Title Thermal analysis of enzyme reactions : report I. Invertaseaction

Author(s) 神前, 武和

Citation 物理化學の進歩 (1938), 12(2): 21-46

Issue Date 1938-04-30

URL http://hdl.handle.net/2433/46135

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

''•

~,

.,~ ,-

~o ~ 2~i No. 2

THERMAL ANALYSIS OF ENZYME REACTIONS*.

Report I. Invertase Action.

By TAKEKAZII I{OSAKI.

The invertase action has long been studied by many investigators, as invertase is relatively stable and obtained in a large amount. 4Villstfitter, fiuler, Nelson

and others have already reported various results of the investigation. All of them have employed the method of measuring the change of rotating power during the

inversion or the reducing power of monoses formed for the observation of the reaction velocity. Though the dilatatometric method of measuring the volume

increase of the reaction system during the inversion has been proposed, yet there

is no report on the invertase action employing the method. In those methods,

except the dilatatometric method, a part of the reaction system must be taken out each time to observe the reaction velocity, so it is difficult to make continued observation always tinder the same condition.

"1'he writer attempted to study the invertase action employing the thenno-

analytical method originated by Prof. Shinkichi Horiba'1. He measured the reaction velocity, observing the rise of the temperature of the reaction system due

to the inversion heat by means of a simple glass calorime[er'~. This thermo-

ana]ytical tnethod is expected to make up (or the defects of [he above mentioned methods. Dforeover, he attempted to measure the inversion heat of sucrose

accurately and to accomplish therma] analysis of various enzyme reactions, espe-cially of those having no perfect method (or its measurement, and so he selected

at first invertase.

(I) Materials,

(I) The Invertase Solution. Yeast whose time value had been made relatively small by cultivation was for long hours left to stand without being diluted for neutral autolysis. The autolytic liquid thus obtained was pudfied hvice by the alcohol precipitation method and then being adsorbed with non-treated nw kaolin it was desorhed with dilute ammonia. By such a simple procedure as this, considerably large quantity of relatively pure invertase solution

• This pnper is the English tnnslntion of tlce some article whiClt nnlxarcd in lhi' fora'ual, 9, I51 (x 934)•

r) ti. Iioriha an<l '1'. Ichiknrva, Rru. Plyr. Cduir., 1, r45 (r9z7)7 4, x (x93o). S. Fiorihn and 1[, ltaln, kry. Pkyr. Clrenr, 6, 47 (x93'-)•

z) 5. Flnrihn and K, Snto, Rev. Phyr. C/rern., 6, x6 Q93=)•

r _ l _ _ .._s L._ ~ -~~r.w' _

(1

a

K

s

r~

~~ k: ,~

9fiT~1t~~it€1 Vol. 12n No. 2 (1938)

22 T. KOSAKI V°I, XII

whose time value was o.zs mold be prepared.

(z) Sucrose Sucrose was dissolved in water to remove impurities by filtration, and made syrupy by vacuum distillation. Alcohol-.being added to t>o~, the precipitate formed was

sepazated. Sucrose .thus treated, being washed with alcohol for several times and then with

ether, .rbc completely dried. Repeating this treatment two days hefora the experiment, and,

on the preceding day, ascertaining that the rotating power of the preparation was [a~=6G.6°

without any reducing power, it was used.

Method of Measurement.

"I'he thermal analysis of a chemical reaction is a method to know the reaction velocity

from the following equation by observing the temperature change of the reaction system ~~~ due m a chemical reaction

dT _ dT _ Q da (t) dt dt - IP dE

The cooling velocity r~T, which is characteristic of the reaction vessel and is caused by the temperature difference between the reacfion system and its surroutding medium, the water

eyuiyalent IP of the system, including the reaction vessel, were measured and further the

reaction heat Q was determined. r~l of the liyuid system can he measured directly by a simple glass calorimeter, different from thlt of the gaseous system. d4' tan be known From dt

the.ohs~vadon of ~E in the case when dl =o, i.e the cooling curve. rat' obeys Arewton's law as ascertained by Horiba and his m-workers and also by the present author:

dt

where k is a constant and dT is the temperature difference between the reaction s}'stem and

its surrounding medium.

To determine If', dE was observe) by giving constantly n certain quantity of heat q' per, unit time to the reaction system with the electric current after the reaction, and iT was

calculated from the equation : - •

r . The Tesult of this measurement was also compared with that obtained with warm.

The reaction heat Q was determined directly as follows. Equa6on (t) can he written as

If w•e find the relation between the time t and the. quantity of heat produced by the

reaction system per unit time ~Q from this equation, and then calculate ~~~rdQ from the beginning of the reaction Iv to its termination t by the graphical integration, Q can be obtained.

In case the reaction is not complete, measure the amount of the substance which has reacted

9fiT~1t~~i~1 Vol. 12n No.

N°. 2 '1'I Iii RhtAl. ANALYSIS OF EN2YMS RI•:ACTION5 23

during the time interval from to to t, by the observaton of the roLltiuq power of the reaction

system after [I (mm [he beginning, and (~ will be obtained.

For the olaervalioo of dE ,which is the. fundamental element of the present research, such a calorimeter as shown in Fig. 1. was employed.

A is a Dewar vessel about tycm. in depth. B a

]3eckmann thermometer, C a stirrer, D a heater, and 'r B the platinum wire d' (radius o.r mm.. length zo.q cm.)

e' attached u the end of the glass tube d is connected

_ - - _ = with the conducting wire d" by the intermedialion of

_ - _ mercury in d. E is a glu, vessel, which holds about E'

zj c.c. of water, and communicates with the Dewar vessel

by the rubber tube a and the glass tube c' and also with ~

~ e r 'open air ],y aid of e". If F, is brought to the position • -'E- E", the contents of F. can he removed into the Detvar

vessel almost instantaneously. The whole apparatus is

- - Q e' sunk in a 4hermostat as shown in the figure.

The Dewar vessel was filled with roo.o c.c. of

sucrose solution o(a certain concentration prepared with

Borh the buBer solution and E aIW with zo.z c.c. of a dilute d' enzyme solution. Leaving it for about j hours in the

rye I bath [o let the tem peralure of the content _of A become

equal to that of the Mth, the temperanve change of the contents of A after the transfer of

the enzyme solution into A was observed. The time elapsing from the transfer of [he enzyme

solution to the beginning of the elevation of [he~tempersmre was always tj acconds in every

experiment anJ the time from the closing or the cutting of the circuit in the case of electric

heating to the b~inning of the change of the temperature was also t5 seconds'>. So the lime

when the temperature began to ris^, namely tj seconds after the transfer, was taken as the

zero-point of the time of observation. '

k and I!' were mEaasured after the observation of dT at every time. For this purpose, an accumulator of a Large capacity, an accurate ammeter and a rheostat were connected with

D" in series. The tempemwre change was observed by heating with a certain yuamity of

electricity per unit time~and also after shutting oN the electric current. The resistance of the

platinum wire was measured preliminarily at 39.o°C. by means of Wheatstone's bridge. For the measurements of k and ii; the reaction system avas employed to know how they changed

with the kind and concentration of substances in the reaction system and to compare them

with lhosc of the distilled water.

,•{) In ibis case an nqueous solution of melh}9ene. blue was transferred from C inm A to olaerve Ilre mixing role and it was mixed almost instantnneously with the contents of A.

C

c'

E

Barh

E

r

,e

IQ -_ --

N

(1938)2

J

9fit~lt~mi~~ Vol. 12n No. 2

2q 'I'. K(15AKI Vol. a:It

The results of the preliminary esperimelit show that the temperature and the hydrogen

ion concentration suitable for the present enzyme preparation are 37.o°C. and px=q•z respec-

IIYCI}S /~CCOI'dingh'• the experiments were carried out in the following four groups.

rs[ group. A sucrose so]ution whose concentration w;is ri9o; px=q•z; 37.o°C. The

amount of the ori~{htal enzyme solo«on was changed.

znd group. r3..j c.c. of the enzyrne solution; px=q.z; i7•o°C. The concentration of thu sucrose solution e•as changed.

3rd group. A sucrose solution .aliose mncentmtion was t5.ego' ; t3.j c.c. of enz}'me solo«on; 37•o°C. px was changed.

qth group. A sucrose solution whose concentration was t5.o%; i3.5 c.c. of the enzyme silnlion; pry=q.z. T'he temperature was changed.

For the buffer the following solutions were employed.

For px = z.q q cc. of ~ secondar}~ salium citrate solution. fi c.c. of ~ hvdro- ro io chloric acid.

For N px = q•z S.zB c.c. of -secondary sodinm phosphate solution. t t.9q c.c, of o citric acid.

r

For px=g•rr qe.c, of to secondary sodium citn[e solution. t c.c. of o caustic soda solution.

troy px=6.z ,o c.c. of ~ primary potassium phosphate solution. S.fi c.c. of N 5 caustic soda solution.

For p„ = y.o so ac of Y primary potassium phosphate s<lution. zq.6g c.c. of N

caustic soda solution.

Experimental.

(I) The Reaction Beat.

(t) The cooling constant fi and the water equivalent !V obtained by

emitlo}~ing r?o.oc.c. of distilled hater are given in Table r.

'['able I.

Water xso.o c.c. Temp. of Bath 37a°C.

No. of 1?xp.~amR) (cl.) mean mean

I 0.736

o.7I q

o.6g3

$A63

7.950

asa3

I65.7I

I65.7z

I65.7a

O.OIy7

o.olg7

o.olg7

k and J•V observed b}- employing the reaction system are given in the column " Blank Test " of "Table 2 and almost no difference can be seen between the

value, of k and ff' in the reaction system and those in distilled water.

(1938)

No. 2 TI [F.RDtA L ANALI'SIS OP ENl.VNE

'fable z.

1fii~~lt~mit€~

Rr•.ncruly~

Va . 12n No. 2 (1938)

•':i

Quantity Quantilyof Tempera-

\ieaeun:ment of IIlauk 'iwrR

cnctinn Heat -

rifSucrose

(G•)

]dnzymeSol W ion

(c.c.)

Rcactimi(Pn)

turcof Bath

(°C)

W'eigbt ofInvcrted Sectinn Papertiucrose omupied by

(~$) the t-g cun-e(!;•)

ReaclicnHOnt k

(caLf_ g.nvd.)

fl~

(cal.)

I5A SA q.2 37A lao.o og78q gAZC. o.oIy7 I55.7I

IoA lOO.O 0.3350 q.orp 0.0197 Ifi5.7_

13.5 loo.o 0.3326 gA65 o.oig6 I65~7.;

IQO Iao.o a333o gA69 o.oI98 I65•T-

ISA Iaao o.33zy q.0(ig OAIt~$ I65.72

20A loo.0 0.,;710 4ASq ~ 0.0195 163.70

2A 13.5 IOOA OA5O3 gAIS ~ o.oI97 165.T

4A loa0 o.IOZB d.1o; ooi97 IGj.63

$.o Ioo.o o.1 z4.3 3.yG5 0.0197 165.71

7.5 Ioao 0.1913 gA31 o.o1g6 i65.72

loo Ioao o.z57( q.nl o.mg8 I65.71

Iz.S Io0.O a3x30 ga25 ooI99 165.7I

2DA I00.0 0.5t32 gAyz o.0193 ?65.P

2jA ys•3 o.fi1o8 q.o63 oAIgS 165.70

SOA yo.Q 0.70I5 q.072 O.OIy3 165.7z

35.0 97•z o.3490 3.98o O.m97 165.7 r

25A I3.5 7A 3]A 17A7 o.afi4z d.00] O.Oly7 165•l.i

6s Sz.z o.3l00 q,00$ O.Olyfi 165~70

$.11 100.0 0,33aj q.oS3 0.0195 16j.7o

^^-•9 Ioo.o 0.3313 q.o(,2 o.m 97 165.72

4•"- 42A 39.4 o•33:d ;.y65 oot96 165.71

38A rooo 0.3703 q.052 OAI97 I65•P

35.0 (() laoo a39or q.t5o o,oly6 I65.7o

3sA(IJ 97A o.3fi3o q.o3z o.olg6 165.71

32A loo.o o.;g[9 ga7o o.olgy 165.7a

\ican q.o58 oAI97 165.7I

btenn Syunre h:rnrt to.o515 to.oool09 footo3

(2) The Determination of the Reaction Heat.

Observing the JT-C cun~e at various conditions, the relation bchvccn `fir :urd ~ .vas measured and the value of ~~~ or q for each 1 calculated from equation (.}), applying k=oAt97 and li = [ 65.7 [. The results of this calculation are given

in Tables 3. 4 and 5.. From the atQ -[ curve (this is correslx~nding to that of Fig. z tvhoseordinate ~X was exchanged with AQ , the unit of 41ie ordinate

I

:..~

9fi7~1t~miil~ Vol. 12n No. 2 (1938)

~8 T. KOSARI Vol. XIi

being cal.~min. and that of the abscissa min.) Q was graphically obtained. The

mean value of Q was 4.[ cal., which was in good agreement in every experiment. When the seactiou had nbt terminated, the decomposition rate was calculated from the rotating power of the reaction system measured immediately after the interrup-

tion and then the reaction heat per t g. mot of sucrose-J4z.z4g. calculated.

Ie is apparent Gom the above table that-the determination of the reaction ]teat by

the present method provides a sufficiently reliable result and accordingly that the

thermal anal}~sis of the reaction velocity based upon the ziQ -! relation is reliable.

(3) Comparison of the Observed Valae with that obtained

thermochemically.

The inversion of sucrose proceeds according to the following equation:

Therefore

C„H~O„ + H.,U=C,H,_Oe+ CeH,,Oe.

glucose (nictose

the inversion heat can be calculated as follows:

(Gs I IKOnAq.)= CCixl hO„] -c

CCeH,sOs] =(CeII,sOaAq.) +L -̂•tt?~+ [C,YH~O„] = I z0~+ I t (H,O) +x

6COp+6(Hs0)=[C,H,_O,)+ t zOr-y + 6C0,+6(H:O)=(CeH„Oe]+rz0>-s

(5)

(glucose) (fructose)

(glucos-e) (fructose)

(C„Ha,O„Aq.)+(H:O)=a(CeH,,Oenq.)+a+6-c+x-y-z. (6)

Substituting the following values into equation (6), tse can obtain q.t cal.

per r g. mot for O_.

rz=-o.9 cal.' ~ti= t 353.5 cal:'t

G=-z.3 cal.'> y= 674.0 cal s, c=-z.3 cal.'t a= 67 i.6 cal.e>

But the results of the combustion heat measurement by various investigators do

not coincide with respect to the numbers smaller than the first decimals of the large calorie value. Therefore the value of Q fluctuates from z.OCal. to to.ocal., if it is calculated by employing various values. Un the other hand, calculating

from the heats of the formation of C,rHaO„Aq., H.U, CeH,aO,;pq. glucose and

q) Tablr axxra!!rs uYrnmf., 4 Qgzx} g) landolt, Pkynk. Ckrm. Tab.r P9x3b

;~AI~1t~~itt1 Vol. 12n No. 2

Na 2 '1'I[F.RiltAL ANALYSIS OF liN%Y11LG ItEACTIUNS 37

C.~II„O~Aq. fructose, namely 534.8 cal., 69.o cal., 300.4 cal. and 300.4 cal sI respec-

tively, avalue-3.ocal. per t g. mol for Q-can be obtained. As the above ealues are all within the limit of the measurement error they arc not all accurate, and

only indicate a rough standard. The value obtained by the present research lies within the lint of this rough standard indicated by the value calculated from the

combustion heat, and so the present value, namely Q for [ g. mol=4.[ cal., is

certainly a reliable one, and consequently it seems to ensure again the applicability of the present analytical method.

(II) Thermal Analysis of the Invertase Action.

Observing t-dT in a number of esperimen[s performed under the above-

mentioned conditions to obtain `~~ q was calculated, and then dividing i[ by Q per [ mg. mol=4.t cal., ~a was calculated. Further, in the present research the relation s-t was unknown and the relation !fit -t or q-t was known and so from this relation k„ u•as calculated as follows.

dx =k~ a-x) (7) rft (

Integrating this we have '

k,,,t =1 n a-x

Then a-x=ae k"r (8)

Substituting (8) in (7), we have

ttl - rtk„C-k„d (9)

Putting the values of dt at 1, and t~ as \ ~i )~ and ~ dit /r, respectively, we have

In ~ rlt ~r -In ~ dt le,-k"'V -4) log {( ~t ~e,l ~ ~dt /r,l .. k,. _

0.4343 (rx-tt)

0 4343 (~=-tt)~

6) Berlhelot, Tkrrwrantimiq 2, 6g6 & 7~(i (x897}

(1938)

9fiT~1t~~i~1 Vol. 12n No.

34 ~ T. KOSAKI Vnl. XTI

where ~n and qy are the values o(q or ̀~ at A and t_ respectively. Using this equation, k„ can be easily calculated from the relation g-t.

Lt this calculation the value of k„ fluctuated when both !, and i }were freely

hakes, and so it was calculated, taking only t, to a

be a certain constant value. From the relation x

between d[ and t aitd that behveen d[ and ̀ -_ k„ the reaction was analysed as will be seen

later. ell ~ As is seen from the following tables and

figures the results obtained in the present-eXperi- ~ o b m

meets show drat the sucrose inversion by inver- -. r (n,in.)

tale takes a tyhe quite different from that of nag' ''

the first order reaction in its earlier stage and similar to it in its later stage-tlte

reaction consists of three parts, SIB, BC and CD, as is shown in Pig. x.

Since the BC part seems to be the transition part from tIB to CD as will

be also mentioned later, the velocity formulae of only the hvo parts, tIB and CD,

and .the influence of various conditions oit these parts will be considered.

(1) The AB-Part.

The relation between ~~ and t is linear as is seen in Figs. 6, 9, 13 and t5. and the velocity equation was derived as follows.

Let a' and 6 represent t10 and tan is respectively in Fig. 3, and the equation of the straight line AB is expressed by

rte =6l+ar. (1 t) dt

Integrating this, we have

.r= b tz+dt+C.

where C=o, as s=o when t=o.

Therefore .r= ~' t'+dt.

Hence t= -d+ ~R~yy-x-r. (The negative sign is unfit.) Substituting this in (t 1),

2 (1938)

No.2 TIIERTf

rfx = ~ dt

Putting +/2b=k~ an

dr - ~,` dt

Prom this equation n and

k, and n, obtained.

a 2 ~e`

i

0

~r Fig. 3.

/•„, is almost constant, dr and k„ is linear as d

6 equation was derived as

Let bi and c rcpresen

line CD is expressed by

~ rtt +k„

And k„= dt

Therefore, !t =6, If ac-I• [ is replaced by ne,

dx =b, . .fc

bl and c were obtained an

(l) Amo

As for pepsin, Schiitz' g

7) E. &hm:, ~. pnrmt. c., s, s» (~885A

9fiT~1t~~it€1 Vol. 12n No.

Ai. ANALYSIS OPEN7.YhiL• REACC[ONS 29

.e'"+ zbx .

N d ab =a, ,

+~ai-i-x (i2)

b were calculated under various conditions, and then

B

_ ~ I°

~- 1 p o

0

~.

Fig. q.

(2) The CD-Part.

but, strictly speaking, it is not. The relation between

seen in Digs. q, to, t3 and t6. and so the velocity

ollows.

t OD and cot ~ respectively in Pig. ¢. and the straight

=b~ • ([ 3)

I n-x

ru+t-cx ti-c(a-x)

then

T (n-r) (i4)r n,-cx

d then rr., was calculated.

unt of Enzyme and Reaction Velocity.

T reported that . the followin relation held behveen the

2 (1938)

-!

9fit~lt~mi~~ Vol. 12n No. 2 (1938)

,

30 T. Kl)SAKI Vol. }CII

amount of enzyme and the .reaction velocity:

where k is a constant, I% the amount of enzyme, x the amount of the split protein

(or the. time t. As for invertase, the results of i~vestigatorswt arc in agreement,

showing the amount of ffie. split sucrose for a given time is directly proportional

to the amount of enzyme

Theo, let .~ be the initial velocity, and v=k • F.

Further, it was admitted that this relation was justified 6y the assumption

that [he invertase action was a Lomngeneous reaction, whose velocity is propor-

tional to the product of the concentrations of enzyme and sucrose. Haldane'~

considers that the nzynte reaction is by no means a reaction in the homogeneous

system. Therefore, it s interesting to sec the influence of the amount of enzyme

on the rate of this reaction which seems to be consecutive.

Experimental Results. Experiments were carried out whit 5.0, io.o, t3.5,

Table 3. Enzyme 5 e.o

t(min.

dT(°CJ

dTdt

(°C./minJ

9(cnl.jmin.)

dxCr

(mol/min.)rm

I(min.j

9T'(°G)

dTdt

(°G/min.~G11./nlltl.~ds

de(mnl/min.)

k,.

a 0 OA12Q2 z.oSS 5.a qoA 0.363 oAO37o I397 5.4 0.o[23I

IA OAI2 OAI2ga zo9fi 5.1 -mwcS5°a 0393 omzo6 L6z3 3.9 oAit6z

z.a oAZS ooxzgz z.t39 5.a -OA201S fi0A odo6 oAOO6o Lga3 3.5 ooizofi

3.0 OA3] O.OI242 z177 5•.; -om _mS 7oA o.go5 oAOO77 1.19 .; 2.9 ooi3o9

4A oASo AOI242 z.zz0 5~4 -oozmS 8oa 0.390 oaot95 0•949 z.3 o.ol46q

5.0

7,0

oA6z

0,0$7

o.otzgz

o.olzgz

z.z6o

x.3gt

S•5

5'7

-DA203$

-OA2039

go.oI 0.36]

taoo~ 0.338

omz63

0.00301

0.760

0.603

1.$

Lq

0.o157z

oAI659

(}O O.IIO 0.ei3i2 z..;66 5.8 -e.oxoo8 It0.0 o.,;o] ooo3tz 0.~83 LI OAI]al

Ia.S 0.15i O.OIIg1 _.:$'- 5.8 -OAOa$5 I aDA 0.275 o.ao3oG og89 0.9 oAI765

15A O.I79 o.olo8q z•379 5.$ 0.00039 I30A o.zg6 o.oogi] o.I u o.z6 oul7gz

I7~5 0.20] oAto3o z.38I 5.$ -o.aogoa I40A o.zlg oAO389 OA69 0.16 OAI]q$

zoA o.z30 o.oo9gz s,;u 5.G oell8o ISOA o.I95 0.00375 o.ot5 0.03 oAI738

z5.o o.z7q 0.oo79t z.zo3 5.4 o.olozq I6oA o.t7q o.oo3z3 o.ooz 0.005 0.01768

3o.a o.31R 0.oo65S 2.I0] 5.t 0.00976

8J

9)

C. G 7-[. R.

J.

O'Sullivun. R-F. N. Tompson, J. C..Sd. Lrndaq 57, Syy R SQS (tS9o} 5. Iiudsun, Anr. J. C. S, 30, 1564 ~ t573 (t9o$)• v. Ealer fi O. SvanF.erg, z. pkyeiol. C., 107, z6g S z75 (t9t9)• ~VillstStteq J. G~user & R. Ruhh, Z. phyrial. C., 123, 7z ([qza).

S, S. F[aldane, Eri ~wr.r (t93a}

No. _3

u

e Cr a

~,

a from

6!

/~6°

(min.)

dr _ k di

9fiI~lt~mit~1 Vol. 12n No.

THER1fAL ANALYSIS OF F.N7.YME. REACTIONS 31

1 S.o, and 20.o c.c. of the enzyme

solutions whose concentration was

t 5 % ~ Pn=4.2, at ~y.o°C., and the

results obtained art shown in Pig. 5. ^JP` The observed values are tabulated .

in Tables 3, 4 and 5. d tvas

calculated from the value of d

at t=o and G also from the ~~

m

-b curve in Fig. 6, and hence l.•1

1~'s' S' and a~ ; G„ c and a, were calculated

,,, curve in Fig. q. These values are given in Table 6.

TaAlc a.

Enzyme 13•Sr..c.

2 (1938)

the

r (min.)

0

z.o

q.o

6.0

S.z

I0..3

x 5,3

u.6

30.0

OT ("C.)

0

0.05

o.xo

o.t5

o.zo

o•z5

0.35

0.45

o.53a

dT de

`G/min .

o.oz473

aAZ473

0~~473

OAaQtO

o.oz3t6

ooa6g

oAxS38

OAI290

oAO7o3

d~

(cal.~min, df mn]fmin.7

q.ogS

q.z6a

4~4z4

q.gSz

q.48o

4.409

q.x87

3•~5

z.goi

to.o

xo.q

xaS

to.g

xa9

xo.7

xo.z

S.S

7.x

t psaa

QOA

-o.ozo ,i9 50.0

-o.ozo39 60.0

-0.oo5ot 7oa

O SO:O

O.OOQ7I 90A

b.ooSl9 IooA

0.00x6 I10.0

o,ot979

dT Cf ("C.) Je

0:563 ~ o.oooS3 o.55I o.oo3l9 o.5ot o.oo58q o.ggS aoo539 o.3S7 0.00603. 0.3.52 0.00616 o.z8q 0.00535 o.2Qq O.OOgSI

9 cal./min.

t.99o

L26g

0.666

o.g85

0.263

o.o6z

o.ogo

O.OOq

dx dr

m01/min.J

q.8

.i.I

L6

LI

o.b

O.13

O.OS

OAS

a~,

o.ozSgS

o.030I5

0.03676

0.03593

0.03945

0.03y50

oA3g62

OA3930

Ta61c

F:nryme

i~

zo c.c.

t' (min.)

0

z.o

q.o

S.o

I2.0

I6,o

20.a

zq.o

zS.o

32.0

36A

dT (°C.)

0

0.070

oago

o.z73

0.383

0.470

o.5go

0.590

o.6zo

0.635

0.637

dT

G/min.

0.o355a

0,0355[

0.0355 a

o.oz7z8

o.ozgG7

onag73

o~oa495

0.00935

om558

o.ooag6

0.ooo4a

dr

(cnL7min.) dt kmol f min.).5.884

6a u

6..i40

5.4x0

5•.137

4.Sao

gs38

3.474

=•947

z.396

z.mo

xq.4

xq.9

IS•5

x 3•z

x3.o

xx-7

xo.3

&5

7.z

5•$

M9

k,,,

-o.ozo39

-o.ozo39

o.o3gzz

o,ozo67

o.ozz45

o.ozgya

o.ozg9z

o.o3tS8

o.o3g6q

0.03584

t (min.J

qOA

qq:o

qSA

jz.o

j6A

60.0

Gq.o

fiSA

7z.o

76A

dT (°C.)

o.6z8

o:Go7

o.SS.i

o.55S

0.530

0.500

o.g7a

o.ggz

0 39a

dT

(°C min.J

aoogzz

0.00554

ooo6gq

0.00656 oAO7 tz

0.00767 I oAO8z8

I oAO8t8

oAO79g

0.00768

(ral./mi0.J

x.3jo

tA6x

a.835

0.734 o.jja

036[ atGS

0.086 o.ozz

oAO3

ds ee

(mol/miu.J

33

z.5

z.o

[.7

[$

0.8

o.q

o,z

0.05

oAOB

k„

oAgz9o oAggb[ aog6oq oAg698 OAj Rj

oAStoj ao5zot a05z[a oA5tz5 oA5t5o

9fi~~lt~mit€~ Vol. 12n No. 2 (1938)

32 T. KOSAKi Vof. XI]

b

X c

c c

bb

i

bn

MOe.

Js ee

0 X c .~

0

+~`.

i0

Fig. 6.

y b M ...

fable 6.

t°

~:x

a ppl aW _~ km

rs. ~.

I:nayme d(x 1a~1 ~~ X IOS~ 6y(X IO~) n~(X 10 (i a a.

SA c.c. SA IAo Lql I =4 0.013 1.12 LogQS

IoA „ 8.5 :.87 1.93 L92 OA29 2.m LoBaa

Ii5 ~. loa z.o3 2OI 2.qq OAQO 2AS L0832

t6.a ~. It.7 z63 ' "29 z6o OAQ_ 1.3G 1•0544

IS.o , Iz6 z.63 '~29 3A0 OAgS 2.C0 1.0$72

20A v Iq-0 2.50 x.;G 3.63 OASO 1.03 Lo768

11s for the i1B part, k, could be regarded as almost constant, and had a

tendency to increase in proportion to the increase of the enzyme amount; ar had

a similar tendency.

!ls for the CD part, b~ increased almost in proportion to the amount of

enzyme ; c showed a remarkable fluctuation ; a, was ahvays constant regardless of -th

e hmount of enzyme.

Again it was found that bi and k, could be represented by b~ F and k, F

respectively in the case where h( and kr` were constants indifferent to the amount

of enzyme and F was the amount of enzyme. The fact that k, and b, corres-

ponding to the velocity constants of the reaction can be represented by k~ F and 6, F is in agreement tvith the results obtained by various investigators though nut

discussed in the same breath.

The duration of the /1B part is about ¢-5 minutes though a little longer in

the case where the. amount of enzyme is small. The larger the ~~ value of the 111i part, the shorter the duration of the BC part is, and at last the BC part

seems to be a transition point from the AB part to the CD.

9fi~~lt~mit€~ Vol. 12n No. 2 (1938)

No. 3 TI[NRhtAI. ANALY575 OF L•'NZYhtR RI?ACTIONS a3

(3J Concentration of Sucrose and Reaction Velocity.

Hrown"'t reported that in the range behveen 5-qo/ the reaction ve]ocity

increased in proportion to the concentration of sucrose, namely, the velocity

constant of the first order reaction could be always given, and accordingly the

sucrose inversion by succharase satisfied ~s•hat the first order reaction required.

The results obtained by other investigators"~, however, proved that below q / the

reaction velocity increased till k„-const., but not above 5 ̂ /o and also tliat in the

range behveen 5-zo/ the velocity reached the maximum with 5^/o according to

the expression k„ x c=const. (c is the concentration denoted by /.) The latter

(act can not be satisfactorily interpreted by the theory of the first order reaction

already admitted. In order to know which of the te•o, sucrose or water, had the

main influence upon the reaction velocity, Nelson and IngersolP'I changed the

concentrations of sucrose and mater in the reaction s}'stem by replacing part of

them with alcohol which would not take part in the reaction and ascertained that

the concentration of water higher than 5,0/ mainly affected the reaction velocity.

Here Nelson" t suggests that the deviation of .this enzyme reaction from the first

order reaction, namely the existence of tl3e maximum value with respecC to the

concentration of sucrose, may easily be explained by the assumption that it is a

reaction of the heterogeneous system based upon the adsorption phenomenon,

taking the concentration of water into consideration.

Experimental Results. f-~.

~,.

~, '~ The results of the experiments

in which the concentrations of the

sucruse used were 2.0, q.o, j.o, i.5,

ro.o, i a.5. i 5.0, ^o.o, X5.0, 30.0

and 35.oq'o, are shown in Fig. Sand

Tables 7, S and 9. The d[ -t curve and ~t -kM curve obtained from the values tabulated in these

'v

.~

a~ \ \ ~

~d ~~~~ +..

c values tabulated in these '-' r (min.)

A. ti. ftrnwn, J. C..Snr. Lardou. 81, 373 (t902} 1.. Michnelis & bi. L Menteo, Bioeh. Z., 49, 333 (t9t3}

J. 9T. Nclson g VV. C. VosLurgh, /.:1. C. S. 39, 790 (t9t7} L..Michaclis, L'inrhun. 7.., 115, 2&~ (cy2t ).

J.Tf. Nelson Sc.M. D. SchuUert, J. :1. C..5.. 50, z[88 (xyz5). C. Il. Inp rsoll, Bx11. tor. chine. biaL, 8, 26y R z76 (t926}

J. ht. Nelson, Ckwr. Brn„ 12, t (ty33)•

rl~, s.

to) tt)

t21

t3)

b x

c c

ale

1fii~~lt~mit€~ VoI 12n No. 2 (1938)

:N'1.̀ K(1SAR1 Vol. XII

tables

a, are

are shown in Figs, g

given in Table to.

and lo. and the

Table 7.

Sucrose zg6.

velocity constants and

(min.7dT

(°G)

dT 9d~ , cal./min.)

dsd! k„

(min.J9T

(°C.)

d7e~ (cal./mio.N.

drdi k„

(°Cy mm.) (mol/min.) PC./min.) molJnun.J

a 0 o.ozo55 3.go5 8.3 to.a o.IIS oAO2o5 o.7lq t7 o.I7538

0.5 oo~ o.ozai5 3d36 S.q -oogo37 xz.5 o.ix7 o.ooot i o.3Gz 0.8 oa96g2

Lo OA1 0.02055 3.469 8.5 -0.04037 ISA O.I I5 n.n0100 o.zo8 0.5 o.zoo9l

2A OAq o.m758 3A4z 7.4 o.I3o98 XlA 6I ID oAOIG7 OAEO O.iS o.x6x85

3A OA57 ooI593 2.825 G.g o.o99go 3oa o.IOI oAOx87 OAI9 o.oq aA9974

SA oA83 mIOSB zA73 5•i o.IZ8x7 qoA oAy3 oAOi83 a e oA7776

7.5 oao5 om64o Lgol 3~4 o.I39o6

Tabla S.

Sucrose z5ya,

(min.

0

z.z

q.o

6.t

S.t

to.;

~z.7

~5•~

~7~

ToS

T4A

2~A

dT ~°~ )

0

OA5

o.[o

O.I$

o.zo

o.z5

0.30

0.35

O.qO

045

0.50

0.55

df fl

°G/min .

o.m~zo

OA2q?O

OAS,f20

OA2¢'A

ooz363

OA21~

o.on

,,['o~ OAI~u

OAI )5q

0.015]$

ootgz8

o.otz77

r cnl. min.

q.oto

q.i]2

4336

4.499

4d6$

4.441

4.475

4.366

q.2 tz

M1Ati3

3.998

3A1o

ds dt

nud/mina

}R

taz

tab

tm

tL1

30.}{

to.g

tab

to.;

9.9

A7

9S

,r,.

-OAiSj3

-o.ozz67

-OAIy42

-Om50I

O.OOSy]

roA0416

om35S

X496

oAa}62

0.00401

om3TI

t (min.

32A

37.3

45A

jjA

65A

]jA

gjA

95.0

105A

I IjA

t-5A

dT (°C.)

0.60

0.6;

0.70

aT"-5

o.7i5

0.675

o.6z3

0.535

o.48z

0.412

0347

eT e~

°C./min.J

0.01277

om7y8

o.twg7o

oAOO75

Om2sn

Om4;0

om6z6

om7o6

0.00726

oAO667

021

(cnl./min.

3.7 [ t

3.443

3A63

z.ggo

1.86y

ig56

0.995

o.G4i

0.379

o.z3&

0.102

ds dr

utnl/min.J

y.o

3.4

7A

f.o

4.5

:•i

2.q

a.5

0.y

0.5

o.z

.~~

oaogxu

omgg9

0.00508

om597

om7z3

oAO78x

OAWp2

OAI025

ooubl

OAI2.~5

oncgbz

~Y$;

r `$ 4

._ a.

-~

.+

L (mueJ

b

~h

i

5

w

~~

Y

a~

}'ig. 9• ..

-. ~.eY

r•~s. to.

m. ow m aro 6il

9fiT~1t~~it€1 Vol. 12n No. 2 (1938)

No. 2'I'IfF:R\iAI . ANALI'SIS OfENZY\fE REACTIONS

TaUle q.

Sucrose ;59a.

:i6

t(min.;

dT(°G)

dT

',,°Gf min.~~(cnl.~nin.Jdr

(moI f min.)~'m

t(min.

dT(°C.J

dT

dt (oal.~min.J(°Gfmin.

dr

(molfmin.~k„

0 0 oAZOao 3314 S.I ! 85.a 0•737 o.oox7o z.13x 5.z oAO833

t.zi OA2i oA21]OD 3.395 S.3 -OA2g3i 195A a71z o.ao3I I 1.807 4.4 oAO93z

z.5o O.O$O OA 3.476 $.' -OA12I7 IoSA a67i oAO387 1.560 ' .g O.O~

3.75 oA75 OA2000 i•557 8.7 -oAZg35 I15A a6;q o.oogzq L;65 3.3 DAIDZG

im o.lm oAZOOa 3.6go 3.9 -o.oz435 Iz5•o a58g o.DOgi2 LI73 z.S oA1o7o

6.zi o.t25 OA2000 3.7n 9.I -o.ozg35 i I35.D o.5gz 0,00490 0,956 z.3 oAt t48

7•So o.I io OA_f1]O 3.So3 s3 -o.oszl7 IgiA o•i94 o.DOg68 o.B;G 2A oA1I6z

IoA o.zao o.otg7l 3•YI9 9.G -o.ot63x I iiA o.g5o oAOg3q 0•749 IB OAI i60

12.5 D.260 oA18z5 3.839 9~4 O.ao7aG I65A o.g07 0.00421 o.6zg Lj OAI39]

t5.3 o,?oo OAI694 3.786 A3 0.00393 I75A 0.365 oAO395 0.536 t.3 mluz

zo.D 0•375 o.oI486 3.GSi 9A o.aog65 I SiA a3z8 0.00347 0•495 1.3 OAI I97

2SA 0.444 OA1302 3.Go5 S.8 0.00437 195.0 az95 oAO3Iz 0•445 IA OAI I90

30A o.iafi om146' 3.549 8.7 D.OOg2] 205A az65 OA0292 o,;8i o.g o.m zo8

35A 0.560 onaoi3 3.5oG 8.6 o.ao377 2ISA o,z37 aooz&t o.3a 0.7 OAI16fi

45A o.6g6 oAO7oS 3.z81 Sa 0.00534 zziA azto omz6S o.zgo o.; OAt31z

i5A a7oi oAOgSz 3.049 7•i o.ooi8a z35A aI83 o.oozi7 o.I7o o.q OAIgO$

b5A 0•735 OAOl9q a.71y 6.7 0.oo69z zio.o o.lgfi o.oozgq OA71 o.z oA1687

75A a745 o.00008 x.444 GA 0,00750

Table to.

tiucrose d(x lo+) h(x IoF) ~~(x ta) ~r~(X I0=) 6, n.

z.oq 8.3 n6o I,79 z.I6 o.zo7 t3.zo Ia7gz

QA .+ 8.3 L60 I•79 aI6 0.I30 7.76 IA222

$A +• 10.E zAj 2A1 z.Cn O.IQO 464 I A713

7.5 ,~ [Lj zA3 2A1 ;.Iz oAyq 3.68 1A832

m.o •, loz zA; 2A1 z56 o.o6q 2A0 IA600

I2.5 n 10.9 2.Oi zA1 {•Q.R 0.0(.3 }.12 Ltl6$

IS.o ~. xo.a zA3 z.0i 2.QQ OAQO 2A$ IAS;z

zoe ,• Io.B z.o3 2A1 3.49 OA25 [.OQ IA6zq

z5.o,~ 9.8 I•77 L38 z.7z OA[1 O.j? ]A2Q0

jOA+ S.o 1.60 t.79 2A0 OA20 1.20 3.1080

;f5.0 +f ~.I 2.60 I•79 z.oq O.OI I o.;z ' IA3rfi

As for the A13 pazt, k, increased a ]ittle below j?o, took quite a constant

value (or 5-sog6, and decreased slightly for more than 20%. Generally it seems

to be indifferent to the concentration of sucrose. a, increased a little in propor-

tion to the concentration of sucrose below 7.g/, and as a whole it tended to

decrease though /luchiating below 2o.o/v. Above 2og°/, it showed a tendency

similar to k,. k~ had almost no relation to the concentration of sucrose, and a,

9fi1~1t~mi>~~ Vol. 12n No. 2 (1938)

36 1'. K(15AKJ Vol. XII

tvas influenced by the amount of sucrose, decreasing as the concentration of sucrose

was increased except in the case of low concentration. Therefore, as for this part

it was found that the results obtained was not in agreement with those of other

investigators.

As (or the CD part, both b, and c remarkably decreased with the increase

of the amount of sucrose within the limit of y.5/, and became constant beyond

the limit. n~ was also constant ]n short, k, and a> are the amounts indifferent

to the concentration of sucrose ; a, decreased with the increase of the concentra-

tion except in the range behveen 2.o-y.5 ~, ; b, and c can he regarded as constants

indifferent to the concentration of sucrose except in the case of low concentration.

The duration of the AB part was about ?-[ z minutes and the lower the

initial concentration of sucrose, the shorter it was. The lower the concentration

of sucrose, the shorter [he duration of the BC part, and for lower concentrations

the BC part was not observed.

(q) Hydrogen Ion Concentration and Reaction Velocity.

The influence of the hydrogen ion concentration upon the invertase action has

been investigated at 5z.5°C. by Sj~rensen" 1 and at IS.o°C. by Michaelis1BJ. The

results obtained by [he former can he unreliable, because invertase must have

been destroyed at such a high temperature as 5z.5°C. According to the ]after,

the relation behveen the hydrogen ion concentration and the invert:cse activity

can be denoted by a cun'e just +like the dissociation curve having its maximum

value at p„=q.5, and so invertase is an amphoteric electrolyte, whose isoelectric

point is pu=q.5, and the non-dissociated part acts as a catalyser for the invzrsion of sucrose. Further, judging from the fact that inevertase would be destroyed in

the medium whose pn value is smaller that q.o. Nelson and 131oomfield'el concluded

that the isoelectric Point is not. necessarit}- the optimum point oFthe invertase

action as has been stated by Michaelis. There is, however, no satisfactory theory

to take the place of that of Michaelis.

Experimental Results.

The results of experiments at which pu was 2.9, q.2, 5.t [, 6.?, and y.o are

shown in Fig. I I and Tables I 1 and [ x. The ̀fir -t curve and d-"t -k„ curve

[q) S. I'. L Sgrenxn, h'roch. Z., 2l, 268 (r9o9). r5) L pTichaelis & li. Uavidwn, Rix4. %., 35, 3Ft6 (r9>>).

I6) J. JT. Nelwn & G. Bloom(ield, J .~. C. S, 48, [oz5 (t9zq}

9fiT~1t~~it€1 Vol. 12n No.

No. 3 TIIFhTtAL ANALYSIS.O& ISN7.Y\th: RA:ACI'IONS 37

obtained are shown in Figs, 1z and t3. The constants, k1, a„ L1, ~, and n2,

calculated similarly are tabulated in Table 13.

As for the dB part, ahough k, fluctuated a liale at pR=3.9-5.11, reaching

the maximum at p,1=4.z, yet in general it seemed to be almost constant in this

range. At the ptl value larger than 5.n, however, it markedly decreased. a,

gradually increased below pll=G.z, and suddenly decreased at pn=y.o.

Table I I.

tnt 70•

2 (1938)

t (min.J

0

j-o

IOA

1 jA

2jA

3jA

QjA

er (°L.)

0 D.ODj

0.010

o.oq

OA28

oA3g

0.050

er Ci

O.Jmin.

oAO11o

0.001 m

0.00110

OAOI 10

omuo

oAO1Ia

oaoo9t

, cal. min.

0.[82

0.197

0.2I i

0.236

073

o.31.i

0.313

Js

At ~(molJ~nin.j o.q

o.q

o.j

o.j

0.6

0.7

0.7

~ ~.

-OAI~f'iri

-OAgQbt

-OA2106

-oA1862

-oao8j3

0

t min.J

SSA

65A

~ 75A

S5A

~~ u5.o

I j0.0

dT ('C•)

0.057 oA6q

OA70

oA75

oA76 X77

oA78

dT d1

(°C.f min:

0.00072 0.00065 O.OOD51 omoz8 omoxa oAaooB oAOmB

(calf min.

0.304 o.3x6

o.3xi

o.z89

0.163

o.1G3 o.z66

er dt nu9fmin.j

0.7

0.7 0.7

0.7

ob

ob ob

k„

0.00:97

-~4M

0000(

0.00430

om5zo

om363

000153

'fable i i.

Pu z-g

t pnin.j

0

L25

z.3a

3.50

S.o

7.5

coA

xz.5

x5A

t7.5

20A

df (°C.)

0

oA2i

OA50

oA7i

O.tOS

0.151

o.xti

o.a5~

o.3xs

0.iii

a:i9l

d!' ~ ds df pl.~min. df C.~mio. ~(mnl~min.

o.ou48

o.ozx4S

o.ozt43

oAZxgS

o.ovg8

oazxgS

o.w_t3fi

oAlyz6

oA1735

OAI560

out3z3

3.559

3.640

i.7zx

3.So3

yyto

gASq

4zto

q.o6l

3sy2

.3.74.i

i•46S

8.7

S.9

4x

'J•3

yG

!O-0

to;

IOA

9.5

9.z

S.5

k.. ~ t ~Gnin.

-o.oz435

-o.ozyoo

-0.oz536

-o.oz7zo

-o.otfi3z

-0.o163z'

0.01567

oAt537

0.0162]

oAISSS

25.0

30.0

35.0

qo.o

50.0

60A

70A

So.o

90A

lOOA

i

dT ~°G)

o.g3a

0.493

0.5[7

o.5x7

o.5m

o{G5

o.q1;

0357

o.3oz

0.x51

dT Ar

°G/min .

onroz8

0.00675

om3zy

oAOO61

oAO;6o

0.00500

ooo5g6

0.oo63q

o.ao5S3

OAO./yQ

9 I dr call min.)~ dr '~(

mol/min.

;.i7i

x.7z7

z.z3z

1.Sx1

,.036

o.68y

O.gg3

o.uq

O.Ot0

O

7.$

G.7

5.5

4i

z.5

1.6

IA

o.z5

OA2

O

k,

oo1S99

oAZ18y

o.oz543

ooaSo3

0.03519

oA36;b

0.03766

oA4c73

oAg656

OAQ7$a

•ranl~ ,;.

mi a'(x:w) d(x xo°) k,(x IoI) .,,(x Io) G, u,

7.a 0.q oA3 o.zt a1z 0.007 zA8 ,As;z

6: Lfi oA3 o.v 5•Iz oAO7 z.o8 IAS~z

$.tI 3.5 Lf5 s~ z•7z aogo x.o8 LoS3z

4z IOA z.o3 2A1 z.qq O.O¢O z.o8 IA83z

z.9 3.7 s~ 1.93 2m O.OgO sAs iA83z

38

3

ti

a

1

•r. xosnx~

~s

P

ie

9fi~~lt~mit€~ Vol. 12n No. 2 (1938)

b

X c ~E

E

e Ib

As

below Ih

pH value

as the v

constant

decrease

dissociati

cerning i

on or fn

of the m

the inflm

sucrose ~

base

a, fl

d up

uctu;

The

G «and ~

'•9 - 5•~

be found

~ f (min.lrtg. I:.

0

u

, ~ n n Y A A 1 • n n ~ ~. d

-~ f f IfOIL} Fls. I2

As for the CD part, L, showed a tendency sim

below hu=S.tt and decreased remarkabh'. Roth

pn value of the medium. Lt other words, k, an

as the velocity constant of each hart, showed

constant below p„=S.tI, being indifferent to the

decreased markedly at larger p„ values. This fa

dissociation curve of Michaelis and others. It is

cerning the preparation of invcrtase that the adsor

on or from kaolin and other adsorbing substances

of the medium and this influence is similar to th

the influence of pI, upon k, and h, may be Basil

sucrose due to invcrtase is assumed to be a react

based upon the adsorption phenomenon. a, and c

a, fluctuated in the neighbourhood of a constant

The duration of the AB part was almost con

and G, were very small. The duration of the B

~.g-5.t I ; it was considerably long at pn=6.2-

be found at pn=y.o.

Vol. XII

b ' X

d Q ~E y, o =

E

ele

i C aoz aoI

-~ kq

t'/g. rq.

ilar to L•, : i[ was quite constant

c and n..vere indifferent to the

d L„ which are to be regarded

2 similar tendency: they were

hydrogen ion concentration and

ct is a little different from the

evident from many reports con-

ption or the elusion of invcrtase

is influenced by the pn ealue

at upon k, and LI. Accordingly,

y explained if the inversion of ion in the heterogeneous system

wire indifferent to the Pu value.

value.

scant at plr=6.z-7.o, where d•,

C part was not observed at prl=

7.0 ; and the CD part could not

9fiI~lt~mii¥1 Vol. 12n No. 2 (1938)

No. 2 TIi}bRBIAI. ANAT.\'515 OF RN%YMR. RP:ACTIONS 39

(5) Temperature and Reaction Velocity.

The influence of temperature upon the invertase action has been studied for a long time by various investigators. Ilttording to them, the equilibrium constant

is slightly influenced by temperature on account of the smallness of the inversion

heat as in the case of an acid catalysis, As for the reaction velocity, it has been

admiited''1 that the reaction velocity has an optimum point with respect to

temperature, because it increases with the rise of temperature according to van't

I-Ioffs law and, on the other hand, it decreases with the rise of temperature on -account of, the heat inactivation of eoz}'me. As to the optimmm point, however,

any accurate value has not been obtained and yet it is considered to be about

55.o°C1nl As the. temperature coefficient, the value of 1.58" 1 is given in the temperature range between 30.0°-4o.o°C. It is reported that the value of the

activation heat, E, calculated from ArrUenius' equation~l is 3,8oocals. and is far

less than that of the acid catalysis-z450~cals.

Experimental Results.

A number of experiments were carried out at 3z.o°, 35.0°, 37.0, ;S.o° and

4z.o°C. Moreover, in order to see the change of [he reaction velocity due to temperature under the same influence by the heat inactivation an experiment was

carried out at 15.o°C., employing the material preliminarily kept at qz.o°C. for one hour, and the result of this experiment will be shown as " 35.o°C. (II) ". "The results obtained are shown in Fig. Iq, and some of the. observed values are

tabulated in Tables t4 and 15. The `tX -l crave and dx -km curve are ire dt

shown Figs. t5 and t6. and the velocity constants d•„ rrr, G„ c and n. in Table 16.

As for the AB part, k[ increased with the rise of temperature (till 37.o°C.), and decreased suddenly in the temperahrre range behveen 37.0° and 33.o°C. and

then gradually decreased till 4z.o°C. TLe heat inactivation began to come forth

at 35.o°C. and it was affected most in the range between 37.0° and 38.o°C. and

and tltcn gradually increased. a, increased till 35.o°C. and decreased a little a[

35.0°-37.o°C. and then gradually at 37.o°-4z.o°C. On the whole it may be regarded as constant

t7) R'. Bi. Bayliss, [YQi//YC aj F.)r.•ynu Adiau, 93 f[9r4) r8) J. B. 5. Haldane, R.r }•rner, 65 ([93°b

t9) H. v. Eul~s & J: Iaurin, Z. Pbytiar. C., 108, 64 (r9r9~. zo) Sv. Anheoius, Z. phy,i,t. C., 4, z56 ([88q).

9fii~lt~mi~~ Vol. 12n No. 2 (1938)

40 T. KOSAIU

Tahle i;.

3z.o°C.

Vol. \Ii

t (min.j

O

t.3

z.6

q.o

5.0

7.5

xo.o

Is,S

t5.o

zo:o

z5A

i0:0

dT (°G)

0

o.ozj

0.050

0.08;

o:I Io

o.I53

azxz

o.z66

o.3xz

0.39= 0.458 a.SoS

dT dt

°C./min.cnl.f min:)

o.ozx37

aozx37

o.ozl37

o.ozx37

OA~I37

OAx13]

OA213J

o.ox99z

o.ol7g6

0.0143q

ao[ I35

o.oo7S6

3.541

i.6zz

3.704

3.SII

3.899

4.057

4•=3z

q.tb9

3.9I I

3.656

3•.i75

z.959

dr d~

nudfmina

S.]

3.9

yI

9.3

9.6

Ioo

tO.q

Ia.z

q.6

g.o

3..i

7.z

t,

-o .oz34[

-0.oz34I

-0.02I]5

-o.ogoSl

-0.o163z

-o .m 63z

0m395

o.oI537

0.01397

a.oI487

OAI7S6

t (min.j

35.0

qOA

45A

5a.0

55.0

65A

75.0

S5A

95.0

[o5A

I x5A

IzSA

9T (°C.)

o.5gz

o.56x

0.567

0.563

0.554

o.$I7

o.g65

o.goy

0.355

0:io5

0:!61

O.33t

dT or

(°C./min.

0.00550

o.ooz36

o.oomq

oml3o

o.ooz3o

omgSo

om5ga

0.00554

ooo5v

0.oo5.i7

0.00495

o.ao;z9

dr

z.679

z.zzz

x.556

x.6zz

x.4z6

x.S9x

o.Gz3

o.gt5

o.z86

o.xo{

0.032

0.009

6.6

5.4

4.5

3A

3.5

2.i

I5

L0

0.7

o.z5

0.06

O.O?

k.

OAISOO

oozl38

o.oz35z

o-oz387 OAZg10

o.ozSzli

o.o3I56 "

oA3093

o.o,;i67

oo,i169 0.03146

O.O_i?SO

Table 15.

35.o°C, pI)

f(niin.)

JT(°G)

dT

der

(cal.~min.jdrd1

(molfmin.)Em

(mio.).1 %'

(°G)

dTJ[

(°C.fmin.)

i

(a11. min.j

drdi

(Inol/min.)~,..

0 0 0.009371 I•SSa 3.3 35A o.zsq oAOg77 Lbj2 q.o 0.00438

La aooS 0.00937 I•577 3.3 -OAxOIS qoA o.zS7 o.oogz6 L64z 4.0 oAO386

zo oal7 i o.00937 ~ Lfio7 3.9 -ao3o45 45•0 0.307 0.00366 Lso7•

3.9 0.oo38q

y0 o.ozS i o.00937 Lfig3 4.a -oA3o45 50.0 o.3zq oAOZS7 t.53z 3.7 oAOSzz

4:0 0,037 o.oog37 L67a 4I -0.03045 55A 0337 o.oozl5 I~454 3.5 o.ooso5

5.0 oAg7 o.oog37 I•7o5 q.z -o.o3oa5 60.0 o.3g6 o.ool7~ I•g3l 3~4 oAO5R9

7.5 0.070 o.oog37 L77y 4.3 -OAI?I7 7o.a o. 360 o.ooogz L3a] oAO59S

Io.o o.o9q a.oo9ofi LSo7 4~4 -0.01?f 7 Soo 0.365 o.aooxfi LzI7 z.g oAO649

Iz.S o.Ils o.oo3g6 1.779 4.3 0.oo79I qo.o a363 o.ooozG 1.14I z.8 o.ao653

I5.0 o.I36 0.00803 L773 4.3 o.oollg tOOA 0.360 oAOOsO ~.075 z.g oA06ga

zo.o ro.I7gl 0.00733I•73I 4.3 oaozoo no.o 0.343 o.ool5z o•3R3 z.I o.ao7y6

a5.o o,ao9 oAO6g4 I•74R 4.3 o.mly8 I zo.o o.3z8 omtg8 o.7gz L8 0.00897

30.0 o.z38 oAO5431 L633 4•I 0.00589

Table t6.

Temperature(°C.)

d(x toq G(x Io") k,(x Id) n,(lo x=) /.~ a_

3z,o 8.7 LS7 t.93 z.oo o.o3z t.bo t.obgo

35A (1~ 9.7 L87 t•93 z.qS o.o3g t.zS IAStx

37A l O.O 2A3 zot 2.qq OAgO 2A8 LoS3z

38.0 7.R I•So I•7z 2.oq oA35 t.68 L0672

qz.o 5.S I_L i •49 i.qS o.oI9 i.z8 I ASIz

35•0 (I ) 3~ o.So Is6 o.So o:o1l I =R i IA$12

9fi~~lt~mit€~ Vol. 12n No. 2 (1938)

No.

U

C 4

d

THF.RNAI. ANALYSIS OT )iN%YIiE REACTIONS

ssoem

~bp

m

O

X e .~

c

:'Z

1

w

-~ 1 (min.J f i~. i4.

~~ ~~

~= ~.~'

.~: /40

x c 'c

•-• Sb

le

T

Y

V4

~~A N

~~

97

O adz

-.. k,.

Pig. x6.

a00

~ - . a a .~ : m .e .... .. Fig. r5.

As for the CD part, 6, gradually ipcreased till 37-o°C. and then suddenly

decreased. The Leat inactivation seems to have come forth at 35.o°C. t tvas almost indifferent to temperature and almost cgnstant though with slight fluctua-

tion. a~, n•as also constant. In short, k„ a, and 6, have a similar tendency and the result is in agreement

with those already published by others. In the present research, however, the

optimum point is 37.o°C., heing different from that hitherto obtained. c and a,

have no relation to the temperature. The duration of the AB part was short at 42.o°C. and 35.o°C. (II), and at

32.o°-3S.o°C. it was indifferent to the temperature. The BC part- was very short except at 35.o°C. (II).

I"rom the data obtained, calculating the temperature coefficients 6•, and 6,

«•hich correspond to the velocity constants of the 11T and CD parts respectively. the activation heat E was calculated from Arrhenius' equation, .and the results

were obtained thus:

Temperature coefficient in the. range behveen 32.0° and qz.o°C.

Afi part (k,) x.26

CD part (G,) 2.03.

Both are different a little from each other, but they are approximate to the

i

9fiI~lt~mi~~ Vol. 12n No. 2 (1938)

A2. - T. KOSAKI Vol. XII

values hitherto obtained.

Activation heat.

AB part gol3 cols.

CD part 15175 Gals.

The discrepancy bchccen these can be considered as a matter of course, for

the reaction velocity of each part quite differs and its velocity constant does not

contain the same factor. These values are far smaller than ?5,500o call. obtained in

the inversion by acid catalysis. Thus, as far as the influence of temperature upon

the Invertase action is concerned, the results obtained .were almost similar to those

of other investigators.

Theoretical Consideration of the Invertase.

By the thermal analysis of the inverta_se action it was ascertained that the

sucrose inversion by Invertase ,is a reaction consisting of two stages, and not of

one stage. This fact, therefore, cart never be explained by the velocity equations

already proposed, but it may be explained if the Invertase action is considered to

6e a reaction in the heterogeneous system. -fhe enzyme solution is in fact a

colloidal system and not a homogeneous one, so the reaction should not be

treated as a reaction in the homogeneous system. Therefore, assuming that the

reaction is _due to the contact catalysis of the colloidal system, theoretical formulae will be derived and compared with the above-mentioned empirical ones.

Theoretical Derivation of the Velocity Equations.

First let us consider the mechanism of the reaction. The surface of enzyme

is a homogeneous adsorptive surface'1 as is stated by Langmuir-1, on which [he

molecules of sucrose and-water can be adsorbed in a monomolecular layer. These

adsorbed molecules are activated by the adsorption and among them reactions

take place. The adsorption coefficient of sucrose is far larger than that of water,

so that at the instant of the mixing with the sucrose solution the surface of

enzyme which has been occupied by the water molecules comes to be occupied

by the sucrose molecules and almost all the water molecules are driven from the

v) An (nr vs a metal catalyst is concerned, it has been found by further research That the surface of a melnl is not homogenrnus, and the active centre should l.e lakeo into acwunl. Langmuir's

simple Theory 1,+• been ndoplcd here (or simplicity, and it explains the results n( the present experiment well.

zz) J. Iangmuip f. A. C. S, 40, Igtit ([9t8). J. Iangmuir, Tmnt. Artrnd. .Stray 17, 6zr (tyzz}

9fiI~lt~mi~1 Vol. 12n No.

No. 2 '19lF.RDiAi. ANALYSIS OF AN7.Y\fF, REACTIONS A9

surface. The area occupied by the sucrose molecules becomes smaller as the concentration of sucrose decreases during the progress of the reaction. Accordingly,

at the earlier stage, in which the area occupied by sucrose is very large, the

reaction velocity depends mainly upon the adsorbed water, while at the later stage, in which the area occupied by .sucrose is very- small, it depends upon the

adsorbed sucrose. Furtlfer, water is adsorbed on the surface of enzyme, not in a molecular state, but in a dissociated state, such as H+ and OIi-.

Fron] this assumption ]et us derive velocity formulae. Let S represent the whole surface of enzyme, which is a quantity related to the dispcrsiq• and the

concentration of the enz}-me solution. Ixt Bs and Bn,n be the fractions of the

enzyme surface occupied by the sucrose and water molecules respectively (water

was first considered to be adsorbed in its molecular state for simplicity.). Then the reaction velocity is proportional to S•B,b;,o for the earlier srige where it

depends upon water, and [o S•Ils for the later stage where it depends upon sucrose. According to Langmuir's adsorption equilibrium, DQ and O,,,n will be as

follows : ,

H., = d,~C,, t

hn,o Cn~, (t 3) and Beau- t t GxCs-F ~'uMiCii,o

where Gs and b,,,o arc the adsorption coefficients of sucrose -and water, and Cs

and C~,,o are [he concentrations of sucrose. and water respectively.

In equations (iy) and (t8), 6s~bn,o and Ci,,,, can be regarded as a constant,

so

1+65C3+6A,oCu,of f+hgCs.

Therefore, equations (ty) and (t3) can be rewritten as follows:

__ hsC,e B, 1 +L9C,,

Buao= ~uaoCn,~~ f +6,Cs

=Bn~Cia,~i ~ f _L-~ G . l~,.

2 (1938)

.~

9fiI~lt~mit~~ Vol. 12n No. 2 (1938)

49 /P. ROSAKI Vol. XII

Hence the velocity equation for

dr _ k S~ aft

the earlizr stage can

by

I -a

6s empirical

be obtained thus,

6n~oCn~n 63 ~~~x,oCx,a

-a +x } (~~)

Let kr and al represent k • S~/

theoretical formula of the same

dr

rtl - I

Similarly, the velocity equ

da- =k' S

by type

k,'~ [r }x

aO and

as the

respectively, then we have a

formula

ation (or the later stage is obtained as follows ;

b~C,

dt t t b,Cs

Let G, and c represent ~~ • S • Gs and by respectively, then we have a theoretical

fornuala of the same type as the empirical formula

A1ext, ]ct us examine whether the velocity constants experimentally obtained can

satisfy the theoretical values or not and then consider the physical meaning of

these constants.

Comparison of the Theoretical Formulae with

the Empirical Formulae.

(1) The A'CG part. First, let us discuss dr=k • S`/ bmo/i C11N• which is con-sidered to correspond to.the velocity constant of the earlier stage. brl,~'!'Ct,,r' is .V

a constant and S IS relative to the amODUt Of C11ZYR]C. It {01101\'S, therefore, that

k, should be increased at a certain rate with the increase of the amount of enryme

and in fact this was experimentally proved.

As to the concentration of sucrose, klshould be indif{cren[, because it contains

no (actor concerning the concentration of sucrose and this was also experimentally

confirmed. IIoty can the fact be explained that ~y is very small at p„=5.1 i-~.o 7

This seems to be related to S, and it is perhaps clue to the fact that the area to

adsorb has considerably been limited before the beginning of the reaction at such

plt values. ~~hethcr this limitation is ascribed to the change of dispcrsity or to

the change of the surface owing to unknown substances though dispcrsity is un-

9fiI~lt~mitt~ Vol. 12n No. 2 (1938)

No. ̂ 'hliL•'R;,1AL ANALYSIS ON ENZYME REACTIONS 4u

changed can not be easily determined, but it is probable from the general natrue

of the colloidal solution that the changeo6 dispersity is the cause.

The duration of the AB part should be the function of the initial area of the

surface of enzyme occupied by the sucrose molecules, Eor the part lasts until the

area occupied by sucrose becomes smaller. However, in N,r= bga = I

i t Gsa f + ~ Gea

the larger the value of a, the larger is tae value of N,. Therefore, the duration

of the dB part should be proportional to the increase of the initial sucrose con-centration. This was, in fact, justified by the experimental results. The influences

of the ]lydrogen ion concentration and temperature upon the duration of tbis part,

.vhich were experimentally ascertained, can be well explained by the consideration

that the adsorption surface is remarkably limitted as above said.

(2) The CD part. G„ which can be regarded as the velocity constant of [he later stage, contains S, so it must be proportional to the increase of the

amount of enzyme, and in fact this was experimentally confirmed. Theoretically

6, contains no factor concerning the sucrose cencentra[ion, and the experimental results show that it is considered to be constant except at very low concentration

of sucrose. To the hydrogen ion concentration bs is not related, but S is.

Therefore, G, must he markedly small at p„=5.11-7.o due to tllc limitation of

the adsorption surface as in the case of k„ and this was experimentally confirmed, too. "I'I1e influence of temperature can be similarly explained.

Summary.

(I) A relatively pure imertase which has such a small time value as o.z5 has been prepared (ronl yeast cells by a simple method.

(z) The sucrose inversion has been im•estigated 6y thermal analysis, employ-ing the invertase thus obtained.

(3) The observed value of the inversion heat has been 4.t cal. per g. mol.

(4) 1'he influences of the enzyme amount, the sucrose conceirtration, the hydrogen ion concentration and the temperature upon the invertase action have been examined by thermal analysis.

(5) The results obtained by thermal analysis have shown that the inversion

by invertase proceeds according to the equations: !t =k, +/ a, tx at. its earlier stage and rlx - 6,(a-x) at its later stage.

(% t-c(a-x)

(6) The theoretical formulae derived from the assumption that the catalytic

46 T. KOSAKI

action of invertase is due. to the adsorptive phenomenon

have been well satisfied by the experimental results-(q)

The author wishes to express his cordial thanks to (or his kind direction and unfailing encouragement.

Y7~e Second Jledical Clinic, Kyoto Imperial Usi,xraity.

9fi7~1t~mit€1 Vol. 12n No.

Vol. XII

of a colloidal solution

and (~).

Pro(. Shinkichi Horiba

2 (1938)