Dynamic regulation of yeast glycolytic oscillations by mitochondrial

functions

M. A. AON1'*, S. CORTASSA1, H. V. WESTERHOFF1, J. A. BERDEN1, E. VAN SPRONSEN2

and K. VAN DAM1

1E. C. Slater Institute for Biochemical Research and Biotechnological Center, University of Amsterdam, Plantage Muidergracht 12,NL-1018 TV Amsterdam, The Netherlands^Department of Molecular Cell Biology, Section of Molecular Cytology, University of Amsterdam, Plantage Muidergracht 14, NL-1018TV Amsterdam, The Netherlands

* Author for correspondence at present address: Centro de Investigaciones en Quimica Biologica de Cordoba (CIQUTBIC), Facultadde Ciencias Quimicas, Universidad Nacional de Cordoba, C.C. 61, 5016 - Cordoba, Argentina

Summary

The control exerted in vivo by mitochondrial func-tions on the dynamics of glycolysis was investigatedin starved yeast cells that were metabolizing glucosesemianaerobically. Glycolytic oscillations were trig-gered after a pulse of glucose by inhibition ofmitochondrial respiration with KCN, myxothiazoland antimycin A or in mutants in the bcl complex(ubiquinol:cytochrome c reductase) that were largelydeficient in respiratory capacity. Inhibition of theadenine nucleotide translocator by preincubationwith bongkrekic acid also triggered a train ofdamped sinusoidal oscillations after glucose ad-dition. The oscillations consisted of cycles of re-duction and oxidation of the intracellular pool ofnicotinamide nucleotides with periods of 45 s to 1 minand amplitudes of 0.8 mH or lower.

Preincubation with the uncoupler carbonyl cya-mide p-(trifluoromethoxy)phenylhydrazone (FCCP)annihilated cyanide-induced oscillations ofNAD(P)H. Evidence for de-energization of mitochon-drial membranes in vivo was obtained by mitochon-drial staining with dimethylaminostyryl-methyl-

pyridiniumiodine (DASPMI) of starved cells. The lowrates of NADH reoxidation shown by respiratorymutants and the FCCP-treated X2180 strain open upthe possibility that mitochondrial dehydrogenasesalso control glycolytic oscillations. Low rates ofcytosolic NADH reoxidation induced by pyrazole, aninhibitor of alcohol dehydrogenase, were also associ-ated with the disappearance of glycolytic oscil-lations.

From experimental evidence and model calcu-lations we conclude that the modulation of the levelsof cytosolic ATP by mitochondrial functions in turnmodulates the approach of the dynamic behavior ofglycolysis to an oscillatory domain. The mitochon-drial NADH dehydrogenase and the glycolytic stepsassociated with NADH reoxidation downstreamfrom pyruvate appear to provide another controllevel of glycolysis dynamics in vivo.

Key words: oscillations, glycolysis, mitochondrial function,bifurcations.

Introduction

The glycolytic flux and the concentration of glycolyticintermediates in intact cells oscillate under some con-ditions (Chance et al. 1964; Hess and Boiteux, 1973;Shulmann, 1988). Possible mechanisms for the glycolyticoscillations have been elucidated. In cell-free extracts ofyeast it was demonstrated that phosphofructokinase(PFK) is involved (Hess and Boiteux, 1971, 1973; Pye,1973; Boiteux et al 1975; Higgins et al. 1973; see Winfree,1980, for a review). Modelling revealed that this involve-ment could result from allosteric effects at the PFK itself(Boiteux et al. 1975) or from the stoichiometric nature ofglycolysis when one of the pathway products is used toprime the first reactions (Sel'kov, 1975; Cortassa et al.1990). In most of the proposed mechanisms the adeninenucleotides play an important role (Hess and Boiteux,1971; Sel'kov, 1975; Cortassa et al. 1990)..

Although the previous models explain many of the

Journal of Cell Science 99, 326-334 (1991)Printed in Great Britain © The Company of Biologists Limited 1991

observations made on the glycolytic oscillations in yeast,others remain unexplained as already pointed out (Pye,1973). An unclear point was the possible effect onoscillations by the NAD+/NADH system (Pye, 1973). Theredox couples NAD+/NADH and NADP+/NADPH play acentral role in the metabolism of sugars by yeast (vanDijken and Scheffers, 1986). Therefore, important ques-tions for physiology remain as to which factors controlglycolytic oscillations in vivo. Such questions cannot beaddressed in cell-free systems in the absence of importantprocesses, e.g. such as those catalysed by the mitochon-dria.

Because of the important role of adenine and nicotina-mide nucleotides in the dynamic behavior of glycolysis, weasked to what extent mitochondrial functions, such asthose related to the regulation of the cytosolic ATP andNADH levels, control glycolysis dynamics in vivo. Themain results obtained suggest that mitochondrial func-tions through the regulation of cytosolic ATP and NADH

325

levels in turn regulate the dynamic behavior of glycolysis.In starved yeast cells, glycolysis probably operates near aHopf bifurcation point, i.e. around which damped orsustained oscillations appear.

Materials and methods

Microorganism and growth conditionsSaccharomyces cereviseae, strain X2180 (a/a, SUC2, mal melgal2CUPI, diploid strain; Yeast Genetic Stock Center, Berkeley,California) was maintained on malt agar slopes. Cells were grownaerobically in batches at 30°C, pH5, in defined medium (YNB).Glucose (1 %) served as a carbon source. Cells were harvested atmid-exponential growth, unless otherwise specified, washed twicewith 0 . 1 M phosphate buffer, pH 6.8, and resuspended in the samebuffer at a concentration of 2xlO6 to 4x10* cells per ml andstarved for 3 h in a rotary shaker (120 revsmin" ) at 30°C.Preliminary studies showed that 3 h of starvation were optimal asjudged from the amplitude of NAD(P)H oscillations. Therespiratory-deficient mutants HR2 14", HR2 40" and HR2 17"obtained from Saccharomyces cerevisiae wild-type strain HR2(Berden et al. 1988) were cultured under similar conditions tostrain X2180 supplemented with 50 jigml"1 histidine, leucine anduracil and 20/igml"1 tryptophan.

Measurement of NAD(P)H kineticsIntracellular pyridine nucleotide reduction was monitored withan Eppendorf fluorimeter at excitation wavelengths of316-366 ran, emission being measured from 400 to 450 ran.Unless otherwise specified, all the experiments were performed ata cell concentration of 107 cells per ml in a thermostated cuvetteat 25 °C with stirring. Cells were kept on ice until assayed. Sinceexperiments lasted from 2 to 4h, controls were performed bystudying the oscillatory behavior as a function of time and nodifference in the ability of cells to oscillate (amplitude andfrequency) could be detected for up to 7 h while keeping the cellson ice.

All the fluorescence traces shown represent a typical resultcorresponding to duplicates or triplicates for each cell batch andfor three independent experiments. Controls with2-deoxy-o-glucose (Sigma, Grade II), a non-metabolized sugar,showed that the observed oscillations originated from glucosemetabolism.

Respiration measurementsYeast cell suspensions under the same conditions as in thefluorescence measurements were assayed for oxygen uptake witha Clark oxygen electrode (Yellow Springs Instruments, YellowSprings OH, USA) in a magnetically stirred oxygraph vessel. At25 °C, 495 IOA of atomic oxygen is dissolved in air-saturated 0.1 Mphosphate buffer, pH6.8. This value was used for the calculationsof oxygen consumption by yeast cells.

Inhibitor and uncoupler treatmentAntimycin A (Sigma Chem. Co, St Louis, USA) from Streptomyceskitazawaensis; myxothiazol (Fluka Chemie AG, Buchs, Switzer-land) from Myxobacterium myxococcus fulvus and carbonylcyanide p-(trifluoromethyoxy)phenylhydrazone (FCCP; AldrichChemie N.V./S-A., Brussels) were dissolved in ethanol. For allthe inhibitors, controls were run by adding the same amount ofethanol alone. The calculated percentages of respiratory inhi-bition were referred to the controls. Bongkrekic acid was used asan aqueous solution in 2 M NH4OH and its addition to the cellsuspension did not provoke measurable pH changes.

Fluorescent staining of mitochondriaMitochondria of yeast cells (107 cells ml"1) were stained byincubation in 0 . 1 M Tris-HCl buffer, pH8, with 5//M DASPMI(Bereiter-Hahn, 1976; Bereiter-Hahn et al. 1983) for 30min atroom temperature. Fluorescence-labelled cells were incubated in

the presence of glucose and inhibitors as described in each caseand a sample of 6 /J was placed between a slide and coverslip andthen sealed. Video films of the fluorescence-labelled cells weremade with a Zeiss Universal photomicroscope equipped with animage intensifier (Videoscope, International Ltd, WashingtonDC) with a CCD camera (Grundig, Germany). Pictures of the cellssubjected to different treatments were taken directly from thevideo films.

Modelling and computationsGlycolysis and the interactions with mitochondria (Scheme I)were modelled as described in Appendix A. The ordinarydifferential equations (ODEs) system (eqns (1) to (4)) wasnumerically integrated on an IBM PS2/80 using the programSCoP with an Adams method (Duke University, 1987). Theanalysis of the stability and bifurcation properties of the ODEssystem (eqns (1) to (4)) were performed with AUTO (E- Doedle,1986; Concordia University, Canada).

Results

Regulatory effects of mitochondrial function on glycolysissuggested by a simulation studyA quantitative model of glycolysis and its interactionswith mitochondrial function was allied to the experimen-tal work (Scheme I). This model is an elaboration of theone we developed previously (Cortassa et al. 1990; Aon andCortassa, 1991) and describes realistic glycolytic oscil-lations. Oscillations reported in the literature for exper-iments with intact yeast cells and with yeast extractscould be simulated (Cortassa et al. 1990, and results notshown). The dynamic behavior of a metabolic pathwaydepends on the values of its kinetic and stoichiometricparameters. For the glycolytic model (ODEs, eqns (1) to(4)) a systematic analysis of this dependence was per-formed by the use of the program AUTO (see Appendix).Fig. 1A,B shows the results for a variation of the loadrepresented by mitochondria (by varying the parameterKp) and variation of the rate at which glucose entered thesystem (Vjn) (Fig. IB). The continuous line refers toparameter values where the ensuing steady state is stable.In Fig. 1A the steady state concentration of ATP droppedas the work load increased, up to a work load of 1.1 mMs"1.As the load was increased further, the ensuing steadystate became unstable, which is indicated by the brokenline in Fig. 1A. Such a transition from stable to unstablesteady state is called a bifurcation. When KP was takenslightly above its bifurcation value, the system did notrelax to a single state but to a sustained oscillation (limitcycle). The point where that transition occurs is a Hopfbifurcation (HB). Variation of the rate at which glucoseentered the system revealed two HB points (Fig. IB).Another change in dynamic behavior is given by therelaxation behavior around a steady state throughdamped oscillations (such transition is delimited by asmall arrow and the HB on the continuous line inFig. 1A,B).

Taken together, the results of Fig. 1 predict that (1)increasing the work load towards the glycolytic ATP-synthesizing machinery, or (2) decreasing or increasingthe influx of glucose into the system, enhance the tendencyof the system to exhibit oscillations. The former predictionsuggests that elimination of mitochondrial oxidativephosphorylation so that the entire work load of producingthe ATP needed for intracellular free-energy transductionbefalls glycolysis, will cause oscillatory behavior. Atmoderate work loads, this should be noticeable asrelaxation towards a steady state through damped

326 M. A. Aon et al.

Vin

Scheme 1

oscillations. At extreme work loads, this might lead tosustained oscillations.

The activity of NADH reoxidizing processes would alsoaffect the dynamics of glycolysis. According to modelcalculations, under conditions of high ATP load thefollowing may be predicted: (1) high rates of NADHreoxidation provoke the appearance of sinusoidal damped

S 2 •

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A1-A \

A

NADH

ATP

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6

5

4 •

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/

/A.

/

y—-\/ ATP \

^ - — "NADH

B

\ HB

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0.2 0.4 0.6

K,n(mMS-')

0.8

oscillations; (2) a decrease in the rate of NADH reoxi-dation would tend to abolish oscillations; (3) at low rates ofNADH reoxidation, if the ATP load is even increased theappearance of square type oscillations is possible.

The plausibility of model predictions was investigatedby changing in different ways the cytosolic levels of ATPand NADH and looking for the appearance (approximat-ing a Hopf bifurcation) or disappearance (further awayfrom a Hopf bifurcation) of glycolytic oscillations (Fig. 1).

Mitochondria! processes involved in the decrease in thelevels of cytosolic ATP that affect the dynamics ofglycolysisThe hypothesis proposing that a drain of cytosolic ATPmediated by mitochondrial function would trigger glyco-lytic oscillations was experimentally tested by the use ofrespiratory inhibitors (Thierbach et al. 1981; von Jagowand Engel, 1981). Fig. 2A-C shows that the addition ofmyxothiazol or KCN after a pulse of glucose did give rise

Fig. 1. Stability analysis of the glycolytic model. The stabilityanalysis of the ODEs system ((l)-(4); see Appendix) wasperformed numerically with AUTO (see Materials andmethods). The stable ( ) and unstable ( ) branches of thesteady-state solutions and the Hopf bifurcations were computedautomatically. The bifurcation diagram was obtained with thefollowing parameter values: (A) Vin (mMS~1)=0.26; £i(mM-1s-1)=0.0949; k3 ( m M - ' f 1 ) ^ , (s'^kj ( m M - W o . l ;*9=0.05 (s"1); T=0.83; Ap°(V)=-0.3. The kinetic parameters ofthe proton pump were: ifM=^M=2mM; VM = VM=0.5mMS~1.The total nucleotides (CA) and phosphate pool (Pt) were both10 mM while the nicotinamide nucleotide pool (CN) was 5 mM.The steady state (ss) ATP and NADH values represented onthe y-axis were obtained as a function of the bifurcationparameter Kv, i.e. the ATP load introduced in the system bythe mitochondrial ATPase. (B) The rate constants, kineticparameters of the proton pump, the total nucleotide (CA) andphosphate pool (Pt) were as in (A) except for Kp(mMS"1)=0.751. The steady state (ss) ATP and NADH valuesrepresented on the y-axis were obtained as a function of thebifurcation parameter Vin (mMs"1), i.e. the substrate inputrate. Large arrows point to the values of the bifurcationparameters for which a Hopf bifurcation (HB) appears.Arrowheads delimit parametric regions, starting at HB, wherethe relaxation of the system to a new steady state is viadamped oscillations.

Mitochondrial regulation of glycolysis 327

GI

1 min

NAD(P)H

Fig. 2. Effect of respiratory inhibitors on the appearance ofglycolytic NAD(P)H oscillations. A suspension of yeast cells(107 cells per ml) grown, harvested and starved as described inMaterials and methods, were pulsed with 20 mM glucose in thecuvette of the fluorimeter at 25 °C with stirring, followed by10 mM KCN (A) or preincubated with 4 /£M myxothiazol (1 min)and followed by successive glucose additions (arrows) of 2 mMeach one (B) or antimycin A addition (1 or 3 ^M) after theglucose pulse (C). G, glucose; c, KCN; a, antimycin A. Theremaining extracellular glucose after the 20 mM pulse was of80 % (first 3 min) and an additional 10 % was consumed 15 minafter KCN addition. The scale of fluorescence corresponds to1.5/*MNAD(P)H.

to glycolytic oscillations, in both the wild-type HR2 (notshown) and the X2180 strain, after a pulse of 20 mMglucose and KCN addition (10 mM) (Fig. 2). Oscillationswere also triggered by a pulse of 20 mM glucose in the

presence of myxothiazol, by increasing concentrations ofKCN (from 5 to 15 mM) after a pulse of 20 mM glucose or by1 min preincubation with KCN (or myxothiazol: Fig. 2B)and subsequent glucose addition. The oscillations con-sisted of cycles of reduction and oxidation of the intracellu-lar pool of pyridine nucleotides with periods of 46 s to 1 minand amplitudes of 0.8 mM or lower. Antimycin A only gaverise to quickly damped oscillations (Fig. 2C). KCN(10 HIM), myxothiazol (4/iM) and antimycin (2/.IM) in-hibited >95%, 72% and 75% O2 consumption in yeastcells, respectively. Also, mutants in the bcl complex(ubiquinolxytochrome c reductase) that were largelydeficient in respiratory capacity exhibited oscillatorytransients following pulses of glucose (Fig. 3 traces B andC). In a similar experiment, the wild-type HE2 did notshow oscillations following pulses of glucose and reached asteady state value in NAD(P)H fluorescence after the thirdglucose pulse (Fig. 3, trace A). The S. cereviseae HR2 40"and HR2 14" mutants showed only 28% and 5%,respectively, of the wild-type strain's respiratory capacity.The HR2 40" mutant respiratory capacity (28%) wassimilar to the residual respiration of the wild-type HR2and X2180 strains after treatment with 4 ,UM myxothiazol.

Further insight into the regulatory mechanisms ofglycolytic oscillations by mitochondrial activity wasprovided by experiments performed in the presence ofbongkrekic acid (BKA), an inhibitor of the adeninenucleotide translocator in living cells (Gbelska et al. 1983;Lumbach et al. 1970). Starved yeast cells preincubatedwith BKA showed oscillatory transients after glucoseaddition (Fig. 4C). The same cells preincubated with BKAwere still able to show damped oscillations after KCN andglucose additions (not shown). Yeast cells respiration wasnot affected by preincubation with BKA. The effect of BKAwas concentration dependent; inhibitor concentrations inthe range of 10-30 /igml"1 gave rise to oscillations. Theseresults suggested that the adenine nucleotide translocatoraffects the oscillatory mechanism, probably through thecontrol of the cytoplasmic-mitochondrial ATP/ADPexchange.

The disappearance of oscillatory behavior in the pres-ence of FCCP (Fig. 4B) or FCCP plus BKA (Fig. 4D)indicated that the inner mitochondrial membrane AjtHplays a role in the triggering of glycolytic oscillations.Evidence for the uncoupling of mitochondrial membranesin vivo in one of the mutants (HR2 40~) (Fig. 3) and in thestrain X2180 was obtained by fluorescent staining ofmitochondria with dimethylaminostyryl-methylpyridin-iumiodine (DASPMI; Bereiter-Hahn, 1976) (Fig. 5). Mito-chondria of strain X2180 stained with DASPMI(Fig. 5A,B) revealed the presence of an apparentlycontinuous mitochondrial network or 'mitochondrion'(Davison and Garland, 1977; Skulachev, 1990). The wild-type strain and the 17" HR2 mutant exhibited similarDASPMI distribution to that shown by the X2180 strain(Fig. 5A,B) in the presence of glucose (results not shown).In the presence of FCCP, DASPMI was uniformlydistributed in the cytoplasm of strain X2180 (Fig. 5D). Asimilar effect of the uncoupler on DASPMI distribution inthe wild-type HR2 strain and 17~ HR2 mutant wasobserved (results not shown). Judging from the distri-bution of the dye, the mitochondria of the mutant HR40"(without FCCP) appear not to have much A^H (Fig. 5C). Itmust be pointed out that the respiratory-deficient mutantHR2 40" only showed 28% of the respiratory capacitywhen compared with the wild-type strain. The uncouplingeffect provokes a release of the dye by annihilation of the

328 M. A. Aon et al.

NAD(P)H

Time1 min

Fig. 3. Respiratory mutants of S. cerevisiae in the bclcomplex. Respiratory mutants from S. cerevisiae strain HR2were grown under batch conditions, harvested, starved and thetemporal evolution of NAD(P)H was monitored as described inMaterials and methods. (A) Wild-type HR2; and (B) and (C) theHR^ 14" and HR2 40" mutants. Arrows point to glucoseadditions (2 HIM). The remaining extracellular glucose was 90 %after the first pulse. The fluorescence scale is 1.5 /IM NAD(P)H.

transmembrane electric potential, since it is known thatDASPMI is distributed in mitochondria according to themembrane potential (Bereiter-Hahn etal. 1983). Althougha decrease in fluorescence was noticed, the distribution ofDASPMI was not affected in strain X2180 metabolizingglucose after preincubation with BKA or additions of KCN

or myxothiazol (results not shown) under the sameconditions as described for Figs 2—4.

Cytosolic NADH reoxidation also affects glycolyticdynamicsThe model suggested that at low rates of NADHreoxidation and high ATP load, square-type oscillationscould appear (see point (3) in Regulatory effects ofmitochondrial function). This specific prediction wastested by inhibiting the alcohol dehydrogenase withpyrazole (Lieber et al. 1978) and the results are presentedin Fig. 6. Square-like oscillations in NAD(P)H wereobtained at 0.1 mM pyrazole (Fig. 6, trace B) while atendency for the oscillations to become square-likeappears already at 0.01 mM of the inhibitor (Fig. 6, traceC). Preincubation of starved yeast cells with pyrazole (0.01to 0.1 mM) did not affect the rate of O2 consumption.

A correlation between a continuous reduction of theNADH pool and de-energization of mitochondrial mem-branes was provided by the use of mutants in the bclcomplex and FCCP. By carefully inspecting the kinetics ofNAD(P)H in the respiratory mutants (Fig. 3, traces B,C)one may confirm that a continuous reduction in the pool ofnicotinamide nucleotides occurs (at least in the interval ofobservation) while in the wild type a steady level of redoxpotential is attained (Fig. 3, trace A). The latter tendencyof the intracellular NAD(P)H pool is taken as anindication of lower rates of NADH reoxidation. Themitochondria of the mutant HR2 40" (without FCCP)appear to be de-energized as judged from the uniformdistribution of DASPMI (Fig. 5C). When cells of strainX2180 were treated with FCCP (10 nM: 40% increase inthe rate of O2 consumption with respect to the control), atendency of the intracellular pool of NAD(P)H to becomemore reduced after a glucose pulse, could be verified(Fig. 4B). Under the same conditions, the uncouplerabolished the KCN-induced oscillations and uncoupledmitochondrial membranes as could be shown by fluor-escence microscopy of DASPMI (Fig. 5D). Taken together,these results suggest that low rates of NADH reoxidationin the FCCP-treated X2180 strain or the HE2 40~ mutantare associated to de-energized mitochondrial membranes.

Discussion

In the present work the regulation in vivo of the dynamicsof glycolysis by mitochondrial activity in starved yeast cellsuspensions was investigated. The main results obtainedpoint to the existence of control exerted by mitochondrialfunctions through the cytosolic ATP and NADH levels onthe appearance of glycolytic oscillations. Model calcu-lations predict (Fig. 1) and experiments suggest (Figs 2-4,6) that glycolysis in starved yeast cells may operate closeto a Hopf bifurcation.

The model simulations describe qualitatively andquantitatively well the experimental results in thefollowing aspects: (1) the amplitude, frequency and shapeof the oscillations. By shape of the oscillations we meantheir sinusoidal-, square-type or the damping of successiveoscillatory cycles. Previous results obtained with a similarmodel of glycolysis gave good quantitative agreement withreported data in period, amplitude, substrate input rateand decrease in oscillatory frequency with substrate input(Cortassa et al. 1990). (2) The phase relationship betweenNADH and ATP was investigated by phase plane analysis(not shown) giving values that were close to reported

Mitochondrial regulation of glycolysis 329

NAD(P)H

D

1 min

Time

Fig. 4. Effect of preincubating withbongkrekic acid and FCCP on NAD(P)Hoscillations in starved yeast cells. Asuspension of starved yeaat cells (107 cells perml) was preincubated for 10 min at 26 °C withstirring and in the absence (A) or in thepresence of FCCP 10 HM (B), BKA OO^gmT1

(O) or a mixture of BKA and FCCPOO/igml"1 and 0.1 mM, respectively (D)).After preincubation, 20 mM glucose (G) and10 mM KCN (c) were added as indicated bythe arrows in the upper and lower tracesexcept for the BKA treatment (C) where onlyglucose (G) was added. The fluorescence scaleis 1.5 /an NAD(P)H.

experimental data (Hess and Boiteux, 1971). (3) Thecatabolic flux sustained by starved yeast cells (107 cellsml"1 harvested in the exponential phase of growth:A640=2.2) was calculated to be 33 / M S " 1 . From modelsimulations, values of glycolytic fluxes that oscillatedaround 210 and 240 jais"1 were obtained at high and lowenergy loads, respectively, that are of the same order ofmagnitude of those experimentally determined. In starvedyeast cells the drain of cytosolic ATP under the experimen-tal, semianaerobic conditions reported here appears to be akey event triggering glycolytic oscillations (Figs 2-4).Essentially, mitochondria by modulating the level ofcytosolic ATP, in turn modulate the approach of thedynamic behavior of glycolysis to an oscillatory region(Fig. 1). The experimental situation described in Fig. 2(i.e. inhibition of mitochondrial oxidative phosphoryl-

ation) is reflected in Fig. 1A as an increase in the ATPload, namely a decrease in the steady state levels ofcytosolic ATP.

Two regulatory levels appear to be implicated in theregulation of the cytoplasmic ATP pool by mitochondria:(1) the A^H and (2) the adenine nucleotide translocator.Regulation of the ATP export to the cytosol by the adeninenucleotide translocator appears to be involved in thetriggering of glycolytic oscillations (Fig. 4). Interestingly,the BKA effect appears to be rather specific, since 62consumption of starved yeast cells was not altered in thepresence of the inhibitor. The results presented (Figs 1,2-4) strongly suggest that glycolysis dynamics in starvedyeast cells operates very clpse to a Hopf bifurcation that isapproached when the cytosolic ATP decreases.

When glycolysis approaches the oscillatory region at

330 M. A. Aon et al.

5A

B

D

Fig. 5. Vital mitochondrial staining with DASPMI of starved yeast cells metabolizing glucose. Yeast cells were grown, harvested,starved and stained as described in Materials and methods. The strains X2180 (A, B, D) and HR2 40~ (C) were stained withDASPMI and monitored by video techniques under the following conditions: (A-C) 20 mM glucose; (D) preincubated with 10 nMFCCP for 5 min and then plus 20 mM glucose. The pictures are representative fields, i.e. >95 % of the cells exhibited the pattern ofstaining shown. Bar, 5/an.

high ATP load, the rate of NADH reoxidation may triggeroscillations. Transient changes in the rate of NADHreoxidation by mitochondria triggered oscillations inmodel simulations (results not shown). Experimentalevidence supporting predictions I and II (see section above:Regulatory effects of mitochondrial function) is presentedin Fig. 2 (trace A), Fig. 3 (traces B,C) and Fig. 4B. Asimilar result to that obtained with the mutants (Fig. 3,traces B,C), i.e. a continuous reduction of the nicotinamidenucleotide pool and quickly damped oscillations after athird pulse of 2mM glucose, was observed with cells ofstrain X2180 preincubated with 10 nM FCCP (Fig. 3 andresults not shown). Two experimental observationssuggest that de-energization of the mitochondria corre-lates with low rates of NADH reoxidation: (1) the HR2 40"mutant showed a low glycolytic flux (given by thesteepness of the temporal change in NAD(P)H; Fig. 3) anda tendency to increase the intracellular pool of NAD(P)Hafter successive pulses of glucose (Fig. 3); (2) a similarpattern of behavior was shown by the X2180 strain whensubjected to a pulse of glucose after preincubation with

FCCP (compare the control (A) with the FCCP-treatedcells (B) in Fig. 4). At high ATP drains, the rate ofcytoplasmic NADH reoxidation by mitochondrial dehydro-genase (Alexander and Jeffries, 1990; Bruinenberg et al.1985) and alcohol dehydrogenases provide another regu-latory level of the dynamics of glycolysis. This additionalregulatory level influences not only the approach ofglycolysis to the oscillatory region (Fig. 1) but, once inside,it further regulates the shape of the oscillations (sinus-oidal-, square-type: Fig. 6 and results not shown).

The metabolic features shown in Figs 3 and 4 (points (1),(2): see previous paragraph) correlated with unenergizedmitochondrial membranes in starved yeast cells stainedwith DASPMI and metabolizing glucose (Fig. 5C,D).When mitochondrial membranes are unenergized, KCN-induced oscillations are quickly damped or tend todisappear as shown by the respiratory mutants (Fig. 3)and FCCP treatment (Fig. 4B), respectively. Takentogether, these results suggest that low rates of NADHreoxidation in the FCCP-treated X2180 strain or the HR240~ mutant are associated with de-energized mitochon-

Mitochondrial regulation of glycolysis 331

NAD(P)H

1 min

Time

Fig. 6. The effect of the rate of cytosolicNADH reoxidation on glycolyticoscillations. A suspension of yeast cells(107 cells per ml) grown, harvested andstarved as described in Materials andmethods were pulsed with 20 mil glucosein the cuvette of the fluorimeter at 25 °Cwith stirring followed by 10 rain KCNafter 3-5 min, without (A) or withpreincubation for 5 min with 0.1 mM (B) or0.01 mM (C) pyrazole. The fluorescencescale is 1.5/IM NAD(P)H. G, glucose; c,KCN.

drial membranes (Figs 4, 5). If the transmembrane electricpotential controls the rate of NADH reoxidation throughthe outer mitochondrial membrane dehydrogenase de-serves further investigation.

The glycolytic model and the interactions with mito-chondrial activity (Scheme I) used in the present work todescribe the experimental data are stoichiometric (Sel'-kov, 1975) with the non-linear kinetic mechanism given bythe stoichiometries of ATP production in anaerobicglycolysis (Cortassa et al. 1990; Aon and Cortassa, 1991).In yeast extracts, the allosteric properties of phosphofruc-tokinase were shown to be the source of oscillations (Hessand Boiteux, 1968; Higgins et al. 1973; Boiteux et al. 1975).The question arises as to whether in vivo the triggering ofglycolytic oscillations can be also explained by allostericeffects on PFK. Experimental evidence now sheds doubton the latter possibility: (1) the control of PFK underPasteur effect conditions could not be ascribed to changesin any one particular effector but rather to contributionsfrom a variety of effectors (Reibstein et al. 1986).Furthermore, Fru-2, §-P2 was the only effector thatappreciably changed between the anaerobic and aerobic

condition. These observations suggest that, in vivo, theallosteric properties of the PFK could hardly be mani-fested at least in aerobic-anaerobic transitions; (2) thepresent work shows that the autocatalytic mechanismgiven by the stoichiometry of glycolysis coupled tomitochondrial activity through the ATP and NADHcytoplasmic pools may constitute another regulatory levelof glycolysis in vivo; (3) in yeast extracts the presence of acomplex type of oscillations apart from sinusoidal, i.e.spike-like or square-type, was experimentally demon-strated (Hess and Boiteux, 1968; Hess and Boiteux, 1973).The stoichiometric model without taking into accountallosteric effects was able to exhibit sinusoidal-, square-and spike-like oscillations (not shown); (4) great deal ofexperimental evidence supports the notion of severalcontrol steps in glycolysis apart from PFK (den Hollanderet al. 1986; Reibstein et al. 1986). According to our results,the dynamics of glycolysis in starved yeast cells undersemianaerobic conditions may attain oscillatory regionsaccording to the following relevant physiological para-meters: the rates of substrate input and substratephosphorylation, the load induced by the non-glycolytic

332 M. A. Aon et al.

ATP-consuming processes and the rate of cytoplasmicNADH reoxidation. At present the possibility cannot beexcluded that the effects of ATP/ADP and cellular redoxstates may run in part through allostericity of PFK and inpart through the autocatalytic nature of the pathway.

Under growing conditions a main contribution to theNADPH balance in yeast cells is expected to occur throughthe functioning of the hexose monophosphate pathway(HMP) (Bruinenberg et al. 1985; van Dijken and Scheffers,1986). Under those conditions a leak in hexose phosphatefrom glycolysis should be expected. The extent of the leakof phosphorylated intermediates may drive glycolysis intosustained oscillations at low substrate influx (Cortassaand Aon, 1991, unpublished data). However, since cellgrowth does not occur under the experimental conditionsdescribed in this work (Galazzo and Bailey, 1989), theNADPH turnover is expected to be very low or non-existent.

Summarising, the results presented strongly suggestthat mitochondrial functions are able to regulate in vivothe dynamics of glycolysis in starved yeast cells throughcytoplasmic ATP and NADH levels. The regulation of theATP and NADH pools in vivo by mitochondria may beachieved at various levels: the mitochondrial protonmotive force through the regulation of the ATP syntheticor hydrolytic fluxes; the adenine nucleotide translocatorpresumably through the regulation of the rate of cytoplas-mic-mitochondrial ATP/ADP exchange, and the mito-chondrial dehydrogenases by regulating the rate of NADHreoxidation. Additionally, a further regulatory level inglycolysis when the cells are operating at high ATP loadsmay be provided by the alcohol dehydrogenase. Whetherthese potential regulatory interactions function in physio-logical transitions remains to be investigated.

The authors thank Dr J. A. Duine (Technical University ofDelft, The Netherlands) for a generous gift of bongkrekic acid andDr Bereiter-Hahn (J. W. Goethe Universitat, Frankfurt) forkindly providing us with DASPMI. Also the assistance in AUTOinstallation and helpful advice of Dr E. Doedle (Dept of ComputerScience, Concordia University, Canada) and Mr R. Belleman(Biophysics Department, Netherlands Cancer Institute) aregratefully acknowledged. We are indebted to the NationalBiomedical Simulation Resource (Duke University, Durham,USA) for providing us with information about SCoP. M.A.A., S.C.and H.V.W. thank the Commission of European Communities andthe Netherlands Organisation for the Advancement of PureResearch (NWO) for financial support.

Appendix

Description of the modelThe interactions of glycolysis and mitochondria aredepicted in Scheme I. Glycolysis was modelled in twolumped steps. The first five steps (upper part) orpreparatory phase (Lehninger, 1982) are represented byGlc—>I, with rate constant ki, and I representing the poolof glyceraldehyde 3-phosphate. The second phase ofglycolysis (lower part), is lumped in I^>Pyr, with rateconstant k3. 2 and 4 in equation (2), below, are stoichio-metric coefficients accounting for the two ATPs expendedin the upper part of glycolysis and the four ATPs producedin the lower part of glycolysis.

Pyruvate does not appear explicitely as an ODE becausecovariation with NADH is assumed (eqns (4) and (11)). Tothe steps of glycolytic NADH production (k3) and consump-tion (&7) (Scheme I: heavy arrows), the cytosolic NADH

reoxidation by the inner mitochondrial membrane de-hydrogenase (k10, Scheme I: light arrow) (Alexander andJeffries, 1990) was added to simulate transient behaviorand was not included in the stability analysis. Addition-ally, the input rate of glucose (Vin) is considered to beconstant.

The non-glycolytic ATP-consuming processes that rep-resent the ATP load are captured by kg and themitochondrial ATPase. The reactions describing eitherATP synthesis (V^) or hydrolysis (Vpi) by the mitochon-drial H+ pump were assumed to follow Michaelis-Mentenkinetics as a function of ADP or ATP concentrations,respectively (Scheme I and eqns (2,12,13)). Mitochondrialrespiration was only implicitly taken into account throughA^H generation. Additional general properties of thepresent model have been described by Cortassa et al.(1990) and Aon and Cortassa (1991).

Stability analysis is the study of the qualitativedynamic behavior of any system in terms of the stability ofthe steady states as a function of a bifurcation parameter.The parameter values for which the stability propertieschange (e.g. from stable to unstable steady states) arecalled bifurcation points (Fig. 1A,B). A Hopf bifurcationindicates a change in the dynamic behavior of a systemfrom a region of stable steady states (attained afteroscillatory transients or damped oscillations) to a region ofsustained oscillations (limit cycles). A thorough stabilityanalysis of the present model conclusively demonstratedthat the overall stoichiometry of ATP production ofglycolysis is in itself the autocatalytic mechanism givingrise to the oscillations or more precisely to the appearanceof Hopf bifurcations (Cortassa et al. 1990, unpublisheddata). The model is described by a set of four non-linearODEs (l)-(4) and three conservation equations (5)-(7):

d[Glc]dt

d[ATP]dt

4V3-V9-VP1-Vi 'P2

dtd[NADH]

dt= 2V 3 -2V 7

(1)

(2)

(3)

(4)

CA = [ATP] + [ADP]; CN = [NAD] + [NADH];

Pt = P; + 2[I] + [ATP] (5)-(7)

with the following fluxes:

V1 = fe1[ATP]tGlc] (8)

V3 = *3 [ADP] [I] [PJ [NAD] (9)

(10)

(11)

= Kv

V7 = k7 [NADH] [NADH]

[ATP] . „ __„(12)

[ADP]

NomenclatureCA, total concentration of adenine nucleotides([ATP] + [ADP]); CN, total concentration of nicotinamidenucleotides ([NAD]+[NADH]); Ap°, reversal potential ofthe proton pump; AjiH> proton motive force; [Glc],

Mitochondrial regulation of glycolysis 333

intracellular concentration of glucose; U], intracellularconcentration of glycolytic intermediate(s) pool; klt k3, k5,k7, kg, rate constants; P;, total intracellular concentrationof inorganic phosphate; Pt, intracellular concentration ofphosphate; Vin, input rate of glucose; VM, V^, KM, KM,kinetic constants of the mitochondrial proton pump; VP1,Vp2, fluxes of ATP hydrolysis and ATP synthesis; T, ratiobetween H+ conductance and membrane capacitance.

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