Kinetic studies of multifunctional reactions catalysed by lipoamide dehydrogenase

1°C..I Riochvm. Vol II~pp. 407 t* 413 6 Pergamon Press Ltd 1980 Printed tn Great Br~taln

KINETIC STUDIES OF MULTIFUNCTIONAL REACTIONS CATALYSED BY LIPOAMIDE DEHYDROGENASE C. S. TSAI Department of Chemistry and Institute of Bjochemistry, Carleton University, Ottawa, Ontario, Canada (Received

3 1 August 1979)

Abstract-Lipoamide dehydrogenase from pig heart, in addition to catalyzing the reversible oxidation of dihydroiipoamide, displays various NADH-mediated activities including hydrogen transfer between nicotinamide nucleotides, electron transfer to inorganic acceptors and redox reaction of quinones. Kinetic studies of these reactions were carried out by measuring initial rate over a wide range of substrate con~ntrations and analyzing product inhibitions at different temperatures. Double reciprocal plots are generally nonlinear. Product inhibitions in some cases do not follow the patterns predictable from simple bisubstrate mechanisms, A kinetic scheme which consists of a random mechanism with a pingpong loop is proposed for multifunctional reactions catalyzed by iipoamide dehydrogenase.

Lipaamide dehydrogenase (NADH : lipoamide oxidoreductase, EC 1.6.4.3) is the flavoprotein component of a-keto acid dehydrogenase complexes catalysing NAD+-linked oxidation of protein-bound dihydrolipamide (Read, 1974). The enzyme has been isolated

in the free form (Savage, 1957; Massey ef al., 1960) and shown to catalyse the reversible dehydrogenase (DHase*) reaction between nicotinamide nucleotide and lipoamide, In addition, the enzyme also mediates other NADH-linked reactions such as hydrogen transfer to nicotinamide nucleotides (THase reaction), electron transfer to inorganic acceptors (ETase reaction) and reduction of quinone dyes (DPase reaction). In view of recent interest in the mechanism and physiological implication of multifunctional enzymes (Kirschner & Bisswanger, 1976; Stark, 1977), this project was initiated to obtain the experimental parameters defining the multifunctionality of pig heart lipoamide dehydrogenase. Because of the complexity with which the flavoprotein participates in the reactions and the diversity in which the multifunctional activities are affected by various reagents and treatments (Masssy. 1963; Williams, 1976), there is a need for systematic and detailed kinetic studies of the reactions catalysed by lipoamide dehydrogenase. Although kinetic studies of the DHase reaction have been reported previously, its mechanism remains uncertain (Visser ef al.; Read, 1973). Furthermore, parallel studies on the THase, ETase and DPase reactions are either incomplete or

* Abbreviations used are: DHase, dehydrogenase assayed by NAD’ + Li~SH)*NH* or NADH + LipStNHz ; THase, transhy~o~ena~ assayed by NADH + TNAD’ ; ETase, electron transferase assayed by NADH + K,Fe(CN), ; DPase. diaphorase assayed by DCIP, 2,6-dichioroindophenol; NADH + DCIP; D.L-dihydroiipoamide; LipS,NH2, D,LLip(SH,)NH,, lipoamide; TNAD+, thionicotinamide adenine dinucieotide. 407

neglected. The present inv~tigation is an attempt aimed at bridging the gap. Kinetic studies were carried out by measuring initial rates over a wide range of substrate concentrations and analyzing product inhibitions. A kinetic mechanism common to all the reactions catalysed by pig heart lipoamide dehydrogenase is proposed. MATERIALS AND

METHODS

Materials Pig heart lipoamide dehydrogenase (3.3 x lo-’ Kat/mg) was purchased from Boehringer Mannheim Canada Ltd., St. Laurent, Quebec, Canada and Sigma Chemical Co. The enzyme was checked for purity by electrophoresis, spectrophotometry (Also/A 450 = 6.0 f 0.5) and atomic absorption for trace cupric ion prior to the use. Enzyme concentrations were determined at 455 nm using an extinction coefficient of 11.3 mM_’ cm-’ and calculated on the basis of FAD content. NAD’, NADH and D,L-lipoamide (LipS,NH2) were obtained from Sigma Chemical Co. Thionicotinam~de adenine dinucfeotide (TNAD+) was the product of P-L Biochemicais Inc. 2,6-Dichioroindophenoi (DCIP) was purchased from Fisher Chemical Comp. DJ_Dihydroiipoamide (Lip(SH),NH,) was prepared by reduction with NaBH., (Reed et al., 19.58). Sodium phosphate buffers at pH 7.5 were prepared as described (Gomori. 1955). Kinetic srudies Kinetic studies were carried out in a Perkin-Elmer spectrophotometer (Coleman model 124) equipped with a variable output recorder (Coiemen model 165) and a thermostat circulator maintained al 25 or 45 f O.S,‘C. All reagents were prepared in 0.050 M sodium- phosphate buffer, RH 7.5 containing 1.0 mM EDTA. The DHase reactions were studied in both directions. In the lipoamide reduction, concentrations of Lip&NH2 varied from 0.050 to l.OmM and NADH from 0.020 to 0.3mM. Reactions were initiated by the addition of 20 nM of the enzyme and initial rates were followed at 340nm. In the dihvdrolioo_ r amide oxidation, concentrations of Lip(SH),NH, range from 0.050 to 0.75 mM and NAD * from 0.025 to 0.75 mM. Rates of reactions were followed at 340nm immediately

C. S. TSAI

408

after adding 20nM of the enzyme. The THase reactions were studied at 395 nm of raction mixtures containing the enzyme (20 nM), NADH varied from 0.020 to 0.30 mM and TNAD+ from 0.025 to 0.75 mM. Initial rates of the ETase reactions were followed at 420 nm after adding 20 nM of the enzyme to mixtures containing NADH ranging from 0.010 to 0.30mM and KaFe(CN), from 0.050 to l.OmM. The DPase reactions were studied by following changes in absorbance at 600nm of raction mixtures containing the enzyme (20 nM), NADH varied from 0.010 to 0.30 mM and DCIP from 0.0050 to 0.10 mM. Initial rates were checked graphically prior to computer analyses. Experimental data in the linear (asymptotic) region were fitted to equation (I) for parallel reciprocal plots (ping-pong mechanism): VAB

nonlinear

(Figs 1 and 2). Similar observations previously (Visser et al., 1970). The

were

nonlinearity was also noted for the reaction catalyzed by the rat liver enzyme at a low temperature. However. linearization was reported to occur at an elevated temperature (Read, 1973). Such a temperature effect was not observed in this study with pig heart enzyme when kinetic measurements were carried out at 25 and 45’C. Figs 1 and 2 differ in that plots for NAD+ reduction are concave downward whereas those for NADH oxidation are concave upward. This kinetic behaviour is described by equation (5) for S = NAD+ or NADH at fixed concentrations of Lip(SH)2NH2 or Lip!&NH,. The condition. m = n > I. predicts the concave down or up cutves (Fig. I ) unless for a dead-

reported

(’ = AB + K,,A + K,B or equation mechanism):

(2) for converging

reciprocal

VAB (‘=-__ AB + KbA + K,B

plots (sequential

(2)

+ Ki,Kb

where V, K.. K, and K,. are maximum velocity. Michaelis constant for nicotinamide nucleotide (A). Michaelis constant for second substrate (B). and inhibition constant for nicotinamide nucleotide respectively according to Cleland’s nomenclature (Cleland. 1963a). The Fortran program described by Cleland (1967) was used for the primary fit while a Fortran program for the linear regression analysis in the secondary fit was written to process data and their standard errors of estimates provided by the primary fit. The calculations were performed by a Sigma IX computer. For experiments with fewer than four sets of 5 x 5 determinations, kinetic parameters were evaluated graphically. Inhibition studies in the presence of product were carried out in an identical manner. Experimental data corresponding to linear competitive inhibition or linear noncompetitive Inhibition were fitted to equation (3) or (4) respectively.

,24

[NAD+]-’

32

40

(~TJM-‘)

vs =G

+ I/K,,)

+ S lzo7

too

where K,, and Ki, are inhibition constants for the product, I which affects the slope or intercept of reciprocal plots of initial rates vs varymg substrate, S(A or B). The nonlinearity in reciprocal plots was analyzed for the n:m function according to equation (5) graphically (Bardsley & Childs. 1975).

60

7 5 E

60

.c E -; 40 > 20

0

where r’ and /j” are kinetic coefficients for the numerator and denominator terms associated with the varying substrate S(A or B) of ith degree respectively.

RESULTS

Initial

of DHase, by pig hydrogenase were carried out. plots for the DHase reaction in DPase

rate studies

reactions

catalysed

THase,

ETase

heart lipoamide Double

and

de-

reciprocal

both directions

are

6

16

32

24 -I

40

(B)

(mM_‘)

Fig. I. Initial rates of dehydrogenase reaction. NAD+ + Lip(SH)ZNHZ at pH 7.5 and 25 C. (A) NADf was varied at fixed concentrations of Lip(SHbNH2 at 0.025, 0.050. 0.10.0.20, 0.25, 0.50 and 0.75 mM. Inset shows r[NAD+] vs [NAD’] at [Lip(SH),NH,] = 0.050 mM where i = m-u of equation (5) (B) Lip(SH)2NHZ was varied at fixed concentrations of NAD’ at 0.025. 0.040. 0.050, 0.10. 0.25. 0.50 and 0.75 mM

Multifunctionality

(A)

o

I

&

mechanisms; ping-pong for [NAD+] < 0.10 mM and sequential for [NAD*] > O.lOmM. Figures 3,4 and 5 show double reciprocal plots for THase, ETase, and DPase reactions catalyzed by lipoamide dehydrogenase. All plots are nonlinear except those for the ETase reaction with NADH as the varied substrate. The concavity of these plots arises from m:n function of equation (5) where m = 11> I. Fitting of experimental data in the linear (asymptotic) region by least squares indicates that the THase reaction proceeds via a ping-pong mechanism (parallel lines) while the ETase and DPase reactions follow the sequential mechanism ~Con~~ergiIlg lines). Kinetic parameters from the initial rate studies in the asymptotic region are given in Table I. The NAD’linked L~P(SH)~NH~ oxidation was analyzed on the basis of two kinetic mechanisms in the two NAD’ concentration regions; ping-pong for NAD’ < 0.10 mM and sequential for NAD’ > O.lOmM. An analogous approach has been adopted by Staal & Veeger (1969) in the analysis of glutathione reductase catalysed reaction. The catalytic efficiency (V/Et) and Michaelis constants agree reasonably well with the reported values (Massey, 1963). A lower catalytic effciency for the DHase reaction may arise from a slight inactivation of the sample.

I

30

40

50

Cm M-l)

[NA;i]-’

409

of lipoamide dehydrogenase

60

-i

z .c E

-i >

60

(B1

I

L

reaction. of dehydrogenase Fig. 2. Initial rates NADH + LipS2NH2 at pH 7.5 and 2.5 C. (A) NADH was varied at fixed concentrations of LipSzNHz at 0.10. 0.15. 0.20, 0.50 and 1.0 mM. Inset shows e[NADH]’ vs [NADH] at [LipS*NH,] = OSOmM where i. = m-n of equation (5). (B) Lip&NH2 was varied at fixed concentrations of NADH at 0.020. 0.030, 0.040. 0.060 and 0.10 mM. The competitive inhibition of NADH at 0.20 and 0.30 mM was also shown in closed circles.

20

40

60

[NADH]-’

60

100

CAM-‘)

60

end substrate curves with

inhibition

when

m > II. concave

up

lim ! = x W-0 1 are expected (Tsai, 1978). The diagnostic test of Bardsky & Childs (1975) agrees with m = n > I, i.e. a random and/or alternative pathways for the NAD’ reduction (Fig. I inset) and m > n. i.e. the formation of the dead-end NADHcomplex for the NADH oxidation (Fig 2 inset). Fitting of the all experimental data (APLGRAF, Carleton University Computer Library) suggests that the concave down curves of Fig. I are best described by two sets of straight lines representing two kinetic

01

IO

1

20

[ TNAD+]-’

30

J

40

CAM-‘)

Fig. 3. Initial rates of transhydrogenase reaction, NADH + TNAD’ at pH 7.5 and 75 C. (A) NADH was varied at fixed concentrations of TNAD’ at 0.025. 0.10 and 0.25 mM. (B) TNAD+ was varied at tixed concentrations of NADH at O.OfO. 0.020. 0.030. 0.040 and O.lOmM.

410

C. S. TSAI

pattern with respect to NADH and Lip&NH,. At high concentrations, NAD+ inhibition vs Lip$NH, was noncompetitive. A transition occurs at O.lOmM NAD+ in agreement with the initial rate studies (Fig. 1). The noncompetitive inhibitions were observed for Lip(SH),NH, with respect to NADH and Lip&NH,. These inhibition patterns are not describable by the known simple bisubstrate reaction mechanisms (Cleland, 1963b) impliciting the operation of alternative mechansism(s). For THase. NAD+ inhibition was noncompetitive with respect to NADH but competitive with respect to TNAD+ in agreement with the ping-pong mechanism. The inhibition patterns of the ETase reaction for NAD+ vs NADH and K,Fe(CN), were noncompetitive, whereas K,Fe(CN), was competitive vs NADH but noncompetitive vs K,Fe(CN), suggesting a random

_y 100 I E .E 60 r i > 60

40

[NADH]-’

‘4001

( mM_’ 1

0’

or

L

I

4

6

12

16

I

20

I

40 [NADH]-’

I

Fzkvl

I

,“”

I loo

I

20

Fig. 4. Initial rates of electron transferase reaction, NADH + K3Fe(CN), at pH 7.5 and 25°C. (A) NADH was varied at fixed concentrations of K,Fe(CN)6 at 0.050. 0.10, 0.15, 0.20 and 0.50 mM. (B) KaFe(CN), was varied at fixed concentrations of NADH at 0.10, 0.020, 0.040, 0.060. 0.10, 0.20 and 0.30 mM.

Kinetic studies in the presence ful techniques for differentiating

of products are usevarious mechanisms in enzymic reactions. To establish the kinetic mechanisms which operate in the asymptotic region, product inhibitions were carried out within the region. Product inhibition constants are summarized in Table 2. For the DHase reaction, NADH inhibited Lip(SHbNH, oxidation competitively with respect to NAD+ and Lip(SH)*NH2 at [NADH] < O.lOmM. However at [NADH] > O.lOmM, the inhibition noncompetitive with respect to pattern was Lip(SH),NH, due to the formation of the dead-end NADH-complex. LipS,NH2 inhibition was competitive vs NAD+ and noncompetitive vs Lip(SHbNH,. In the NADH-linked LipS2NH2 reduction, NAD+ at low concentrations produces competitive inhibition

OY

[DICHLOROINDOPHENOL]-’ (mM_‘)

diaphorase reaction, Fig. 5. Initial rates of NADH + DCIP at pH 7.5 and 25’C. (A) NADH was varied at fixed concentrations of DCIP at 0.0050. 0.010. 0.015. 0.020 and 0.050 mM. (B) DCIP was was varied at fixed concentrations of NADH at 0.010. 0.020. 0.040 and 0.10 mM.

Multifunctionality Table

1. Kinetic

parameters

for reactions

of lipoamide

411

dehydrogenase

by pig heart lipoamide dehydrogenase

catalysed

at pH 7.5

Temp Reactions

(“C)

(FM tk

‘)

DHase:NAD+

+ Lip(SH)2NH,

25” 45” 2Sb 45b

21) 266 738 813

DHase:NADH

+ Lip&NH,

25 45

356 359

THase:NADH

+ TNAD’

25 45

379 564

ETasc: NADH

+ K,Fe(CN),

25 45

277 519

DPase:NADH

+ DCIP

25 45

117 150 705 703

Studies of Massey et al. (1960) have shown that the DHase reaction catalysed by pig heart lipoamide dehydrogenase proceeds via a ping-pong mechanism. The same conclusion was reached for the rat liver enzyme, though a number of product inhibition patterns disagreed with the predicted mechanism unless dead-end inhibitions were assumed (Reed, 1973). The observation that NAD+ binds to the oxidized lipoamide dehydrogenase (Su & Wilson, 1971) suggests a possible involvement of the sequential mechanism.

Table 2. Product inhibition constants for lipoamide

DHase

NADH

893 1003

0 0

17.8 X IO3 18.0 x IO3

183 285

263 444

0 0

19.0 x lo3 28.2 X lo3

177 328

495 685

27.5 25.1

2.77 x IO’ 5.19 x lo3

33.6 34.7

Varied substrate

Kii (PM)

NAD+ Lip(SH),NH, NAD+ Lip(SH),NH,

NAD+

_a

739

dehydrogenase

&) 24. I 16.8

Kii @M)

_a

17.7 13.2

7.77b 170 330

565

202 438

235 _

53.0 84.2

119

121 107

333 75.3

734 639

357 184

371 533

1920

563 758

164 1390

202

243 711

4.06 66.0

161“ NADH TNAD+

ETase

NAD+

NADH FaFe(CN),

384 1150

K.+Fe(CN),

NADH KaFe(CN),

2740

NADH DCIP

344

Kii and Ki, are inhibition [NADH] < 0.10 mM; b, [NAD+] > 0.10 mM.

constants [NADH]

lo3 lo3 lo3 IO-’

1.86 x lo3 2.72 x 10’

reactions

_c

NAD+

NAD+

catalysed

NADH Lip&NH,

THasc

DPase

5.49 7.11

x X x x

consisting of, at least, four sets of 5 x 5 experimental < O.lOmM and b, [NAD+] > O.lOmM which were

7.92b Lip&NH,

127 128

10.6 13.3 36.9 40.7

The work of Visser et al. (1970) implicated the operation of an ordered BiBi mechanism. Nonlinear double reciprocal plots observed in the previous reports and present study further indicate the complexity of the kinetic mechanism. A similar situation was reported for other flavoenzymes (Staal & Veeger, 1969; Mannervik, 1973). Double reciprocal plots are nonlinear for initial rates vs NADf in the DHase reaction; NADH in the DHase, THase and DPase reactions as well as second substrates in the THase, ETase and DPase reactions. The nonlinearity of NADH in the DHase and THase reactions is derived from the n:m (m = n + 1) function, however all the others arise from the n:n (n > 1) function of equation (5). The former indicates the formation of the dead-end NADH-complex while the

DISCUSSION

Product inhibitor

0 0 73.5 67.3

37.7 54.4

pathway. NAD+ inhibited DPase competitively with respect to NADH but noncompetitively with respect to DClP in agreement with the ordered BiBi mechanism.

Reaction

355 421 827 951

59.5 62.0

Kinetic parameters were calculated from the asymptotic regions pomts except the reaction, NAD+ -t Lip(SH)*NH, in a, [NAD+] based on four sets of 4 x 4 data points. Error range = 515%.

VIE, (min-‘)

(k)

_ _

for intercept > O.lOmM;

_c

3.66 I06

49.7*

effect and slope effect respectively. c, [NAD+] < O.lOmM and

a, d,

412

c. s

rSAl

latter implicates the likely contributions of multipathways (Bardsley & Childs. 1975; Tsai, 1978). The deadend NADH complex has been demonstrated spectrophotometrically. The unified mechanism (mixed random Pine-Pone mechanism with dead-end NADH complexes) wh;h agrees with kinetic behaviours of multifunction reactions and consistent with chemical principles, is depicted in the Scheme I.

is equal to, smaller than or larger than (n,,B + II&,>B2+ il,rh,83)2(d,1 + d,>,B + d,*h1B2) + (n,>,B + no,~,lB2)2(dbB + d,>B2 + d,,B3).

c

Similarly, the plots of ~1~ I vs Be ’ are linear, concave up- or downward depending on whether

is equal to, smaller than or larger than (II&, A)2(d,A + d,>A2). At low substrate concentrations in the asymptotic mechanisms; ping-pong region, simple bisubstrate and ordered BiBi, prevail depending on the distribution of EA. Whereas in the concave region at high substrate concentrations, contribution from the alternative pathways becomes important. The ping-pong mechanism is evidenced by the spectroscopic demonstation of F, initial rate studies of DHase and THase reactions (Ki, = 0) as well as product inhibitions of LipS2NH2 on the DHase reaction and NAD+ on the THase oxidation of TNAD+. The ordered BiBi mechanism with NADH as the leading substrate is indicated by the converging double reciprocal plots for the DHase reaction at [NAD’] > 0.1 mM, the ETase and DPase reactions. This mechanism, furthermore. agrees with the product inhibition studies of NADH. Lip(SH)2NH2 on the DHase reaction and NADH on the DPase reaction. The contribution of steady-state random mechanism is substantiated by the following observations: (a) nonlinear reciprocal plots with respect to nicotinamide nucleotides and/or the second substrate for all reactions, (b) interactions of the oxidized enzyme with both NAD+ and Lip(SH)2NH2 and (c) constraint by the concept of microscopic reversibility for the reverse order of substrate addition vs product release indicated by the product inhibition studies of the ETase reaction. Furthermore, the competitive NAD+ patterns observed for inhibition ([NAD+] < O.lOmM) vs NADH and Lip&NH,, NADH ([NADH] < O.lOmM) vs NAD+ and Lip(SH),NH, in the DHase reaction can only be accommodated by the random mechanism.

Scheme I. Proposed kinetic mechanism for multifunctional reactions catalyzed by pig heart lipoamide dehydrogenase. E, F, A. B, P and Q are enzyme (oxidized), enzyme (reduced) intermediate. NADH, oxidized substrate, reduced substrate and NAD+ respectively.

where, E, F. A. B, P and Q are the oxidized enzyme. the reduced enzyme intermediate, NADH. oxidized substrate, reduced substrate and NAD’ respectively. It must be emphasized that not all of the pathways are followed by any given reaction. However the mechanism represents a summary of all the observable pathways. The existence of most of the intermediates, F, EA(FQ). FQB(EAB ti EPQ), EP(FB) and EQ has been demonstrated (Massey, 1963; Williams, 1976). The steady-state rate equation for the mixed random Ping-Pong mechanism (Scheme 1 without FA) in the absence of products (P, Q = 0) was derived according to Fromm’s procedure (Fromm, 1970).

c =

(n,,AB

___~~ &A

+

43

+

&,AB

+

&,A2

+

dts,B2 + d,+A2B

where n,i and dxi are kinetic coefficients for numerator and denominator terms respectively associated with substrate x(A or B) of the ith degree (Tsai, 1978). Equation (6) is 2:2 function in A and 3:3 function in B according to equation (5). It predicts that the plots of 1.-’ vs A-’ are linear, concave up- or downward depending on whether (n,B

+ ndIB2 + ntiJB3)&,B x (d, + d,B

1

2

+ noLbA2B + nab3AB + nalb,A2B2 + n,,,AB3)Et

+ n,+,B’) + d,>B2 + dd,B3)

+ d,,,,,AB’ + db,B3 + dazb,A2B2 + d,,,AB3

(@

At high concentrations, NADH inhibits DHase and THase by interacting with the reduced enzyme intermediate to form the dead-end complex, FA. This is implicated by that (a) the substrate inhibition occurs only in the ping-pong mechanism, i.e. NADH-linked reductions of LipS2NH2 and TNAD+, and (b) the inhibition is competitive with respect to LipS2NH2 (Fig 2B) and TNAD’. The ability of NADH to interact with both E and F affects the denominator of equation (6) in A2 and A2B terms as well as an additional A3 term. This gives rise to the 2:3 function in

Multifunctionality ,4 according ([LipS2NHJ’

to equation (5). Slopes of 13-I vs B-’ or [TNAD’]-I) have the form: dl%-

’

I

dB-’

k,,Et

A +

iL;,k,Et

which can be estimated from the replot of slopes (dt,-‘/dB-‘) vs A. K, values for the DHase and THase reactions are 0.090 and 0.19 mM respectively accounting for the observed inhibitions at [NADH] in excess of 0.10 and 0.20 mM respectively. The operation of alternative mechanisms is disNAD+-linked oxidation of the played by Lip(SH)2NHZ. At low NAD’ concentrations ([N.AD+] c O.lOmM) when klOkZ, g klBkz2Q and k,, + k,,Q, the ping-pong mechanism of the Scheme 1 prevails. However at high NAD+ concentrations ([NAD+] > O.lOmM) when

where k, = k14/k13

kllk,cjQ

ti

(42 + k,s)(k,4 + hd

the ordered BiBi mechanism is favored. Similar concluslon was reported for glutathione reductase (Staal & L’eeger. 1969). Although additional studies are needed to substantiate its validity. the proposed kinetic scheme (Scheme 1) bridges the seemingly conflicting earlier results on the dehydrogenase reaction and provides the kinetic basis for further investiations on the catalytic diversity of flavoenzymes. All of the alternative pathways need not to be followed at one time for any given reaction. The operative mechanism for a given reaction depends on the fluxes of the reactants through the competing pathways (Britten, 1966). A slow conversion of E to F. i.e. k, k5 A/(k,

+ k, + k, B)

< k, k, AB/(kl + k,k,

AB(k,,

+ k, A)

+ k5 + k, B) P k3k,

A faht conversion k, ks A/(k,

+ kg A).

+ k, + k7 B)

9 k,k,AB/(kz

+ k, + k,B) + k, A)

channels anism.

ABl(k4

of E to F riu EA. i.e

+ k,k,

ABl(k,

the reactants

through

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+ k5 + k, B)

favors the flux of reactants through the random mechanism which becomes the ordered BiBi mechansim if k, k, ABl(k2

413

of lipoamide dehydrogenase

the ping-pong

mech-

.4~~no~~lrt/grm~,Irs This work was supported by a grant from the National Sciences and Engineering Research Council of Canada. The author acknowledges the computational assistance of Mr. A. Gullen.

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