Vol. 267, No.20, Issue of July 15,pp. 14084-14093, 1992

THEJOURNAL OF BIOLOGICAL CHEMISTRY

Printed in U.S.A.

Effect of Temperature onthe Creatine Kinase Equilibrium* (Received for publication, December 17, 1991)

Walter E.Teague, Jr. and Geoffrey P. Dobson$ From the National Institute on Alcohol Abuse and Alcoholism, National Institutes of Health, Rockville, Maryland 20852

The effect of temperature on the apparent equilibrium constant of creatine kinase (ATPxreatine Nphosphotransferase (EC2.7.3.2)) was determined. At equilibrium the apparentK' for thebiochemical reaction was defined as

Creatine kinase (ATP:creatine N-phosphotransferase (EC 2.7.3.2)), a dimeric enzyme (Mr 82,600), catalyzes the magnesium-dependent reversible transphosphorylation between phosphocreatine (PCr)' and ATP according to the following biochemical reaction (1, 2).

[ZATP][Cr]

LPCr

K' = [ZADP][ZPCr]

+ BADP = ZATP + Cr

(1)

The transphosphorylation reaction was first described in The symbol 2 denotes the sum of all the ionic and metal complex species of the reactant components in 1934 by Karl Lohmann (3), and a few years later its reversiM. The K' at pH 7.0, 1.0mM free M 8 + , and ionic bility in muscle extracts was demonstrated by Lehmann (4). strength of 0.25 M at experimental conditions was 177 Since that time there has been much interest in the kinetics & 7.0,217f 11,255j : 10,and 307 f 13 (n= 8)at 38, of the enzyme from a variety of tissues (5) and its important 25, 15,and 5 "C, respectively. The standard apparent role in energetic coupling of metabolic processes in excitable enthalpy or heat of the reactionat the specified condi- tissues (6, 7). One of the key functions of creatine kinase in tions (AH'") was calculated from a van't Hoff plot of brain, skeletal, and cardiac muscle is its capacity to maintain log,& versw 1/T, and found to be -11.93 k J mol" (-2852 cal mol-l) in the direction of ATP formation. cytosolic ATP levels relatively constant during steady state The corresponding standard apparent entropy of the activity and duringmodest work transitions despite decreases in PCr (8, 9). It performs this buffer function in vivo by reaction (AS'") was +4.70 J K"mol". Thelinear function ( 3= 0.99)between loglo K' and 1/Kdemon- maintaining near-equilibrium between all reaction compostrates that both AH'" and AS'" are independent of nents (10-15). Past attempts to explain the maintenance of temperature for the creatine kinase reaction, and that near-equilibria in vivo have focused on ( a ) the enzyme being AC,,'", the standard apparent heat capacityof products present at activities in tissue far in excess of the rate of ATP minus reactants in their standard states, isnegligible utilization (16), and ( b ) that it is not kinetically limited by between 5 and 38 "C. We further show from our data either of its substrates since the K, values are in the approxthat the sign and magnitude of the standard apparent imate range of concentrations reported in the tissue (16). Gibbs energy (AG'O) of the creatine kinase reaction It was the maintenance of near-equilibrium of creatine was comprised mostly of the enthalpyof the reaction, kinase, and the combined reactions of glyceraldehyde-3-phoswith 11%coming from the entropy TAS'" term. The phate dehydrogenase, 3-phosphoglycerate kinase, lactate dethermodynamic quantities for the following two reference reactions of creatine kinase were also deter- hydrogenase equilibria in tissue(11-15) that subsequently led to its widespread use in estimating the cytosolic phosphorylmined. ation ratio (ATP/ADP x Pi) and free ADP and Pi in tissues PCr2- + ADPS- + H+ = ATP4- + C r (2) by traditional biochemical methods (11)and more recently by MgPCr + MgADP" + H+ = MgATP2- + Cr + Mg2+ (3) noninvasive 31PNMR (17). The phosphorylation ratio permits calculation of the apparent Gibbs energy of the system, The AH" for Reaction 2 was -16.73 k J mol" (-3998 while free ADP and Pi have been implicated as the primary cal mol") and for Reaction 3 was -23.23 k J mol" kinetic controllers of oxygen consumption (18). (-5652cal mol") over the temperature range 5-38 "C. Despite the early kinetic and thermodynamic studies on The corresponding ASo values for the reactions were creatine kinase (5) and the more recent thermodynamic study +110.43 and +83.49 J K-' mol", respectively. Using the AH'" of -11.93 k J mol", and one K value at one of Lawson and Veech (19) and the31PNMR study of LoPresti temperature, a second K' at a second temperature can and Cohn (20), the quantitative effect of temperature on the be calculated, thus permitting bioenergetic investiga- reaction remains to be investigated. The aim of this study tions of organs and tissues using the creatine kinase was to determine the enthalpy and entropy changes for the equilibria over the entire physiological temperature biochemical reaction at pH 7.0, 1.0 mM free M$+, and an range. ionic strength of 0.25 M and for two chemical reactions over the temperature range of 5-38 "C. The AH'"for the creatine * The costs of publication of this article were defrayed in part by kinase biochemical reaction should have widespread applicathe payment of page charges. This article must therefore be hereby marked "aduertisement" in accordance with 18 U.S.C. Section 1734 tion in those studies on the bioenergetics of animal tissues maintained at temperatures other than 38 "C. solely to indicate this fact. ~

~~

~~

~

~~~

~~~

$ To whom correspondence should be addressed NationalInstitute on AlcoholAbuse and Alcoholism, National Institutes of Health, 12501 Washington Ave., Rockville, MD 20852.

14084

' The abbreviation used is: PCr, phosphocreatine.

Effect of Temperature Creatine theonKinase Equilibrium MATERIALS AND METHODS'

Enzymes and Chemicals Creatine kinase (EC 2.7.3.2) was purchased as the lyophilized powder from rabbit skeletal muscle. Glucose-6-phosphate dehydrogenase (EC 1.1.1.49) Grade 1 from yeast, hexokinase (EC 2.7.1.1) from yeast, lactate dehydrogenase (EC 1.1.1.27) from beef heart, and pyruvate kinase (EC 2.7.1.40) from rabbit skeletal muscle were purchased as the3.2 M ammonium sulfate suspensions from Boehringer Mannheim. Pyruvate-monosodium salt, ATP-crystallized disodium salt, ADPdisodium salt, phosph~nolpyruvate-tricyclohexyl~monium salt, NADH-mono~ium salt (Grade I), and NADP-disodium salt (98%) were obtained from Boehringer Mannheim, D-Glucose, imidazole (low , Trizma-base (tris(hy~oxymethy1)fluorescence blank 0 . ~ 2 % ) and aminomethane), phosphate-potassium salt (mono~asic and dibasic), were purchased from Sigma. EDTA (acid form) powder was purchased from J. T. Baker Chemical Co. All other chemicals were reagent grade. For equilibrium studies, creatine hydrate, phosphate-sodium salt (monobasic and dibasic), potassium chloride, magnesium chloride (anhy~ous), and thepotassium salts of ATP and ADP were purchased from Sigma. Phosphocreatine-disodium salt and creatine kinase (lyophilized) were obtained from Boehringer Mannheim.

I n s t r u ~ n t a t i o nand Equilibrium Determinations NADH or NADP oxidation-reduction was monitored a t 340 nm and 1-cm path length using a Zeiss PMQ-I1 spectrophotometer (Carl Zeiss, Oberkochen, Germany) taking the extinction coefficient of NADH under these conditions to be 6.22 X cm2/mol a t 340 nm. In those instances where the limitations of the Zeiss were reached, for example the measurement of ADP when the equilibrium was approached favoring ATP and creatine formation, the oxidation of NADH was monitored by a change in fluorescence using a Farrand Ratio-2 fluorimeter (Optical Technology Devices, Inc., Elmsford, NY). Fluorometer assay tubes were disposable borosilicate Kimble glass culture tubes (10 X 75 mm) purchased from PGC Scientific (Gaithersburg, MD). The equilibrium mixtures were placed in IO-ml capacity ReactiVials containing Reacti-Vial magnetic stirrers. The Reacti-Vials were housed in an Reacti-Aluminum Block ( E l ) which holds up to eight vials. The vials, stirrers, and block were purchased from Pierce. A water/air-powered magnetic stirrer (GFS Chemicals, Columbus, OH) was built and attached to the bottom of the aluminum block in the water bath. The stirrer was purchased from PGC Scientific. The entire block was suspended in a refrigerated Neslab RTE-110 water bath (Neslab Instrument, Portsmouth, NH). Thetemperature of the water bath could be maintained at k 0.1 "C.The pHof the equilibrium mixtures was measured on a Radiometer PHM 84 research pH meter at 25 "C (Radiometer, Copenhagen). Values of pH were corrected to the experimental temperature in the equilibrium mixtures using a temperature coefficient (ApH/At "C) of -0.0028 for 50 mM phosphate buffer (21). We assumed linearity between the change in pH and temperature for 50 mM phosphate buffer from 5 to 38 "C. Equilibrium incubations were carried outin 50 mM potassium phosphate buffer, pH 7.0, 180 mMKC1, and 3.25 mM total MgC12. The mixtures were prepared by adding the reactants in powder form t o 20 ml of 50 mM monobasic potassium phosphate buffer, 180 mM KCI, 3.25 mM MgCIz. All substrates were analyzed for magnesium using atomic-absorption spectrophotometry and have been taken into account inthe calculations of free Mg2'. Having dissolved the metabolites, the pHwas then adjusted to 7.0 using 3 M KOH. Final volume of solution was adjusted to 25 ml in a volumetric flask, and a final p H was read a t 25 "C. 10-ml aliquots of the equilibrium mixtures were placed in the Reacti-Vials and water bath (5.0 k 0.1 "C). Creatine kinase (13 mg of lyophilized powder) was dissolved in 1.0 ml of 50 mM phosphate buffer, pH 7.0, and 25 plwas added to the10 mi reactvial (about 10 units/mI at 25 "C). After 1-h reaction time, a 1.0-ml aliquot was transferred from the Reacti-Vial to a Centricon-30 spin filter (Amicon, Connecticut, MA) kept at thedesired temperature in the water bath. The spin filter was then placed into a temperaturecontrolled rotor and centrifuged a t 4000 X g for 10 min. The enzymePortions of this paper (including part of "Materials and Methods" and Tables 6 and 7) are presented in miniprint at the end of this paper. Miniprint iseasily read with the aid of a standard magnifying glass. Full size photocopies are included in the microfilm edition of the Journal thatis available from Waverly Press.

14085

free filtrate containing the reactants of the creatine kinase reaction was removed and kept at -89 "C untilanalysis the following day.To ensure that thetemperature was maintained constant from the equilibrium bath to the time of removing the enzyme by centrifugation, great care was taken to keep the centrifuge and rotors at the appropriate experimental temperature. After completing the experiment, the bathtemperature was changed to 15"C using identical procedures described for 5, then 25, and finally 38 "C.

M e t a ~ Assays ~~c Spectrophorometric and fluorometric enzymatic assays were carried out according to theprocedures described in Lowry and Passonneau (22) with the following modifications. Total adenosine 5'-triphosphate (ZATP) was measured in 50 mM Tris-HC1, pH 8.1, 0.4 mM D-glucose, 1 mM MgC12, 0.3 mM NADP containing 0.35 unitsiml glucose-6-phosphate dehydrogenase. The reaction was initiated with 0.7 unitlml hexokinase and complete in 5-10 min. Total creatine phosphate (ZPCr) was measured using the reagent described for ATP except with the addition of that hexokinase (0.7 unit/ml)and ADP (0.4 mMf, The reaction was initiated by the addition of 150 unitslml creatine kinase, and the reaction was complete in 5-10 min. Stock creatinekinase solution was made by slowly dissolving 40 mg of creatine kinase in 0.950 ml of ice-cold 50 mM Tris-HCC pH 8.i. Total creatine (ZCrl was measured in 100 mM imidazole-HCI. DH 7.6, 5 mM, 30 mM Kdl, 0.5 mM phosphoenolpymvate, 1 mM ATP, 0.100 mM NADH containing 5 units/ml lactatedehydrogenase and 5 units/ml pyruvate kinase. The reaction was initiated by the addition of 150 units/ml creatine kinase (for preparation of creatine kinase see creatine phosphate assay above). The reaction was complete in 10 min. Total adenosine 5"diphosphate (ZADP) was assayed in 50 mM phosphate buffer, pH 7.0 (30 mM Na2HP04:20mM NaH2P04),2 mM MgC12, 0.2 mM phosphoenolpyruvate, 0.2 mM EDTA, 0.100 mM NADH containing 1.25 units/ml lactate dehydrogenase. ADP was then measured by the addition of 5.0 units/ml pyruvate kinase. The reactions were over in 5 min. The reagent for the fluorometric assay of ADP was identical to that described for the spectrophotometric assay except that the NADHwasreduced to 0.005 mM and the reaction initiated with 0.2 unit/ml pyruvate kinase.

Theory and Equations Used to Calculate

A

H

'

O

Relationship between the Standard Apparent Gibbs Energy, Standard Apparent Enthalpy, and Standard Apparent Entropy inBiochemical Systems-The second law of thermodynamics provides the basis for the predictions of the effects of temperature on all chemical and physical equilibrium (23). As with any thermodynamic treatment of a chemical reaction, it is important to emphasize that the amount of heat and work evolved or absorbed by the reacting system when it changes from an initial to a final state depends on the independent variables that are held constant and is independent of pathway. For a biochemical reaction at specified T , P, pH, free M e and I , the standard apparent thermodynamic properties for a reaction can be quantitatively described by the following equation, AG'" = AH'" - TQS'" where AG'" is the standard apparent Gibbs free energy change, is the standard apparent enthalpy change, and AS'" is the standard apparent entropy change of a reaction at theabsolute temperature T in Kelvin. The above equation applies to the change in state of the reacting system from unmixed reactants each a t a standard concentrations of 1 M to unmixed products each at their standard state concentrations of 1 M, except for the solvent water, a t constant temperature and pressure (24). For biochemical systems, the conditions commonly referred to are pH 7.0 and free MgZ+ of 0.5 or 1.0 mM, ionic strength of 0.25 M, temperature 25 or 38 "C, and atmospheric pressure. ~ e f i n i ~ofi oEqu~libr~um ~ and the ~ ~ u i ~Cons~ant-Equilib~ r i u ~ rium may be defined as thatdynamic state where the apparent Gibbs energy of reaction (AG't is zero a t specified T, P, pH, free MgZ+, and I (AG' = AG'" + RT2.303 log K' = 0). When the reactants represent the total ionic species, the equilibrium constant is known as an apparent R', which is often referred in the literature to a Kwp or observed equilibrium constant (KO&) (Table 1). K' may be calculated using the the totalreactant concentrations analytically measured in the laboratory specified a t experimental conditions (e.g. pH 6.96, free M e = 0.94mM, I = 0.25 M, 38 "C), or it maybe calculated a t

14086

Effect of Temperature on the Creatine Kinase Equilibrium TABLE 1 Definitions of thermodynamic quantities, symbols, and units

Symbol

Definition

Units

K'

Apparent equilibrium constant of a biochemical reaction where the reactant concentrations are the sum of all the species at specified pH and free M e . K' may be calculated using the total reactant concentrations analytically measured in the laboratory at experimental conditions (e.g., pH 6.96, free M$+ = 0.94 mM, I = 0.25, 38 "C) or it may be calculated by inputing the experimental data into a computer program and solving for K' a t standard conditions of pH, free M F , ionic strength and temperature (see miniprint for the discussion and an example). The meaning of K' cannot be interpreted unless accompanied by a biochemical equation and specification of the standard stateof each of the reactants. K' has also been referred to in the literature as Kobsor Kapp.

M

Krei

Equilibrium constant of a chemical reaciton in terms of species a t specified temperature, pressure, and ionic (see text for specific reaction). strength. Two K-f were used in the present study, Ki,,, and KMgmmpler

M

Enthalpy or heat contentof a reaction at standardconditions of temperature, pressure, and ionic strength. The symbol denotes standard conditions (hypothetical ideal solution at 1 M). A negative AH' indicates an exothermic reaction and a positive A H * an endothermic reaction.

J mol"

AH'"

Standard apparent or transformed enthalpyof a reaction at specified pH, and free M e , temperature, pressure, and ionic strength.

J mol"

AGO

Standard Gibbs energy of a reaction under standard conditions. G is defined as U K.

In

J mol"

AG'"

Standard apparent or transformed Gibbs energy of a reaction at specified T, P, pH, free M e , and I. AG'" = -RTln K'.

J mol"

AS'

Standard entropy of a reaction under standard conditions.

AS'"

Standard apparentor transformed entropy of a reaction at specified pH, and free MgZf, temperature, pressure, and ionic strength.

ACpo

Standard heat capacity of the products of a reaction minus the heat capacity of the reactants under standard conditions a t constant pressure.

J K" mol"

AC,"

Standard apparent or transformed heat capacity of the products of a reaction minus the heat capacity of the reactants at specified pH, and free M e , temperature, pressure, and ionic strength.

J K" mol"

A H o

+ PV - TS. AGO = -RT

+ t/"C

T

Absolute temperature in Kelvin where T/K = 273.15

R

Gas constant from the ideal gas equation PV = nRT where P is the pressure, n is the amount, Vis thevolume and T i s the temperature. R = 8.3145 J K" mol" (1.9873 cal K" mol").

I

Ionic strength I = 1h Z cg2,where c, is concentrations of the various ions in moles per liter andz, is the charge of the resDective ions.

specified standard conditions of pH, free M F , ionic strength, and temperature (e.g. pH 7.0, free M$' of 1.0 mM, I = 0.25 M, 38 "C, see Miniprint). The biochemical reaction for creatine kinase in this study was Reaction 1 where K' = [ZATP] [Cr]/[ZPCr][BADP] and the symbol Z denotes the sum of all the ionic and metal complex species in M. In addition to the biochemical reaction (Reaction 1) and K', there exist a number of chemical reactions known as reference reactions with equilibrium constants Kref8. Krefs are calculated from the empirical data and knowledge of the acid dissociation constants and metal binding constants for all the reactants and solving for the defined reactant species. In the present study we defined two reference reactions for creatine kinase, PCr2- + ADP3MgPCr

+ H'

+ MgADP" + H'

=

ATP"

+ Cr

= MgATP2- + Cr

(2)

+ MgZ+

(3)

J K" mol" J K" mol"

K J K" mol" M

the conversion factor from loglo to natural log (In), and K' is the apparent equilibrium constant. The variation of K' with temperature is given by the following expression (known as the van't Hoff equation), = -."d log K'

dT

A€F" 2.303RTZ

where AH'" is the standard apparent enthalpy of the reaction, and

K' is the apparent equilibrium constant. The quantitative relation between the apparent equilibrium constant and temperature is commonly derived by integrating Equation 5 (23). A much simpler procedure is to substitute Equation 4 into AG'" = AH'" - TAS'" which yields the following. log K' =

AS'*

-AH'"

+2.303RT 2.303R

with corresponding K,r. of Ki,,ic and K M ~ respectively. ~ ~ ~ ~ I ~ ~ , Equation 6 shows that when log K' is plotted against 1/T, a straight The K commonly used in physical chemistry but not directly line will be generated with a slope equal to -AH'"/2.303 R and y intercept of AS'"/2.303 R when AH'" is independent of temperature. applicable to physicochemical systems is the thermodynamic equilibThus Equation 6 is of the type y = mx b, where m is the slope and rium constantK (Z= 0). K ( I = 0 ) is calculated by extrapolating from b is t h e y intercept a t any defined 1/T value. specified ionic conditions back to zero ionic strength at infinite In order to utilize Equation 6 for purposes of calculating a second dilution where the activity coefficients of each reactant species is K a t another temperature given one K' and the Lw' of the reaction, equal to 1.0. For K (I= 0) to be of use in biochemical systems it must it is written for two temperatures and thedifference is taken to obtain be adjusted to specified conditions of T, P, pH, free MgZfof the Equation 7, i.e. system thought to exist in the cell. A summary of the thermodynamic quantities, symbols, and units used in the present study are presented in Table 1. Dependence of the Standard Apparent Gibbs Energy and K' on +AH'" Tz - Ti =-x Temperature-The relationship between the standard transformed 2.303R TIT, Gibbs energy and theapparent equilibrium constant is the following,

+

(-)

AG'" = -2.303RT log K'

(4)

where R is the gas constant, T i s the temperature in Kelvin, 2.303 is

where K; and K; are the apparent equilibrium constants and temperature Tl and T2,respectively. If AH'" is to be expressed in J mol", R is the gas constant and equal to 8.314 joules of J K" mol" (1.987 cal

Effect of Temperature on the Creatine Kinase Equilibrium

14087

TABLE 2 Acid dissociation and mngnesium binding constants as a function of temperature at I = 0.25 M Equilibrium constants were adjusted to the different temperatures and at ionic strength of 0.25 M, using the procedure described under "Experimental Procedures," Standard enthalpy values (kJ mol-') used in the calculations are reported at an ionic strength of zero and temperature of 25 "C. To convert A H o values to cal mol-' multiply by 1000/4.184. Equilibrium constant AH" ( I = 0) 5 "C 15 "C 25 'C 38 "C Reference Acids (M) HATP3- = H+ + ATP" HADP2- = H+ + ADP3HCrP" = H' + CrPzHzPO:- = H+ + HP0:Magnesium complexes W 1 M%+ + ATP" = MgATPZM%+ HATP3- = Mg-

+ M%++ ADP3- = MgADP" M%++ HADPZ- = MgADP Me2' + H P O F = MaHPO, Mg2+ + CrP2- = MgCrP

-7.03 -5.73 +2.66 +2.84

3.86 X 10-7 3.62 X 10-~3.43 X 5.20 X 10-7 4.92 X 10-7 4.69 X 2.91 X 10-~3.09 X 10-~3.27 X 1.97 X 2.09 X 2.23 X

[MgATPz-]/[ATP"][Mp2f]

+18.77

5.58 X 10'~ 6.82 X 10+~ 8.14 x

[MgATP"]/[HATP3-][M%+]

+11.67

6.84 X

[MgADP"]/[ADP3-][M%+]

+18.79

lo+' 5.83 X lo+'

[MgATPz-]/[ATP"][M$+]

+10.85

1.84 x 10'2.08

[MgHP04]/[HPO:-][M%+]

+12.13

2.88

[ATP4-][H']/[HATP3-l [ADP3-][H+]/[HADPz-l [CrP"][H+]/[HCrP"] [HP0,2-][H+]/[HzPO:-l

10-~ 3.53 X 10" 2.41 X

)

ATP"

I

10-7 3.23 X 10-7 10-7 4.45 X 10-7

[MgCrP]/[CrP2-][M%+]

+8.19 1.46

K-' mol"). Equation 7 can therefore be used to calculate the apparent equilibrium constant ( K i ) for a reaction at an absolute temperature ( T2)from the value K ; at temperature T1provided the standard apparent enthalpy of reaction (AH') at specified T,P, pH, free M e , and I is known. Alternatively, if the equilibrium constants have been determined a t two or more temperatures, the heat of the reaction can be calculated from the slope of the plot of log K' versus 1/T. Method of Adjusting hH" and Equilibrium Constants K to an Ionic Strength of 0.25 "-The L\H" values for the acid-dissociation and magnesium binding reactions used in the present study were for the most part those recently tabulated in Alberty and Goldberg3 after Goldberg and Tewari (26). The values were reported a t 25 "C and an ionic strength of zero ( I = 0) (Table 2). The published AiT values for the PCr series were at I = 0.20 M (27) and 0.25 M (28) and were adjusted to I = 0 using the following equation,

9.90 x 10+~

7.67 X

lo+'

7.27

X

10"

lo+' 8.87 X lofz

x

lo+'

2.32 x

lo+'

10"4.34

8.47

X

X

10''

3.31 X

lo+'

3.76

X

lo+'

1.59 X

lo+'

1.70 X 10"

X

9.42

X

lo+'

1.11 X

2.62 x 10" X

lo+'

1.84 X 10"

(28)

number of simultaneous equations, and the ionic reactant species, free M e , and all the buffer components, were calculated (see Miniprint for details). Since the potassium binding constants for phosphocreatine and their enthalpies are not known, it was decided that all potassium binding contributions of PCr and the other reactants should be omitted in ourcalculations of equilibrium concentrations. Statistical significance between the equilibrium constants andtemperature was assessed using Student's t test. RESULTS

Equilibrium was judged complete when the apparent K , defined as [ ZATP] [Cr]/[ ZADP] [ ZPCr] at experimental conditions of pH, free M e , and ionic strength, agreed to within 10-15% when the reaction was approached from both directions. For example, at 38 "C in the direction of ATP formation, the apparent K' was 164 8.4 (n = 4) and 190 +. 5.70 ( n = 4) when approached from the opposite direction (Table X (2.2 products - 22' reactants) (8) 3). Longer incubation times of 6 and 24 h resulted in no differences in the experimental K' values. Given the limits of where 1.4775 and 1.60 are constants and 2 2 is the sum of the squared the assay methods employed (45%),the criteria of equilibrium individual charges of the reactant species (26). The equilibrium constants for the acid-dissociations and magne- under our experimental conditions at the different temperasium binding reactions used in the present study were from Alberty tures was considered satisfactory. The primary experimental and Goldberg (25), Smith and Alberty (27), and Woledge (28). All data for all other temperatures including the pH and total constants reported at I = 0.25 M were first adjusted to I = 0 M a t magnesium concentrations can be found in Table 6 (Mini25 "C using Equation 9, print). Since the apparent K' calculated in this way for each experiment represents conditions of approximately pH of 7.0, II-y products K ( I = 0) = K ( 1 ) X and approximately free M$' of 0.5-0.8 mM, and because the II? reactants equilibrium is highly sensitive to changes in both ions (19), where K is the equilibrium constant and Ily is the product of the we decided to calculate K at pH 7.0, free M e of1.0mM, activity coefficients of the species at I = 0.25 M. The equilibrium and ionic strength of 0.25 M. The theory and an example of constants were then calculated a t the different experimental temperatures (5, 15, 38 'C) using the integrated form of the van't Hoff the procedure used is described in the Miniprint Supplement. equation (Equation 7). The last stepwas to convert the equilibrium It was K' (pH 7.0, free M$+ = 1.0 mM, I = 0.25 M ) that was constants from I = 0 to 0.25 M at the four temperatures using the used in all subsequent thermodynamic calculations. extended Debye-Huckel equation and temperature-dependent A valFrom a plot of the log K (pH 7.0, free M$+ 1.0 mM, I = ues of Clarke and Glew (29). It was assumed that H for all reactions 0.25 M) versus temperature (l/T), the AH'" for the reaction was temperature-independent. The standard enthalpies and equilib- was calculated from the slope of the line and found to be rium constants at 5, 15, 25, and 38 "C ( I = 0.25 M) are presented in -11.93 kJ mol-' (- 2852 cal mol-') in the direction of ATP Table 2. Calculation of the Concentrationsof Free Magnesium Ions and Other formation (Fig. 1).The corresponding entropy ( A S o ) for I(' 4.70 J K" mol". The equation for the line was y = Ionic Species of the Creatine Kinase Reaction-The free [ M e ] and was concentration of ionic species of reactants were calculated using a 0.2428 -t 623x and R2= 0.99. The linear relation (R2= 0.99) computer program written in the language of MathematicaTM (Wol- between log K' and 1/T demonstrates that AH'" and AS" fram Research, Massachusetts). The totalconcentrations of reactants are both independentof temperature. of the creatine kinase reaction measured a t equilibrium, together with The A W and ASo values for the two reference reactions the total magnesium and ionic strength and the appropriate aciddissociation and metal binding constants, were substituted into a are presented in Table 4. The values for ICionic of creatine kinase (Kionic= [ATP4-][Cr]/[ADP3-][PCr2-][H+]), at the R. A. Alberty and R. N. Goldberg, unpublished data. different temperatures were 3.77 X 10' M-' at 38 "c,4.93 X

+

~~

Effect of Temperature on the Creatine Kinase Equilibrium

230

1

/.I

/

/

AH''

=

-11.93 kJlmol

2.25

4

0.0036

0.0035

0.0034

0.0033

2.20 0.0032

1

1fT

(K)

FIG. 1. van't Hoff plot of the effect of temperature on the apparent equilibrium constant of the creatine kinasereaction ZADP + ZPCr = ZATP + Cr where log K' is defined as log [ZATP][Cr]/[ZADP] [ZPCr] at pH 7.0, free Mg2+ 1.0 mM, and ionic strength of 0.25 M. Each point represents the mean k S.E. (n = 8 ) at 5, 15, 25, and 38 "C (see "Materials and Methods"). The

+

623n with R2 = 0.99. The equation to the line was y = 0.2428 standard apparent heat of the reaction, AH'", was calculated from the slope of the line (slope = -AH"/2.303 R, where R is the gas constant andequal to 8,314 J/mol K-'). The intercept of log K' uersus l / T at 1/T = 0 is equal to AS'"/2.303 R, where AS'" is defined as the standard apparent entropy of the reaction under the conditions defined. The standard apparent AH'' for the creatine kinase reaction in the direction of ATP formation was -11.93 kJ mol" (-2852 cal mol"), and AS'"= +4.70 J K" mol" (at 38 "C).

10' M" at 25 " c , 6.19 X 10' M" at 15 "c,and 8.15 X 10' M" at 5 "C. The equation to the line was y = 5.763 874x with R2= 0.99 (graph not shown). The standard enthalpy for the reaction was -16.73 k J mol"(-3998 cal mol-') and corresponding standard entropy was +110.43 J K"mol" (Table

+

4). The values for K Mof creatine ~ kinase ~ at the ~ different ~ temperatures ( K Mcomplex ~ = [MgATP2-][Cr] [Mg2+]/[ MgADP"][MgPCr][H+] were 1.82 x 10' at 38 "C,2.66 x 10' at 25 "C,3.66 X lO'at 15 "C,and 5.31 X lo8 at 5 "C.The equation to the line was y = 4.356 + 1213x with R2 = 0.99 (graph not shown). The standardenthalpy for the reaction was 23.23 kJ mol" (-5552 cal mol") and corresponding standard entropy over the temperature range 5-38 "C was 83.49 J K"mol" (Table 4). The thermodynamic data compiled in Table 4 also show that the relative contributions of the enthalpy and entropic terms to theGibbs energy (AG'" and AG") vary widely for the biochemical and chemical reactions of creatine kinase at 38 "C. For the biochemical Reaction 1, involving the sum concentrations of all reactants, the energy of AG'" is made up of 89% AH'" and 11%of the TAS'" term. For Reaction 2, the ionic reaction, 33% of the energy in AGO is from AH'" and 67% from the TAS" term. For Reaction 3, the magnesium complex reaction, 47% of the energy in AGO is from AH'"and 53% from the TAS" term. At present we have no adequate explanation for these different contributions of the enthalpy and entropy to theGibbs energy of reaction. The method of calculating Krerfrom the measured metabolites at different temperatures taking intoaccount the effect of temperature on the acid-dissociation and metal complex binding constants is presented in the Miniprint.

~

Effect of Temperature on

the Creatine Kinase Equilibrium

14089

TABLE 4 Thermodynamic properties of the creatine kinase reaction Thermodynamic properties for biochemical reaction 1 are at pH 7.0, free M e of 1.0 mM, ionic strength of 0.25 M. The symbol Z denotes the sum of all the ionic and metal complex species of the reactant components in M. The prime (') on the thermodynamic quantities applied only to reaction 1 at the defined experimental conditions. The thermodynamic properties for chemical reactions 2 and 3 are for I = 0.25 M. The species of reference reactions 1 and 2 were calculated using the computer language of Mathematics@ (see Table 2, "Experimental Procedures," and miniprint). TAS" kJ mol", AS" J mol" K-', AG'" kJ mol", AH'" kJ mol", Biochemical reaction 5-38 "C 38 "C 5-38 "C 38 "C 1. ZPCr

+ ZADP = Cr + BATP Chemical reactions

+

2. PCP- + ADP3- H' = Cr + ATP" 3. MgPCr MgADP" + H' = Cr + MgATP2+ Mg2f

+

-13.39 AG" kJ mol", 38 'C

-11.93 kJ mol",

-51.09 -49.21

+4.70

+1.46

5-38 "C

AS ' J mol" K-', 5-38 "C

TAS' kJ mol", 38 "C

-16.73 -23.23

+110.43 +83.49

+34.36 +25.98

A H o

TABLE 5 Historical summary of values for the enthalpy of the creatine kinase reaction in the direction of ATP formation Date AH'" (kJ mol") Conditions Reference and method Calorimetric measurement of heats of (31) 1951 +5.44 to +7.53 hydrolysis of ATP and PCr at pH 7.0, obtained in the 1930s by Meyerhof and Lohmann and corrected in 1951 by Oesper. 1954

+12.55 to +25.10

Experimentally determined from van't Hoff plot of log K' us. 1/T. K' calculated from total ionic species present at 20 mM total M e , 100 mM glycine and pHof 9.0. Calorimetric measurement of heats of hydrolysis ATPand PCr, pH 8.0. 1 mM CaC12, no M e , 45 mM TrisHC1,150 mM KC1.25 "C. Recalculation of 1951 data correcting for heat capacity changes due to buffer ionization and neutralizations, and heats of dilution. Heats of metal complex formation were not corrected. Calorimetry 30 mM phosphate, pH 7.0, 10 mM total M e , 25 "C. Derived from analyzing published K' values at different temperatures but with inadequate knowledge of ionic conditions.

1960

-15.48

1962

+4.18 to +8.37

1972

-4.35

1973

+2.10 k 20.92

1992

-10.00

Calculated from direct calorimetric measurement of heats of hydrolysis for ATP(pH 7.0) andPCr(pH 8.0), free M e = 1.0 mM, ionic strength 0.20 M.

Calculated by Teague and Dobson. Data from Alberty (personal communication) and Ref. 28.

1992

-11.93

van't Hoff plot of logK' us. 1/T, pH 7.0, free M e = 1.0 mM, ionic streneth 0.25 M.

Teague and Dobson (this study).

DISCUSSION

This study examined, in a quantitative manner, the effect of temperature on the creatine kinase reaction. The qualitative effect of temperature on chemical equilibrium is given by the general principle of Le Chatelier, and its exact mathematical formulation by Jacobus Henricus van't Hoff in 1885 (30). In his Lectures on Theoretical and Physical Chemistry, 1898, van't Hoff stated the law as follows: "all equilibria are displaced at high temperatures toward the side that is formed with absorption of heat; whilst at low temperatures adisplacement in the opposite sense takes place "(30). The mathematical expression of van't Hoff can be graphically represented ' calculated from as a plot of log K' uers'sus 1/T, and the AH"

(5)

Calculated by Teague and Dobson from data in Refs. 32 and 33.

(6)

the slope of the line (slope = -AH'"/2.303 R ) where R is the gas constant. The threedifferent forms of the creatine kinase reaction analyzed in this way were as follows:

+ ZADP = Cr + ZATP + ADP3- + H+ = Cr + ATP4-

ZPCr PCr"

+ MgADP" + H+ = Cr- + MgATP' + Mg2'

A H ' O

=

-11.93 kJ mol"

(1)

H = -16.73 kJ mol"

(2)

H = -23.23 kJ mol"

(3)

MgPCr

Reaction 1was studied at pH of 7.0, free Mg+*of 1.0 mM, and ionic strength of 0.25 M. The symbol Z denotes the sum of all the ionic and metal complex species of the reactant compo-

Effect of Temperature on the Creatine Kinase Equilibrium

14090

nents. For biochemical purposes, Reaction 1 has the greatest utility since each reactant component represents what is actually measured in the tissue. The AH'" for this reaction was -11.93 kJ mol" (-2852 cal mol") (Fig. 1, Table 4). The standard apparent entropy (AS") for Reaction 1 was +4.70 J K-' mol". The highly linear function between log K' uersw 1/T (R2= 0.99; Fig. l), demonstrates thatthestandard apparent enthalpy and entropyof the reaction are independent of temperature over the range 5-38 "C, and further that AC,", the standard apparentheat capacity at constant pressure of the products less that of the reactants, approaches zero. Kirchoffs law states that for a given process operating at constant pressure d(AH'")/dT = AC,". The AH'" of -11.93 kJ mol" for the creatine kinase Reaction 1 is in close agreement with the value of -10.00 kJ mol" calculated from estimates of the heats of hydrolysis of ATP andPCr determined under similar ionic conditions (Table 5 ) . The apparent enthalpy change for the hydrolysis of ATP is -25 kJ mol" at pH 7.0, free Mg2+ of 1.0 D M , Z = 0.20 M (Alberty (23)), and -35 kJ mol" for the overall heat of hydrolysis of PCr at pH 7.0, free M P of 1.0 mM ,Z = 0.20 M (28). The heat of the reaction for creatine kinase estimated from theheats of hydrolysis at pH 7.0 was calculated as follows. ZPCr

+ H20= Cr + ZPi

AH'" hydrol = -35.0 kJmol"

+ ZADP = ZATP + H20 AH"

ZPi

hydrol = +25.0 kJ mol-'

Net: ZPCr

+ ZADP = ZATP + Cr

AH'"

= -10.0

kJmol"

From a literature survey of the past 40 years, estimates of AH'"for the creatine kinase reaction in the direction of ATP formation vary widely in both sign and magnitude (Table 5 ) . The discrepancy among the estimates calculated from the older calorimetric data of Meyerhof, later to be recalculated and tabulated by Oesper (31), was most likely due to an inadequate knowledge of the contributing heat changes due to buffer ionizations and neutralizations, heats of dilution and mixing, and heats of metal complex formations in the calorimeter (see Ref. 6). Another study carried out in the early 1950s involving equilibrium measurements calculated a AH'" of creatine kinase in the ATP direction of 12.55-25.10 k J mol" (3000-6000 cal mol")(5), which is opposite in sign to the value reported in this study. Reasons for this major discrepancy are complex but may relate to the methodology employed in measuring the reactant components of the creatine kinase reaction. Because enzymatic analysis of metabolites was not available at thetime, the equilibrium concentrations of ATP, ADP, and Cr were calculated from the single measurement of creatine phosphate using a molybdate acidhydrolyzable phosphorus method (5). Having presented some of the important thermodynamic quantities for creatine kinase reaction under specified conditions,it was of interest from a theoretical standpoint to calculate the A.W' and ASo for two reference reactions, the ionic reaction (Reaction 2) and the magnesium complex reandthe complex action (Reaction 3). The A.W' for Kionic was -16.73 kJ mol" (-3998 cal mol") and -23.23 kJ mol" (-5552 cal mol"), respectively, at Z = 0.25 M (Table 4). The corresponding ASo were 110.43 and 83.49 J K" mol-', respectively. The AW of -16.73 kJ mol-' for Reaction 2, a reaction that is magnesium- and pH-independent, compared very favorably with the value of -15.48 kJ mol" calculated from the heats of hydrolysis of PCr and ATP under similar conditions from the calorimetric data of Gellert and Sturtevant (32) and Podolsky and Sturtevant (33). The value of -15.48 kJ mol" was calculated in the following way. The enthalpy for PCr

hydrolysis in 45 mM Tris-HC1 buffer, pH 8.0, 1.0 mM CaC12, 150 mMKC1 at 25 "C, was-37.67 kJ mol" (-9000 cal mol"). Under similar conditions the enthalpy for ATP hydrolysis was 22.18 k J mol" (-5300 cal mol"). The AW estimated for the creatine kinase reaction in the direction of ATP formation from the heats of hydrolysis with no magnesium present was therefore -15.48 kJ mol" (-3700 cal mol-') at pH 8.0. In summary, the AH'" value for the creatinekinase reaction at pH 7.0, free of 1.0 mM, and ionic strength of 0.25 M was calculated from a van't Hoff plot and found to be -11.93 kJ mol". By knowing the of the creatine kinase reactions under specified conditions and one K' at temperature, T I ,a second K' can be calculated at another temperature, T2, using the integrated form of the van't Hoff equation. The study also showed that under physiological conditions of pH 7.0, free M P of 1.0 mM, and ionic strength of 0.25, the sign and magnitude of the standardapparent Gibbs energy (AG'O) of the creatine kinase reaction was comprised mostly of energy from the AH" (89%))with the remaining 11% coming from the entropy TAS'" term. A Z T 0

Acknowledgments-We thank Professor Emeritus R.A. Alberty (Massachusetts Instituteof Technology) for critical comments on the manuscript and in particular for scholarship on thermodynamic theory, equations, and calculations. We thank Dr. Robert N. Goldberg (National Institute of Standards and Technology) for assistance with ionic strength theory and calculations. We also thank Dr. R. L. Veech (National Institute on Alcohol Abuse and Alcoholism) for permitting this work as part of the Laboratory of Metabolism and Molecular BioIogy research program. REFERENCES 1. Watts. D. C. (1973) in TheEnzvmes (Bover. P. D.. ed) nn. 384-4.5.5. --Academic Press, New York ' ~' 2. Kenyon, G. L., and Reed, G. H., (1983)Adu. Enzymol. Re[.Areas Mol. Biol. 54,367-426 3. Lohmann, K. (1934) Biochem. 2. 271,264-277 4. Lehmann. H. (1936) Biochem. Z. - 286.336-342 ~. 5. Noda, L.,'Kuby, S . A., and~lardy,H. A. (1954) J. Biol. Chem. 2 1 0 , 83-95 6. Kuby, S.A., and Noltmann, E. A. (1962) in The Enzymes (Boyer, P. D., Lardy, H., and Myrback, K., eds) pp. 515-603, Academic Press, New York 7. Kushmerick, M. J. (1983) in Handbook of Physwlogy, Section IO, Skeletal Muscle (Peachey, L. D., ed) pp. 189-236, American Physiological Society, Bethesda, M D 8. Hohorst, H. J., Reim, M., and Bartels, H. (1962) Biochem. Biophys. Res. Commun. 7 , 142-146 9. Danforth, W. H. (1965) in Control of Energy Metabolism (Chance, B., and Estabrook, R. W., eds)pp. 287-297, Academic Press, New York 10. Carlson, F. D., and Siger, A. (1959) J. Gen. Physiol. 4 3 , 301-313 11. Veech. R. L.. Lawson. J. W. R.. Cornell. N. W.. and Krebs.,~ H. A.. (1979) .~~,~J. Biol. Chem. 264,6538-6547' 12. Gadian, D. G., Radda, G. K., Brown, T. R., Chance, E. M., Dawson, M. J., and Wilkie, D. R. (1981) Biochem. J. 194,215-228 13. Matthews, P. M., Bland, J. L., Gadian, D. G., and Radda, G. K. (1981) Biochem. Biophys. Res. Commun. 1 0 3 , 1052-1059 14. Bittl, J. A,, and Ingwall, J. S. (1985) J . Biol. Chem. 2 6 0 , 3512-3517 15. Dobson, G. P., Veech, R. L., Passonneau, J. V., Kobayashi, K., Inubushi, T., Wehrii, S., Nioka, S.,and Chance, B. C. (1991) N M R Biomed. 5,2028 16. Kuby, S. A., Noda, L., and Lardy, H. A. (1954) J. Biol. Chem. 210,135-82 17. Chance, B., Leigh, J. S., Jr., Clark, B. J., Maris, J., Kent, J., and Smith, D. (1985) Proc. Natl. Acad. Sei. U. S. A. 82,8384-8388 18. Chance, B., and Williams, G. R. (1955) J . Biol. Chem. 217,383-393 19. Lawson,,J. W. R., and Veech, R. L. (1979) J. Biol. Chem. 2 5 4 , 6528-6537 20. LoPrestl, P., and Cohn, M. (1989) Biochem. Biophys. Acta 998, 317-320 21. Bates, R. G. (1964) Determination of pH: Theory and Practlce, p. 128, John Wiley and Sons, New York 22. Lowry, 0.H., and Passonneau, J. V. (1972) A Flexible System of Enzymatic Analysis, Academic Press, New York 23. Alberty, R. A. (1987) Physical Chemistry, Ed. 7, p. 934, John Wiley and Sons. New ... . ., . .. Vork . . 24. Alberty, R. A. (1991) Biophys. Chem. 4 2 , 117-131 25. Woledge, R. C. (1972) Cold Spring Harbor Symp. 37,629-634 26. Goldberg, R. N., and Tewari, Y. B. (1991) Bioph s Chem 40, 241-261 27. Smith, R. M., and AlbeFy, R. A. (1956) J.,Am. d&m. Soc. 78,2376-2380 28. Woledge, R. C., and Redly, P. J. (1988) Btophys. J. 5 4 , 97-104 29. Clarke, E. C. W., and Glew. D. N., (1980) J. Chem. SOC.Faraday Trans. 76. 1911-1916 30. van't'Hoff, J. H. (1898) Lectures on Theoretical and Physical Chemistry, Edward Arnold, London 31. Oesper, P. (1951) in Phosphorus Metabolism (McElroy, W. D., and Glass, B., eds) pp. 523-536, Johns Hopkins University Press, Baltimore 32. Gellert, M., and Sturtevant, J.M. (1960) J. Am. Chem. SOC.82,1497-1499 33. Podolsky, R. J., and Sturtevant, J. M. (1955) J. Biol. Chem. 217,603-606 I

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--->

Effect of Temperature on the Creatine Kinase Equilibrium SUPPLEMENT TO ElfeCl 01 Temperature On the Creatine Klnase Equilibrium by: W. E. Teag~eJr. and Gmnrey P. Dobson

14091

Effect of Temperature on the Creatine Kinase Equilibrium

14092

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Effect of Temperature on the Creatine Kinase Equilibrium Table 1

Aad-dissociation and Magnesium binding constants

HATP' = H*+ ATP'

HPCr' = H f + PC?

brndine Mg2++ A P 4 = MgATP'

wumu

Mg2'+ HAT= ' MgHATP

Mg2*+ADP'=

MgADP

Mg'*+ HADP2.= MgHADP

Mg*'+ PCrl'= MgPCr

14093