A kinetic model of phosphofructokinase from Plasmodium berhei. Influence of ATP and fructose-6-phosphate

Molecular and Biochemical Parasitology, 27 (1988) 225-232

225

Elsevier MBP 00915

A kinetic model of phosphofructokinase from Plasmodium berghei. Influence of ATP and fructose-6-phosphate Detlef Buckwitz, Gisela Jacobasch, Christa Gerth, Hermann-Georg Holzhtitter and Richard Thamm Institute of Biochemistry, Humboldt-University, Berlin, G.D.R. (Received 8 May 1987; accepted 8 September 1987)

Phosphofructokinase (PFK) from the malarial parasite Plasmodium berghei shows the following kinetic features: the more the pH is decreased, the more the enzyme is inhibited by ATP; in contrast to PFK from erythrocytes, this inhibition is less potent by two orders of magnitude; as in the red cell, fructose-6-phosphate (F6P) is a positive effector. Kinetic modelling of PFK from P. berghei has been performed by taking the pH-dependence of activity into regard, implicitly by the estimation of pH-dependent kinetic parameters for the inhibition by ATP and the activation by F6P and explicitly by the assumption of protonation-steps involved in allosteric regulation. By means of a novel procedure of model discrimination [D. Buckwitz and H.-G. Holzhtitter: A new method to discriminate between enzyme-kinetic models. In: Application of Computational Methods in Medicine (Gy6ri, I., ed.), Akademai, Budapest, in press] we have selected among several kinetic models the best rate equation which provides an adequate quantitative description of the kinetic behaviour of the enzyme in the relevant ranges of substrate concentrations and pH (5.8-7.6). It thus becomes clear how the highly increased glycolytic flux in malaria-infected cells could be affected through PFK. Key words: Plasmodium berghei; Phosphofructokinase; Kinetic model; pH; ATP inhibition; Monod model

Introduction

Erythrocytes infected with the malarial parasite Plasmodium berghei show a 10-30-fold increased glucose consumption via glycolysis [1,2] which is catalysed by parasite-specific enzymes differing electrophoretically and kinetically from the host cell, including phosphofructokinase (PFK) [3]. This enzyme is considered to be one of the most important control enzymes of red blood cell glycolysis [4-6]. From studies on enzyme activities [7] as well as from cross-over plots of intermediate concentration [8], it is clear that PFK is of regulatory importance also in the malaria parasite. Its kinetic properties allow a high glycolytic flux at low pH-values occurring in parCorrespondence address: Prof. Dr. sc. nat. Jacobasch, Institut ftir Biochemie, Hessische Str. 3-4, Berlin, DDR - 1040. Abbreviations: PFK, phosphofructokinase (EC 2.7.1.11); F6P, fructose-6-phosphate; MgATP, Mg2+-complexed ATP; SQ, weighted sum of least squares; ~r, experimental error.

asitised red cells [9] where host cell glycolysis is strongly inhibited [10]. These findings have been confirmed by our own results [11] and similar resuits have been obtained with Plasmodium knowlesi-infected erythrocytes [12]. Apparently, the glycolytic pathway seems to be regulated in a different way to that of red cells. To obtain insight into metabolic control of malarial energy metabolism it is necessary to characterize its regulatory enzymes such as PFK kinetically. In this paper a mathematical model of PFK is presented which describes the kinetic behaviour of the enzyme in the relevant ranges of concentrations of the substrates Mg2+-complexed ATP (MgATP) and fructose-6-phosphate (F6P). Since the pH-value decreases during parasitemia of red blood cells the pH-dependence of PFK-activity has also to be considered. The model takes into regard the dependence on the pH-value between pH 6.0-7.6. Using statistical tests it is shown that the accuracy of the proposed model is adequate for the experimental data under consideration.

0166-6851/88/$03.50 O 1988 Elsevier Science Publishers B.V. (Biomedical Division)

226

Materials and Methods

The kinetic measurements were carried out with the lysates of parasite cells. After washing the red cells of 5-10 ml blood from mice infected with P. berghei strain L N K 65 (hematocrit 15-30%, parasitemia 80-90%) three times with isotonic sodium chloride and removal of the leucocytes, the erythrocytes were hemolysed osmotically (1 part suspension with a hematocrit of 30% and 2 parts aqua dest.). The parasites were separated by centrifugation at 4000 x g for 10 min. Next they were washed with a solution of 150 m M a m m o n i u m chloride and then centrifuged at 3500 × g for 10 min. The sediment was resuspended using isotonic sodium chloride containing 4.0 m M phenylmethylsulfonyl fluoride and 0.5 m M leupeptin. Afterwards the parasites were lysed by three times freezing and thawing. After centrifugation at 10000 x g for 20 min we obtained a stroma-free lysate (SFL). The activity of P F K was measured with an Epp e n d o r f - p h o t o m e t e r at 366 nm with the following assay: 0.2 m M N A D H , 1.0 m M MgC12, 90 m M KC1, 1.0 m M K2HPO4, 8.0 Ixg aldolase, 3.3 txg triose phosphate isomerase, 3.3 Ixg glycerol-3phosphate dehydrogenase in 0.08 M Tris-buffer ( T = 37°C). The concentrations of the substrates varied in the ranges 0.03-3.0 m M F6P and 0.04--4.8 m M A T P . T h e m e a s u r e m e n t s were carried out in the range p H 5.8-7.6. All fine-chemicals used were from Boehringer-Mannheim, all other substances were of analytical purity. The experimental data used for modelling are derived from at least two repetitions. From these and from additional investigations we have estimated an experimental error of ~r = 0.035 Vmax which we suppose to be constant. This assumption is in a g r e e m e n t with other studies on the error structure of kinetic m e a s u r e m e n t s [13]. For the estimation of the kinetic p a r a m e t e r s a nonlinear regression procedure based on a modified G a u s s - N e w t o n algorithm was used minimizing the weighted sum of least squares N

SQ =

~] i -

where

W i [12 i - -

V (Xi, #)]2

(1)

1

v(xi, 15)

is rate law dependent on the

vector of concentrations xi at the i-th data-point and the estimate 15 of the p a r a m e t e r vector p; Vl is measured activity; w i is weighting factor; N is n u m b e r of data. The program calculated the p a r a m e t e r values of all possible models one by one and discriminated between the models on the basis of the statistical tests described in Appendix I. All calculations were carried out on a 64 kbyte microcomputer. Linear methods and linearized plots failed because of the complexity of the models and the fact that free ATP, M g A T P and Mg 2+ had always been present simultaneously in varying concentrations (eqs. 2, 3). Results

Implicit consideration of pH-dependence.

As a first approach, the dependence of the kinetic properties of PFK on p H is described by the estimation of p H - d e p e n d e n t kinetic parameters. The plot of the activity versus the concentration of F6P (Fig. 1) is generally sigmoid, i.e. F6P is both a substrate and a positive effector. The dependence on the concentration of A T P is also biphasic (Figs. 2 and 3), due to its function both as a substrate and an inhibitor. Therefore, a Monod-type model [14] has been suggested. According to this model, increasing p H shifts the equilibrium towards the R-

0o~

£ 05 F6P(mM)10 •

15

Fig. 1. Activity in dependence on F6P concentration at several pH-values and ATP-concentrations; ATP = 0.4 mM (o), 0.8 mM (A) and 1.0 mM ([3) at pH 7.2; ATP = 0.2 mM (T), 0.4 mM (e), and 0.8 mM (A) at pH 6.8; ATP = 0.4 mM (*) at pH 6.5; lines correspond to model a4.

227

state. At pH 7.2 a nearly hyperbolic dependence on F6P results also at inhibiting concentrations (1.0 mM) of ATP (Fig. 1). On the other hand this plot becomes sigmoid at decreasing pH (6.8 and 6.5, respectively) and increasing ATP concentrations, which is explained by a transition to the Tstate. The inhibition by ATP depends also on the pHvalue. The enzyme is strongly inhibited at pH 6.5 whereas this effect is marginal at pH 7.2 (Fig. 2). As is obvious from Fig. 3, the activity of malarial PFK as a function of [ATP] increases with higher concentrations of F6P although the biphasic ATP effect itself remains unchanged. In contrast to this the Km-value of ATP seems to be independent of the pH-value (Fig. 2) as well as of the concentration of F6P (Fig. 3). Despite the dual function of ATP as substrate and inhibitor and the resulting overlap of the two effects it is evident that the K mvalue is much smaller than the pH-dependent inhibition constant. MgATP has been assumed to be the real substrate as this is generally known to be the case for kinases. Its concentration was calculated from the total concentrations of ATP and Mg 2÷ ([ATPT] and [MgT]) by

KA =

[Mg 2÷1 [ATP] [MgATP]

(2)

10

0.8

.~..

"-" " " ~ .

06

>~

04

-\ 02

0

-f----~

.~-___ o 5

--.... 10 ATP (raM)

?5

2.0

Fig. 2. Activity in dependence on the total concentration of ATP at several pH-values; p H = 6.5 (m), 6.8 (e), and 7.2 (&); F6P = 1.0 mM; the fits correspond to model a4 ( ), al ( - - - ) and b4 ( - - . - - ) .

1 [MgATP] = ~ (KA + [ATPTI + [MgT]) --

[~ (K,, +

[ATPr] + [Mgr]) z - [ATP-r] [MgT]]

l'=

(3)

The dissociation constant, K A = 0.081 mM, may be regarded as pH-independent [15]. To describe the reaction mechanism, three models have been taken into account by specifying the general kinetic rate-law of two-substrate reactions under steady-state conditions [16--18] extended by an allosteric term of Monod type [14]: V ~

v ~ [MgATP l [F6Pl 1 [MgATP] [F6P] + Kr [MgATP] + Km~ [F6P] + K.~ K~ 1 + L

(4) 1 + [ATPTI-] n

K~LJ Kn

where is maximum activity; are Michaelis constants for MgATP and F6P; g m a , Kif are dissociation constants for MgATP and F6P; Lo is equilibrium constant for the transition between the R-state and the Tstate; n is number of subunits (this value had not been fixed but estimated together with the other parameters); Kal is inhibition constant for total ATP; gfl is activation constant for F6P (kinetic nomenclature according to Cleland [18] and Monod et al. [14]; the index i denotes a dissociation constant and not an inhibition constant). M o d e l a: sequential mechanism with Kima = Kma and Kif = Kf (presupposing the rapid-equilibrium assumption [19] and independent binding of both substrates). M o d e l b: ordered mechanism with MgATP as the first substrate: Kif = 0; Kma = 0. M o d e l c: ordered mechanism with F6P as the first substrate: Kima = 0; Kf = 0. Vrnax Kma, K f

228

been fitted to the N = 172 data. So only the allosteric constants of F6P and ATP are dependent on pH:

10--

o8~-

l"max [MgATP] [F6PI

V =

([MgATPI + Kma) ([F6P] + K0 > ~04

[ATPd7 n 0 .... 0

I 05

_

I 10 ATP ( m M )

15

20

Fig. 3. Activity in dependence on the total concentration of A T P at several F6P concentrations; F6P = 0.2 m M ( I ) , 0.5 m M (at), and 1.0 m M (o) at p H 6.8 and F6P = 0.2 m M (r~) at p H 7.2; ( ) p H 6.8, ( - - - ) p H 7.2 (model a4).

The sums of least squares SQ remaining after regression, which correspond to the degree to which the regression model describes the experimental data, are given in Table I. Because it produces the smallest SQ-value, model a is favoured. Furthermore model b can be rejected due to the fact that the apparent Kin-values of MgATP (Kma) do not depend on the concentration of F6P (Fig. 3). Comparing the parameter values of model a estimated for different pH-values (Table II), Kma, Kf, Lo and n seem to be constant. Note that these 4 parameters have been assumed to be pH-independent in a modified model a* which has 10~

O8

06

02

(5)

I+[F6Pl | KflpH -]

(estimated parameter values: Table II, 2nd section). By this simplification only 10 instead of 18 parameter values are necessary to describe the data-set without a significant loss of accuracy of the model. The resulting model is well suited to characterize the kinetic properties of malarial PFK at the pH-values considered here but fails for instance when continuous pH-transitions are to be investigated by mathematical models of the parasite metabolism.

Explicit consideration of the pH-dependence. The effect of pH has been considered explicitly by the introduction of one or two parameters into the allosteric term of the rate law corresponding to fictive H+-dissociations. This procedure is based on the idea of Michaelis and Davidson [16] of using the H+-concentration in rate equations to describe pH-dependences. It should be stressed that this strategy can lead to a good phenomenological but never mechanistical model of the data. From a family of models corresponding to different reaction mechanisms and models of alloTABLE I

L

(35.6

l+Lo

6.0

6.a

6IB

172

L

1~

76

Sums of least squares SQ and test statistics U (see Appendix I) after fitting models a, b, and c to the N = 172 data

pH

Fig. 4. Activity in dependence on the pH-value at several A T P concentrations; A T P v = 0.3 m M (V), 0.6 m M (at), 1.0 m M ( I ) , and 1.5 m M (e); F6P = 1.0 raM; full lines correspond to model a4. (o) M e a s u r e m e n t s for red blood cell PFK from rat obtained under comparable conditions ( A T P = 1.5 m M ) [22].

Model

SQ

U

a b c

0.129 0.395 0.271

0.81 a 8.10 2.81

a A d e q u a t e model for a = 5%.

229 TABLE II Estimated parameter values of model a and a*, respectively in comparison to PFK from red cells measured under identical conditions [20] Parameter

pH 6.5

pH 6.8

pH 7.2

red cell PFK pH 7.2

0.022 0.035 0.70 1.21 2.81 3.81

0.037 0.028 1.02 0.58 3.60 3.87

0.027 0.032 3.69 0.32 4.12 3.83

0.07 0.15 0.01 0.15 0.05 4

0.71 1.37

0.032 0.036 1.01 0.57 2.87 3.80

3.59 0.32

model a

Km~ Kf Kal Kfl Lo n model a*

Kma Kf Kal,~ Kfl..e~" Lo n

In model a* Kma, Kf, Lo, and n are kept pH-independent a priori. All parameters except Lo and n in mM.

steric regulation the 6 most suited rate laws were involved in model discrimination. (A list of the rate equations of the other models considered is available from the authors.) Model a4 gives the best overall fit to the data: v.~, [MgATP] [F6P] 1 v = ([MgATP] + K~) (F6P] + Kr) 1 + L + (1 +[H÷]] ( 1 + [ K ~ ( 1 + L=I+Lo

•

Khl /

(6) [ATP]

+

[MgATP]]) ] n

K~l

Kraal

/

1 + [n__]+ [F6P] Khl

Kn

Estimated parameter values of model a4 (eq. 6) gma

Kal Kraal

K, Kh, gh2 Lo n

a Corresponds to pK 1 = 7.72 and pK2=5.50.

Discussion The kinetic properties of malarial PFK have to be seen in the light of special metabolic requirements during parasitemia of the red cell. The need for large quantities of energy in the form of ATP for the multiplication of the parasites can only be met by glycolysis. The high glycolytic activity leads to lactate accumulation and metabolic acidosis

[7,21].

TABLE III

K,

It is a random mechanism assuming two sites for H+-dissociations. ATPfree and MgATP can only be bound to their protonated allosteric site and F6P is only bound to its unprotonated one (H ÷ has a competitive effect on F6P activation) (for parameter values see Table III).

0.031 mM 0.034 mM 0.023 mM 0.090 mM 0.064 mM 0.019 ~M a 3.16 ~M a 3.54 3.79

The dependence of PFK activity on pH in model a4 (eq. 6) is shown in Fig. 4. In the pH range considered there is a good agreement with the experimental data. Hence the assumptions which have been made with regard to the pH-effect seem to be reasonable. It is evident that the enzyme is more inhibited by ATP as the pH decreases. But in contrast to PFK from red cells the inhibition constants differ by two orders of magnitude (cf. Table II). Thus there is still a remarkable flux through malarial glycolysis while at lower

230 T A B L E IV Discrimination between models with explicit regard to p H test statistics Trs defined by eq. (8) Model r

al a2 a3 a4 b4 c4

Model s al

a2

a3

a4

b4

c4

0

-4.78 0

7.77 8.50 0

7.97 8.42 1.92 a 0

4.90 5.58 -4.26 -4.28 0

5.56 5.98 -0.90 a - 1.44 a 4.00 0

a No significant difference at a level of a = 5%.

pH-values the pathway of the host cell is nearly totally inhibited. Our kinetic analysis does not allow us to decide whether the inhibition is caused by MgATP and free ATP or only by the latter, since the fit of the favoured model is not significantly better than that of a model assuming only inhibition by free ATP at a level of 5% (see Appendix I). It seems to be likely that malarial PFK is affected by ATPtree only, similar to PFK from other origins. A shift from pH 7.2 to 6.5 causes only a slight decrease of the amount of MgATP 2- (by the factor 1.12-1.21 independent of [ATPT]) but the partition of ATP 4- decreases by the factor 1.1-2.2 while H A T P 3- increases drastically (factor 2.24.3) (see Appendix II). The amount of MgH A T P - and its changes are marginal (< 0.6% of [ATPT] ). The constancy of [MgATP 2-] is in agreement with the pH-independence of the Michaelis-constant for MgATP. On the other hand we cannot decide whether the increased inhibition of PFK by ATP is due to a protonation of the enzyme or if it is only caused by an increasing amount of H A T P 3-. Compared with the red cell enzyme [20] the affinity for F6P is increased threefold whereas its activation effect is decreased. The first fact could be important at lower F6P concentrations because according to the model a lack of F6P could not be compensated by an excess of the other substrate. Moreover, for the host cell enzyme the pH-dependence of F6P affinity is much more pronounced. Changes from pH 7.2 to 6.8 lead to a decrease of the apparent S0 5-value by a factor of 9 ([ATP] = 2.0 mM) and a factor of 12 ([ATP] = 0.2 mM) [22], respectively, compared with a less

than 2-fold decrease of F6P activation in the parasites. A decrease of pH from 7.2 to 6.5 results in a shift of the ratio [F6p2-]/[HF6P -] from 12.3 to 2.45. Obviously, the K m for F6P is not influenced by changes of the ionization of the substrate. The pH-dependence of activation of the enzyme by F6P cannot be explained by the ionization of the substrate only, since despite the large shift of the ratio [F6p2-]/[HF6P -] the absolute amount of F6P 2- decreases by only 23% while the activation constant rises 4.3-fold. Thus a protonation of the protein seems to be more likely. The pH-dependence of activation is synergistic to that of inhibition by ATP. Assuming that the concentration of ATP is kept relatively constant due to the regulation of the glycolytic system as is the case in mammalian red cells, F6P rather than ATP would be an important effector for short-time regulation. The estimated value of n = 3.8 makes it rather probable that the native form of PFK has four catalytic subunits. The in vivo activity of malarial PFK estimated from the glycolytic flux of infected erythrocytes amounts to 5% of maximum activity. This rate is much higher than that of PFK in uninfected cells which is inhibited to more than 99% of maximum activity at pH 7.2. It is problematic to characterize the physiological importance of these and other effectors because this would require a better knowledge of the metabolite concentrations in the parasites which is not available up to now. But it is very probable that the activation by F6P as well as the inhibition by ATP and decreasing pH play an important role in the regulation of this control enzyme.

231

Appendix I Discrimination between alternative models of malarial PFK. When fitting a more phenomenological model to experimental data two questions have to be answered: Is the model which is favoured because of the smallest SQ generally better suited to describe the kinetics of an enzyme than other rate laws (model discrimination) ? Does the model reflect the data in an adequate manner (model testing)? Therefore two statistical tests developed by Zwanzig [23] were used the applicability of which to enzymatic data had been proved by Buckwitz and Holzhiitter [24]. By the first test the ratio between the differences of least squares of the models and a suitable defined distance between them is tested for significance. The distance between model r and s is defined by:

CJVr

-

vs/wv,

-

vs

=

N

-

i z

1

wi [~i (x~, p) - v~ (xi, $)]~

(7)

with explicit regard to pH are listed it follows that the differences between models a3, a4, and c4 are not significant at this level of a. From the statistical point of view it is not reasonable to discriminate between them when using this set of experimental data. On the other hand these 3 models fit the data significantly better than all other models do. The following test allows a decision whether a model describes the data in an adequate manner, i.e. that the model error Af is zero, or not. The model error is defined to be the minimal distance between the real behaviour of the enzyme (errorfree data or an infinite number of data) and the model: A f=

W

min

(9)

Vi - - V(Xi, i0)

N---~ oo a f which is unknown on principle is one part of the sum of least squares SQ besides the variance o-2 caused by the error of the data. For each model the hypothesis h f = 0 is tested using the test statistics

v [SV ' °q

The test statistic is u =

N

x,5

S Q r (/~) - SQs (B)

(10)

2 wi i=1

2 ~ ~ wp [v~ (xi, ~o) - ~ (xi, ~o)1~ ~

o"i experimental error (here o i

=

constant = or)

The following decision rule holds: Trs > Ul-oa2 model s is chosen; ITrsl < ul-o~2 no significant difference between the models with respect to the data; Trs < -Ul_~/2model r is chosen; where u1-~/2 denotes the (1-a/2)-quantile of the normal distribution. For a level of significance of 5% it follows ul-oa2 = 1.96. Comparing models a, b, and c we obtained Tab = --7.60, Tac = - 2 . 0 9 and Tbc = 5.61. Thus it is possible to decide in favour of the random mechanism (model a). From Table IV where the Trs-values of 6 models

The model is accepted to be adequate when u < Ul_ed2 and rejected otherwise. Only the errors of model a of the first and model a4 of the second approach may be regarded to be equal to zero, statistically. Although the real mechanism of the enzyme is unknown, models a and a4, respectively, may be considered as correct models to describe the kinetic properties of PFK from P. berghei. For all other rate laws the hypothesis Af = 0 has to be rejected (incorrect models).

Appendix II Ionization and Mg-complexes of the substrates. The ionization and Mg2+-complexation of A T P and F6P, respectively in dependence of p H have been elucidated based on the equilibria [15]:

232

K. (ATP)

Kb (ATP 4 )

[H+] [ATp4-] [HATP3_] - 1.08 x 10-7M

[MgATp2 ] - 1.39 x 10 -4 M 1 [Mg2÷1 [ATP 4-1

Kb (HATP 3 ) =

[MgHATP-] = 35.5 M -1 [Mg2+l [HATP 3-]

(11) (12)

K, (F6P) - [H+] [F6p2-] - 7.76 x 10 -7 M [HF6P ]

(14)

a n d t h e c o n s t a n c y o f t h e s u m s o f [ A T P T ] , [F6PT], a n d [MgT].

(13)

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13 Tommasini, R., Endrenyi, L., Taylor, P.A., Mahuran, D.J. and Lowden, J.A. (1985) A statistical comparison of parameter estimation for the Michaelis-Menten kinetics of human placental hexaminidase. Can. J. Biochem. Cell. Biol. 63,225-230. 14 Monod, J., Wyman, J. and Changreux, J.P. (1965) On the nature of allosteric transitions: a plausible model. J. Mol. Biol. 12, 88-118. 15 Lawson, J.W.R. and Veech, R.L. (1979) Effects of pH and free Mg 2÷ on the equilibrium constant of the creatine kinase reaction and other phosphate hydrolyses and phosphate transfer reactions. J. Biol. Chem. 254, 6528-6537. 16 Dixon, M. and Webb, E.C. (1964) Enzymes, 2nd edn., Academic Press, New York. 17 Hayashi, K. and Sakamoto, N. (1985) Dynamic Analysis of Enzyme Systems, Springer-Verlag, Tokyo. 18 Cleland, W.W. (1963) The kinetics of enzyme catalyzed reactions with more substrates and products. I. Nomenclature and rate equations. Biochim. Biophys. Acta 67, 104-137. 19 King, E.L. and Airman, C. (1956) A schematic method of deriving the rate laws for enzyme-catalyzed reactions. J. Phys. Chem. 60, 1375-1378. 20 Otto, M., Heinrich, R., Kuhn, B. and Jacobasch, G. (1974) A mathematical model for the influence of F6P, ATP, K ÷, NH2, and Mg 2+ on the phosphofructokinase from rat erythrocytes. Eur. J. Biochem. 49, 169-178. 21 Deslauriers, R., Ekiel, I., Kraft, T. and Smith, I.C.P. (1982) NMR studies of malaria - 31p nuclear magnetic resonance of blood from mice infected with Plasmodium berghei. Biochim. Biophys. Acta 721,449-457. 22 Kfihn, B., Jacobasch, G. and Rapoport, S.M. (1969) Some properties of phosphofructokinase of rat erythrocytes. Acta Biol. Med. Germ. 23, 1-17. 23 Zwanzig, S. (1980) The choice of approximative models in nonlinear regression. Math. Oper. Stat. Ser. Stat. 11, 23-47. 24 Buckwitz, D. and Holzhiitter, H.-G. (In Press) A new method to discriminate between enzyme-kinetic models. In: Application of Computational Methods in Medicine (Gy6ri, I., ed.), Akademai, Budapest.