of Vq, the limits on V':, drop somewhat, but even for a constant, very rapid exchange at aldolase, the minimal values for V':, are 35, 90, and 150 nmol/lO" cells/h at 0 to 20, 20 to 40, and 40 to 60 min, respectively. If V, is permitted to increase with time, then the increase in V':, becomes less pronounced; but in order to have V':, remain nearly constant, it is required that V, increase by 3 to 4 orders of magnitude during the hour, which is highly unlikely since aldolase is not generally considered to be regulated and since the activity of this enzyme as assayed in vitro is large (Table IV).
The conclusion that there is simultaneous operation of the  V Incorporation of 6-'4C-glucose into carbon 1 of glucose in glycogen Cells were grown and incubated for times up to 1 h with the standard substrate mixture containing LG-"Clglucose. Glycogen was isolated and the glucose decarboxylated as described under "Materials and Methods." The percentage of radioactivity in glucose released by decarboxylation is given in the row labeled Observed for two experiments (labeled I and II); each value represents the mean of a triplicate determination. The reaction rates from Table IV were used with the model to compute the relative specific activity of the glucose-6-P pool, and the percentage of label calculated to be in Position 1 is given in the row marked Calculated.
% phosphofructokinase and fructose-1,6-diphosphatase reactions suggested that experiments be performed measuring the amount of label appearing in Carbon 1 of glucose-6-P when [6-'YJglucose was the labeled substrate, because this is the only combination of reactions which will cause such a redistribution of carbon. Since glycogen is assumed to have glucose-6-P as its precursor, experiments were performed in which cells were incubated with [6-'4Clglucose, and the glycogen was degraded to glucose and decarboxylated as described under "Materials and Methods" (Appendix II). The results (Table V) show that label does appear in Carbon 1 of glucose-6-P, thereby confirming the operation of a futile cycle at V:$ and V',. That the measured incorporation of [6-'Qglucose into Carbon 1 of glucose-6-P is comparable to the amount predicted at each time from the flux values of Fig. 1 constitutes strong support for the values of V:$ and V':, chosen in the best fit. It should also be recalled that the amount of label appearing in Carbon 1 of glucose-6-P also depends on other flux values. The agreement between predicted and measured values thus further supports the entire flux configuration of Fig. 1.
Although, on the whole, the model gives a close fit to the data, in some cases the predicted values for incorporation of label into product do not agree well with the observed values. For example, the model predicts that incorporation of [l-'Qglucose and [2-'QZ]glucose into both glycogen and lipid glycerol should be practically equal (see Table III) whereas about 20% more [l-'4C]glucose than [2J4C]glucose was incorporated into glycogen and slightly less into lipid glycerol. No choice of fluxes was capable of producing this result. While it is possible that some additional pathway might be added which would account for this discrepancy, the magnitude of the difference is not, in our opinion, sufficient to warrant a conclusion that the metabolic scheme needs modification. Similarly, although the predicted values for incorporation of [U-'YJribose into glycogen are lower than the observed values, it seems unlikely that there is a metabolic pathway we have overlooked that might improve the fit to these data. Another discrepancy between the data and the predictions of the model occurs for the incorporation of [U-'YJglucose into lipid glycerol. This almost certainly represents a technical error of some sort since at later times the value from [UJ4Clglucose into lipid is lower than that from either [l-or 6-'Qglucose, which is impossible.
It is not surprising that the model does not fit the data for incorporation of [UJ4C]fructose into lipid glycerol (Table III).
This measurement, it will be recalled, was unique in that its time course showed biphasic kinetics, with a rapid initial rate of incorporation, a slowing, and another increase in the last time interval. The model predicts a steadily increasing rate of incorporation, as it does for [l-'Qfructose.
In the latter case, however, the predicted values agree with the data throughout the course of the incubation (Table III). We have no explanations for the puzzling behavior of [U-llC]fructose with respect to its incorporation into lipid glycerol since even if fructokinase were present in Tetrahymena (which does not seem to be the case (8)), it is difficult to see how operation of this pathway would produce data of the type found here.
It will be noted that the predicted values for incorporation of [IY-'~C]-and at later times [2J'Clglucose and of {2-'Y!Jglycerol into CO, are considerably below the measured values (Table  III). This may come about because the metabolic fates of pyruvate and acetyl-CoA are greatly oversimplified in this model. Earlier work has shown a much different rate of incorporation of [2J4C]-and [3J4Clpyruvate into CO, (11, which cannot be taken into account by the reactions shown in Fig. 1. (It should be noted that although CO, production at steps V, and V,, is not explicitly shown in Fig. 1, the yields in CO2 from these steps are accounted for in the computer program.) For V,, > 0, this metabolic scheme will produce a difference in label incorporation into CO, from [1-"Cjpyruvate as compared to that from [2-'4C]-and [3-'Qpyruvate.
Since label in carbon 1 of pyruvate is derived from carbons 3 and 4 of glucose, a significant contribution of V,. would serve to augment the incorporation of label from LU-'"Clglucose relative to that from [l-, 2-, and 6-"Clglucose as observed. The small contribution of fatty acid synthesis (cf. Fig. 4) is not sufficient to account for the discrepancy but conversion of acetyl-CoA to some other product (such as amino acid) at an appreciable rate might permit a closer fit.
The discrepancy between predicted and observed incorporation from [2J4Clglycerol and [2-'4C]glucose into CO, may also arise from the highly oversimplified representation of acetyl-CoA metabolism. By virtue of recycling via the glyoxylate cycle, label from [2-"Clpyruvate (and thus also from  is converted to CO, at a rate greater than that from [3-'Qpyruvate. The closer fit of predicted CO, formation from [2-'Qglucose in the 0 to 20-min interval rather than at later times (Table III) supports this possibility since recycling is more likely to contribute significantly at later times.

DISCUSSION
The present work quantitates the flux of carbon through the reactions of glycolysis and the pentose phosphate pathway in Tetrahymena, thus complementing earlier work analyzing the 2-and 3-carbon metabolism of this ciliate (1). In contrast to our earlier studies, however, the metabolism of Tetrahymena upon exposure to carbohydrates was time-dependent, i.e. the rates of incorporation of label from substrates into some of the products measured changed during the l-h incubation.
Although the model used to analyze our data was developed for steady state conditions, it was found to be applicable for several reasons. First, in each 20-min interval the incorporation data into all products from all labeled substrates was nearly linear, as expected for a system in the steady state. Second, measurements of the pool sizes of glucose-6-P and fructose-6-P (the two intermediates which might be expected to undergo the largest changes in amount) indicated that they change only slowly after the first 5 min of incubation. Therefore the Analysis of Pentose Phosphate and Glycolytic Pathways 1597 pools change size slowly relative to the flux through them, so that the conditions for isotopic and metabolic steady state are closely approximated. Third, that cycloheximide prevents the acceleration in rate of incorporation of label from glucose into CO, suggests that slow changes in enzyme levels are responsible for the observed nonlinearity.
Therefore, at least after the first few minutes, the system can be treated as a quasi-steady state system in which changes in enzyme levels and pool sizes are so slow that the steady state derivation is applicable. Although we may expect that the flux values computed for the first 20-min interval to be less accurate than for the two subsequent intervals, the general closeness of the computed values to the data even in the first IO-min period supports the validity of the analysis. The patterns shown in Fig. 1 thus constitute a realistic picture of carbon flow along the glycolytic and pentose phosphate pathways in Tetrahymena during the 1st h of adaptation to addition of a mixture of glucose, fructose, glycerol, and ribose to cells in the transition phase of growth.

Glucose
Utilization and Glycogenesis -It is well known that Tetrahymena has a high capacity for glyconeogenesis (21) and for glycogen synthesis from glucose (5,8). Glucose uptake appears to be mediated by a phlorizin-sensitive, sodium-dependent, stereospecific carrier-mediated process (26). Glucose uptake was very high even during the first 20 min after addition of the substrate mixture and rose significantly with time ( Fig. 1). Fructose, which is thought to be transported by the same carrier system (26), however, is used at a constant rate throughout the hour. The disparity between the constancy of fructose utilization and the small but important increase in glucose utilization is difficult to explain since it is thought that the two sugars are transported by the same carrier and phosphorylated by the same kinase. It is noteworthy that glycogen synthesis during the first 20-min interval proceeded at over 96% of the rate attained in the subsequent intervals. Thus, it appears that Tetrahymena, growing in the absence of carbohydrates, maintains a near maximal capacity for hexose transport, phosphorylation, and glycogen synthesis. If there are changes in the activities of the enzymes involved in glycogen synthesis from glucose-6-P in Tetrahymena they must occur very rapidly. It is highly unlikely, therefore, that the decrease in levels of adenyl cyclase and of cyclic AMP which occur in response to long term growth of Tetrahymena in proteose/peptone media supplemented with glucose (271, play any role in the regulation of glycogen synthesis from glucose in the present experiments. Glycolysis -During the hour of incubation an ever increasing amount of carbon enters the glycolytic pathway. The observations that the appearance of label from glycerol in CO* and of label from glucose and fructose in glycogen are linear with time (Table II, Appendix II) localize the controlled step(s) between the hexose phosphates and the triose phosphates. Flux through phosphofructokinase, which is smallest of all the reactions of the upper portion of the glycolytic pathway (Fig. 1) increases 7-fold over the course of the hour. In view of the known regulatory properties of this enzyme (281, it seems likely that the increase in flux at this step is of primary importance in producing the acceleration of glycolysis. This cannot be the only control point, however, since the increase in flux through phosphofructokinase is accomplished without a decrease in the pool size of fructose-6-P (Table I, Appendix II). This indicates that an increase in input of this pool must occur. Part of this must result from the increase in glucose phosphorylation (Vo). Although this increase appears small (going from 930 to 1045 nmol/lOS cells/h), it is not accompanied by an increase in glycogen synthesis and thus must result in an increase in catabolism. It should be noted, however, that the net flux through hexose phosphate isomerase is in the direction of glycogen synthesis. Thus the increase in rate of glucose-6-P formation is accompanied by a decreasing utilization of fructose-6-P for glycogen synthesis and the increasing catabolism of this intermediate.
It appears, therefore, that both hexokinase and phosphofructokinase mediate the augmentation of glycolysis, which is of interest since both enzymes have been reported to be rate-limiting in Tetrahymena (3, 10) and both enzymes are in large part localized on the mitochondria of this cell (11,12). Several roles for this sort of partitioning are possible: (a) bound enzyme may be closer to the site of ATP production and hence more effective in phosphorylation; (b) bound enzyme may have different kinetics from the free enzyme; (c) adsorption to particles may make the enzyme inaccessible to the cytosolic pool of substrate, possibly creating separate pools of substrates. Experiments on cells grown to the logarithmic and stationary phases of growth with or without glucose supplementation failed to reveal any changes in intracellular distribution of phosphofructokinase (12) or hexokinase (ll), but such experiments do not rule out the possibility of more rapid changes in localization or in kinetic properties of these enzymes. In view of these considerations and the finding that cycloheximide prevented the acceleration of glycolysis, further experiments on the intracellular distribution and properties of these enzymes are warranted. Gumaa and McLean (29), in an extensive study of the pentose phosphate pathway in ascites tumor cells, found that prior to the addition of glucose, the ratio fructose-6-P/glucose-6-P was about 0.86. Within 10 min after glucose addition, a steady state was achieved in which this ratio dropped to 0.36, a value close to the apparent equilibrium constant (0.32 to 0.47; see Table 5 of Ref. 29) of hexose phosphate isomerase. In Tetruhymenu the ratio in proteose/peptone was 0.14 ( Table I, Appendix II). Within 5 min this ratio rose to 0.54 and by 30 min after the addition of the substrate mixture dropped slightly to 0.41. Thus the mass action ratio for hexose phosphate isomerase changes in the opposite direction to that observed in ascites cells (possibly because of the addition of fructose as well as glucose), but is never very far from the ratio expected if the reaction were close to equilibrium.
The 3.5fold increase in bidirectional flux through this step is presumably a consequence of the increase in pool sizes of both fructose-6-P and glucose-6-P. Initially, the flux in each direction is only about 5 times the net flux, but this increases to 16 times and 35 times the net flux in the 20 to 40-and 40 to 60-min intervals, respectively, so that one would anticipate that fructose-6-P and glucose-6-P would be at isotopic equilibrium.
In fact, however, examination of the computed specific activities of each carbon of glucose-6-P and of fructose-6-P shows that even in the 40 to 60-min interval complete equilibration is not achieved. In the 40 to 66-min interval, with [1-'Qglucose as the labeled substrate, for example, the specific activities (relative to the [1-'YJglucose in the medium) in Carbon 1 of glucose-6-P and fructose-6-P are 0.78 and 0.71, respectively, and in Carbon 6,0.052 and 0.067, respectively. Thus even a bidirectional flux 35 fold higher than the net flux does not yield isotopic equilibration when, as in the present case, there is a large influx of labeled substrate into one of the two pools under consideration. The effect of the large flux values on pool equilibration is not limited to the case when the label is on an immediate precursor of one of the pools. If the labeled substrate is [U-'4Clribose, for example, the relative specific activi-

Analysis
of Pentose Phosphate and Glycolytic Pathways ties in Carbon 1 of glucose-6-P and fructose-6-P are 0.0024 and the relative specific activities of Carbon 3 of dihydroxyacetone-0.0031, respectively. P and glycerol-P are 0.0063 and 0.0054, respectively, and with there was also a 7-fold increase in flux the relative specific activity of Carbon 2 of dihydroxyacetone-P through fructose-1,6-diphosphatase (Fig. 1). These increases is 0.088 while that of glycerol-P is 0.22. were not only necessary to achieve a fit to the incorporation Pentose Phosphate Pathway -Previous work in our laboradata of Table III but also were verified by the independent tory had indicated that the nonoxidative portions of the pendetermination of the incorporation of label from [6-'"Clglucose tose phosphate pathway played a role in the metabolism of into the 1 position of the glucosyl moiety of glycogen (Table V).
carbohydrates (4, 5) even though the oxidative portion of this It must be emphasized that, contrary to the several uncertain-pathway appeared to be absent (2)(3)(4). In this work we have ties attending interpretation of tritium exchange measurebeen able to quantitate the fluxes through the pentose phosments, as discussed in detail by Katz et al. (25), the present phate pathway under a particular set of conditions. The remeasurement of the magnitude of this apparently futile cycle sults show that the in vivo flux through the oxidative portion depends only on the assumption that the reactions occur ac-(V,) is very small, amounting to less than 1% of glucose cording to the scheme shown in Fig. 1 in a single compart-utilization.
During the first 20 min of incubation, however, it ment, an assumption which in any case is necessary for esti-represents a significant fraction of the total glycolytic flux. mation of this futile cycle by tritium exchange methods. It can The observed flux is very close to the barely measurable in be seen from Fig. 1 that the amount of futile cycling between vitro activity of glucose-6-P dehydrogenase. The function of fructose-6-P and fructose 1,6-diphosphate (defined as 100. V',/ this very small flux is unknown. VJ is very large, ranging from 70 to 80% of the flux through The role of the nonoxidative reactions of the pentose phosthe forward reaction. This is considerably larger than the phate pathway in the synthesis of the pentose moieties of values (ranging up to 40%) estimated for other cells (30,31). nucleic acid has been in dispute. The pattern of label incorpo-The reason for such a large futile cycle is not known; it may be ration from [2J4C1glucose into pentose led earlier workers to related to the very high glyconeogenic capacity of this cell. In conclude that the nonoxidative steps were important (35, 361, cells grown identically but washed free of proteose/peptone but Katz and Rognstad (37) pointed out the necessity of distinand suspended in a mixture of acetate, pyruvate, glutamate, guishing between incorporation of radioactivity via the exhexanoate, and bicarbonate, the glyconeogenic flux from P-change reactions of transketolase and transaldolase and net enolpyruvate was 255 nmol/lO" cells/h (11, which is consider-synthesis of pentose from hexose. Studies with organisms ably larger than the net glycolytic flux (V:, -V',) at the lacking the oxidative enzymes (38)(39)(40)(41) show clearly, however, phosphofructokinase step measured here in the presence of that under some conditions the nonoxidative reactions are glucose and fructose. It should be noted that Sato et al. (32) capable of the net conversion of hexose to pentose. Our results have provided evidence that label exchange via reversal of with Tetrahymena demonstrate that although RNA is synthephosphofructokinase may occur in vitro. If such reversal oc-sized in significant quantities, and label from both ribose and curs in u&o, the magnitude of the futile cycle would be corre-glucose is incorporated into RNA, the net movement of carbon spondingly overestimated.
under these experimental conditions is from pentose to hexose.
Glycerol Metabolism and Fatty Acid Synthesis -Whereas Although the rate of nucleic acid synthesis is less than the in many species carbohydrate is an excellent precursor of fatty uptake of ribose, a close link between the two processes is acids we had earlier reported that practically no label from 1 l-indicated by the temporal correlation between the increase in 'JC]glucose appeared in the fatty acids of Tetrahymena (5). ribose uptake and the increase in RNA synthesis (Fig. 1). It The present results extend this observation; even in the pres-would be interesting to see if the pen&e moieties of RNA can ence of glucose, fructose, ribose, and glycerol, fatty acid synbe synthesized from glucose in the absence of added ribose. thesis became undetectable after the first few minutes of It is generally recognized that the nonoxidative reactions of incubation (Fig. 4). The reason for this cessation of fatty acid the pentose phosphate pathway can serve as a salvage pathsynthesis in the presence of carbohydrate is unknown, but it way for ribose, and the ability of Tetrahymena to synthesize should be noted that triglyceride does not appear to function as glycogen from added ribose (4, 42) clearly testifies to this role. a reserve fuel in Tetrahymena (33). Since earlier work has In nature, where bacteria are thought to be the main food, this shown that Tetrahymena converts exogenous pyruvate to acewould permit utilization of the pentose moieties of the ingested tyl-CoA in a compartment not associated with lipogenesis (341, nucleic acids. The nonoxidative portions of the pentose phosthe present work demonstrates that the metabolism of pyru-phate cycle may also play an important role during starvation, vate from 6-and 3-carbon precursors is similar to that of when large quantities of RNA are degraded (43,44). Although exogenous material. much of the phosphate and bases were released into the me-Although fatty acid synthesis stops soon after the substrate dium, Leboy et al. (43) found that very little ribose was remixture is added, a small amount of lipid glycerol continues to leased unless iodoacetate was added. These results suggest be formed (Fig. 1). Most of the glycerol utilized, however, that Tetrahymena can utilize the pentose moieties that are enters the glycolytic pathway at a rate (-40 nmol/lO" cells/h) made available from RNA degradation during starvation and which does not change appreciably during the incubation.
indicate another function for the nonoxidative portion of the Although it is frequently assumed that the reaction catalyzed pentose phosphate cycle. by glycerol-P dehydrogenase is near isotopic equilibrium, this The present work provides the first quantitative analysis of is clearly not so during the first 20 min after addition of the bidirectional flux through the nonoxidative reactions of the substrate mixture, when the unidirectional fluxes (VOX, V& pentose phosphate cycle for any organism. Although measureare less than 4 times the net flux (Vo, -V,,,). During the 40 to ments considerably in excess of the number of independent 60-min interval, equilibration is approached if the label is in parameters were made and the measurements were fairly well glucose, fructose, or ribose. magnitudes of all these fluxes with precision. Nevertheless, some conclusions are warranted. The fluxes through these steps were about an order of magnitude lower than the glycolytic flux, and the net flux was even smaller. Our finding that the reverse fluxes are of the same order as the forward fluxes is in keeping with the values for the equilibrium constants of these reactions (45,461, and serves as a warning against use of the assumption that fluxes through the transaldolase and transketolase reactions are unidirectional. Some conditions where use of this assumption may be justified are discussed in Appendix I. Our data also show a progressive increase in flux through transaldolase (V,,,, V',,, in Fig. 1) following addition of the substrate mixture. The data do not permit us to rule out a similar increase in transketolase, but if this occurred it would necessitate very large changes in flux through ribulose-5-P epimerase and ribose-5-P isomerase. This emphasizes the need for making an even larger number of well distributed measurements than were made in the present study if one is to obtain a precise analysis of the flux pattern through the nonoxidative portions of the pentose phosphate pathway.
Energetic Considerations -Because of the precision with which many of the flux values have been determined, it is possible to compute the expected rates of production and consumption of ATP for the pathways shown in Fig. 1 under the conditions of these experiments for each ZO-min interval during the l-h incubation. These computations are presented in Table VI. The steps that consume ATP are the phosphorylation of each of the substrates, the phosphofructokinase step, and the synthesis of glycogen from glucose-6-P. (We assume here that utilization of UTP for glycogenesis is energetically equivalent to utilization of ZATP.) Initially 3840 nmol of ATP are consumed/h/lOR cells, and this rate rises to 4078 by the end of the incubation. Line g of Table VI shows the reduction in ATP utilization that would have been realized if there had been no futile cycle (i.e. if the fructose-1,6-diphosphatase activity were zero but the same net flux had gone through the phosphofructokinase step). There would have been only a 1% reduction in ATP utilization in the first ZO-min interval, but during the last 20-min interval a 9% reduction in ATP consumption would be realized if there were no futile cycling. Thus as the cell adapts to the catabolism of carbohydrates, a considerable portion of its consumption of ATP is apparently "wasted." Obviously, we are here neglecting the energy cost of nucleic acid synthesis, ion pumping, swimming, etc. If one could account for these modes of ATP consumption, then even during the 40 to 60-min interval, the fraction of total ATP consumption due to fructose-1,6-diphosphatase activity would be very small. In terms of the consumption of ATP within the framework of the pathways of intermediary metabolism encompassed in Fig. 1, however, the futile cycle does account for an appreciable amount of the ATP consumed in the latter part of the incubation. Of considerable interest is the result that during the first 20 min after addition of the carbohydrate mixture, 583 nmol of ATP are used (per 10" cells) in excess of the amount produced. Since the content of ATP is about 17 nmol/lO" cells (471, this deficit obviously could not be made up by depleting the cell ATP. Thus in the early stages of adaptation to the carbohydrate mixture the cell must use other fuels, probably amino acids from the medium, in order to maintain a positive energy balance. The oxygen consumption results support this. The theoretical Q,. due to oxidation of the added substrates can be computed from the fluxes of Fig. 1 since 0.5 mol of 0, is required to reoxidize every mol of reduced pyridine nucleotide produced. The total production of NADH + NADPH (including NADH generated in the Krebs cycle) is given by the sum 2. V, + V, + VI6 + VOX -V,,, + 4. V,. The rate of 0, consumption due to oxidation of sugars and glycerol is therefore 270 nmol/lO" cells/ ' V,, includes the conversion of G6P to GlP, the formation of UDPG, and the transfer of the glycosyl group to glycogen. ' It is assumed that the PO ratio is 3 when NADH is oxidized in the mitochondria of Tetrahymena. h in the first 20-min interval and increases to 546 and 760 nmol/l(rj cells/h in the next two intervals. Since the measured Qo, is about 5000 nmol/106 cells/h (see Appendix II), the oxidation of material present in the medium is clearly providing most of the ATP for the energy needs of the organism. The small difference between the QoZ in the presence and absence of added substrates is consistent with a small contribution of carbohydrate to the total oxygen consumption. It should be noted that at later times (see Table VI), the glycolytic flux has increased sufficiently so that carbohydrate oxidation alone would be sufficient to meet the energy needs of the cell.

Adequacy of Metabolic
Scheme-Although the model employed gives a detailed description of Tetrahymenu metabolism whose accuracy is demonstrated by the close match of most of the computed incorporations to the experimental data, a few of the measurements were not fit by the model. While some of these failures to achieve excellent fit may represent technical errors, it is also possible that some assumption is not satisfied. Aside from the assumption of the steady state, the validity of which has been discussed in detail, the only other assumptions relate directly to the structure of the metabolic system as depicted in Fig. 1. These fall into two classesdeliberate oversimplifications and possible errors. Several oversimplifications are apparent in Fig. 1. Thus an input of P-enolpyruvate from reactions of the Krebs and glyoxylate cycles and associated pathways has been neglected, and the fate of acetyl-CoA has been reduced to a single reaction. Possible consequences of these simplifications have been discussed where relevant under "Results" and will not be repeated here. The only way to ascertain whether any of the data that are not well fit could be more closely matched would be to set up a complete model in which no simplifications are made, i.e. one which combines the elements of Fig. 1 of this paper with those of Fig. 1 of Raugi et al. (1). Such work is currently in progress.
Of more fundamental concern is whether the scheme shown in Fig. 1 is structurally correct. As noted above, 5 of the glycolytic enzymes in Tetrahymena are known to be particulate as well as cytosolic (3,(11)(12)(13)(14)(15) and it is possible that compartmentation of intermediates, which has been shown to be important in the case of acetyl-CoA (341, plays an important role in the glycolytic pathway. The measurements which necessitate an increasing rate of hexose phosphate isomerase are those of the relative incorporation of fructose and glucose into glycogen. These data could be fit, at least qualitatively, by a model in which there were two pools of glucose-6-P, one fed by glucose and the other by fructose-6-P. If this were the case, the flux through hexose phosphate isomerase could be large and constant, and the observed data reproduced by a progressively greater mixing of the glucose-6-P pools. Although several authors have presented data indicating the presence of two pools of glucose-6-P (and, indeed, of several other glycolytic intermediates) in other tissues (16)(17)(18)(19)48) we believe that it would be premature to invoke the presence of multiple pools of any glycolytic intermediates in Tetruhymena until experiments using a full model with no simplifications have been performed and analyzed.

Kinetics
of Adaptation to Presence of Carbohydrates -Since low concentrations of cycloheximide prevent the increase in rate of "'CO, formation from labeled glucose whether the cycloheximide is added together with the substrate mixture or half way into the hour of incubation, it is reasonable to suppose that protein synthesis or protein modification is responsible in part for the adaptation process. One may therefore ask whether any simple model for the adaptation process would be consistent with the observed shapes of the curves of label incorporation into products with time (see Fig. 2). Suppose that the activity of a rate-limiting enzyme is A, + A, t, where A, is the activity at the start of the incubation and A, is a measure of the rate of increase of activity of this enzyme with time. The amount of product, P, formed by this enzyme would then be given by P = I 0 '(A,, + A,t')dt' = A t + A+ 0 If one assumes that the rate-limiting enzyme of glycolysis is phosphofructokinase, then one would expect a parabolic increase in the amount of label appearing in CO, after the addition of the carbohydrate mixture. We chose to fit the data to a power function of the form I = uP. It can be shown that a parabola of the form P = A,,t + A, F/2 when tit to a power function of the form chosen results in a value of b between 1 and 2, depending on the relative magnitudes of the linear and quadratic terms of P. Since the average value for the exponent b in the equations for '%O, accumulation from [l-'%]glucose and fructose is 1.86, it may be considered that the activity of phosphofructokinase increases linearly with time after addition of the carbohydrate mixture. This does not necessarily imply that the amount of this enzyme is increasing with time, since the rise in activity might be achieved by modification of the enzyme, synthesis of an activator, etc. Further experiments are obviously required to ascertain the factors controlling the increase in flux through phosphofructokinase.
The formalism of Equation 4 can also characterize the shapes of most of the incorporation of label versus time curves for the other products measured. Thus for the ratelimiting step in glycogen synthesis, the choice A, -0, would predict a linear incorporation of label from all substrates into glycogen, as observed (Table II, Appendix II).