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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)