ARCHIVES OF BIOCHEMISTRY AND BIOPHYSICS Vol. 212, No. 2, December, pp. 705-716, 1981

A Mathematical Model Describing the Effect of Temperature and Substrate Concentration on the Activities of M., and H, Lactate

Dehydrogenase from the Big Brown Bat (Epfesicus fuscus)’

ROBERT W. CUDDIHEE2 AND MARGARET L. FONDA3

Department of Biochemistry, University of Louti& Health solaces Center, IaLsvdk, Kentucky .lo292

Received April 28, 1981, and in revised form July 20, 1981

The effect of temperature on the activities of Mr and Hd lactate dehydrogenases (LDH, EC 1.1.1.27) isolated from the big brown bat (Ept&msfzmxs) was examined. Temper- ature effects were dependent on the concentrations of all four LDH substrates, pyruvate, lactate, NADH, and NAD. Arrhenius plots of In vi vs reciprocal of absolute temperature were linear for all but the lowest substrate concentrations. The slopes of these Arrhenius plots were used to calculate the temperature effect parameter (p). Substrate-dependent temperature effects for M4 and & LDH were described by an equation for a rectangular hyperbola, p = [Es + E&HKt + .Sl proposed by G. R. Harbison and J. R. Fisher (1974, Camp Bimhem Physid 47B, 27-32) for adenosine deaminase. The parameters E, (CL at infinitely low substrate concentration), EB (p at infinitely high substrate concentration), and Kt (the concentration of substrate when c = [Em + &j/X) can be used to describe the temperature dependence of LDH activity at any substrate concentration and to compare the substrate-dependent temperature effects on the two isoenzymes. Significantly dif- ferent E, and K1 values for pyruvate-dependent temperature effects and different E,, E,, K,, and E, -Em (the range of possible p values) for lactate-dependent temperature effects were found between M1 and H1 LDH isoenzymes. High lactate concentrations inhibited bat Hg LDH activity to a greater degree at low temperatures than at high temperatures. Thus substrate inhibition plays an important role in the effect of temperature on the activity of H-type LDH at high lactate concentrations. Substrate-dependent temperature effects on bat LDH activity were the result of temperature effects on the apparent K,,, value of the respective substrate. Since both the apparent Km for pyruvate and the K; for the competitive inhibitor oxamate decreased with decreasing temperature, the sub- strate-dependent temperature effects observed for pyruvate probably resulted from an increased affinity between pyruvate and the LDH-NADH complex with decreasing tem- perature.

Although steady-state concentrations of substrates in isolated tissue samples are usually much lower than the concentra- tions required to saturate enzyme systems (l-3), many studies on the effect of tem- perature on enzyme activity at saturating

1 This research was supported in part by grants from the Kentucky Heart Association and from the Commission on Academic Excellence of the Univer- sity of Louisville. A preliminary account of this work has appeared in Fed Prm (1980) 39,2259.

s Present address: Department of Preventive Med- icine, Washington University School of Medicine, St. Louis MO. 63110.

a To whom all correspondence should be addressed.

substrate concentrations have been re- ported (4-13). The effect of temperature on enzyme activity is usually different at physiological substrate concentrations than at saturating substrate concentra- tions (1, 2, 14-21).

Gibson (22) derived a theoretical rela- tionship between substrate concentration and the degree of temperature dependency of enzyme activity (p calculated from the slope of an Arrhenius plot of In u vs l/T) for any enzyme which follows Michaelis- Menten kinetics. Gibson demonstrated that ~1 is related to the effect of temperature on the apparent Km and to the relationship

705 0003-9861/81/140705-12302.00/O Copyright 0 1981 by Academic Press,. Inc. All rigbta of reproduction in any form reserved.

706 CUDDIHEE AND FONDA

between the Km and the chosen substrate concentration:

P=EB+[&]R[~]. Dl

The effect of temperature on apparent Km values has been studied in depth. Em- pirically, temperature effects on Km are associated with substrate-dependent tem- perature effects on enzyme activity (13). When Km varies directly with temperature (positive thermal modulation), the effect of temperature on enzyme activity at low substrate concentration is much less than at high substrate concentration (1, 2, 14, 16, 20, 21, 23, 24). Conversely, when Km varies inversely with temperature (nega- tive thermal modulation), the effect of temperature on enzyme activity at low substrate concentration is much greater than at high substrate concentration (25).

Harbison and Fisher (16) demonstrated that substrate-dependent temperature ef- fects on adenosine deaminase activity could be described by a rectangular hyperbola with the equation,

El

where p equals the temperature effect pa- rameter, EB is ~1 at saturating substrate concentrations (vi = V), E, is p at very low substrate concentrations (vi = V/K,), S is the concentration of substrate, and Kt equals the substrate concentration when p = (E, + E,)/2.

The effect of temperature on the activity of the isoenzymes of lactate dehydroge- nase (LDH,4 L-lactate:NAD+ oxidoreduc- tase EC 1.1.1.27) at saturating substrate concentrations has been studied (4,26-31). LDH isoenzymes that are predominantly H type tend to have a higher Arrhenius energy of activation than do the LDH iso- enzymes that are predominantly M type. Thus at saturating substrate concentra- tions, increasing temperature has a greater effect on H type then M type LDH activity (4, 27, 28, 30).

At substrate concentrations below sat-

4 Abbreviation used: LDH, lactate dehydrogenase.

urating, or physiological concentrations, however, the effect of temperature on H- and M-type LDH activity is less charac- terized. Borgmann and Moon (28) studied the effect of temperature on kat/Km for beef heart and muscle LDH, however, the data were not compared quantitatively. From their data it appears that the kcat/ Km (apparent Km for lactate) for beef heart LDH may be more temperature-de- pendent than the k-,/K, for beef muscle LDH, whereas the temperature effect on kcat/Km (apparent K, for pyruvate) ap- pears to be the same for the two isoen- zymes.

The effect of temperature on the activity of LDH is extremely dependent on the con- centration of substrate (1, 12, 14, 1’7, 21, 28, 31). The research reported here deals with the effect of temperature on the ac- tivity of M4 and H4 LDH isoenzymes iso- lated from the big brown bat (Eptesicus fuscus), a mammal that undergoes large changes in body temperature (4 to 3’7°C). The relationship of bat LDH activity and temperature covering the physiological range of the bat was determined using various substrate and coenzyme concen- trations from below the Km to saturating levels.

MATERIALS AND METHODS

Materids. Pyruvic acid, sodium lactate, NAD+, NADH, potassium oxalate, sodium oxamate, l-ethyl- 3(3-dimethylaminopropyl)carbodiimide, and amino- hexyl-Sepharose 4B were obtained from the Sigma Chemical Company.

All solutions were made with double-distilled water. Measurements of pH were made with a Ra- diometer Model 23 pH meter at 25°C. Phosphate buffer was chosen for the assays since it has a low temperature coefficient. Between 11 and 335°C phos- phate has a pK change of -0.07.

Animal co&&ion Eastern big brown bats (E. jb- cus) were captured in their hibernaculum (limestone caves in Marengo, Ind.). Upon returning to the lah- oratory, they were placed in a light-proof box, pro- vided with water ad lib. and kept at approximately 5°C for 2 to 8 weeks.

Tissue preparation Bats were killed by decapita- tion without arousal from hibernation. The livers were rapidly removed and homogenized in a buffer containing 210 mM mannitol, 10 mM Tris-HCl, 70 m&f sucrose, and 0.1 rnre EDTA, pH 7.3. The liver ho-

TEMPERATURE/SUBSTRATE EFFECT. ON BAT LACTATE DEHYDROGENASES 707

mogenates were centrifuged at 23,000g for 15 min and were immediately frozen (-2O’C).

Enzyme pur&o&m. The M4 and H4 LDH isoen- zymes were purified from E. fvmus liver and heart, respectively, using affinity chromatography on an oxamate aminohexyl-Sepharose 4B column by a modification of the procedure of O’Carra and Barry (32). Coupling of oxalate to aminohexyl-Sepharose 4B was done by the following procedure. To 5 ml of aminohexyl-Sepharose 4B was added 0.5 g of potas- sium oxalate, and the sample was agitated for 15 min. Immediately afterward, 1.25 g of 1-ethyl-3(3-dimeth- ylaminopropyl)carbodiimide was added, and the mix- ture was shaken for 16 h at room temperature. The oxamate-aminohexyl-Sepharose was washed with 200 ml of 1 M KC1 and resuspended in 7.5 ml of 3 mM sodium axide. A 0.5 X lo-cm column was packed with 1.5 ml of oxamate aminohexyl-Sepharose 4B. Follow- ing equilibration of the column with 20 mM sodium phosphate, pH 7.0,0.5 M NaCl, 10 ml (approximately 2 mg of LDH/ml of packed Sepharose) of supernatant containing 10 mM NADH and 0.5 M NaCl was applied to the column at a maximal flow rate (1 ml/min). The column was washed with 20 void vol of 20 m?d sodium phosphate, pH 7.0, plus 0.5 M NaCl and 0.2 mM NADH at a maximal flow rate. LDH was eluted by washing the column with 20 mM sodium phosphate, pH 7.0, containing 0.5 M NaCl (without NADH) at a flow rate of 0.1 to 0.2 ml/min (33). Mq LDH eluted immediately following removal of NADH from the column. H4 LDH eluted from the column at approximately 10 void vol after the NADH had been removed. Poly- acrylamide gel electrophoresis was used to determine the LDH isoenzyme content of the fractions. The LDH isolated from bat liver contained 94.0 + 1.2% (mean f SD) M subunits and is referred to as Mq LDH, whereas, the LDH isolated from bat heart con- tained 99.0 * 1.0% H subunits and is referred to as H, LDH.

Polyacqlamide gel electrophuresis. Samples were applied to 5.5% polyacrylamide gels and run accord- ing to the procedure described by Dietz and Lubrano (34). Isoenzyme profiles were quantitated by plani- metry measurements of densitometer scans of each gel.

Enzyme assay. LDH activity was measured by fol- lowing the change in absorbance at 340 nm or in relative fluorescence (excitation wavelength, 350 nm; emission wavelength, 514 nm). The assay solution contained 67 mrd sodium phosphate, pH 7.4, and var- ious concentrations of pyruvate, lactate, NADH, and NAD+. The reaction was initiated by adding enzyme with an add-a-mixer (Precision Cells, Inc.) at a con- centration which produced linear velocities for at least 30 s. Initial velocities were recorded for sub- strate concentrations from below the K, to approx- imately 10 times the K, at each temperature (11,20, 30, and 38.5”C). All assays were performed in trip-

licate. A Zeiss PMQ II and Beckman Model 35 were used to make spectrophotometric measurements. Fluorometric determinations were made in an Aminco Bowman spectrophotofluorometer (Model 4-810) equipped with a Coleman 165 recorder. Water-jack- eted cuvettes or a temperature-controlled cuvette holder were maintained at the desired temperature by a Forma Temp Jr Bath and Circulator. The tem- perature in the assay cuvette was monitored by a Yellow Springs Telethermometer (Model 451D).

Analysis and treatment of data. The kinetic param- eters, V, apparent K, and V/K,, were determined directly from substrate vs initial velocity curves us- ing computer programs derived by Cleland (35) and modified for our system. The values of the temper- ature-effect parameter, p, were determined from the slopes of Arrhenius plots of In vi vs l/T. E. values were determined from the slopes of Arrhenius plots of In Vvs l/T. E, values were determined from the slopes of Arrhenius plots of In V/K, vs l/T. The values of E, - E, were determined from the slopes of Arrhenius plots of In K, vs l/T, as well as by taking the difference between the two parameters, E, and E,. For each Arrhenius plot, linear regression was used to determine the slope of the line of best fit, and the product moment correlation was used to determine how well the data fit that line.

Theoretical curves for p vs substrate concentration were generated using Eq. [2]. Values for Kt were ob- tained using a linear transformation of Eq. [2],

(EB - ‘) K (l/S). (p- t

Statistical analyses for differences consisted of the Student t test to determine differences between means and a one-way analysis of variance to deter- mine differences among means.

RESULTS

The effect of temperature on bat M., LDH activity with pyruvate concentra- tions ranging from below the Km to nearly saturating is shown in Fig. 1. Replotting these data as initial velocity vs tempera- ture gave a family of curves (Fig. 2) which followed the Arrhenius relationship (36),

or ui zz A~-(F/RT)

ln vi = - I . L + In A, R T [41

where vi equals the initial velocity of the LDH reaction at temperature T (“K), R is the gas constant, and ~1 is the temperature effect parameter. Plots of In vi vs l/T were

708 CUDDIHEE AND FONDA

FIG. 1. The effect of pyruvate concentration on ini- tial velocity of I& LDH at various assay tempera- tures: 0,ll’C; l ,2OoC; q ,3O”C; and n , 385°C. NADH concentration was 1.0 X lo-’ M. LDH activity was assayed by following the decrease in absorbance at 340 nm. Each data point represents the mean of 15 determinations.

linear except with the lowest concentra- tion of pyruvate (Fig. 3, Table I). Values for p were obtained from the slopes and are given in Table I.

A plot of p vs pyruvate concentration demonstrated that the dependency of ~1 on pyruvate concentration followed a rect- angular hyperbola (Fig. 4, open circles). This relationship is similar to that ob- served with mollusk adenosine deaminase, which was shown to be described by Eq. [2] (16). Values for E,, EB, and Kt were cal- culated from our data as described under

1

FIG. 2. The effect of temperature on bat I& LDH activity at different concentrations of pyruvate: 0, 0.05 mM; A, 0.10 mrd; 0,020 ml; 0,0.40 mre; A, 0.30 mbi; n , 1.6 mM; and 0, saturating levels (V). This is a replot of the data in Fig. 1.

1

;i\. 0 5

- q 0

c 5o-\ L.0 0

. . D .

.

30. . . . 319 3.30 3.u 35:

fx 103

FIG. 3. The relationship of In vi for I& LDH with l/T at different concentrations of pyruvate: 0, 0.05 mM; A, 0.10 mM; 0,020 mM; 0,0.40 mM; n , 0.30 mM; A, 1.6 mu; and 0, saturating levels (V). This is a replot of the data in Fig. 2.

Materials and Methods and are presented in Table II. The solid line in Fig. 4 was drawn using Eq. [2] and these values, and the fit is excellent.

To verify further the use of this math- ematical model in describing substrate- dependent temperature effects, initial ve- locities were also measured at 11, 20, 30, and 38.5”C using a range of lactate con- centrations (1.25 to 20 mM) with 1 mM NAD+, a range of NAD+ concentrations (0.313 to 2.5 X 10e4 M) with 30 mM lactate, and a range of NADH concentrations (3.13 to 50 PM) with 1 mM pyruvate. All the data fit Eq. [4] well (Table I). The values for p calculated for each substrate concentra- tion (Table I) were dependent on lactate, NAD, and NADH concentrations (Figs. 5- 7). Values for the parameters E,, E,, and Kt for these substrates are presented in Table II. Data with lactate (Fig. 5, open circles) and NAD (Fig. 6) did fit the model Eq. [Z]; Because of the poor fit to Eq. [2] of the data obtained with various NADH concentrations, a reliable value of Kt could not be calculated (Fig. 7, Table II). There- fore, values of ~1 at various NADH con- centrations were calculated using Eq. [2], EB, E,, and three hypothetical values of Kt. Values of Kt equaling 0.5K,, Km, and 2K, at 25°C were chosen since the values of Kt for the other substrates were similar to their Km values at 25°C (Tables II and

TEMPERATURE/SUBSTRATE EFFECT ON BAT LACTATE DEHYDROGENASES 709

TABLE I

TEMPERATURE EFFECF PARAMETERS (cc) AND PRODUCT MOMENT CORRELATIONS (7) FOR ARRHENIUS PINTS OF INITIAL VELOCITY DATA WITH M4 LDH”

Substrate Concn. (mM)

fib (cal/mol) -9-C

Lactate

NAD+ 0.0313 0.0625 0.125 0.250 0.50 1.00

Pyruvate 0.05 0.10 0.20 0.40 0.80 1.60

0.313 0.625 1.250 2.50 5.00

10.00 20.00

NADH 0.00313 0.00625 0.0125 0.025 0.050

283 0.19 1,320 +- 516 0.68 rf: 0.15 3,225 + 741 0.90 zk 0.01 5,617 f 1,044 0.98 + 0.01 7,367 +- 530 0.99 + 0.00 9,130 f. 460 0.99 k 0.00

9,580d 0.98 + 0.00 9,900d 0.98 k 0.00

10,600 + 250 0.99 + 0.00 11,400 k 300 0.99 + 0.00 12,126 k 375 0.99 z!z 0.01 13,297 + 474 0.99 2 0.00 13,833 + 88 0.99 f. 0.00

10,647 + 314 0.99 + 0.00 11,336 k 201 0.99 2 0.00 13,296 * 145 0.99 2 0.00 13,943 f 33 0.99 f 0.00 14,094 5 253 0.99 2 0.00 14,330 * 70 0.99 + 0.00

6,657 + 1,093 0.94 + 0.03 6,978 + 1,027 0.99 + 0.01 8,492 f 692 0.99 f 0.01 9,767 f 712 0.98 + 0.01

12,531 + 1,183 0.98 + 0.01

a All values represent the means + SD. b Analysis of variance demonstrated significant differences (P < 0.01) for all variable substrates tested. ’ Correlation coefficient for Arrhenius plot. d Theoretically determined from pi values calculated using the Michaelis-Menten equation.

III). None of the calculated lines fit the data obtained with NADH (Fig. 7). Initial velocities at the lower concentrations of NADH were probably not very accurate, and substrate inhibition was observed at high concentrations of NADH, especially at 11°C.

Initial velocities of bat H1 LDH were measured at 11, 20, 30, and 38.5”C using a range of pyruvate concentrations (0.025 to 0.8 mM) with 0.1 mM NADH and a range of lactate concentrations (0.313 to 40.0 mM) with 1 mM NAD. The initial velocities increased with increasing substrate con- centration and with increasing tempera- ture. Plots of In vi vs the reciprocal of ab-

solute temperature were linear except with the lowest concentration of pyruvate. Plots of II vs pyruvate concentration (Fig. 4, closed circles) or lactate concentration (Fig. 5, closed symbols) demonstrate the substrate-dependent temperature effects on H4 LDH activity. Qualitatively these are similar to the substrate-dependent temperature effects we observed with M4 LDH.

Pyruvate-dependent temperature ef- fects for bat l& and M1 LDH activities fit Eq. [2]. The value of EB for bat MI LDH with pyruvate was significantly less than EB for bat H4 LDH. This relationship is in agreement with the effect of temperature

710 CUDDIHEE AND FONDA

I I 0.4 0.8 1.2 1.6

PrmmrE[mt4]

FIG. 4. The effect of pyruvate concentration on p for bat M1 (0) and Ht (0) LDH isoenzymes. The lines represent curves of best fit generated from the equa- tion of ~1 = (E&3 + E&)/(K, + s) and using values for E,, E,, and Kt shown in Table II. The circles rep- resent actual data (mean + SD). The NADH concen- tration was 1.0 X lo-’ M.

on the Vof LDH isoenzymes from humans (27, 30). The values of E, for bat M4 and H4 LDH with pyruvate were similar (Table II). The values of Kt for bat M4 and H4 isoenzymes with pyruvate were signifi- cantly different. Accordingly, the concen- tration of pyruvate required for maximum temperature effects was much lower for H4 LDH than for M4 LDH.

Lactate-dependent temperature effects for bat Mq LDH fit Eq. [2] (Fig. 5), however, the lactate-dependent temperature effects for bat H4 LDH were more complex. H4 LDH activity was inhibited by high lactate concentrations at all temperatures, but the degree of inhibition increased as assay temperature decreased (Fig. 8). Values of P for H4 LDH with high lactate were greater than EB (Fig. 5, Table II) since high lactate concentrations inhibited bat l& LDH more at low temperatures than at high temperatures and because the method used to determine V values re- jected values of initial velocity showing substrate inhibition (35). To determine the fit of the lactate data to Eq. [2], an Eb for H4 LDH was calculated taking into ac-

1 K 1 1 ---= P - Em E,-E, ' s+Es -E,' 151

Using the experimental values for p and E, (Table II), a plot of l/(p-E,) vs l/lac- tate gave a straight line. Eh was deter- mined from the 9 intercept.

The parameters EB, E,, and Kt deter- mined for lactate with Mq, Hq (assuming no substrate inhibition), and H4 (substrate inhibition included) LDH are shown in Table II. The effect of temperature on LDH activity at saturating lactate con- centrations, EB, for M4 LDH was signifi- cantly less than EB or Eb for bat H4 LDH (Table II). This relationship was also shown for the LDH isoenzymes from hu- mans and beef (4,28). The value of EL for l& LDH (substrate inhibition) was signif- icantly greater than the EB for Hq LDH (assuming no substrate inhibition). Thus

FIG. 5. The effect of lactate concentration on p for bat M1 (0), & (actual data with substrate inhibition, 0) and l& (calculated assuming no substrate inhi- bition, n ) LDH isoenzymes. The curved lines (both solid and broken) represent curves of best fit gen- erated from the equation p = (E&T + E&)/(K, + S) using the values for EB. E,, and Kt shown in Table II. The circles represent actual data (mean f SD). The squares are theoretical points obtained by as- suming substrate inhibition did not occur at the low temperatures; these points were determined by cal- culating initial velocities for high lactate concentra- tions using the Michaelis-Menten equation, Vi = V[S]/(K,,, + S). The NAD+ concentration was count the substrate inhibition by lactate.

Eq. [2] can be rearranged to 1 mM.

LACTATE [mM]

TABL

E II

MO

DEL

PAR

AMET

ERS F

OR

M4

LDH

AN

D H

q LD

H”

43

E,

EB -

Em

Iso-

Va

riabl

e en

zym

e su

bstra

te*

cal/m

ol

-r”

Cal

/m01

-r

C

al/m

old

cal/m

ol”

-r (2

)

M4

Pyru

vate

10

,459

+ 5

39

0.99

*

0.00

-3

,488

+

817

0.93

-+

0.03

13

,948

*

1,06

0 13

,903

It

972

0.99

k

0.01

0.

19 +

0.

03

Lact

ate

14,4

85 +

- 259

0.

99 -

+ 0.

00

9,05

4 +-

300

0.

97 -

t 0.

01

5,43

1 f

519

5,49

2 f

731

0.97

*

0.02

3.

60 k

0.

99

NAD

H

9,99

3 0.

99

5,83

1 0.

99

4,16

2 4,

140

0.91

N

AD

14,9

93 *

86

0.

99 z

k 0.

00

10,0

86 +

- 258

0.

98 +

0.0

2 4,

907

+ 34

1 4,

967

-+ 3

73

0.80

+ 0

.07

0.10

H

, Py

ruva

te

11,7

94 +

265

’ 0.

99 _

t 0.

00

-2,8

02

+ 25

1 0.

92 -

+ 0.

08

14,5

96 +

24

4 14

,644

?z

225

0.99

t

0.00

0.

054r

t 0.

003f

La

ctat

e@

25,6

91 f

39

1f

13,9

04 f

311f

0.

93 -

+ 0.

01

11,8

18 +

W

f 7.

23 -

t 0.

87f

Lact

ateh

18

,559

+ 3

805”

0.

99 -

t 0.

00

13,9

94 +

311

f 0.

93 *

0.

01

4,68

5 -c

71

0f

4,67

2 +

714

0.60

f

0.06

0.

99

‘All

valu

es r

epre

sent

th

e m

ean

f SD

. * S

econ

d su

bstra

te

is s

atur

atin

g.

’ Cor

rela

tion

coef

ficie

nt

for

Arrh

eniu

s pl

ot.

d EB

- E

, ob

tain

ed

from

ta

king

th

e di

ffere

nce

betw

een

E,

and

E,.

e EB

- E

, ob

tain

ed

from

plo

t In

K,,,

vs l/

T.

fH,

vs M

q w

ith

the

sam

e su

bstra

te,

P <

0.00

5.

g Ini

tial

velo

citie

s su

bjec

t to

sub

stra

te

inhi

bitio

n in

clud

ed.

h Ini

tial

velo

citie

s su

bjec

t to

sub

stra

te

inhi

bitio

n ex

clud

ed.

* H,

(g)

vs H

q (h

), I’

< 0.

005.

712 CIJDDIHEE AND FONDA

zyme-NADH complex. Initial velocities obtained with M4 LDH using saturating concentrations of NADH, various concen- trations of pyruvate, and three constant oxamate concentrations demonstrated that oxamate was a competitive inhibitor with respect to pyruvate at 11,20,30, and 38.5% (Fig. 9). The values for the Ki for oxamate and the K,,, for pyruvate decreased with decreasing temperature in a similar man- ner (Fig. 10).

NA D* [mM]

FIG. 6. The effect of NAD+ concentration on p for bat I& LDH isoenzyme. The curved line is the curve of best fit generated from Eq. [2] using values for E,, E,, and Kt shown in Table II. The circles represent actual data (mean + SD). The lactate concentration was 30 mM.

substrate inhibition plays an important role in determining the effect of temper- ature on the activity of H-type LDH iso- enzymes at high lactate concentrations. Unlike the data obtained with pyruvate, the value of E, for bat M4 LDH with lac- tate was significantly less than E, for & LDH. The Kt value for H4 LDH (substrate inhibition) was significantly higher than the Kt for M4 LDH.

In an attempt to determine the mech- anism of substrate-dependent tempera- ture effects, the effect of temperature on the apparent Km of the respective sub- strates and the binding of a competitive inhibitor of LDH was studied. Generally, the apparent Km values for pyruvate, lac- tate, NAD, and NADH with M4 LDH and for pyruvate and lactate with Hq LDH in- creased significantly (P < 0.01) with in- creasing temperatures (Table III). No sig- nificant changes were observed for the Km values for M4 LDH with lactate or NAD between 11 and 20°C or with NADH be- tween 20 and 335°C. The Km value for H4 LDH with lactate decreased significantly in going from 11 to 20°C.

The apparent K,,, for pyruvate is made up of several rate constants and is not sim- ply a dissociation constant (14, 37, 38), whereas the Ki for oxamate is the disso- ciation constant for oxamate and the en-

DISCUSSION

The effect of temperature on bat M4 LDH activity was dependent on the con- centrations of all four substrates of LDH:pyruvate and NADH in the pyruvate to lactate direction, lactate and NAD in the lactate to pyruvate direction. These substrate-dependent temperature effects can be described by Eq. [2], P = [E,S + EJJ/[K, + 5’J. This model equation was applied successfully to data obtained with M4 LDH in the presence of various con- centrations of pyruvate, lactate, and NAD+. NADH-dependent temperature effects did not fit the model equation. We feel, how- ever, this was not an inadequacy of the

12 . 1 _____-_--

NADH LM]

FIG. 7. The effect of NADH concentration on P for bat M4 LDH isoenzyme. The concentration of pyru- vate was 1 mM. The circles represent the actual data (mean + SD). The lines were generated from Eq. [2] using the values for EB and E, shown in Table II and Kc equal to 3.13 (- - -), 6.25 (-), and 12.5 pY (- - -).

TEMPERATURE/SUBSTRATE EFFECT ON BAT LACTATE DEHYDROGENASES 713

TABLE III

THE EFFECT OF TEMPERATURE ON THE APPARENT K,,, VALUES OF Mq LDH AND H4 LDH

Iso- enzyme Substrates 11 20 30 38.5

K,,, value (mM)O at designated temperature (“C)

M4

H4

Pyruvate NADH Lactate NAD+ Pyruvate Lactate

0.067 + 0.009 0.121 f 0.018 0.257 + 0.023 0.600 2 0.065 0.0035 r o.ooo7 0.0054 + o.ooo7 0.0068 + o.ooo9 0.0066 + o.ooos 2.10 rt 0.13 2.44 + 0.18 3.53 + 0.33 4.88 5 0.17 0.069 rt_ 0.003 0.056 k 0.006 0.082 5 0.005 0.149 + 0.010 0.016 + 0.001 0.031 f 0.002 0.069 + 0.004 0.162 + 0.007 0.659 5 0.001 0.368 + 0.012 0.640 f 0.036 1.296 f 0.172

’ Values represent the means + SD.

model equation, but rather an inadequacy in the method of our data collection. Since the apparent K, for NADH is extremely low, it was very difficult to measure LDH activity at NADH concentrations below the Km. At high NADH concentrations, inhibition was observed.

Equation [2] was also applied success- fully to data obtained with H4 LDH in the presence of various concentrations of py- ruvate and lactate. The fit of the data with lactate improved when the inhibition by high lactate concentrations was taken into consideration.

The model for substrate-dependent tem- perature effects defines several parame- ters. EB is equal to p at infinite substrate concentration and is the highest value p can attain assuming the enzyme does not

250

100

100 200 300 LOO

LACTATE [mM]

FIG. 8. The effect of lactate concentration on initial velocity of bat H4 LDH at various assay tempera- tures: 0, 11; 0, 20; 0, 30; and n , 38.5”C. The NAD concentration was 1 mrd.

exhibit substrate inhibition. &, is equal to p at zero substrate concentration and is the lowest value p can attain. The value ,?ZB - E,, or the range of values for CL, pro- vides a way of quantitating substrate-de- pendent temperature effects. Kt equals the concentration of substrate when CL = [I$ + I&]/2. As with the Michaelis-Menten curve, the slope of the p vs S curve is great- est at substrate concentrations below the Kt. Consequently, for substrate concentra- tions equal to or less than the &, the tem- perature effect on LDH activity will be extremely dependent on substrate concen- tration.

For all substrates, substrate-dependent temperature effects on bat M4 and H LDH

r I 05 1.0 1.5 20

PYRlJL TE x dt4

FIG. 9. Lineweaver-Burk plot showing oxamate in- hibition of bat M4 LDH at 38.5”C. Oxamate concen- trations were (0) 0.0, (0) 6.0 X lo-‘, (U) 1.2 X lo-*, and (0) 2.4 X lOA td. The concentration of NADH was 1 x 1o-4 M.

714 CUDDIHEE AND FONDA

FIG. 10. The effect of temperature on the apparent K,,, of pyruvate (0) and the apparent Kj of oxamate (0) with hat I& LDH.

activity were associated with a tempera- ture effect on the apparent Km values (Figs. 4-7, Table III). This observation agrees with Hochachka and Somero’s (13) concept that positive and negative thermal modulation are responsible for substrate- dependent temperature effects on enzyme activity.

The model equation can be used to verify mathematically that the temperature ef- fects on the apparent Km are responsible for these substrate-dependent tempera- ture effects. Differentiating Eq. [Z] with respect to S yields

Thus the change in temperature effects on LDH activity with respect to the change in substrate concentration is directly re- lated to the quantity [EB - E,]. However, EB and E, are defined as the temperature- effect parameters of an Arrhenius plot when vi equals V and V/K,, respectively,

lnV=lnA-2$, VI

Taking the difference of Eqs. [7] and [8] and rearranging gives

ln K n

= EB - Ea !. + ln A”

-RT * PI

Finally, taking the derivative of In Km with respect to l/T yields

d In Km ---= EB - E, d(l/T) -R ’

or -Rd In Km

Eb - E‘T = d(l,T) * WI

Substitution of this expression into Eq. [6] yields

dp [-Rd In JUWT)I-K. f11l -= ds (K + q2

Thus the temperature effects on the ap- parent K,,, are directly responsible for the thermal modulation which produces sub- strate-dependent temperature effects. If [EB - Em] is positive, the system shows positive thermal modulation and the ex- tent of the modulation depends on the magnitude of [:E, - E,]. If [EB - E,] is negative, the system shows negative ther- mal modulation. Comparison of [E, - E,] derived from our Km data and [EB - E,] obtained from our E, and E, data dem- onstrate the validity of our derivation (Table II).

The mathematical model enables quan- tification of thermal modulation and thus provides a method for comparative stud- ies. Since the values of E, - E, obtained for both bat M4 and H4 LDH with pyruvate were positive and similar (Table II), these isoenzymes had the same degree of ther- mal modulation. With lactate, however, the values of EB - E, for bat H4 (assuming no substrate inhibition) and M4 LDH were similar and were significantly lower than Eb - E, for H4 (with substrate inhibition). Therefore, because of substrate inhibition by lactate, H4 LDH had greater positive thermal modulation (a greater effect of temperature on the apparent Km) than did M4 LDH.

It has been suggested that thermal mod- ulation (dp/dS) produced by temperature effects on the apparent Km is the result of temperature affecting the binding of substrate to enzyme (13). Evidence for this, however, has been based solely on the assumption that the apparent Km is sim- ilar to the dissociation constant of the en-

TEMPERATURE/SUBSTRATE EFFECT ON BAT LACTATE DEHYDROGENASES 715

zyme-substrate complex. Since, in most cases, the apparent K, is made up of many rate constants and not just the dissocia- tion constant (14, 37, 38), the claim that changes in enzyme-substrate affinity are responsible for thermal modulation may not be justifiable.

To determine if the thermal modulation which produced the pyruvate-dependent temperature effects on LDH activity could be described by the effects of temperature on the affinity of LDH for pyruvate, we investigated the effect of temperature on the affinity of oxamate for M4 LDH-NADH complex. Since oxamate is a competitive inhibitor with respect to pyruvate at all temperatures used (Fig. 9) and its Ki value is a true dissociation constant between oxamate and the enzyme-NADH complex, the effect of temperature on the Ki for oxamate should be similar to the effect of temperature on the dissociation constant of pyruvate from the enzyme-NADH com- plex. Figure 10 demonstrates that both the apparent Km for pyruvate and the Ki for oxamate with bat M4 LDH decreased with decreasing temperature. It appears as if the pyruvate-dependent temperature ef- fects on activity, or positive thermal mod- ulation with pyruvate, resulted from an increased affinity of the enzyme-NADH complex for pyruvate.

Although many enzymes exist as iso- enzymes (39), the physiological purpose of these enzyme variants is still quite spec- ulative. In an effort to understand the role of LDH isoenzymes, the H4 and M4 LDH isoenzymes have been compared (40-45), however, no attempt has been made pre- viously to compare the effect of temper- ature on the activity of the LDH isoen- zymes at low, or physiological, substrate concentrations.

Both bat M4 and H4 LDH activities were controlled by substrate-dependent tem- perature effects with respect to pyruvate and lactate. These temperature effects were described by the model Eq. [2]. All the parameters E,, E,, and Kt must be taken into account to determine the effect of temperature on LDH activity at any substrate concentration. Physiological substrate concentrations are usually at or

below Km levels (l-3) and consequently Kt levels (R. W. Cuddihee and M. L. Fonda, unpublished results). Therefore, E,, the relationship of in vivo substrate concen- tration to K,, and the extent of thermal modulation (E, - EJ are physiologically significant. In the pyruvate to lactate di- rection, the effect of temperature on H4 and M4 LDH activities was the same at infinitely low pyruvate. Since the Kt values were different for the two isoenzymes with pyruvate, the relative amount of temper- ature dependency would depend on the ratio of pyruvate concentration to the re- spective Kti In the lactate to pyruvate di- rection, the activity of H4 LDH showed greater temperature dependency at all lac- tate concentrations and showed greater thermal modulation than the activity of M4 LDH, because H4 LDH activity had a higher E, and was subject to substrate inhibition. The physiological significance of the values of the parameters in Eq. [2] is being studied by determining the tem- perature and substrate concentrations in E. fuscus tissues while the animal is arous- ing from hibernation.

Studies involving the effect of temper- ature on enzyme activity report the effect of temperature usually on V (E,) and less frequently on Km (E, - E,) and perhaps V/K, (EJ. The model equation describes temperature effects on enzyme activity for all substrate concentrations. Since phys- iological substrate concentrations appear to be considerably below those levels re- quired to saturate enzyme systems, an evaluation of the effect of temperature on an enzyme system in viva requires an un- derstanding of the effect of temperature on enzyme systems using substrate con- centrations below saturation.

The model equation developed by Har- bison and Fisher, Eq. [2], can be used to describe the effect of temperature at sub- strate concentrations below saturation for any enzyme that has a temperature-de- pendent apparent Km (Eq. [ll]). Since, in most cases, apparent Km values are tem- perature dependent over an organism’s normal range of habitat temperature (12-14, 19-21, 24, 25, 28, 29), the model equation may be used to describe the effect

716 CUDDIHEE AND FONDA

of temperature on enzyme activity with various substrate concentrations, not only for adenosine deaminase (16) and LDH, but for most enzyme systems.

ACKNOWLEDGMENTS

We thank the Indiana Department of Natural Re- sources Division of Fish and Wildlife for issuing an Indiana scientific collectors license for the collection of bats. We appreciate the assistance of Dr. George H. Herbener in the collection of the animals.

REFERENCES

1. SOMERO, G. N., AND HOCHACHKA, P. W. (1969) Nature (e) 223,194-195.

2. SOMERO, G. N. (1969) Biochmh J. 114,237~2.41. 3. FERSHT, A. (1977) Enzyme Structure and Mech-

anism, p. 256-259, Freeman, Reading/San Francisco.

4. OLSON, S.-O. R. (1975) @q~. Biochem Physid 51B, 5-18.

5. VROMAN, H. E., AND BROWN, J. R. C. (1963) J. Cell Camp P/L&& 61,129-131.

6. DEMENEIX, B. A., AND HENDERSON, N. E. (1978) Cmnp. Bimhen~ Physid 59B, 333-337.

7. RAISON, J. K., ANDLYONS, J. M. (1971) PWC Nat. Acad Sk USA 63,2092-2094.

8. WOODARD, C. B., ANJJ ZIMNY, M. L. (1973) Amer. J. Physid 225,429-431.

9. Low, P. S., AND SOMERO, G. N. (1974) tip Biochem Physid 49B, 307-312.

10. Low, P. S., BADA, J. L., ANDS~MERO, G. N. (1973) Proc Nat Acad Sci USA 70,430-432.

11. SOMERO, G. N., AND SIEBENALLER, J. F. (1979) Nature (Lmdm) 282,1OO-102.

12. NARITA, J., AND HORIUCHI, S. (1979) mp. Biochen~ Phyeiol 64B, 249-253.

13. HOCHACHKA, P. W., AND SOMERO, G. N. (1973) Strategies of Biochemical Adaptation, pp. 222- 245, Saunders, Philadelphia.

14. BORGMANN, U., MOON, T. W., AND LAIDLER, K. J. (1974) Biochemistrg 13,5152-5158.

15. BEHRISCH, H. W. (1971) B&hem. J. 121,399-409. 16. HARBISON, G. R., AND FISHER, J. R. (1974) C!mp

Biochem Physid 47B, 27-32. 17. HOCHACHKA, P. W., AND SOMERO, G. N. (1968)

Conzp Biochem Physid 27.659-668. 18. BEHRISCH, H. W. (1974) Canad J. Biochem 52,

894-902. 19. BORGMANN, A. I., AND MOON, T. W. (1976) J,

Cmp Physid 107.185-199. 20. HOSKINS, M. A. H., AND ALEKSIUK, M. (1973)

Camp Bidwm Physid 45B, 343-353. 21. BALDWIN, J., AND ALEKSIUK, M. (1973) hp

Biochem Physiol 44B, 363-370.

22. GIBSON, K. D. (1953) B&him Biophya Acta lo, 221-229.

23. BEHRISCH, H. W. (1969) Biochem J. 115.687-696. 24. SOMERO, G. N., AND HOCHACHKA, P. W. (1968)

Biochem J. 110,3%-400. 25. SOMERO, G. N., AND HOCHACHKA, P. W. (1971)

Amer. Zcd 11.159-167. 26. GEREZDE BURGOS, N. M., BURGOS, C., GUTIERREZ,

M., AND BLANCO, A. (1973) Biochim. Biaphya Acta 315,25O-258.

27. BIJHL, S. N., JACKSON, K. Y., LUBINSKI, R., AND VANDERLINDE, R. E. (1977) clin Chem 23, 1289-1295.

28. BORGMANN. U., AND MOON, T. W. (1975) Can.& J. Biochem 53.998-1004.

29. TSUGAWA, K. (1980) Camp Biochem Physid 66~, 459-466.

30. BUHL, S. N., JACKSON, K. Y., AND VANDERLINDE, R. E. (1977) Cl& Chim, Acta 80,~270.

31. MOON, T. W. (1978) Cmp Biocha, Physid 59B, 183-190.

32. O’CARRA, P., ANDBARRY, S. (1972) FEBSL.& 21, 281-285.

33. NADAL-GINARD, B. (1978) J. Bid Chem 253,170- 177.

34. DIETZ, A. A., AND LUBRANO, T. (1967) Anal. Biochem 20,246-257.

35. CLELAND, W. W. (1967) Advan Enzynd 29, l- 32.

36. JOHNSON, F., EYRING, H., AND STONER, B. J. (1974) The Theory of Rate Processes in Biology and Medicine, pp. 3-5, Wiley, New York.

37. CLELAND, W. W. (1970) in The Enzymes (Boyer, P., ed.), 3rd ed., Vol. 2, pp. 6-7, Academic Press, New York.

38. DIXON, M., AND WEBB, E. C. (1979) Enzymes, 3rd ed., p. 57, Academic Press, New York.

39. URETA, T. (1977) Curr. !&p CeU Regd 13, 233- 258.

40. EVERSE, J., AND KAPLAN, N. 0. (19’73) Advan EnzymaL 37,61-W.

41. HOLBROOK, J. J., LILIAS, A., STEINDEL, S. J., AND ROSSMAN, M. G. (1975) in The Enzymes (Boyer, P. D., ed.), pp. 191-292, Academic Press, New York.

42. EVERSE, J., AND KAPLAN, N. 0. (1975) in Isoen- zymes, Vol. 2, Physiological Function (Mar- kert, C. L., ed.), pp. 29-43, Academic Press, New York.

43. EVERSE, J., BARNE’IT, R. E., THORNE, C. J. R., AND KAPLAN, N. 0. (1971) Arch. Biochem Biophya 143,444-460.

44. PLAGEMANN, P. G. W., GREGORY, K. F., AND WROEUEWSKI, F. (1960) J. Bid Chem 235, 2282-2287.

45. VESELL, E. S. (1965) sciace l50,159O-1593.