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Molecular and Cellular Biochemistry 184: 409–417, 1998.© 1998 Kluwer Academic Publishers. Printed in the Netherlands.

Metabolic control analysis and mitochondrialpathologies

Thierry Letellier, Monique Malgat, Rodrigue Rossignol and Jean-PierreMazatCJF-INSERM 97-05, Université Victor Ségalen Bordeaux 2, 146 rue Léo Saignat, F-33076, Bordeaux-Cedex, France

Abstract

One of the main salient features recognized in mitochondrial diseases is the existence of a threshold in the degree of amitochondrial deficit for the expression of the disease. When expressed as a function of the degree of heteroplasmy, thevalue of the threshold can be very high, around 90% (mutated DNA/total DNA). This means that 10% of normal DNA is enoughto sustain a quasi normal mitochondrial oxidative phosphorylating flux. We have shown that most of the compensation isdone at the metabolic level: for instance a 70% deficit of cytochrome oxidase decreases the oxidative flux by just 10%.Similar patterns are observed for the other complexes. Using Metabolic Control Anlaysis (MCA), we have shown that thiskind of result is inescapable: the threshold value can be correlated to the control coefficient of the deficient step. The valueof the threshold is reinforced by slight increases at the transcriptional and translational level as we show in a simplemathematical model.

Finally we associate the threshold in the expression of a deficit, to the threshold in the energy demand of different tissues,in order to describe various patterns of onset of mitochondrial diseases (double threshold hypothesis). (Mol Cell Biochem 184:409–417, 1998)

Key words: metabolic control analysis, mitochondrial diseases, heteroplasmy, double threshold hypothesis

Introduction

The unique features of mitochondrialgenetics and pathologies. The conceptof heteroplasmy of mtDNA mutations

Several aspects of mitochondrial genetics have to be takeninto account. Firstly, human mtDNA is a 16,569 nucleotidepair, closed circular molecule which codes for a small (12S)and large (16S) ribosomal RNA (rRNA), 22 transfer RNAs(tRNA) and 13 polypeptides, all of which are componentsof the oxidative phosphorylation system. Several mutationsof mtDNA are known and give rise to now well describedpathologies. However, the complexes of mitochondrialoxidative phosphorylation involve more than 100 subunits,which means that most of them (except the 13 mtDNA-encoded) are coded by the nuclear genome. Thus, despite the

fact that no precise mutation has been described to date inthe nuclear genome that affects mitochondrial oxidativephosphorylation, such mutations are to be expected. Further-more, the nucleus also codes for all the specific machineryoperating inside mitochondria for mtDNA replication,mtDNA transcription, and mtRNA translation. Mutationshave also to be expected in these nuclear-encoded, mito-chondrial enzymes. Some have been described, but notlocalized, such as mutations regulating the number of copiesof mtDNA (mtDNA depletion).

Secondly, mtDNA is particularly prone to mutation sincethe mtDNA lacks protective proteins such as histones andhas a low-efficiency repair system. Hence, the mtDNA hasa more than ten times greater rate of mutation than thenuclear DNA. This high rate of mutation can be used to studyevolution on short scales such as human evolution andmigrations.

Thirdly, mtDNA is inherited through the oocyte cytoplasm,

Address for offprints: T. Letellier, Laboratoire GESBI, Université Victor Ségalen, Bordeaux 2, 146 rue Léo Saignat, F-33076, Bordeaux-Cedex, France

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and thus shows maternal inheritance; from the spermatozoon,only the nucleus usually enters the oocyte. This means thatthere is no mtDNA recombination at fertilization. Hence allmtDNA variation is the product of sequential accumulationof mutations along radiating maternal lineages.

Fourthly, since there are 2–10 copies of mtDNA permitochondria and some hundreds of mitochondria per cell,there are some thousands of mtDNA molecules per cell. Thismeans that one mtDNA encoded gene exists at more than athousand times the copy in number of nuclear DNA encodedgene, which in turn clearly implies regulation of theexpression of these different genes in the building of thosemitochondrial complexes composed of a mixture of nuclearand mitochondrial subunits.

Fifthly, when a new mutation arises in a mtDNA mol-ecule, it creates a mixture of mutant and normal mtDNAsknown as heteroplasmy. Thus, the expression of a mutationin the mtDNA will be a function of the degree of hetero-plasmy.

A new technique has been developed by King and Attardi[3, 4] to study the expression of mtDNA mutations and therelationships between the mitochondrial and nucleargenomes. It consists of production of cell strains lackingmtDNA by long term exposure to low concentrations ofethidium bromide. These cells can survive in the presenceof pyruvate, to regenerate NAD, and uridine, because dihy-droorotate dehydrogenase in UMP biosynthesis requires thepresence of CoQ/CoQH

2. These cells called rho o or

mtDNA-less can be fused with enucleated cells, the mtDNAof which carries a mutation (Fig. 1) [5, 6]. The resultingcells are called cybrids. In this way, it is possible to followthe expression of the mitochondrial mutation and theeffects of its heteroplasmy in a wild type nuclear DNAenvironment.

The threshold effect in the expressionof mitochondrial pathologies

One problem in mitochondrial diseases caused by mtDNAmutations is to know how the heteroplasmy of the mito-chondrial mutation is expressed in the two relevant mito-chondrial fluxes: the respiratory rate and the rate of ATPsynthesis.

As a matter of fact, the answer is known: the group ofAttardi [6] for instance showed that, in the case of theMELAS mutation 3243, 10%, or perhaps less, of wild typeDNA is enough to sustain a normal respiratory rate. Otherauthors have already shown or have recently confirmed that,in the case of other tRNA mutations or in the case of deletions,10% of wild type DNA is usually enough to observe a normalactivity. For instance Sciacco et al. [7] showed that (we quote):

‘85–90% deleted mitochondrial DNA must be reached beforeCOX activity is impaired’. The phenotypic expression of tRNAmutations are complex because they affect all the mitochon-drially encoded subunits, but differentially according to theiramino-acids composition.

An example of an effect on a single complex was given byBindoff and Turnbull in Newcastle [16] who observed thatboth in a patient with cytochrome c oxidase deficiency andin an animal model, a copper-deficient rat, lowering theactivity of complex IV by over 50% did not affect therespiratory flux. More recently, Kuznetsov and Kunz inMagdeburg [17] showed that in a mouse mutant with a severecopper deficiency the activity of COX is only about one halfof the normal activity, but that no difference was found inmaximal rates of respiration; however the control co-efficient was higher in the mutants (0.8 instead of 0.30 forthe control value).

All these authors clearly demonstrate that there is athreshold in the heteroplasmy of the mutation around 90%.Above this threshold, when there is more than 90% ofmutation, the mutation leads to pathological behaviour.Below, the fluxes of respiration and of ATP synthesis arenormal, and even the activities of some complexes are at thenormal level. This rises the question of the mechanismleading to this threshold behaviour i.e. the question of theeffect of the heteroplasmy at each step of the processleading from the mutation to the respiratory rate or to ATPsynthesis.

We will consider each process in turn and we will beginwith the last step which, as we have shown, is probably themost important for generating the threshold. This will answerthe question: ‘How does a variation in the activity of acomplex influence the flux of respiration or of ATPsynthesis’.

The explanation of the threshold effectin terms of metabolic control analysis(MCA)

It is rather easy to mimic a complex deficiency by use ofspecific inhibitors. Figure 2A shows the effect of KCN oncomplex IV activity alone and on the rate of oxygen con-sumption at the same concentrations of KCN. It can be seenthat even at 50% inhibition of complex IV one observes onlya very weak inhibition of the flux through the whole chain andone has to go as far as 90% of inhibition of the isolated stepin order to obtain a substantial inhibition of respiration. Thisis more obvious when represented as in Fig. 2B where wehave plotted the inhibition of the respiratory flux as a functionof the complex IV inhibition for the same KCN concentrations.What we observe is a clear-cut threshold: until 90% inhibition

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Fig. 1. Construction of cybrid cells with a wild type nucleus from ro cells and the mutated mtDNA.

of complex IV, the respiratory rate decreases slowly; but,beyond 90% of complex IV inhibition, the respiratory rateabruptly decreases to reach the zero level.

The same pattern is observed in the case of the inhibitionof other complexes [8].

We have already interpreted this behaviour in the frame-work of the metabolic control theory [10–12]. In this theoryan important parameter is defined: the control coefficientwhich quantitatively expresses the effect on a flux of aperturbation of a step. For instance a control coefficient of

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0.1 for complex IV means that a perturbation of 10% of theactivity of this complex will only entail a change of 1% in therespiration rate. Thus the value of control coefficient appearsclearly as the initial slope of the curve in Fig. 2B.

A very important consequence of the definition of controlcoefficient is the summation theorem, stating that in ametabolic network, the sum of the flux control coefficients

of every step of the network on any one flux is equal to one: N FΣ C = 1 which means, for instance that:i=1

i

CV(O2)CplxI

+ CV(O2)CplxIII

+ CV(O2)CplxIV

+ CV(O2)ATPase

+ ....... = 1 or

CV(ATP)CplxI

+ CV(ATP)CplxIII

+ CV(ATP)CplxIV

+ CV(ATP)ATPase

+ ....... = 1

Fig. 2. (A) Complex IV inhibition by KCN of respiratory rate (n) and of isolated cytochrome c oxidase activity (¨). The theoretical inhibition curve of theglobal flux and the isolated step have been fitted according to [25] and [26]. (B) Respiratory rate as a function of the complex IV inhibition drawn using thetheoretical curves of Fig. 2A.

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Fig. 3. Constraints on the flux inhibition curve as a function of the controlcoefficient value. The curve represents the step inhibition curve. The initialslope to the flux inhibition curve is drawn in accordance with a low controlcoefficient by comparison with the initial slope to the step inhibition curve.The final slope to the flux inhibition curve is imposed by the requirement forthis curve to reach the x-axis when the step is completely inhibited.

Table 1. The threshold value of the defect is expressed as a function of thecontrol coefficients of the different complexes of respiratory chain on therate of oxygen consumption (rat muscle mitochondria, after [9])

Control coefficient Threshold(% of defect)

Complex I 0.07 90%Complex III 0.23 60%Complex IV (COX) 0.14 70%

Table 2. Control coefficients of cytochrome c oxidase and of ATP/ADPtranslocator in different tissues at state 3 respiration

Tissue Muscle Heart Liver Brain Kidney

Control coefficient of 0,20 0,12 0,01 0,01 0,03cytochrome c oxidaseControl coefficient of 0,04 0,04 0,01 0,07 0,06ATP/ADP translocator

Experimental results have largely confirmed this theoreticalprediction ([9, 13, 14] for instance.

All the experimental results now show that most of thecontrol coefficients are very low. Most of them have to bepositive in the case of oxidative phosphorylation, and in orderto give a sum equal to 1 it is necessary that most of themshould be close to zero. This is an unescapable consequenceof the summation theorem (see [15] for a more generaldiscussion). The shape of Fig. 2B is also imposed by thesmall value of the control coefficients as shown in Fig. 3:at the beginning (small deficit), a quasi horizontal slope isobserved due to the low control coefficient. On the contrary,at a very low activity of the step both curves must meet again,due to the fact that the flux becomes zero when the step is

being completely inactivated. This unavoidable behaviourleads to a sigmoid inhibition shape of the flux inhibition curveand to a threshold effect when the flux is plotted as a functionof the inhibition of one of its steps. Furthermore, Table 1 showsthat the lower the control coefficient, the higher is thethreshold.

We have shown that this threshold effect is also observedin a model of oxidative phosphorylation developed byBernard Korzeniewski in our laboratory [18].

This observation lead us to the following hypothesis: wehave demonstrated that the threshold effect observed on aflux value when a specific activity is modulated is mainly theconsequence of the value of the control coefficient of thestep on the flux. We know that the control coefficient of agiven step can vary according to different types of mito-chondria. This led us to propose the hypothesis that part ofthe tissue specificity in the metabolic expression of mito-chondrial mutations could be due to the differences in controlcoefficients. Thus we measured the control coefficients ofthe cytochrome c oxidase and of the nucleotide adenylictranslocator in different types of tissues: heart, muscle, liver,kidney and brain. The results we obtain (Table 2) show that,in some cases at least, the variation in the expression of amitochondrial mutation in different tissues could be due tothe tissue variation of the control coefficients of the variouscomplexes.

The reinforcement of the threshold at transcription andtranslation steps

Next, we will look at the effect of the heteroplasmy in thefirst steps of the expression of mitochondrial mutations, thatis on transcription and translation steps.

Unfortunately, there are, to our knowledge, only two,incomplete, quantitative reports in the literature.

One of them comes from the laboratory of Serge Alziariin Clemmont-Ferrand [19, 20] (Table 3) and concerns a deletionin the mitochondrial DNA of a Drosophila species. The resultsexhibit a slight elevation of the wild type compounds at eachstep of the process: a wild type mRNA ratio slightly higherthan the corresponding wild type DNA ratio and a percentageof complex activities slightly higher than the corresponding

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Table 3. Expression of the heteroplasmy of a large deletion in themitochondrial genome of a Drosophila subobscura strain. After [19] and[20]

Relative level in the mutant (%)

mtDNA total 150mt DNA normal 30∆ mtDNA 120ND5 mRNA 35ND1 mRNA 45ND4 mRNA 55Cyto b mRNA 66∆ mRNA 45Complex I activity 60Complex III activity 70Complex IV activity 107Resp. (Glu-Mal) 70Resp. (Succ.) 100

Table 4. Expression of the heteroplasmy of a mtDNA deletion inlymphoblasts derived from a patient with Pearson’s syndrome. After [21].(ND4 and Cox II are included in the deletion)

Relative level in the patient (%)

mtDNA total 140mtDNA normal 4 0∆ mtDNA 100ND4 mRNA 55COX II mRNA 40COX I mRNA 100COX IV mRNA 100COX VI mRNA 100COX activity 81–88ATP synthesis 100

200*WTmRNACplx = (2)

KmRNA + WTmRNA

200* WTmtDNAWTmRNA = (1)

KmtDNA + WTmtDNAwild type mRNA ratio. Finally, this ends up with a quasinormal recovery of the respiratory flux.

The other comes from the laboratory of Coby van denBogert in Amsterdam [21] (Table 4), and shows the samephenomenon with a normal rate of ATP synthesis despitethe fact that the content in wild type mitochondrial DNAis only 40%.

Fig. 4. Percentage of WT mRNA (or WT tRNA) as a function of thepercentage in WT mtDNA according to equation (1).

A simple model of the threshold as a function ofheteroplasmy

We have developed a simple model which considers theexpression of a mitochondrial mutation according toScheme 1. We have used simple functions to express theresult of each step of this scheme: – the normalized quantityof WT mRNA and WT tRNA (between 0–100%; 100% isthe normal wild type (WT) quantity) is given as a functionof the normalized quantity of WT mtDNA (between 0–100)by the hyperbolic function, with KmtDNA = 100:

This function is equal to 100 for mtDNA = 100 (normalsituation); it gives a slight increase in mRNA or tRNAbetween 0–100 as it can be seen in Fig. 4). – the normalizedquantity of a complex is given by the same type of function:

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2*WTmRNA 2* WTtRNACPlx = 100* * (2′)

KmRNA +WTmRNA KtRNA + WTtRNA

If Cplx ≤ Cplxth then we define VO2

th = C*Cplx

th, + 100 (1-C)

andVO2 = VO2

th/Cplx

th * Cplx (3′)

The double threshold hypothesis

Douglas Wallace, some years ago, also proposed the conceptof a threshold in the expression of mitochondrial mutationsbut of a slightly different nature [1, 22]. This threshold mainlyconcerns the energy demand of a tissue, with a classificationof the tissues according to their energetic needs; this explainswhy some tissues that have higher energy demands, such asbrain and muscles, are also more sensitive to mitochondrialdiseases. If the supply of ATP by mitochondria falls downunder the particular threshold of the tissue, pathological signsappear. A decrease in the mitochondrial power due to agingor to an increase in heteroplasmy can lead to pass under thethreshold.

In order to explain the tissue variability of mitochondrialdiseases, we propose combining both concepts of thethreshold into what we call the double threshold model(Fig. 7).

The intercept of the two curves separates the normalfunctioning of the mitochondria from the pathologic state.It can be evidenced on Fig. 7 two types of intercept whichcan lead to different types of pathologies. In the case ofintercept of type 1 (Fig. 7A) one can expect a progressiveinstallation of a pathological state as is observed in thechronic encephalomyopathies in the adults (Kearns-Sayre;MELAS or MERRF). The intercept of type 2 (Fig. 7B) willcorrespond to an abrupt passage towards a pathologic stateas observed in fatal infantile myopathies.

This gives also a slight increase in the quantity of complexcompared to the corresponding quantity of mRNA. Weadditionally hypothesise that the decreased quantity of tRNAis not limiting until a threshold tRNA

o. If tRNA < tRNA

o then

the quantity of complex becomes:

Fig. 5. Percentage of normal respiratory rate as a function of the percentage in the activity of a complex (equations) C is the control coefficient of the step onthe respiratory flux and Cplxth is the threshold as defined in the text.

– the rate of respiration is given by a function simulating thethreshold effect described in Fig. 2. We have described thistype of curve simply by two straight lines (see Fig. 5):If Cplx ≥ Cplx

th then VO2 = C*Cplx + 100 (1-C) (3), where C is

the control coefficient of the step catalyzed by the complex.

With these equations and for tRNAo = 0.2 (20% of tRNA is

enough to translate the quantity of WTmRNA), we obtain thecurve of Fig. 6 which is very similar to the Fig. 1 in [6] andexhibits a strong threshold in the expression of the mtDNAmutation in the rate of oxygen consumption around 15% ofmtDNA.

It can be seen in the simulation that for instance, 30% ofWT mtDNA gives 46% of the corresponding WT mRNA(involved in the mutation) and 63% of the correspondingcomplex itself and then 96% in the rate of respiration.

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Conclusion

Mitochondrial metabolism and genetics exhibit severalparticularities which force us to consider them differentlyfrom cytosolic metabolism, particularly in the case ofinborn errors of metabolism affecting oxidative phos-phorylation.

Several mutations of mitochondrial DNA have beendescribed that can lead to different pathologies as a functionof the heteroplasmy of the mutation in the various tissues.

One of the main salient features recognized in mito-chondrial diseases is the existence of a threshold in thedegree of a mitochondrial deficit for the expression of thedisease. When expressed as a function of the degree ofheteroplasmy the value of the threshold can be very high,around 90% (mutated DNA/total DNA). This means that10% of normal DNA is enough to sustain a quasi normalmitochondrial oxidative phosphorylating flux. We haveshown that most of the compensation is done at the metaboliclevel: for instance a 70% deficit of cytochrome oxidasedecrease the oxidative flux by just 10%. Similar patterns areobserved for the other complexes in accordance withmetabolic control theory. The value of the threshold isreinforced by slight increases at the transcriptional andtranslational level.

In fact this result, though clearly apparent in mitochondria,because the heteroplasmy phenomenon allows a complete

Fig. 6. Percentage of respiratory rate as a function of the percentage ofWT mtDNA resulting from the combination of the equations (1) to (3′).

range of variation of a mutation between 0–100%, is moregeneral and had already been depicted particularly by Kacser[23]. It is an inescapable result of MCA and more particularlyof the summation theorem as shown on Fig. 3.

The fact that different tissues not only have differences inenergy demands, but also have different types of mitochondriaand thus different control coefficients (and associatedthreshold) at each step can explain the tissue differencesexpression of mitochondrial mutations. The combinationof these two concepts leads us to the double thresholdhypothesis.

Acknowledgements

This work was supported by the Association Française contreles Myopathies (A.F.M), the Université Bordeaux II, theRégion Aquitaine, INSERM and the French Ministry of HighEducation and Research. The authors wish to thank Dr. D.Fell for many valuable comments.

Fig. 7. The double threshold hypothesis.

tissue 1

tissue 2

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