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Kinetics of the lactate dehydrogenase reaction in high-viscosity media
Biochimica et Biophysica .4cta, 998 (1989) 196-203 Elsevier
196
BBAPRO33~5
Kinetics of the lactate dehydrogenase reaction in high-viscosity media Alexander P. Demchenko 1, Oksana I. Rusyn 1 and Ekaterina A. Saburova 2 l The.4. V. Palladin Institute of Biochemistry of the Ukrainian S.S.R. Academy of Sciences, Kieo (U.S.S.R.) and 2 The Institute of Biological Physics of the U.S.S.R. Academy of Sciences, Pushchino, Moscow Region (U.S.S.R.)
(Received 29 May 1989)
Key words: Lactate dehydrogenase; Viscosity; Enzyme kinetics; Protein dynamics
The effect of the medium viscosity on kinetics parameters of lactate dehydrogenase reaction was studied. The viscosity increase results in a sharp decline in the catalytic rate for ~ ath the pyruvate reduction and lactate oxidation reactions. It is shown that the catalytic step and its associated confm~afional motions is the only step which is considerably retarded when the viscosity increases. The reaction is not ~ns~.tive to changes in the dielectric properties of the medium. An inverse power function observed between the rate constant and viscosity cannot be explained by the theory of absolute reaction rates. However, it can easily be interpreted o~ the basis of the Kramers theory dealing with the transition over the activation barrier as a diffusional motion in the field of random forces. The influence of the mediums viscosity on the kinetic parameters indicates the existence of strong coupling between the dynamics of the solvent and the conformational motions of the protein molecule, which are correlated with the catalytic step.
Introduction
Despite the long-term efforts, the subject of the mechanisms of action of enzymes is still far from being understood. We are still unable to predict the rate and the way of regulation of the catalytic reaction on the basis of structural information about proteins, even at the atomic level of resolution. Apart from the structure of the ground state of the enzyme-substrate complex, the mechanisn:~ of the activation steps and the nature of the activated (transition) states and sub-states have to be known as well. There are many theories attempting to explain the physical mechanisms of enzymic catalysis [1-4], and, despite the basic differences between them, they have the common point of postulating the role of protein structure beyond the catalytic centre and correlating protein dynamics with the catalytic steps. Further progress requires application of new experimental approaches for the analysis of protein dynamics associated with the catalytic function. Along this line, it was proposed recently to make use of the medium's viscosity as an independent variable to study protein dynamics [5-7]. The critical point is that the absolute-
Correspondence: A.P. Demchenko, A.V. Palladin Institute of Biochemistry, Ukrainian S.S.R. Academy of Sciences, Kiev 252030, U.S.SoR.
rate theory (the theory of activated complex) [8] which neglects the effect of medium (and its dynamics) on the reaction rate, and is unable to interpret the recently obtained data showing that the catalytic rate constants for carboxypeptidase [6] and myosin ATPase [9] considerably decline with the increase of solvent viscosity. Viscosity dependence was also observed for a non-enzymic activation process - the reassociation of myoglobin with ligands following the photodissociation caused by a laser flash [5]. But such a dependence was not observed for enzyme kinetics of chymotrypsin [10]. The alternative Kramers theory [11], regarding the process of transition over the activational barrier as a diffusional motion within a field of random forces, was used to interpret these data. The question of generality of the observed viscosity effects and the applicability of the Kramers theory to enzymic processes still remains unclear. The present study deals with the viscosity effects on the ~dnetic parameters of lactate dehydrogenase. Viscosity was changed by addition of different cosolvents such as glycerol, sucrose and other monomeric and polymeric viscogenes and the reaction was followed in both the forward and reversed directions. Unlike the previously studied hydrolytic reactions [6,9,10], this reaction occurs within the enzyme matrix, totally shielded from the aqueous solvent. The complex mechanism of regulation makes it possible to investigate the influence of viscous
0167-4838/89/$03.50 © 1989 Elsevier Science Publishers B.V. (Biomedical Division)
197 environment on the inhibition and formation of nonproductive complexes. For the first time it is shown for redox reactions that the catalytic reaction rate constant critically depends on the medium's viscosity and that it can be accounted for by the Kramers theory. Materials and Methods
Lactate dehydrogenase ((S)-lactate:NAD + oxidoreductase, EC 1.1.1.27) was isolated from pig skeletal muscles (M4 isoform) using the method of Jecsai [12], involving fractional salting out, and 4-fold recrystaUization in an ammonium sulfate solution. Additional purification was performed by an ion-exchange chromatography column with DEAE-Sephadex A-50 (Pharmacia) [13]. The preparation was homogeneous according to the usual electrophoretic criteria. The specific activity was 320/~M NADH rain -1 at pH 6.2 and 25 ° C. The steady-state reaction kinetics were recorded at 340 nm (absorption band of NADH) using Specord UV-VIS spectrophotometer (Carl Zeiss) in a thermostated call at 25°C. The initial rate was determined irom the inclination of the tangent line with respect to the initial portion of the kinetic curve, recorded during the first 30 s. The reactio~ was started by introducing a small amount of enzyme stock solution into the medium containing coenzyme, substrate and viscogeneous cosolvent in 0.1 M phosphate buffer. When studying the reduction of pyruvate, the ptl was kept at 6.2, and the N A D H concentration was 2-10 - 4 M. During investigation of lactate oxidation pH was 9.5 and NAD + concentration was 4 mM. These pH values were chosen in order to avoid the strong pH-dependence of the reaction due to histidine group protonation with pK 7.6. The enzyme concentration was 1/~g/ml. Circular dichroism spectra were recorded by a dichrograph Jasco M-40 (Japan). Protein concentration was 1 mg/ml. The lactate dehydrogenase concentration was determined spectrophotometricaUy, using the known absorption factor ~280nm/;' mg/ml 1 = 1.29. The kinetic parameters (Vmax and Km) were found using the Hanes transformation ([S]/V vs. [S] relationship) [14] with the aid of the least-square method. The viscosity values for solutions of glycerol, sucrose and alcohols were taken from Ref. 15. Viscosities of all the other solutions were measured experimentally using a thermostatted glass capillary viscometer (the capillary diameter was 0.73 mm). Results
In our experiments the sucrose concentration varied from 0 to 44% (w/w), while that of glycerol varied from 0 to 63% (w/w), which results in the variation of viscosity from 0.89 to 7.1 cP and to 10.2 cP, respectively. Under these conditions the reaction rate decreases by an order of magnitude. Fig. I shows the relationship between the initial reaction rate (V) and the pyruvate concentration at excess of NADH for various sucrose and glycerol concentrations. The results presented in Fig. 1 were obtained for the reaction of pyruvate reduction in the presence of 0.5 M KCI. These conditions were chosen since it is known that C1-eliminates the substrate inhibition appearing at high substrate concentrations [16]. Similar results (considerable deceleration of the reaction rate resulting from the addition of glycerol and sucrose) were also obtained in the absence of KCL In the latter case, the reaction in the v~scous i~ediurn re~tains the characteristic feature of substrate inhibition, i.e., the decline of the V vs. [S] relationship at high (> 2 mM) pyruvate concentrations. Ethylene glycol (30 and 50% (w/w)) was also used to vary viscosity in the solution. For the reaction of pyruvate reduction the maximal rate Vma~decreased from 3.26 relative units in buffer (viscosity 7/= 0.89 cP) down to 2.26 relative units in a 3070 solution (?/= 1.84 cP) and 1.32 relative units in a 5070 solution (T/= 3.13 cP) of ethylene glycol.
A
3.
I
® . = ~
®
,SS':
o I
~ 0 / 0
x ~r6
~^Jx ~ x 0 ~---
El
.7
I
2
[sl (raM)
3
x 8
4
5
B +
2 5 0 >
C
0
I I
I 2
I 3
I 4
I 5
Is] (raM)
Kinetics of the lactate dehydrogenase reaction in highviscosity media In the studies of the rate of the lactate dehydrogenase reaction as a function of sucrose or glycerol concentration, a sharp monotonous decline is observed.
Fig. 1. Initial rate, V, of pyruvate reduction as a function cf substrate concentration [S] in 0.5 M KCI solutions at different concentrations of glycerol (A) and sucrose (B). For glycerol: 1, control: 2, 17%; 3, 25%; 4, 33%; 5, 41%; 6, 48%; 7, 55%; and 8, 63%. For sucrose, 1 control; 2, 8.6%; 3, 17%; 4, 24%; 5, 31%; 6, 37%, and 7, 43%.
198 A
~liB
~.(nm)
22o
23o
24o
2so
?.60 -
270
~
280
~.(nrn) 290
300
310
320
~
/
Fig. 2. Circular dichroism spectrum of lactate dehydrogenase in 0.1 M phosphate buffer and in 30~ sucrose solution, pH 6.2. (A) 210-240 nm region; (B) 250-300 nm region.
A substantial reduction of the reaction rate with the increase of viscogen concentration is also observed for the reverse reaction of lactate oxidation when NAD + is the cofactor. The ma.umal rate, Vm=,, decreases from 8.5 relative units in buffer to 1.5 units in 44% sucrose and 1.3 units in 63% glycerol. Similarity of ~he observed effects caused by different viscous cosolvents (sucrose, glycerol, ethylene glycol) and the absence of any correlation with other solvent properties (hydrophobicity, dielectric constant) suggests that it is the viscosity that was the common property of the solvents, which is responsible for this phenomenon. The reduction of the reaction rate in the glycerol, sucrose and ethylene glycol solutions cannot be accounted for by irreversible enzyme inactivation (the activity remains unchanged during several hours of incubation at the maximum concentrations of these cosolvents). The effect is completely reversible: when the viscous solvent is diluted with aqueous buffer during the kinetic run, the sharply increased rate of the reaction is observed.
buffer in a 30% sucrose solution. This indicates that the cosolvents in question do not induce any substantial change in the a-helical content of protein (210-240 nm region, and in the environment of tryptophan residues (250-300 nm region). Some finer structural changes in the enzyme, influencing the transitions between the sub-states involved in the catalytic process, cannot be ruled out. However, as it will be shown below, the addition of concentrated solutions of sucrose and glycerol does not change the regulatory properties of the enzyme: formation of inhibitory complexes with substrate and inhibition by anions. For the redox reaction of charge transfer it is possible that the solvent affects the catalytic rate by modifying the dielectric character of the environment, as it was described for hydrolytic enzymes [21]. Taking into account such a possibility, the effects of special watercosolvent mixtures with low dielectric constant (e) (30% mixtures of methanol, ethanol and dioxane with water) were studied as well. The data obtained do not reveal an appreciable effect of ( on the kinetics of the lactate
Possible cosolvent effects on the catalytic rate
The possibility of the effect of dissociation of lactate dehydrogenase tetrameric molecule into subunits in the presence of viscogenic cosolvents can be easily ruled out. The rotational relaxation time of molecule, recorded by the fluorescence depolarization technique is unchanged in concentrated glycerol solutions [17]. Besides, as follows from kinetic experiments [18,19], the studies of hybridization of M- and H-isoenzymes [16] and examination of the activity of immobilized subunits [20], the lactate dehydrogenase subunits are independent and kinetically identical. The question arises whether there is any reversible conformational change in response to the addition of the viscogenic agents. As is shown in Fig. 2, the circular dichroism spectrum is identical to that in the aqueous
TABLE I Kinetic constants Vm, x and K,n for lactate dehydrogenase reaction as functions of solvent dielectric constant E Solvent
Water Glycerol (30~) Ethylene glycol
e a
1] b
limax
Km
(cP)
(relative units)
(mM)
78 70 69.8
0.89 2.16 1.84
2.96 + 0.13 1.96+0.05 2.26 + 0.10
0.19 ± 0.03 0.10+0.01 0.15 ± 0.05
58 52
2.18 1.6 c
2.25 + 0.14 2.74 + 0.39
0.18 + 0.04 0.20 + 0.06
(30~) Ethanol (30%) Dioxane (30~)
a Ref. 22. b Ref. 15. c Measured by viscometer.
199 dehydrogenase reaction (Table I). This corroborates the fact known from X-ray crystallographic data [23,24] that in this catalytic process the charge transfer occurs within the hydrophobic cavity inaccessible to the solvent, and the dielectric screening of the surface charged group should exert no effect on the catalytic rate. A number of polyhydroxylic substances, including sucrose and glycerol, are known to stabiliTe the native conformation of proteins in aqueous solutions [25-28]. The addition of sucrose increases stability of lactate dehydrogenase toward thermal denaturation [29]. This may be due to prevaifing hydration of protein in a mixed solvent and exclusion of organic cosolvent from the hydration !~er. Such a stabilizing effect may create an addition~ tension in the native protein globule, which i s likely to cause its decreased mobility. It is difficult to distinguish this effect, if it contributes to the catalysis, from the solvent viscosity effect. However, for a series of cosolvents (sucrose, glycerol, ethylene glycol, etc.) the magnitude of the protein-stabilizing effect does not correlate with the viscosity [25]. Therefore, this effect is unable to explain the influence of viscogenic cosolvent on the catalytic rate which we observed.
The effect of viscosity on different steps of the lactate dehydrogenase reaction. The general mechanism of the lactate dehydrogenase reaction includes substrate inhibition and formation of non-productive enzyme-substrate complexes [16,30]. The binding of substrates is sequential: the binding of N,~DH proceedes that of pyruvate. The formation of the ternary E-NADH-pyruvate complex is accompanied by conformational rearrangements of the protein. Anions of neutral salts, in particular C1- ions, are specific regulators of the lactate dehydrogenase reaction [30,31]. Depending on the conditions CI- may act either as an inhibitor or activator. At small substrate concentrations ([S] Km), when the ternary non-productive E-NAD+pyruvate complex is formed, CI- displaces substrate from this complex, in this way resulting in activation of the reaction [30]. We have studied viscosity effects on formation of enzyme-substrate complex, inhibitory binding of anions and elimination by anions of substrate inhibition. The change of the Michaelis constant (Kin) was studied at increasing concentrations of sucrose (up to 44~ (w/w)) and glycerol (up to 63~ (w/w)). A 5-fold decrease in K m was observed from 0.1 to 0.02 mM for pyruvate reduction and from 20 to 2-5 mM for lactate oxidation. Regarding the reaction of the pyruvate rec~uction, the plots of the reaction rate against the pyruvate concentration in the presence of inhibitor (0.5 M KCI) were
2.0 D
1
-.I
d >
1.0
o o
I
I
I
I
04
08
:2
~6
CI
1.O
0.5
_J
-15I
,og 1.o
-05
'
0.5 Fig. 3. Initial reaction rate of pyruvate reduction as a function of KCI concentration (A) and same function in the Hill coordinates (B). 1, control; 2, 40% sucrose; 3, 50~ glycerol. Pyruvate concentration, 20 mM.
used to obtain the apparent Michaelis constant (Km.app). At high concentrations of sucrose and glycerol we observed a similar decrease of this parameter. Having the Kfm values from separate experiments and calculating Kmapp,this way one can obtain K l, the dissociation constant of the inhibitor, from the equation
[3o1: Km,app ffi Km~l -t- [|] '~
(1)
where [I] is the inhibitor concentration. In 40% sucrose and 50% glycerol the value for K~ are 0.09 + 0.03 M, which does not differ significantly from the reference value 0.1 + 0.02 M in the aqueous buffer. This shows that the presence of sucrose or glycerol produces virtually no effect on the binding of anions in the enzyme active centre. The effect of C1- concentration on reaction rate at inhibitory pyruvate concentration (Fig. 3) demonstrates that these ions increase the initial rate of the reaction by 2-2.5-times irrespectively of the presence of viscogenic cosolvent.
200 The dissociation constant of C I - in the ternary nonproductive complex is found from the previously suggested equation [27] for the stationary rate in the Hill coordinates: I VlAl-.oo--_~+lgV[Ai--oo = lg[A]-lg KA g U --/)[A] ---,oo
UIA] ---.0
5 ~
~
+(o3
.
,
(2) r.
'
_
where VIAl-.0 and VtA l _. ~ are rates at zero and saturating anion concentrations [A]. A plot constructed in these coordinates is identical with and without viscous cosolvents. The obtained K A ( C I - ) values for buffer, 4070 sucrose and 5070 glycerol were 0.19 _+ 0.05, 0.19 + 0.05 and 0.16 + 0.05, respectively. Thus, the most pronounced viscogenic cosolvent effects are observed at the catalytic steps. Judging from the reduced value of K m, there also occurs a certain strengthening of the enzyme-substrate complexes, while the remaining steps, including the processes of competitive inhibition by C I - and the decay of non-productive enzyme-substrate complex do not appear to experience any effect of viscosity. All components of the catalytic lactate dehydrogenase mechanism and its regulation are retained in viscous medium.
~
~
3
2.
~ 0
I 1 I n r/ ( c P )
I 2
Fig. 4. Rate constant, kcat, for pyruvate reduction reaction in sucrose and glycerol solutions as a function of solvent viscosity 7, plotted in the double logarithmic coordinates. 1: sucrose (0-44%), pyruvate, 0.02-2 raM, 8 = 0.74:t:0.08; 2: sucrose (0-44%), 0.5 M KCI, pyruvate 0.2-5 raM, 8 -- 0,67 -+0.04. 3: Glycerol (0-63%), pyruvate 0.02-2 mM, 8 -- 0.98+0.04. 4: glycerol (0-63%), 0.5 M KCI, pyruvate 0.2-5 raM, 8 =1.13_+0.05. 6-
Reaction rate constant as a function o f m e d i u m viscosity
We have observed that the reaction rate constant, in all cases shows a clear-cut reverse power relationship to the medium viscosity, T/. If the activational character of the reaction is taken into account, the reaction rate constant can be presented in a form: kca t (keatS--gmax//[E]),
k,:.t = A. 7 -+ e E-/kr
4
I 0
I I 1 2 in 17cop) Fig. 5. Rate constant, K~,, for pyruvate reduction reaction in alCohols solutions as a function of solvent viscosity, 7, plotted in the double logarithmic coordinates, o, methanol (0%, 10%, 30%); <>, ethanol (0%, 10%, 30%); +, ethylene glycol (0%, 30%, 50%); pyruvate 0.02-2 mM, 8 = 0.74-+0.14.
(3)
where k T is the product of the Boltzmann constant and the absolute temperature, E a is the activation energy, and A and 8 are the empirical coefficients. By using double logarithmic plots, we obtain the straight lines of functions In k~at vs. In ~ from the slopes of which the parameter 8 can be obtained. In the case of pyruvate reduction (see Fig. 4), the ~t value is approx. 0.7 in the case of sucrose and it is close to 0.9 for glycerol. N o significant difference is observed between its values with and without 0.5 M KC1. Similar 8 values are observed with methanol, ethanol and ethylene glycol (Fig. 5). Several polymeric cosolvents (polyacrylamide, polyvinyl alcohol and poly(ethylene glycol)s) were also tested as viscogenic agents. We have observed similar but qualitatively smaller effects in terms of viscosity (Fig. 6). The influence of polymeric cosolvents on the catalytic rate is expected to be complex, and requires special investigation, with allowance for the excluded volume, hydration and other effects being taken into account. Besides, in this case, microscopic and macroscopic
viscosities may deviate significantly, and this does not allow to compare quantitatively the results with the data on other viscogens. Qualitatively, however, the results obtained on polymeric cosolvents are also in favour of the postulated general solvent viscosity effect. Interestingly, that for the reaction of lactate oxidation (Fig. 7), the function ha kcat vs. In +7, is similar to
A "7 01
O
~5
#¢&
e-
4
I 0
I 1 In !?(cP)
I 2
Fig. 6. Rate constant, Kcat, for pyruvate reduction reaction in polymers solutions as a function of solvent viscosity, 7, plotted in the double logarithmic coordinates, o, control; +, poly(ethylene glycol), Mr 600 (105[), m, polyvinyl alcohol (1%), ~t, poly(ethylene glycol) M, 6000 (10%), A, poly(ethylene glycol), Mr 6000 (11%), ×, polyacrylamide (0,16%), pyruvate 0.02-2 mM, 8 = 0.38 +0.15.
201 fluence the Michaelis constant (K m = (K_I + k 2 ) / k l ) . Under certain conditions (when k_ 1 >> k2), k a can be calculated as:
L3
k a = kca t / K m
,,e e-
(6)
-2
1
t 0
I 1 In 7/ (cP)
I
2
Fig. 7. Rate constant, Kcat, for lactate oxidation reaction in sucrose
and glycerol solutions as a function of solvent viscosity, 17, plotted in the double logarithmic coordinates. 1, sucrose (0-44~), 8 = 0.80+ 0.04; 2, glycerol (0-63~), 8 = 0.77+0.04, lactate 1-100 raM.
that of pyruvate reduction reaction with 8 = 0.8 for both glycerol and sucrose used as viscogenic cosolvents. Discussion The effect of viscogenic cosolvents on biocatalytic reactions The simple explanation of viscosity effects in terms of the slowdown in diffusion of substrates in viscous media does not correspond t.o our data. At saturating substrate concentrations its diffusion should not influence the reaction rate. In more general case, if the reaction depends both on the chemical steps and diffusion, its rate constant can take the following form [32]: 1/Ka = 1/kD + 1/Kc '
(4)
where k a ( i n c m 3- s - 1 ) is the experimentally observed bimolecular rate constant; kc is the bimolecular rate constant that applies when diffusion is very fast. k o is the diffusion rate constant, which according to the Stokes-Einstein equation is inversely proportional to the medium viscosity, ~1. For diffusion-controlled reactions 1 / k a = 1 / k o, and this value is proportional to rl. Therefore, to find out whether an enzymic reaction is diffusion-controlled or not, it was proposed to study the 1 / k a vs rl relationship, being assumed that kca t does not depend on the viscosity [32,33]. For the simple reaction scheme kt k2 E + S ~ E S ~ EP k_ 1
The dependence of k a o n Ti was used by several authors [34-37] to arrive at the conclusion that the particular enzymic reaction they have studied involves the diffusion limit. This approach should be valid only in cases when kca t is viscosity-independent. This is not the ease for lactate dehydrogenase reaction. We observe the weakly pronounced kent/Kin relationship, since both these parameters decline simultaneously as viscosity increases. Generally, the cosolvent effects on substrate binding-dissociation and on the catalytic rate are different in origin, and the difference of their change in sign and magnitude is quite probable. The mechanism of viscogenic solvent influence on Km is most probably related to the solvent effect on the affinity of enzyme for substrate. Since the variation of ionic strength within a wide range of values does not change the affinity of lactate dehydrogenase for pyruvate [30,31], one may suggest that the energy of Coulomb interaction with the substrate in the enzyme active centre is not influenced by solvent composition. Probably, the changes in Km depend on the hydration term in the binding energy. This assumption is in good agreement with the data on the relationship of the dissociation constant for various anions to fit the Hoffmeister series showing the relationship between the affinity to enzyme and their hydration energy [31].
(5)
k-2
where E is the enzyme; S, the substrate, and P, the product. Kinetic constants k - i and k 2 a r e not diffusion-controlled by definition. So diffusion control may be only in kl. If the complex formation between enzyme and substrate is diffusion-controlled, it could in-
Conformational adiabatic character of lactate dehydrogenase reaction It is important to single out the rate-limiting steps of the lactate dehydrogenase reaction which must be influenced by changes in medium viscosity. It is established that the release or trapping of a proton from medium does not limit the reaction rate in either forward or reverse directions [18]. The proton produced as a result of lactate oxidation goes over to the catalytic group His-195, staying with the ternary complex until the release of the product. The trapping of a proton from solution during the reduction of pyruvate goes on before the formation of the ternary complex of enzyme with N A D H and pyruvate occurs. Thus, all transitions in the ternary complex take place with the charge retained within the complex. This condition can only be met in case of a complete shielding of the reaction centre from the aqueous environment. As shown by kinetic studies [18,38-40], the limiting step of the pyruvate reduction reaction is not the catalytic transfer of hydride ion but the conformational
202 isomerization of the ternary enzyme-substrate complex, which either accompanies or proceedes this transfer:
H÷E
NADH
NADH
NAD +
pyruvate
pyruvate
lactate
(7)
Proof of the conformational relationship of this step is provided by observation of the lack of kinetic isotope effect in case of substitution of NADH with its deuterated analogue, [2H]NAD [41]. If the limiting step of this reaction were the catalytic hydride ion transfer proper, the substitution would decrease the reaction rate by 5-6-times. According to X-ray crystallographic data, the apoenzyme of lactate dehydrogenase and its ternary complex are significantly different in conformation [23,24]. The complex formation is accompanied by a shift of the loop, containing residues 98-110, which leads to a complete shielding of the reaction centre from the solvent. The stop-flow experiments [40-42] enabled identification of the rate-limiting isomerization step with the transition to the conformation of ternary complex observed in crystallographic studies. If the reaction proceeds in the direction of lactate oxidation and NAD + reduction, the study of deuterated lactate also reveals a complete absence of the kinetic isotope effect [38]. This means that in this case also the reaction rate cannot be limited by the rate of the catalytic charge transfer process. According to kinetic data, the rate is governed probably not by the rate of charge transfer in the ternary complex or by that of passage through the preceding steps, but by the subsequent processes of dissociation of products or related conformational isomerization of the enzyme: NADH
/ NADH
(8) pyruvate H+ +pyruvate
NADH
Some kinetic experiments [16,18] are in agreement with the notion that the conformational isomerization which limits the reaction rate, occurs after the splittingoff the proton and pyruvate and is connected with the dissociation of NADH. However, as yet there is no complete clarity regarding this issue [43]. If the product dissociation is the rate-limiting step for the lactate oxidation reaction, the viscosity effect should slow down the reaction according to relationship e-m2 [3,44], while in the case of rate-limiting conformational isomerization, the effect is expected to be a function of ~-8 (Eqn. 3) with a coupling factor 0 < 8 ~< 1. Our finding that the viscosity effect has the form of ~-8 and 8 is about the same for both the forward and reverse reaction indicates that a conformational motion is rate-limiting for both directions of the reaction and viscosity affects this motion. According to the ideas developed by Dogonadze et
al. [45,46] the manifestation that the chemical or conformational step is a factor limiting the reaction rate is dependent on the relaxation times of the system along the corresponding degrees of freedom (reaction coordinates). Depending on their relative magnitudes, the process can be either conformational-adiabatic, or electronically adiabatic with respect to the conformational transitions. Strongly pronounced effects of medium viscosity, combined with the absence of primary kinetic isotope effect [47] point to the electronic adiabatic character of the reaction in question. This implies that the electronic state of substrates depends critically on the motion in the conformational coordinates of protein globule. The reverse power relationship between the reaction rate constant and solvent viscosity (Eqn. 3) suggests the application of Kramers theory for interpretation of the data [11]. At high viscosities, it describes the reaction rate constant, kr, as an explicit function of viscosity: kr(71r,T) = ( A / ~ r ) e -Ea/kr
(9)
where T/is a parameter which describes the dissipation of energy (internal friction) in the process of activational transition, i.e., local viscosity in the region of the reaction centre. The two parameters: ~ (Eqn. 3) and l~r (Eqn. 10) differ by a factor 8 which describes the coupling between the dynamics of protein and that of solvent molecules [5,6]. Because the values taken on by 8 are rather high (0.5 < 8 < 1), this coupling is significant. In enzyme catalysis the Kramers theory is expected to be applicable for those processes where the elementary act is connected with conformational change of protein [47]. It is, probably, this feature that is common to different enzymes, such as carboxypeptidase [6], myosin [9] and lactate dehydrogenase (this study) where conformational alterations play a key role in catalysis and where considerable effects of medium viscosity are observed.
Acknowledgements The authors are sincerely thankful to L.I. Krishtalik, B. Somogyi, D.E. Hoshtariya, V.I. Tishkov and Yu.F. Krupyansky for their valuable advice given in the course of experimental work, and to N.N. Veliky for reading the manuscript and critical remarks°
References 1 Cared, G., Fasella,P. and Gratton, E. (1979)Annu.Rev. Biophys. Bioeng. 8, 69-97. 2 Welch, G.R., Somogyi, B. and Damjanovich, S. (1982) Prog. Biophys. Mol. Biol. 39, 109-146. 3 Somogyi,B., Welch, G.R. and Damjanovich,S. (1984) Biochim. Biophys. Acta 768, 81-112.
203 4 Cared, G. and Gratton, E. (1986) in The Fluctuating Enzyme (Welch, G.R., ed.), pp. 227-262, John Wiley & Sons, New York. 5 Beece, D., Eisenstein, L., Frauenfelder, H., Good, D., Marden, M.C., Reinisch, L., Reynolds, A.H., Sorensen, L.B. and Yue, K.T. (1980) Biochemistry 19, 5147-5157. 6 Gavish, B. and Werber, M.M. (1979) Biochemistry 18, 1629-1275. 7 Somogyi, B., Norman, J.A. and Rosenberg, A. (1986) Biophys. J. 50, 55-61. 8 Gandour, R.D. and Schowen, R.L. (eds.) (1978) Transition States of Biochemical Processes pp. 1-616, Plenum Press, New York. 9 Khoshtaria, D.E. and Goguadze, N.G. (1986) Biophysica (U.S.S.R.) 31, 220-222. 10 Khoshta~a, D.E. and Goguadze, N.G. (1985) Bioorgan Klfim. (U.S.S.R.) 11, 1621-1626. 11 Kramers, H~A. (1940) Physica 7, 284-304. 12 Jecsai, G. (1961) Acta Physiol. Acad. Sci. Hung. 20, 339-341. 13 Wartman, B. (1960) Biochim. Biophys. Res. Commun. 2, 179-183. 14 Cornish-Bowden, A. (1979) Principles of Enzyme Kinetics, p. 45, Mir, Moscow. 15 Chemist's Reference book (1965) 2nd Edn., Vol. 3, pp. 715-720, Chemistry, Moscow. 16 Holbrook, J.J., Liljas, A., Steindel, S.J. and Rossmann, M.G. (1975) In The Enzymes (Boyer, P.D., ed.), 3rd Edn., VoL 11, pp. 191-293, Academic Press, New York. 17 Markovich, D.S. (1980) preprint N1512-80, pp. 1-273, VINITI, Moscow. 18 Holbrook, J.J. and Gutfreund, H. (1973) FEBS Lett. 31, 157-169. 19 Whitaker, J.R., Yates, D.W., Bennett, N.G., Holbrook, J.J. and Gutfreund, H. (1974) Biochem. L 139, 677-697. 20 Nagradova, N.K. and Muronec, V.I. (1985) Uspekhi Sovremennoi Khimii (U.S.S.R.) 26, 83-108. 21 Bernard, M.L. and Laidler, K.J. (1952) J. Am. Chem. Soc. 74, 6099-6101. 22 Akhadov, Ya.Yy. (1977) Dieletric properties of binary solutions, pp. 1-366, Nauka, Moscow. 23 White, D.B., Hackert, M.L., Buehner, M., Adan~, M.J., Ford, G.C., Lentz, P.J., Smiley, I.E., Steindel, S.J. and Rossmann, M.G. (1976) J. Mol. Biol. 102, 759-779. 24 Grau, V.M., Trommer, W.E. and Rossmann, M.G. (1981) J. Mol. Biol. 151, 289-307. 25 Back, J.F., Oakenfull, D. and Smith, M.B. (1979) Biochemistry 18, 5191-5196.
26 Arakawa, T. and Timasheff, S.N. (1982) Biochemistry 21, 6536-6544. 27 Arakawa, T. and Timasheff, S.N. (1985) Biochemistry 24, 6756-6762. 28 Lee, J.C. and Timasheff, S.N. (1981) Biochemistry 256, 7193-7201. 29 Jacobson, A.L. and Braun, H. (1977) Biochim. Biophys. Acta 493, 142-153. 30 Saburova, E.A. and Markovich, D.S. (1978) Mol. Biol. (Moscow) 12, 737-746. 31 Yagodina, L.O., Saburova, ~:~.A.,Marcovich, D.S. and Volkenstein, M.V. (1986) Doklady Acid. Sci. USSR, 288, 491-494. 32 Berg, O.G. and Von Hippel, P.H. (1985) Annu. Rev. Biophys. Chem. 14, 131-160. 33 Dunford, H,B. and Hasinoff, B.B. (1986) J. Inorg. Biochem. 28, 263-269. 34 Brouner, A.C. and Kitsch, J.F. (1982) Biochemistry, 21,1302-1307. 35 Hardy, L.W. and Kitsch, J.F. (1984) Biochemistry 23, 1275-1282. 36 Baselyanski, M., Robey, E. and Kitsch, J.F. (1986) Biochemistry 25, 125-130. 37 Hasinoff, B.B., Dreher, R. and Davey, J.P. (1986) Biochim. Biophys. Acta 911, 53-58. 38 Bennett, N.G. and Gutfreund, H. (1973) Biochem. J. 135, 81-85. 39 Parker, D.M., Jeckel, D. and Holbrook, J.J. (1982) Biochem. J. 201, 465-471. 40 Waldman, A.D.B., Clark, A.R. and Holbrook, J.J. (1985) Biochem. Soc. Trans. 13, 257-260. 41 Stinson, R.A. and Gutfreund, H. (1971) Biochem. J. 121, 235-240. 42 Waldman, A.D.B., Hart, K.W., Clarke, A.R., Wigley, D.B., Barstow, D.A., Atkinson, T., Chia, W.N. and Holbrook, J.J. (1988) Biochem. Biophys. Res. Commun. 150, 752-759. 43 Dalziel, K. (1975) In The Enzymes (Boyer, P., ed.), 3rd Edn., Vol. 11, pp. 2-60, Academic Press, New York. 44 Somogyi, B. and Damijanovicb, S. (1986) In The fluctuating Enzyme (Welch, G.R., ed.), Wiley & Sons, New York, pp. 341-368. 45 Dogonadze, R.R., Kuznetsov, A.M. and Marsagishvili, T.A. (1980) Electrochim. Acta 25, 1-28. 46 Dogonadze, R.R., Kuzaetsov, A.M. and Utstrup, J. (1977) J. Theor. Biol. 69, 239-263. 47 Khoshtaria, D.E. (1986) Biophysika (U.S.S.R.) 31, 391-395.
196
BBAPRO33~5
Kinetics of the lactate dehydrogenase reaction in high-viscosity media Alexander P. Demchenko 1, Oksana I. Rusyn 1 and Ekaterina A. Saburova 2 l The.4. V. Palladin Institute of Biochemistry of the Ukrainian S.S.R. Academy of Sciences, Kieo (U.S.S.R.) and 2 The Institute of Biological Physics of the U.S.S.R. Academy of Sciences, Pushchino, Moscow Region (U.S.S.R.)
(Received 29 May 1989)
Key words: Lactate dehydrogenase; Viscosity; Enzyme kinetics; Protein dynamics
The effect of the medium viscosity on kinetics parameters of lactate dehydrogenase reaction was studied. The viscosity increase results in a sharp decline in the catalytic rate for ~ ath the pyruvate reduction and lactate oxidation reactions. It is shown that the catalytic step and its associated confm~afional motions is the only step which is considerably retarded when the viscosity increases. The reaction is not ~ns~.tive to changes in the dielectric properties of the medium. An inverse power function observed between the rate constant and viscosity cannot be explained by the theory of absolute reaction rates. However, it can easily be interpreted o~ the basis of the Kramers theory dealing with the transition over the activation barrier as a diffusional motion in the field of random forces. The influence of the mediums viscosity on the kinetic parameters indicates the existence of strong coupling between the dynamics of the solvent and the conformational motions of the protein molecule, which are correlated with the catalytic step.
Introduction
Despite the long-term efforts, the subject of the mechanisms of action of enzymes is still far from being understood. We are still unable to predict the rate and the way of regulation of the catalytic reaction on the basis of structural information about proteins, even at the atomic level of resolution. Apart from the structure of the ground state of the enzyme-substrate complex, the mechanisn:~ of the activation steps and the nature of the activated (transition) states and sub-states have to be known as well. There are many theories attempting to explain the physical mechanisms of enzymic catalysis [1-4], and, despite the basic differences between them, they have the common point of postulating the role of protein structure beyond the catalytic centre and correlating protein dynamics with the catalytic steps. Further progress requires application of new experimental approaches for the analysis of protein dynamics associated with the catalytic function. Along this line, it was proposed recently to make use of the medium's viscosity as an independent variable to study protein dynamics [5-7]. The critical point is that the absolute-
Correspondence: A.P. Demchenko, A.V. Palladin Institute of Biochemistry, Ukrainian S.S.R. Academy of Sciences, Kiev 252030, U.S.SoR.
rate theory (the theory of activated complex) [8] which neglects the effect of medium (and its dynamics) on the reaction rate, and is unable to interpret the recently obtained data showing that the catalytic rate constants for carboxypeptidase [6] and myosin ATPase [9] considerably decline with the increase of solvent viscosity. Viscosity dependence was also observed for a non-enzymic activation process - the reassociation of myoglobin with ligands following the photodissociation caused by a laser flash [5]. But such a dependence was not observed for enzyme kinetics of chymotrypsin [10]. The alternative Kramers theory [11], regarding the process of transition over the activational barrier as a diffusional motion within a field of random forces, was used to interpret these data. The question of generality of the observed viscosity effects and the applicability of the Kramers theory to enzymic processes still remains unclear. The present study deals with the viscosity effects on the ~dnetic parameters of lactate dehydrogenase. Viscosity was changed by addition of different cosolvents such as glycerol, sucrose and other monomeric and polymeric viscogenes and the reaction was followed in both the forward and reversed directions. Unlike the previously studied hydrolytic reactions [6,9,10], this reaction occurs within the enzyme matrix, totally shielded from the aqueous solvent. The complex mechanism of regulation makes it possible to investigate the influence of viscous
0167-4838/89/$03.50 © 1989 Elsevier Science Publishers B.V. (Biomedical Division)
197 environment on the inhibition and formation of nonproductive complexes. For the first time it is shown for redox reactions that the catalytic reaction rate constant critically depends on the medium's viscosity and that it can be accounted for by the Kramers theory. Materials and Methods
Lactate dehydrogenase ((S)-lactate:NAD + oxidoreductase, EC 1.1.1.27) was isolated from pig skeletal muscles (M4 isoform) using the method of Jecsai [12], involving fractional salting out, and 4-fold recrystaUization in an ammonium sulfate solution. Additional purification was performed by an ion-exchange chromatography column with DEAE-Sephadex A-50 (Pharmacia) [13]. The preparation was homogeneous according to the usual electrophoretic criteria. The specific activity was 320/~M NADH rain -1 at pH 6.2 and 25 ° C. The steady-state reaction kinetics were recorded at 340 nm (absorption band of NADH) using Specord UV-VIS spectrophotometer (Carl Zeiss) in a thermostated call at 25°C. The initial rate was determined irom the inclination of the tangent line with respect to the initial portion of the kinetic curve, recorded during the first 30 s. The reactio~ was started by introducing a small amount of enzyme stock solution into the medium containing coenzyme, substrate and viscogeneous cosolvent in 0.1 M phosphate buffer. When studying the reduction of pyruvate, the ptl was kept at 6.2, and the N A D H concentration was 2-10 - 4 M. During investigation of lactate oxidation pH was 9.5 and NAD + concentration was 4 mM. These pH values were chosen in order to avoid the strong pH-dependence of the reaction due to histidine group protonation with pK 7.6. The enzyme concentration was 1/~g/ml. Circular dichroism spectra were recorded by a dichrograph Jasco M-40 (Japan). Protein concentration was 1 mg/ml. The lactate dehydrogenase concentration was determined spectrophotometricaUy, using the known absorption factor ~280nm/;' mg/ml 1 = 1.29. The kinetic parameters (Vmax and Km) were found using the Hanes transformation ([S]/V vs. [S] relationship) [14] with the aid of the least-square method. The viscosity values for solutions of glycerol, sucrose and alcohols were taken from Ref. 15. Viscosities of all the other solutions were measured experimentally using a thermostatted glass capillary viscometer (the capillary diameter was 0.73 mm). Results
In our experiments the sucrose concentration varied from 0 to 44% (w/w), while that of glycerol varied from 0 to 63% (w/w), which results in the variation of viscosity from 0.89 to 7.1 cP and to 10.2 cP, respectively. Under these conditions the reaction rate decreases by an order of magnitude. Fig. I shows the relationship between the initial reaction rate (V) and the pyruvate concentration at excess of NADH for various sucrose and glycerol concentrations. The results presented in Fig. 1 were obtained for the reaction of pyruvate reduction in the presence of 0.5 M KCI. These conditions were chosen since it is known that C1-eliminates the substrate inhibition appearing at high substrate concentrations [16]. Similar results (considerable deceleration of the reaction rate resulting from the addition of glycerol and sucrose) were also obtained in the absence of KCL In the latter case, the reaction in the v~scous i~ediurn re~tains the characteristic feature of substrate inhibition, i.e., the decline of the V vs. [S] relationship at high (> 2 mM) pyruvate concentrations. Ethylene glycol (30 and 50% (w/w)) was also used to vary viscosity in the solution. For the reaction of pyruvate reduction the maximal rate Vma~decreased from 3.26 relative units in buffer (viscosity 7/= 0.89 cP) down to 2.26 relative units in a 3070 solution (?/= 1.84 cP) and 1.32 relative units in a 5070 solution (T/= 3.13 cP) of ethylene glycol.
A
3.
I
® . = ~
®
,SS':
o I
~ 0 / 0
x ~r6
~^Jx ~ x 0 ~---
El
.7
I
2
[sl (raM)
3
x 8
4
5
B +
2 5 0 >
C
0
I I
I 2
I 3
I 4
I 5
Is] (raM)
Kinetics of the lactate dehydrogenase reaction in highviscosity media In the studies of the rate of the lactate dehydrogenase reaction as a function of sucrose or glycerol concentration, a sharp monotonous decline is observed.
Fig. 1. Initial rate, V, of pyruvate reduction as a function cf substrate concentration [S] in 0.5 M KCI solutions at different concentrations of glycerol (A) and sucrose (B). For glycerol: 1, control: 2, 17%; 3, 25%; 4, 33%; 5, 41%; 6, 48%; 7, 55%; and 8, 63%. For sucrose, 1 control; 2, 8.6%; 3, 17%; 4, 24%; 5, 31%; 6, 37%, and 7, 43%.
198 A
~liB
~.(nm)
22o
23o
24o
2so
?.60 -
270
~
280
~.(nrn) 290
300
310
320
~
/
Fig. 2. Circular dichroism spectrum of lactate dehydrogenase in 0.1 M phosphate buffer and in 30~ sucrose solution, pH 6.2. (A) 210-240 nm region; (B) 250-300 nm region.
A substantial reduction of the reaction rate with the increase of viscogen concentration is also observed for the reverse reaction of lactate oxidation when NAD + is the cofactor. The ma.umal rate, Vm=,, decreases from 8.5 relative units in buffer to 1.5 units in 44% sucrose and 1.3 units in 63% glycerol. Similarity of ~he observed effects caused by different viscous cosolvents (sucrose, glycerol, ethylene glycol) and the absence of any correlation with other solvent properties (hydrophobicity, dielectric constant) suggests that it is the viscosity that was the common property of the solvents, which is responsible for this phenomenon. The reduction of the reaction rate in the glycerol, sucrose and ethylene glycol solutions cannot be accounted for by irreversible enzyme inactivation (the activity remains unchanged during several hours of incubation at the maximum concentrations of these cosolvents). The effect is completely reversible: when the viscous solvent is diluted with aqueous buffer during the kinetic run, the sharply increased rate of the reaction is observed.
buffer in a 30% sucrose solution. This indicates that the cosolvents in question do not induce any substantial change in the a-helical content of protein (210-240 nm region, and in the environment of tryptophan residues (250-300 nm region). Some finer structural changes in the enzyme, influencing the transitions between the sub-states involved in the catalytic process, cannot be ruled out. However, as it will be shown below, the addition of concentrated solutions of sucrose and glycerol does not change the regulatory properties of the enzyme: formation of inhibitory complexes with substrate and inhibition by anions. For the redox reaction of charge transfer it is possible that the solvent affects the catalytic rate by modifying the dielectric character of the environment, as it was described for hydrolytic enzymes [21]. Taking into account such a possibility, the effects of special watercosolvent mixtures with low dielectric constant (e) (30% mixtures of methanol, ethanol and dioxane with water) were studied as well. The data obtained do not reveal an appreciable effect of ( on the kinetics of the lactate
Possible cosolvent effects on the catalytic rate
The possibility of the effect of dissociation of lactate dehydrogenase tetrameric molecule into subunits in the presence of viscogenic cosolvents can be easily ruled out. The rotational relaxation time of molecule, recorded by the fluorescence depolarization technique is unchanged in concentrated glycerol solutions [17]. Besides, as follows from kinetic experiments [18,19], the studies of hybridization of M- and H-isoenzymes [16] and examination of the activity of immobilized subunits [20], the lactate dehydrogenase subunits are independent and kinetically identical. The question arises whether there is any reversible conformational change in response to the addition of the viscogenic agents. As is shown in Fig. 2, the circular dichroism spectrum is identical to that in the aqueous
TABLE I Kinetic constants Vm, x and K,n for lactate dehydrogenase reaction as functions of solvent dielectric constant E Solvent
Water Glycerol (30~) Ethylene glycol
e a
1] b
limax
Km
(cP)
(relative units)
(mM)
78 70 69.8
0.89 2.16 1.84
2.96 + 0.13 1.96+0.05 2.26 + 0.10
0.19 ± 0.03 0.10+0.01 0.15 ± 0.05
58 52
2.18 1.6 c
2.25 + 0.14 2.74 + 0.39
0.18 + 0.04 0.20 + 0.06
(30~) Ethanol (30%) Dioxane (30~)
a Ref. 22. b Ref. 15. c Measured by viscometer.
199 dehydrogenase reaction (Table I). This corroborates the fact known from X-ray crystallographic data [23,24] that in this catalytic process the charge transfer occurs within the hydrophobic cavity inaccessible to the solvent, and the dielectric screening of the surface charged group should exert no effect on the catalytic rate. A number of polyhydroxylic substances, including sucrose and glycerol, are known to stabiliTe the native conformation of proteins in aqueous solutions [25-28]. The addition of sucrose increases stability of lactate dehydrogenase toward thermal denaturation [29]. This may be due to prevaifing hydration of protein in a mixed solvent and exclusion of organic cosolvent from the hydration !~er. Such a stabilizing effect may create an addition~ tension in the native protein globule, which i s likely to cause its decreased mobility. It is difficult to distinguish this effect, if it contributes to the catalysis, from the solvent viscosity effect. However, for a series of cosolvents (sucrose, glycerol, ethylene glycol, etc.) the magnitude of the protein-stabilizing effect does not correlate with the viscosity [25]. Therefore, this effect is unable to explain the influence of viscogenic cosolvent on the catalytic rate which we observed.
The effect of viscosity on different steps of the lactate dehydrogenase reaction. The general mechanism of the lactate dehydrogenase reaction includes substrate inhibition and formation of non-productive enzyme-substrate complexes [16,30]. The binding of substrates is sequential: the binding of N,~DH proceedes that of pyruvate. The formation of the ternary E-NADH-pyruvate complex is accompanied by conformational rearrangements of the protein. Anions of neutral salts, in particular C1- ions, are specific regulators of the lactate dehydrogenase reaction [30,31]. Depending on the conditions CI- may act either as an inhibitor or activator. At small substrate concentrations ([S]
2.0 D
1
-.I
d >
1.0
o o
I
I
I
I
04
08
:2
~6
CI
1.O
0.5
_J
-15I
,og 1.o
-05
'
0.5 Fig. 3. Initial reaction rate of pyruvate reduction as a function of KCI concentration (A) and same function in the Hill coordinates (B). 1, control; 2, 40% sucrose; 3, 50~ glycerol. Pyruvate concentration, 20 mM.
used to obtain the apparent Michaelis constant (Km.app). At high concentrations of sucrose and glycerol we observed a similar decrease of this parameter. Having the Kfm values from separate experiments and calculating Kmapp,this way one can obtain K l, the dissociation constant of the inhibitor, from the equation
[3o1: Km,app ffi Km~l -t- [|] '~
(1)
where [I] is the inhibitor concentration. In 40% sucrose and 50% glycerol the value for K~ are 0.09 + 0.03 M, which does not differ significantly from the reference value 0.1 + 0.02 M in the aqueous buffer. This shows that the presence of sucrose or glycerol produces virtually no effect on the binding of anions in the enzyme active centre. The effect of C1- concentration on reaction rate at inhibitory pyruvate concentration (Fig. 3) demonstrates that these ions increase the initial rate of the reaction by 2-2.5-times irrespectively of the presence of viscogenic cosolvent.
200 The dissociation constant of C I - in the ternary nonproductive complex is found from the previously suggested equation [27] for the stationary rate in the Hill coordinates: I VlAl-.oo--_~+lgV[Ai--oo = lg[A]-lg KA g U --/)[A] ---,oo
UIA] ---.0
5 ~
~
+(o3
.
,
(2) r.
'
_
where VIAl-.0 and VtA l _. ~ are rates at zero and saturating anion concentrations [A]. A plot constructed in these coordinates is identical with and without viscous cosolvents. The obtained K A ( C I - ) values for buffer, 4070 sucrose and 5070 glycerol were 0.19 _+ 0.05, 0.19 + 0.05 and 0.16 + 0.05, respectively. Thus, the most pronounced viscogenic cosolvent effects are observed at the catalytic steps. Judging from the reduced value of K m, there also occurs a certain strengthening of the enzyme-substrate complexes, while the remaining steps, including the processes of competitive inhibition by C I - and the decay of non-productive enzyme-substrate complex do not appear to experience any effect of viscosity. All components of the catalytic lactate dehydrogenase mechanism and its regulation are retained in viscous medium.
~
~
3
2.
~ 0
I 1 I n r/ ( c P )
I 2
Fig. 4. Rate constant, kcat, for pyruvate reduction reaction in sucrose and glycerol solutions as a function of solvent viscosity 7, plotted in the double logarithmic coordinates. 1: sucrose (0-44%), pyruvate, 0.02-2 raM, 8 = 0.74:t:0.08; 2: sucrose (0-44%), 0.5 M KCI, pyruvate 0.2-5 raM, 8 -- 0,67 -+0.04. 3: Glycerol (0-63%), pyruvate 0.02-2 mM, 8 -- 0.98+0.04. 4: glycerol (0-63%), 0.5 M KCI, pyruvate 0.2-5 raM, 8 =1.13_+0.05. 6-
Reaction rate constant as a function o f m e d i u m viscosity
We have observed that the reaction rate constant, in all cases shows a clear-cut reverse power relationship to the medium viscosity, T/. If the activational character of the reaction is taken into account, the reaction rate constant can be presented in a form: kca t (keatS--gmax//[E]),
k,:.t = A. 7 -+ e E-/kr
4
I 0
I I 1 2 in 17cop) Fig. 5. Rate constant, K~,, for pyruvate reduction reaction in alCohols solutions as a function of solvent viscosity, 7, plotted in the double logarithmic coordinates, o, methanol (0%, 10%, 30%); <>, ethanol (0%, 10%, 30%); +, ethylene glycol (0%, 30%, 50%); pyruvate 0.02-2 mM, 8 = 0.74-+0.14.
(3)
where k T is the product of the Boltzmann constant and the absolute temperature, E a is the activation energy, and A and 8 are the empirical coefficients. By using double logarithmic plots, we obtain the straight lines of functions In k~at vs. In ~ from the slopes of which the parameter 8 can be obtained. In the case of pyruvate reduction (see Fig. 4), the ~t value is approx. 0.7 in the case of sucrose and it is close to 0.9 for glycerol. N o significant difference is observed between its values with and without 0.5 M KC1. Similar 8 values are observed with methanol, ethanol and ethylene glycol (Fig. 5). Several polymeric cosolvents (polyacrylamide, polyvinyl alcohol and poly(ethylene glycol)s) were also tested as viscogenic agents. We have observed similar but qualitatively smaller effects in terms of viscosity (Fig. 6). The influence of polymeric cosolvents on the catalytic rate is expected to be complex, and requires special investigation, with allowance for the excluded volume, hydration and other effects being taken into account. Besides, in this case, microscopic and macroscopic
viscosities may deviate significantly, and this does not allow to compare quantitatively the results with the data on other viscogens. Qualitatively, however, the results obtained on polymeric cosolvents are also in favour of the postulated general solvent viscosity effect. Interestingly, that for the reaction of lactate oxidation (Fig. 7), the function ha kcat vs. In +7, is similar to
A "7 01
O
~5
#¢&
e-
4
I 0
I 1 In !?(cP)
I 2
Fig. 6. Rate constant, Kcat, for pyruvate reduction reaction in polymers solutions as a function of solvent viscosity, 7, plotted in the double logarithmic coordinates, o, control; +, poly(ethylene glycol), Mr 600 (105[), m, polyvinyl alcohol (1%), ~t, poly(ethylene glycol) M, 6000 (10%), A, poly(ethylene glycol), Mr 6000 (11%), ×, polyacrylamide (0,16%), pyruvate 0.02-2 mM, 8 = 0.38 +0.15.
201 fluence the Michaelis constant (K m = (K_I + k 2 ) / k l ) . Under certain conditions (when k_ 1 >> k2), k a can be calculated as:
L3
k a = kca t / K m
,,e e-
(6)
-2
1
t 0
I 1 In 7/ (cP)
I
2
Fig. 7. Rate constant, Kcat, for lactate oxidation reaction in sucrose
and glycerol solutions as a function of solvent viscosity, 17, plotted in the double logarithmic coordinates. 1, sucrose (0-44~), 8 = 0.80+ 0.04; 2, glycerol (0-63~), 8 = 0.77+0.04, lactate 1-100 raM.
that of pyruvate reduction reaction with 8 = 0.8 for both glycerol and sucrose used as viscogenic cosolvents. Discussion The effect of viscogenic cosolvents on biocatalytic reactions The simple explanation of viscosity effects in terms of the slowdown in diffusion of substrates in viscous media does not correspond t.o our data. At saturating substrate concentrations its diffusion should not influence the reaction rate. In more general case, if the reaction depends both on the chemical steps and diffusion, its rate constant can take the following form [32]: 1/Ka = 1/kD + 1/Kc '
(4)
where k a ( i n c m 3- s - 1 ) is the experimentally observed bimolecular rate constant; kc is the bimolecular rate constant that applies when diffusion is very fast. k o is the diffusion rate constant, which according to the Stokes-Einstein equation is inversely proportional to the medium viscosity, ~1. For diffusion-controlled reactions 1 / k a = 1 / k o, and this value is proportional to rl. Therefore, to find out whether an enzymic reaction is diffusion-controlled or not, it was proposed to study the 1 / k a vs rl relationship, being assumed that kca t does not depend on the viscosity [32,33]. For the simple reaction scheme kt k2 E + S ~ E S ~ EP k_ 1
The dependence of k a o n Ti was used by several authors [34-37] to arrive at the conclusion that the particular enzymic reaction they have studied involves the diffusion limit. This approach should be valid only in cases when kca t is viscosity-independent. This is not the ease for lactate dehydrogenase reaction. We observe the weakly pronounced kent/Kin relationship, since both these parameters decline simultaneously as viscosity increases. Generally, the cosolvent effects on substrate binding-dissociation and on the catalytic rate are different in origin, and the difference of their change in sign and magnitude is quite probable. The mechanism of viscogenic solvent influence on Km is most probably related to the solvent effect on the affinity of enzyme for substrate. Since the variation of ionic strength within a wide range of values does not change the affinity of lactate dehydrogenase for pyruvate [30,31], one may suggest that the energy of Coulomb interaction with the substrate in the enzyme active centre is not influenced by solvent composition. Probably, the changes in Km depend on the hydration term in the binding energy. This assumption is in good agreement with the data on the relationship of the dissociation constant for various anions to fit the Hoffmeister series showing the relationship between the affinity to enzyme and their hydration energy [31].
(5)
k-2
where E is the enzyme; S, the substrate, and P, the product. Kinetic constants k - i and k 2 a r e not diffusion-controlled by definition. So diffusion control may be only in kl. If the complex formation between enzyme and substrate is diffusion-controlled, it could in-
Conformational adiabatic character of lactate dehydrogenase reaction It is important to single out the rate-limiting steps of the lactate dehydrogenase reaction which must be influenced by changes in medium viscosity. It is established that the release or trapping of a proton from medium does not limit the reaction rate in either forward or reverse directions [18]. The proton produced as a result of lactate oxidation goes over to the catalytic group His-195, staying with the ternary complex until the release of the product. The trapping of a proton from solution during the reduction of pyruvate goes on before the formation of the ternary complex of enzyme with N A D H and pyruvate occurs. Thus, all transitions in the ternary complex take place with the charge retained within the complex. This condition can only be met in case of a complete shielding of the reaction centre from the aqueous environment. As shown by kinetic studies [18,38-40], the limiting step of the pyruvate reduction reaction is not the catalytic transfer of hydride ion but the conformational
202 isomerization of the ternary enzyme-substrate complex, which either accompanies or proceedes this transfer:
H÷E
NADH
NADH
NAD +
pyruvate
pyruvate
lactate
(7)
Proof of the conformational relationship of this step is provided by observation of the lack of kinetic isotope effect in case of substitution of NADH with its deuterated analogue, [2H]NAD [41]. If the limiting step of this reaction were the catalytic hydride ion transfer proper, the substitution would decrease the reaction rate by 5-6-times. According to X-ray crystallographic data, the apoenzyme of lactate dehydrogenase and its ternary complex are significantly different in conformation [23,24]. The complex formation is accompanied by a shift of the loop, containing residues 98-110, which leads to a complete shielding of the reaction centre from the solvent. The stop-flow experiments [40-42] enabled identification of the rate-limiting isomerization step with the transition to the conformation of ternary complex observed in crystallographic studies. If the reaction proceeds in the direction of lactate oxidation and NAD + reduction, the study of deuterated lactate also reveals a complete absence of the kinetic isotope effect [38]. This means that in this case also the reaction rate cannot be limited by the rate of the catalytic charge transfer process. According to kinetic data, the rate is governed probably not by the rate of charge transfer in the ternary complex or by that of passage through the preceding steps, but by the subsequent processes of dissociation of products or related conformational isomerization of the enzyme: NADH
/ NADH
(8) pyruvate H+ +pyruvate
NADH
Some kinetic experiments [16,18] are in agreement with the notion that the conformational isomerization which limits the reaction rate, occurs after the splittingoff the proton and pyruvate and is connected with the dissociation of NADH. However, as yet there is no complete clarity regarding this issue [43]. If the product dissociation is the rate-limiting step for the lactate oxidation reaction, the viscosity effect should slow down the reaction according to relationship e-m2 [3,44], while in the case of rate-limiting conformational isomerization, the effect is expected to be a function of ~-8 (Eqn. 3) with a coupling factor 0 < 8 ~< 1. Our finding that the viscosity effect has the form of ~-8 and 8 is about the same for both the forward and reverse reaction indicates that a conformational motion is rate-limiting for both directions of the reaction and viscosity affects this motion. According to the ideas developed by Dogonadze et
al. [45,46] the manifestation that the chemical or conformational step is a factor limiting the reaction rate is dependent on the relaxation times of the system along the corresponding degrees of freedom (reaction coordinates). Depending on their relative magnitudes, the process can be either conformational-adiabatic, or electronically adiabatic with respect to the conformational transitions. Strongly pronounced effects of medium viscosity, combined with the absence of primary kinetic isotope effect [47] point to the electronic adiabatic character of the reaction in question. This implies that the electronic state of substrates depends critically on the motion in the conformational coordinates of protein globule. The reverse power relationship between the reaction rate constant and solvent viscosity (Eqn. 3) suggests the application of Kramers theory for interpretation of the data [11]. At high viscosities, it describes the reaction rate constant, kr, as an explicit function of viscosity: kr(71r,T) = ( A / ~ r ) e -Ea/kr
(9)
where T/is a parameter which describes the dissipation of energy (internal friction) in the process of activational transition, i.e., local viscosity in the region of the reaction centre. The two parameters: ~ (Eqn. 3) and l~r (Eqn. 10) differ by a factor 8 which describes the coupling between the dynamics of protein and that of solvent molecules [5,6]. Because the values taken on by 8 are rather high (0.5 < 8 < 1), this coupling is significant. In enzyme catalysis the Kramers theory is expected to be applicable for those processes where the elementary act is connected with conformational change of protein [47]. It is, probably, this feature that is common to different enzymes, such as carboxypeptidase [6], myosin [9] and lactate dehydrogenase (this study) where conformational alterations play a key role in catalysis and where considerable effects of medium viscosity are observed.
Acknowledgements The authors are sincerely thankful to L.I. Krishtalik, B. Somogyi, D.E. Hoshtariya, V.I. Tishkov and Yu.F. Krupyansky for their valuable advice given in the course of experimental work, and to N.N. Veliky for reading the manuscript and critical remarks°
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