BIOCHIMICA ET BIOPHYSICA ACTA 317

P H Y S I C A L F A C T O R S I N F L U E N C I N G CATALASE R A T E CONSTANTS

G. K. STROTHER AND E. ACKERMAN*

Physics Department, The Pennsylvania State University, University Park, Pa. (U.S.A.)

(Received July 2rid, 196o)

SUMMARY

The rate constants for the catalase--hydrogen peroxide reaction are determined as a function of temperature over the range + 45 ° to - - 2 0 ° and as a function of viscosity of the medium over the range 0.87 to 80 centipoise at room temperature. Both an accelerated-flow mixing apparatus and Beckman cuvettes were used to determine the reaction rates. The results indicate that at room temperature the formation of the enzyme-substrate complex is accompanied by a negative entropy change of 24.6 mole -I degree -1, and is diffusion-controlled for viscosities higher than about 6 centipoise. The rate of formation of free enzyme plus products from the enzyme-substrate complex yields a straight-line Arrhenius plot with an observed heat of activation of 5.1 + 0.6 kcal/mole.

INTRODUCTION

Catalase is a heme enzyme found in practically all forms of life. There are four heme groups per molecule for bacterial catalase, but only three heme groups for beef liver catalase 1. The molecular weight of catalase is about 248,ooo, depending somewhat upon the source 1.

The reaction between catalase and hydrogen peroxide is particularly suited for s tudy of the effects of physical factors. The rate constants are well known and are among the fastest determined to date for reactions in solution. The reaction involves the formation of an enzyme-substrate complex with an absorption peak in the visible range. In addition, the substrate (hydrogen peroxide) absorbs in the u.v. Spectro- photometric recording of the time course of the reaction is therefore possible, and has been employed here.

The pr imary purpose of the investigations reported in this article was to study all enzyme reaction at the molecular level. For this the variation of the reaction rate constants were measured as functions of temperature and viscosity of the suspending medium. From the temperature studies, one can find a characteristic heat of activa- tion. Using absolute rate theory, these indicate the entropy changes which occur during the reactions. From the viscosity data, one can determine the effects of changing the diffusion coefficient. Taken together, all these types of data help us to determine the molecular nature of this enzyme reaction.

Theory The reaction between catalase and hydrogen peroxide has been described in

detail by CHANCE 1 . The first par t of the reaction involves the formation of an enzyme-

* Present Address: Mayo Clinic, Rochester, Minn. (U.S.A.).

Biochim. Biophys. dcta, 47 (1961) 317-326

3 1 8 G . K . STROTHER, E. ACKERMAN

substrate complex; in the second par t this complex breaks down into free enzyme plu~ products, as shown below.

cat + H202 ~Io~ cat. H20=

cat . H~O~ k4~ cat + 2H~O + O~

At suitable concentrations of the reactants, k= may be ignored, and a steady state analysis yields the following relationships:

h i = p_~l (kl + k4) (I) kl ~ _ _ k l ' (3)

8 k l ' hi' (2) k4 = - - (4)

I I + 8 Pl kl k4 e

where Pl is the maximum concentration of the enzyme-substrate complex produced by the reaction, and e is the initial enzyme concentration; k 1 and k 4 are second order rate constants describing the formation of the enzyme-substrate complex and the formation of free enzyme plus products, respectively. The overall disappearance of hydrogen peroxide is described by the rate constant kl' .

Both catalase and its hydrogen peroxide complex have absorption bands in the visible region, and the formation of the enzyme-substrate complex can be observed at 405 mt, by means of the decrease in O.D. as the reaction takes place. The value of (k 1 + k~) can therefore be determined from data taken at 4o5 m/, using formula 1

i . i l n 2 k l + k4 = - - (5)

x0 t0 .5

where x o is the initial concentration of hydrogen peroxide and t0. 5 is the reaction half- time, defined as the time required for p to increase to half its maximum value.

By noting the relative changes in O.D. after hydrogen peroxide is put into a catalase solution, the value of pz/e is obtained at a wavelength of 405 m/,. By sub- stitution of this value into eqn. (I), experimental values of k x and k 4 are obtained.

Since hydrogen peroxide has appreciable absorption at a wavelength of 23o ml z, a value for k 1' can be obtained at this wavelength by recording the overall catalase reaction, i.e. the disappearance of hydrogen peroxide. The value of k 1' can be deter- mined from the formula I

in 2 kl' = (6)

eto. ff

where to.5' is the half-time for the overall reaction. Using eqns. (3) and (4) calculated values of kj and k4 can be compared with the values obtained at 4o5 mt~.

MATERIALS AND METHODS Instrumentation

The rate constants under investigation are among the fastest determined for enzyme reactions. The room temperature value of k x, the association rate constant for hydrogen peroxide and catalase, is on the order of lO T M -1 sec -1. The actual value of this constant is obtained by measuring the half-time, to. v of the association reaction at a given initial concentration, x0, of substrate. From eqn. (5) one can observe tha t

Biochim. Biophys. Acta, 47 (196I) 317-326

EFFECTS OF PHYSICAL FACTORS ON CATALASE KINETICS 319

the measured half-time is inversely proportional to the substrate concentration. Thus one can slow down the reaction by decreasing the initial hydrogen peroxide concentration as long as x 0 is greater than e. The hmiting factor here is that the O.D. change due to the formation of enzyme-substrate complex decreases if e is decreased. These conditions put two maj or requirements on the instrumentat ion necessary to ob- serve the association reaction: (a) the response t ime must be as fast as a msec or less, and (b) the instrument must be responsive to O.D. changes, as low as lO -40.D. units, or less.

In order to achieve these requirements, an apparatus similar to that described by CHANCE 2 was constructed z,4. The basic instrumentation consists of a Beckman Model DU spectrophotometer with a photomultiplier a t tachment suitably modified for recording, into which can be placed a reaction flow system. The flow system is suitable for either stopped flow or accelerated flow determinations 1. By means of two manually driven syringes, the reactants are simultaneously forced into a plastic mixing chamber, where mixing is completed in about 0.2 msec. After mixing, the reactants flow through an observation tube located in the path of the monochromatic light beam of the spectrophotometer. The optical path length is 2 ram, and the tube is rectangular. The tube was used at viscosities up to about IOO centipoise.

The O.D. changes associated with the course of the reaction are detected and amplified by means of the photomultip]ier a t tachment of the Beckman spectrophoto- meter. The signal from the photomultiplier is fed to a chopper amplifier, where it is compared with a reference voltage 60 times/sec, thus permitt ing a.c. amplification. The signals of interest are of short duration, low amplitude, and occur at a set wave- length, therefore long time drift is not a problem. The a.c. output of the chopper amplifier is fed directly to a Bruel and Kjaer sound level recorder, modified only b y the use of a linear input potentiometer. In order to observe small changes in O.D. the fluctuations due to light source instabil i ty were minimized. This was achieved by voltage regulation of the Beckman lamp supply3, 4.

In order to obtain reaction curves at temperatures below freezing, the flow system was wrapped with removable cooling coils. An alcohol-dry ice mixture was pumped through the coils and also through two Beckman thermospacers. The temperature was monitored with a copper-constantin thermocouple junction inserted directly into the flow system. For the high temperature runs a temperature control system was used in conjunction with heating elements placed in the cooling system reservoir.

For experiments in the u.v. a hydrogen discharge lamp with its associated Beckman power supply was used. When the reaction flow system was used in the u.v., a special mixing chamber with synthetic sapphire windows in the observation tube 3, 4 was utilized. The sapphire windows have roughly the same transmission as quartz in the ultra violet.

Determination of rate constants

In order to completely determine the catalase rate constants, two types of measurements were used. The first experiment determined the half-time associated with the overall reaction, to.5', as denoted in eqn. (6). From this the value of kl', the overall rate constant, was calculated. A second experiment was used to determine the value of the ratio Pile, indicating the maximum amount of enzyme substrate complex formed. These experiments were performed over the viscosity range, 0.87 to about 90 centipoise and separately over the temperature range + 4 5 ° to - - 2 0 °. The rate

Biochim. Biophys. Acta, 47 (I96x) 317-326

320 G.K. STROTHER, E. ACKERMAN

constants were also determined at room temperature in sucrose and methylcellulose media in order to determine the effect of changes in viscous media.

To determine kl', the spectrophotometer was set to a wavelength of 230 my. Known amounts of catalase and hydrogen peroxide were manually mixed together in the Beckman cuvette. The resulting change in O.D. due to the disappearance of hydrogen peroxide was recorded and a half-time for the reaction was determined from the tape record. All curves used were exponential; at least three curves were measured for each determination. Catalase concentration for this series of experiments was about 2. 4- lO 4 M, while hydrogen peroxide concentration was about 1.6. lO -3 M. These concentrations were determined exactly for each experiment.

The determination of p x/e was made at a wavelength setting of 405 m/,. The value of the ratio was obtained by noting the maximum O.D. change as a small amount of hydrogen peroxide was stirred into a I -cm cuvette containing the cataiase solution. The readings were taken manually using only the Beckman spectrophotometer.

As a check on the reaction mechanism, k 1 and k4 were determined directly from observations made at 405 m~ using the accelerated flow technique 1, 3, 4. These experi- ments were performed over the entire temperature range of + 45 o to - - 2 0 °. Reaction half-times were obtained by displaying O.D. on the y-axis and flow velocity on the x-axis of an oscilloscope3, 4. At least three reaction curves were used for each (k 1 + k4) determination. Catalase concentration was about o.12/zM and hydrogen peroxide concentration was about 13 ~M. These values were determined exactly for each experiment. For room temperature (27 ° ) data at water viscosity, the observed half-times were on the order of 2.5 msec.

All reactants were buffered at pH 7.5 with o.15 M phosphate buffer. Viscosities were determined by the Ostwald method. Crystalline beef liver catalase was purchased from the Mann laboratories; the bacterial catalase was prepared by A. BRILL at the Johnson Research Foundation, University of Pennsylvania. Chemically pure glycerol was mixed with appropriate buffer and water for the viscous media. C. P. 3 °/o hydroger~ peroxide was used for the substrate, and its concentration was checked both with the Beckman spectrophotometer and chemically.

RESULTS

Fig. I shows the variation of k( , the rate constant for the overall reaction, with temperature over the range + 4 5 ° to - - 2 o °. The da ta were taken at 230 mt~ and the values of k 1' were determined using eqn. (6). Room temperature water viscosity values of 5.0" lO T and 2.3" lO 7 M -1 sec -1 for k 1' (bacterial) and k 1' (beef liver) respec- t ively agree with published values1, 5 within experimental error ( ± 5 °/0). Previous data on the temperature behavior of this rate constant from 35 ° to o ° have been summarized by CHANCE d. Heats of activation of 1.4 and 0.6 kcal/mole for bacterial and beef liver catalase respectively were reported. The present data agree with previous results and extend the temperature range, indicating a break in the Arrhenius plot at room temperature not previously suspected for the temperature range above o °. Since k 1' is not a simple rate constant any heat of activation obtained from an Arrhenius plot is not considered significant from a theoretical viewpoint. Below 5 ° the reactions were run in glycerol-water (54:46) to prevent freezing. Above 5 c, the values of k 1' were not affected by the addition of this amount of glycerol.

Biochim. Biophys. ,4cta, 47 (1961) 3t7-32(~

EFFECTS OF PHYSICAL FACTORS 01~ CATALASE KINETICS 32I

At room temperature the viscosity of this mixture was found to be 6.3 centipoise. At - - 2 o °, the viscosity of this mixture was increased to roughly 80 centipoise. Fig. I indicates tha t k 1' is independent of temperature over the range 45 ° to 25 °, and decreases by a factor of io (for bacterial catalase) over the range + 25 ° to - -20 °.

The variation of px/e with temperature is shown in Fig. 2. Since Pl is the maximum concentration of the enzyme-substrate complex and e is the initial free enzyme con- centration, their ratio is an indication of the maximum amount of enzyme which has actually gone into the formation of the E. S complex. At room temperature and water viscosity, the values of pl/e for bacterial catalase and beef liver catalase were found to be 0.40 and 0.33 respectively, in agreement with published values1,6, ~. The determinations were made at 405 m/z using the Beckman cuvettes and mixing manually. No change was found in the value of pile as the glycerol content wa~

log~o k~

7.8-

7.6

7.4,

Z 2 -

7 . 0 -

6 .8 -

6 . 6 -

6 . 4 -

,31

( ~ (~) - BACTERIAL CATALASE O O o ~ . ~ ~ , BEEF LIVER CATAI.ASE

"~'N\ X

45"C --20"C / /

i i t i , I I ¢ .32 .33 .34 .35 .36 .37 .38 .39

T - I X 102, *K

Fig. I. Log 1° k~ vs T -1 in glycerol medium.

P*

.40-

.35-

.30-

.25-

.20

,15.

.I .31

x

t . . . . .

- //111 Z

I I

/ /x /

/ /

Z ~ ' c : I I I I I I

.32 .33 ~ 4 .3s .36 .37 .~ T -I X IOZ, eK

Fig. ~ . P l l e v s T -x in glycerol medium.

\ -20"C

t ; .$g

Biochim. Biophys . Acta, 47 (z96I) 317-326

322 G . K . STROTHER, E. ACKERMAN

increased to 9 ° ~o by weight, at room temperature. Therefore, the reduction of the pl/e values at low and high temperatures shown by Fig. 2 is thought to be a function of temperature only, and independent of viscosity changes. The rather large spread of the beef liver catalase data in the intermediate temperature range is believed due to a faulty cuvette holder in the Beckman spectrophotometer, subsequently replaced before obtaining the bacterial catalase data. For the bacterial catalase, each plotted point is an average of about eight determinations. The standard deviation for room temperature determinations is ~ o,o26 M -1 sec -1.

Fig. 2 indicates that Pile decreases rapidly as the temperature goes above 25 ° and below o ° for both types of catalase. The effect of high temperature may be heat denaturation of the enzyme. As may be noted from formulas (3) and (4), the variation of pz/e with temperature is an indication that the variations of the rate constants k I and k4 with temperature will be different. In all cases the low temperature medium is 54 % glycerol.

The variation of k I and k 4 with temperature for bacterial catalase is shown in Fig. 3. The plotted points are calculated from data taken at 230 mF on the overall reaction using eqns. (3) and (4).

Values of k 1 ~ I.O. lO 7 M -1 sec -z and k4 ~- 1.6. lO 7 M -z sec -1 obtained here at room temperature and water viscosity for bacterial catalase agree with the published values z.

Values of k 1 and k4 determined with the accelerated flow technique are not listed since the rate constants calculated from k 1' determinations as compared with those calculated from (k 1 + k4) determinations agreed within 25 % in the range - - 5 ° to + 2 5 °, with a somewhat higher spread at the high and low temperature extremes. A factor of 2 previously noted by CHANCE 1 between calculated and observed rate constants for bacterial catalase at room temperature was not observed here.

The variations of the rate constants k z and k4 with temperature are considered to be more meaningful than the variation of k 1' because these are true second order rate constants. I t is apparent from Fig. 3 that the Arrhenius plot for k 1 is broken into three separate regions. In the range 45 ° to 15 °, the rate of enzyme substrate formation is independent of temperature. This is in agreement with previous results 3, 4 on beef

IOgio k

Z2-

7.0-

E6

6.4-

6.2-

6.0-

5.8 - 45oc . 2 0 o c

, . , I I I L i I I .31 .32 .33 .34 .35 .36 .37 .38 .39 .,tO

T - I X l O t , o K

Fig. 3- Loglo kl and k 4 vs T -1 for bacterial catalase in glycerol medium.

B i o c h i m . B i o p h y s . Ac ta , 47 (1961) 317-326

EFFECTS OF PHYSICAL FACTORS ON CATALASE KINETICS 3 2 3

l iver catalase. In the range + 15 ° to - - 5 °, k 1 decreases b y about a factor of 2. The heat of activation in this region is determined from the slope to be 5.1 ± 0.6 kcal/mole. In the range - - 5 ° to - - 2 0 °, k 1 decreases sharply to a value of 8.2. lO s M -1 sec -z at the extreme temperature.

The behavior of the rate of formation of free enzyme and products, as denoted by k4, is very different from that of k 1. Apparently k 4 is not affected adversely by the temperature extremes, since it shows a steady decrease with temperature, yielding a heat of activation of 5.1 ± 0.6 kcal/mole throughout the range covered. The spread of the plotted points at the low temperature is not considered significant.

The effects of viscosity of the medium on the rate constants kz and k 4 are indicated in Fig. 4, which is a plot of the rate constants v e r s u s the change in the FICK diffusion coefficient, D, for hydrogen peroxide in glycerol-water mixtures. The values of D used here were obtained by means of a rotating platinum electrode and associated circuitry constructed in this laboratory s. The procedure employed was to stir a known amount of H~O 2 into selected glycerol-water mixtures surrounding the rotating electrode and record the cell current as a function of time. The H20 ~ concentration was 1.45. lO -3 M and the glycerol-water mixtures were o, 50, 7 o, 80, and 90 ~o glycerol by weight. The relationship between cell current and the FICK diffusion coefficient was determined by putt ing known concentrations of oxygen into glycerol solutions, for which the values of D have been determined 9. By this means the cell current was found to be proportional to D °'6 for this particular rotating electrode at high glycerol concentrations.

The kinetic data represented in Fig. 4 were taken at room temperature in glycerol- water mixtures of increasing viscosity. The most viscous (9 ° ~o glycerol) values were obtained using 405 mF data, since a reaction at 230 mF could not be observed. The rest of the values plotted were obtained at a wavelength of 230 mF. Fig. 4 shows tha t the rate constants k~ and k 4 become diffusion controlled at about 6 centipoise viscosity, and are diffusion independent for lower viscosity values. The values of kz and k 4 tend to become equal as the viscosity increases, so k s drops more sharply than k 1 as D

16-

1 4 -

12-

I O -

~B. . J

0 0

X106 u '~

~4, BACTERIAL CATALASE

m ®

® k¢,BEEF LIVER CATALASE

0 x k l= BACTERIAL CATALASE

0 q O~ kI ,BEEF LIVER CATALASE 0

I I I I I I I I I I0 20 30 40 50 60 70 80 9 0

0 X I0 -7 It; cm 2 l ee - I

Fig. 4- k : and k 4 as a f unc t i on of D (H202) .

I I 0 0

Biochim. Biophys. Acta, 47 (1961) 317-326.

324 c . K . S T R O T H E R , E. A C K E R M A N

decreases. Since the rate constants will be zero for no diffusion, the curves shown in Fig. 4 must terminate at the origin, as shown.

In order to determine the effects of different media on the reaction rates, the rate constants were determined in sucrose and in methylcellulose media. Table I shows

T A B L E I

VALUES OF P i l e ; k l ' , k 4 AND k 1 FOR BACTERIAL CATALASE AS A FUNCTION OF VISCOSITY FOR DIFFERENT MEDIA

k l t ' Z o -7 k 1 "I0 7 k 4 . I 0 - 7

in centipoise* Medium pt/e M -x sec x M - t sec-t M_X sec-~

6. 3 G l y c e r o l o ,4o 5 .o i .o i .6 63 G l y c e r o l o .4 ° o . 9 o o . i 9 o . 2 8

7 S u c r o s e 0 .42 4 .5 0 . 9 7 1 .34 6 7 S u c r o s e o .4 ° 1.3 o . 2 7 o .4 °

7 M e t h o c e l * * 0 .37 5 .6 i . i 1 .9 7 ° M e t h o c e l 0 .37 i .7 o .34 0 .57

* S u c r o s e a n d m e t h y l c e l l u l o s e v i s c o s i t i e s a r e ~ i o ~o. ** D o w C h e m i c a l C o m p a n y , m e t h y l c e l l u l o s e , v i s c o s i t y t y p e IOO.

the values of pile, k 1, k 4, and k~' for bacterial catalase obtained at room temperature for similar viscosities in different media. Some difficulty was experienced with the methylcellulose solutions due to formation of bubbles upon mixing. The standard deviation for the Methocel Pile determinations is 4- 0.03. Table I shows there is no significant effect on the reaction rates due to change in the medium. A separate series of determinations in glycine-water mixtures indicated no changes in the rate constants due to dielectric effects 15.

D I S C U S S I O N

One of the first questions one might ask concerning the behavior of the rate constntsa at temperature and viscosity extremes is whether the reaction mechanism remains un- changed.The agreement between the values of the rate constants k 1 and k 4 calculated from data obtained at 4o5 m~ and those from data taken at 23o m~ indicates tha t the reaction mechanism is valid over the temperature and viscosity ranges used.

The behavior of the rate constant k 1 describing the association of the enzyme and substrate to form the intermediate complex is extremely interesting. This rate constant is apparently independent of temperature in the range 25 ° to 45 ° . In addition, kl is diffusion independent for values of ~ up to about 6 centipoise. The behavior of kx is therefore not in general accord with absolute reaction rate theory. In discussing the theory of absolute reaction rates 1°, it has been stated that if a reaction requires an activation energy of about I2 kcal/mole or more, it will be diffusion in- dependent. For reactions with activation energies less than this, the theory predicts tha t diffusion of the reacting molecules should be the limiting factor. These predic- tions are contradicted by the results reported in this paper. Since k 1 is independent of temperature from 25 ° to 45 °, the activation energy is zero (or very nearly zero) over a range where the reaction is diffusion independent.

In the temperature independent region, absolute rate theory predicts tha t the association reaction should be accompanied by a large negative entropy of activation

B i o c h i m . B i o p h y s . A c t a , 47 (1961) 3 1 7 - 3 2 6

EFFECTS OF PHYSICAL FACTORS ON CATALASE KINETICS 325

AS*, relative to the standard state given below. The value of k 1 is related to AS* by the formula

kl = - e (7) Nh

where R is the gas constant, T is the absolute temperature, N is Avogadro's number, h is Planck's constant, and AS* is the entropy of activation. Using the value k 1 = i .o. IoTM -1 sec -1 and T = 300 ° K, eqn. (7) yields the value AS* = - -24 .6 cal/mole/degree, where the change in entropy is referred to a standard state for catalase, H~O,, and intermediate complex concentrations of I mole/1 in water. I t is of interest to see if this entropy loss can be the result of the a t tachment of the hydrogen peroxide molecule to the enzyme. The absolute entropy of Ha02 in the solution may be estimated using the expression

S (H~O~) = St, + SM (8)

where SL is the absolute entropy of pure liquid H , O , at 25 ° and SM is the change in the partial molal entropy due to mixing with water.

The value of SL for H ,02 is estimated as followsll:

(z~s due to raising the temperature to - -2 °) (AS due to fusion) (AS due to raising the temperature from --2 ° to 27 ° )

+ 9* + 9.3, + 1.5

+ 19.8 e.u./mole

where the starred values were taken from data given for H20. The entropy of mixing, SM, is calculated to be 8 e.u./mole using I mole/1 as the reference state for H ,O 2 and 55 moles/1 as the reference state for water.

On forming the activated complex, all of the entropy of mixing, (SM) and some of the entropy of the liquid H,O, , (SL) should be lost. Thus one may calculate that 8 < A S * < 28.

A comparison with the experimental result, - -24 .6 cal/mole/degree, shows tha t the observed AS* is well within this range. Further it indicates that most of the entropy associated with the H ,02 molecule is lost in forming the act ivated complex.

In spite of the good fit between theory and experiment evidenced above, the writers feel that some caution should be exercised regarding the above calculations. There is an increasing amount of evidence 12 that these enzyme reactions involve the displacement of water molecules at the active site. This subject has been discussed by CHANCE 13 for the catalase molecule. Thus one would expect an increase in entropy due to the displaced water molecule, which does not appear in the above calculation. Water has an absolute entropy of 16.7 e.u./mole at 25 °, and one would normally expect much of this to be gained when it was released from the active site. Investiga- tion of the O z-hemoglobin association reaction indicates this entropy increase occursZ, 4.

The observed behavior of the rate constant k 1 with the viscosity of the media is best approached from a molecular viewpoint. The molecules in a liquid are believed to move by taking small discrete jumps between quasi-equilibrium positions 1°. Thus a collision process is at work, and the number of encounters per second between a catalase and a hydrogen peroxide molecule is proportional to the diffusion constant. I f these encounters are very brief, then most encounters will not lead to a reaction. Under these circumstances the reaction rate will depend upon the number of effective

Biochim. Biophys. Acta, 47 (196I) 317-326

326 G . K . STROTHER, E. ACKERMAN

encounters, which will be proportional to the product of the length of an encounter times the encounter rate. The reaction rate will be diffusion independent in this case.

If one increases the viscosity, then the encounter rate decreases and the en- counter length increases until it is feasible that every encounter leads to a reaction. In this case the reaction will be diffusion controlled. The results of the present investigation indicate that the rate constants k 1 and k 4 are diffusion independent up to about 6 centipoise viscosity, whereupon they then appear to become diffusion controlled.

I t is of interest to compare some observed values of k 1 with values calculated on the basis of collision theory. For diffusion controlled reactions the encounter rate is given by the expression 1*

Z ~ 2~D (ra + rb) N lO -8 M -1 sec -1

where D is the diffusion coefficient, ra and rb are the radii of the active areas of the colliding molecules and N is Avogadro's number. This should be equal to the chemical rate constant k in the diffusion controlled range. A value for Z can be calculated if D, ra and rb are known.

Applying the above formula to one of the extreme points on Fig. 4, gives

Z ~ 1.8. lO 7 M -1 sec -1 if

ra + rb -- IO -8 c m

and D ~ 5" lO-7 cm2 sec-1

The value of Z calculated above is based on the assumption that two spherical molecules of approx, the same radius are colliding. In the present case, a very small H,O s molecule collides with an active site on a very large catalase molecule. Thus the geometrical factor of 2~r may be approximated by the value ~r for the data given here. This reduces the calculated value of Z so that Z - - o.9" 10 7 M -x sec -x. Using a value from Fig. 4 of k4 ----- 5" I@ at D : 5" IO-7 cm~/s ec, a value of (ra + rb) ~-~ o.6/k is obtained for the radius of the active site. This number is the same order of magnitude as the radius of an iron atom, which is what one might expect for a heme site.

R E F E R E N C E S

1 ]3. CHAliCE, in S. L. FRIESS ANn A. WEISBERGER, Technique o[ Organic Chemistry, Vol. vi i i , Inves t iga t ion of Rates and Mechanisms of Reactions, Interscience Press, N.Y., 1953.

2 B. CHAliCE, Rev. Sci. Instr., 22 (1951) 619. 8 G. K. STROTHER, P h . D . Thesis, The Pennsylvania State University, 1957. 4 R. L. BERGER, P h . D . Thesis, The Pennsylvania State University, 1956.

B. CHANCE, in F. JOHNSON, Influence o] Temperature on Biological Systems, The American Physiological Society, 1957.

s R. F. BEERS AND I. W. SlZXR, J . Phys. Chem., 57 (1953) 29o. R. F. BEERS AND I. W. SIZER, J. Biol. Chem., 195 (1952) 133.

s E. H. STRICKLAND, P h . D . Thesis, The Pennsylvania Sta te Univ., Feb. 1961. 9 j . JORDAN, E. ACKERMAN AND R. L. BERGER, J. Am. Chem. Soc., 78 (1956) 2979.

10 S. GLASSTONE, K. LAIDLER AND H. EYRING, Theory o /Rate Processes, McGraw Hill, N.Y., 1941 . 11 Circular 500, National Bureau o] Standards. x, D. RITTE~B~RG, in S. GROFF, Essays in Biochemistry, J o h n Wiley, N.Y., 1956. as ]3. CHAlice, J. Biol. Chem., 194 (1952) 471. x* E. A. MOELWYI~-HuGHES, Physical Chemistry, Oxford Press, England, 1957. 15 E. ACKERMAN, personal communicat ion.

Biochim. Biophys. Acta, 47 (1961) 317-326