A Kninetic Analysis of Endogenous Respiration of Bakers Yeast

7/26/2019 A Kninetic Analysis of Endogenous Respiration of Bakers Yeast

1/17

A K I N E T I C A N A L Y S I S O F T H E E N D O G E N O U S

R E S P I R A T I O N O F B A K E R S ' Y E A S T

Bx T.

J.

B. STIER AND J. N. STANNARD

From the Biological Laboratories, Harvard University, Cambridge)

(Accepted for publica tion, July 9, 1935)

I

We wil l d iscuss in th is paper the k inet ics of endogenous respirat ion

of bakers ' yeas t ; tha t is , the respirat ion of in tac t yea s t cells suspended

in non-nutr ient media . In succeeding papers resul ts growing f rom

an examinat ion of the nature of the me tabol ic processes involved wil l

be presented. The purpo se of th is ser ies is to demo nstrate the neces-

s i ty of descr ibing the behavior of metabol ic sys tems at their nat ive

loci by the use of

n v vo

procedures . By deal ing with exper ime ntal ly

ver if iable ra te-control l ing s teps in the var ious m etabol ic sys tems we

wil l show how these complex chains of react ions ma y b ehave as dis t inct

funct ional uni ts a t one t ime and, dep ending upon the imposed exper i-

men tal condi t ions , as in ter related but yet coordinated sys tems. S ince

the overal l metab ol ic act iv i ty can be shown to be governed by these

rate-control l ing loci, '1 in tegrated act ion of the myriad s of s imul-

taneous react ions is achieved within a cel l. I t i s fel t tha t th is meth od

of inves t igat ion is a necessary procedure which should precede any

f inal appl icat ion of the resul ts of in

v tro

s tudies of enzym e act ion to

the dyn amical organizat ion of

n v vo

meta bolic processes.

As a general rule in plant cells and tissues the rate of respiration

under s tarvat ion condi t ions sooner or la ter decreases with t ime af ter th e

s tored mater ia l has been reduced below a cer ta in cr i t ical concentra-

1 Obviously in all but zero order reactions (for an example,

cf.

p. 471) the

instantaneous rate of respiration may be a fu nction of the con centrati on of react-

ing materials. The rate co nstant in these cases is then the appropriate consta nt

describing the activity of the pace-setting locus; e.g., a first order constant. We

imply that the behavior of the descriptive consta nt for the rate of decomposition

of a relatively large amou nt of substrat e reflects the physical and chemical char-

acteristics of this locus, whatever its real nature may be.

461

The Journal of General Physiology


2/17

462

~..NDOGENOUS RESPIRATION O1 BAKERS YEAST

tion. This has been shown in A s p e r g i l l u s n i g e r by Kosinski (1902)

and in yeast most recently by Geiger-Huber (1934). It is assumed

that bacteria maintain themselves in non-nutrient solutions by de-

composition of their internal stores (Rahn, 1932).

The term autofermentation has been applied to the decomposition

of internally stored carbohydrates or their products of hydrolysis in

yeast juices, dried yeast, pressed yeast, and intact yeast c f . Harden,

1932; yon Euler and Lindner, 1915). Harden and Young (1902)

showed that glycogen is the principal carbohydrate reserve of yeast

and it is generally held that the ultimate substrate in autofermentation

is glycogen

c f .

Harden, 1932;~ Warburg, 1927;3 Meyerhof, 1925;

Warkany, 1924).

The tacit assumption has been that autofermentation proceeded by

the same general mechanism as the respiration and fermentation of

sugar added to the medium. The work which we are to describe

emphasizes the necessity for exercising great care in the use of the

term autofermentation. The metabolic utilization of reserve sub-

stances exhibits such differences in intact living yeas t as compared

with variously treated preparations, that the t erm autofermentation

is not stri ctly applicable to the former. For reasons which will be

given in another paper we prefer the term e n d o g e n o u s r e s p i ra t io n and

will reserve autofermenta tion for those cases in which the metabolism

can be shown to be of a truly fermentative type as is evidently the

case with yeast juice and pressed yeast.

II

EXPERIM-ENTAL PROCEDURES

Two strains of bakers' yeast, S a c c h a r o m y c e s c e r e v i s i a e , were em-

ployed; one was a pure strain grown in the laboratory, the other a

pure strain grown in large quantiti es under commercial conditions and

obtained from the Fleischmann Company through the kindness of Dr.

Charles N. Frey. This latter strain is essentially commercial bakers'

yeast, but is handled under such conditions as to exclude almost all

possible contaminants. The time at which each lot was separated

from its culture medium was noted on each package; the yeast was

2 pp. 33, 34, 40, 143, 161, and 186.

8 P. 364.


3/17

T. I . B . STIER AND I . N . STANBIARD 46 3

k e p t u n d e r r e fr i g er a t i o n e n r o u t e f r o m t h e f a c t o r y t o o u r L a b o r a t o r y .

T h i s s t r a i n w i l l b e r e f e r r e d t o a s G M y e a s t . T h e p u r e s t r a i n w h i c h

w e c u l t i v a t e d w a s o n e a l re a d y e m p l o y e d i n c o n n e c t i o n w i t h s e v e r al

s t u d i e s m a d e i n t h i s L a b o r a t o r y ( R i c h a r d s , 1 9 2 8 ; O s t e r , 1 9 3 4 - 3 5 ) .

I t w a s

Sacchar om yces ce r ev i s i ae

H a n s e n , o b t a i n a b l e f r o m t h e A m e r i c a n

T y p e C u l t u r e C o l le c t i o n , C h i c a g o ; f o r m e r l y N o . 2 3 3 5, a n d n o w r e -

n u m b e r e d N o . 4 3 60 . W e w il l r e f e r t o t h is s t r a in a s S t r a i n 4 3 6 0.

S tock cu l tu res o f S t ra in 4360 were main ta ined a t low tempera tu re (7C.) on

a g a r s l a n t s m a d e u p w i t h 1 .5 p e r c e n t m a l t e x t r a c t b r o t h ( D i fc o ) a n d 2 p e r c e n t

agar , s t e r i li zed 20 minu tes a t 15 lbs. p ressure . At l eas t 2 weeks p r io r to use the

y e a s t w a s t r a n s f e r re d t o W i l l i a m s ' m e d i u m

of.

Wil l iams , 1920 ; Wi l l i ams , Wi l son ,

a n d y o n d e r A h e , 1 9 27 ) a n d s u b - c u l tu r e s m a d e e v e r y 2 - 3 d a y s . P u r e c u l t u r e

m e t h o d s w e r e u s ed a t a l l t i m e s. D u r i n g a n y o n e p e r io d o f e x p e r i m e n t a t i o n s to c k

cu l tu res were main ta ined in Wi l l i ams ' med ium.

The ac tua l exper imenta l ma te r ia l was incuba ted fo r the des i red t ime in g lass

towers 30 X 3 .5 cm. a t 25-26C. These had a tube sea led in a t the top reach ing

t o w i t h i n ~ c m . o f t h e b o t t o m t o a l lo w a e r a t i o n f r o m a p u r i fi e d c o m p r e s s ed a i r

supp ly . Aera t ion is necessa ry , fo r , a s shown by S t ie r , Arno ld , and S tann ard

( 1 9 33 - 3 4) l a rg e c l u m p s o f y e a s t i n te r f e re w i t h p r o p e r m e a s u r e m e n t o f t h e t u r -

b i d i t y o f t h e s u s p e n s i o n b y t h e p h o t o e l e c t r i c d e n s i t o m e t e r , a n d p r o b a b l y s o m e -

wh a t wi th measurem ent o f the metabo l i sm as we ll . Th e ae ra t ion was su f f icien t ly

v igorous to reduce the num ber o f c lumps con ta in ing over 4 cel ls to l e ss than 5

per cen t o f the to ta l number o f ce l l s .

In the ea r l i e r por t ion o f the work we used t r ans fe r s f rom the o r ig ina l s tock

c u l t u r e o b t a i n e d f r o m th e A m e r i c a n T y p e C u l t u r e C o l le c t io n . A t a l a t e r d a t e

s ing le ce l l s f rom th i s cu l tu re were i so la ted by a d i lu t ion t echn ique employ ing

Pe t r i d i shes and m al t ex t rac t aga r . Th e loc i o f s ing le ce ll s were marke d a f te r

exam ina t ion und er the b inocu la r mic roscope and severa l co lon ies a r i s ing f rom

such s ing le ce l l s were separa te ly inocu la ted on to agar s l an t s and then l a te r in to

Wi l l i ams ' med ium. Th e mos t success fu l one o f these was se lec ted fo r fu tu re work .

W e r e p e a t e d se v e r a l e x p e r im e n t s o n t h i s n e w l y i s o la t e d s t r a i n a n d c o m p a r e d

i t s behav io r wi th tha t o f our o r ig ina l pure l ine . No d i f fe rences in resp i ra to ry

ac t iv i ty o r in i t s me tabo l ic behav io r cou ld be de tec ted .

T h e y e a s t w a s c e n t r i f u g e d a w a y f r o m t h e c u l t u r e m e d i u m a t a p p r o x i m a t e l y

3000 R .P .M . fo r 3 -5 m inu tes . F resh , s t e r il e M/15 KH2PO4 so lu t ion (pH 4 .5 ) , o r

ra re ly S~renson phospha te buf fe r a t a se r ie s o f pH va lues , was added ; the ce l l s

were washed , r ecen t r i fuged , and resuspended a t the p roper concen t ra t ion in the

new medium. One wash ing was su f f icien t to remove the l a s t t races o f the cu l tu re

m e d i u m , b u t n o t e n o u g h t o w a s h o u t a p p r e c i a b l y a n y o f t h e s o l u b l e c o m p o n e n t s

of the cel l .

T h e G M y e a s t w a s s t o r e d i n a r e f ri g e r a to r a t 7 C . a n d w a s u s e d w i t h in 2 4 - 4 8

h o u r s a f te r i t s ar r iv a l . F o r e a c h e x p e r im e n t a p o r t i o n w a s r e m o v e d f r o m t h e


4/17

4 6 4

ENDOGENOUS RESPIRATION OF BAKERS' YEAST

cen te r o f the package in a s t e r i l e t r ans fe r cab ine t and made up to the des i red con-

cen t ra t ion wi th s te r i l e ~ /15 KH2PO4, usua l ly a f te r one cen t r i fuga l wash ing .

The pho toe lec t r i c dens i tomete r (S t ie r , Arno ld , and S tannard , 1933-34) was

u s e d a s a q u i c k a n d a c c u r a t e m e t h o d o f o b t a i n i n g y e a s t s u s p e n s i o n s o f u n i f o r m

and kno wn conce n t ra t ion fo r any se r ies o f experiments~ Th e dens i tom ete r was

ca l ib ra ted in te rms o f d ry we igh t o f yeas t . The den s i ty o f the suspens ions used

f o r t h e e x p e r i m e n t s h e r e r e p o r t e d w a s m a d e h i g h s i n c e t h e r a t e o f e n d o g e n o u s

resp i ra t ion o f in tac t yeas t i s on ly 0 .4 -0 .05 o f tha t o f yeas t suspended in 2 pe r

cen t dex t rose -phospha te so lu t ion cf. W a r b u r g , 1 92 7 ; M e y e r h o f a n d I w a s a k i ,

1930).

T h e o x y g e n c o n s u m p t i o n a n d a e r o b i c C O ~ p r o d u c t i o n w e r e m e a s u r e d i n W a r -

b u r g r e s p ir o m e t er s . T h e C O ~ p r o d u c t i o n w a s m e a s u r e d b y t h e t w o v e s se l m e t h o d

d i s c us s e d b y F r e n c h , K o h n , a n d T a n g ( 1 9 34 - 3 5 ). T h e s h a k e r s p e e d n e c e s s a ry

to insure f reedom f rom th e l imi t s se t by d i f fus ion was ca. 120 comp le te osc i l l a t ions

p e r m i n u t e w i t h a n a m p l i t u d e o f 8 c m . A s t h e r a t e o f r e s p i ra t i o n d e c l in e d t h e

t ime be tween read ings was inc reased so tha t the exper imenta l e r ro r o f r ead ing

ma nom ete r de f lec t ions was he ld to wi th in 4 -2 .5 pe r cen t . Inaccurac ies due to

the re ten t ion o f CO~ by N a~H P04 wh en th i s subs tance i s used in p repar ing buf fe r

s o l u ti o n s f o r m a n o m e t r i c m e a s u r e m e n t s o f m e t a b o l i s m w e r e re d u c e d t o a m i n i m u m

by us ing on ly KH2PO4, as r ecom men ded by Kre bs (1928). Add i t ion o f ac id a t

t h e e n d o f a n e x p e r i m e n t w a s t h u s u n n e c e s s a r y .

The g rowth o f the yeas t r e sp i r ing in s te r i l e ~ /15 KH~PO4 so lu t ion was de te r -

m i n e d b y m e a n s o f t h e d e n s it o m e t e r. T w o s a m p l e s w e r e p r e p a r ed , o n e a t t h e

o r i g in a l c o n c e n t r a t i o n o f y e a s t a n d a n o t h e r d i l u t e d w i t h s t e ri l e p r i m a r y p h o s p h a t e

so lu t ion to a conc en t ra t ion su f f ic ien tly low to e l imina te any g row th inh ib i t ion due

t o c r o w d i n g c f . Stephenson , 1930 ' ) . The samples were kep t in dens i tom ete r

t u b e s w h i c h w e r e i m m e r s e d in a t h e r m o s t a t . N o g r o w t h w a s e v e r o b s e rv e d i n

p u r e p h o s p h a t e s o l u t i on s . T h e n u m b e r o f c el ls t a k i n g u p m e t h y l e n e b lu e a t

t h e b e g i n n i n g a n d e n d o f t h e e x p e r i m e n t w a s f o u n d t o b e l o w a n d c o n s t a n t cf.

Richards , 1932, fo r de ta i l s r egard ing the s ign i f icance o f th i s me thod o f e s t ima t ing

the num ber o f dea d ce il s) . Care was exerc i sed to main ta in reasonab le s te r i l i ty

dur ing a ll phases o f an exper iment . Mic roscop ic exam ina t ion a f te r Gra m s ta in ing

revea led no bac te r ia l g rowth even in exper iments l a s t ing 48 hours .

Al l (o r r ep resen ta t ive ) samples f rom the Warburg vesse l s were t e s ted fo r

c h a n g e i n p H b y t w o m e t h o d s , i n d i c a to r a n d q u i n h y d r o n e e l e c t ro d e w i t h c a l o m e l

ha l f -ce l l , and found to remain cons tan t wi th in 0 .1 pH un i t dur ing 24 hours t ime .

r r r

T h e R a t e o f E n d o g e n o u s R e s p i r a t i o n a s a F u n c t i o n o f T i m e i n a N o n -

N u t r ie n t M e d i u m

F e w s t u di e s o f y e a s t u n d e r s t a r v a t i o n c o n d i t i o n s d o m o r e t h a n s t a t e

t h a t t h e r a t e o f O 3 c o n s u m p t i o n o r C O , p r o d u c t i o n d e c l in e s w i t h t i m e .

4p . 26 .


5/17

T. j. B. ST m R A~CD J. N. STANDARD 465

G e i g e r -H u b e r (1 93 4) i n a r e c e n t p a p e r f i g u re s b o t h d i f f e r e n t i a l a n d

i n t e g r a l c u rv e s f o r t h e o x y g e n c o n s u m p t i o n o f D e l f t b e e r - y e a s t su s -

p e n d e d i n K IS K H 2 P O 4 s o l u t i o n s h o w i n g a n i n i t i a l r a p i d d e c l i n e i n

r a t e t o a c o n s t a n t l e v e l w h i c h p e r s is t e d f o r t h e d u r a t i o n o f t h e e x p e r i -

m e n t , b u t h e d o e s n o t g i v e a k i n e t i c a n a l y s i s o f hi s d a t a .

I f b a k e r s ' y e a s t is s u s p e n d e d i n a p u r e p h o s p h a t e b u f f e r m e d i u m

t h e s u b s e q u e n t r a t e o f r e s p i r a t o r y e x c h a n g e i s a f u n c t i o n o f b o t h t h e

i n it i al a g e o f t h e c e l ls a n d t h e t i m e i n t h e m e d i u m . I f a y o u n g ( 24

h o u r ) c u l t u r e i s u se d , t h e r a t e o f r e s p i r a t io n d e c l in e s w i t h t i m e f r o m

A 6

H ~ . 0 2 4 6 8 I0 12

T i m e

F I G . I . T h e r a t e o f O 2 c o n s u m p t i o n ( c . m m . / 1 0 r a in .) a s a f u n c t i o n o f t i m e f o r

a 1 6 h o u r cu l t u r e s u s p e n d e d in M / I S K H 2 PO 4 s o l u t i o n a t p H 4 . 5 . ( E x p e r i m e n t

a t 2 5 C . ; S t r a i n 4 3 5 0 c u l t u r e d a t 2 5 C . )

t h e f i r s t p o i n t w h i l e i n o l d e r c u l t u r e s a v a r y i n g p e r i o d o f c o n s t a n t

r a t e p r e c e d e s t h e d e c l in e , w h i c h i s s o m e w h a t s lo w e r i n t h is c a s e. F o r

c o n v e n i e n c e w e h a v e t e r m e d t h e s e r a t e - t im e r e l a t i on s t h e d i s s im i l a -

t i o n c u r v e . T h e e v e n t s o c c u r ri n g i n y o u n g c u l t u r e s w i ll b e d is c u s se d

f i rs t , fo l l o w e d b y a s h o r t a c c o u n t o f t h e i n f l u e n c e o f t h e a g e o f t h e

c e l l o n t h e c o u r s e o f t h e d i s s i m i l a t i o n c u rv e .

Young Cul~res

F i g . 1 i l l u s t r a t e s t h e r e l a t i o n o f O , c o n s u m p t i o n t o t i m e i n a 1 6 h o u r

c u l t u re . T h e e x p e r i m e n t s h o w n in t h i s f ig u r e w a s c o n t i n u e d t o 48

h o u r s t o t a l ti m e . T h e r a t e m e r e l y a p p r o a c h e d z e ro a s y m p t o t i c a l l y .


6/17

466

E N D O G E N O U S I (E SP IR AT IO I~ O F B A K E R S Y E A S T

A t t h e c lo s e of t h e e x p e r i m e n t o n l y a s l ig h t i n c re a s e w a s d e t e c t e d i n

t h e n u m b e r o f c e ll s t a k i n g u p m e t h y l e n e b l u e a n d 0 .05 c c . se e d e d i n t o

f r e s h W i l l i a m s m e d i u m g re w p ro l if i c a ll y .

T h e K O H i n t h e i n s e t o f t h e W a r b u r g v e s se l w a s re n e w e d a t i n t e r v a l s w i t h n o

conseq uen t chan ge in ra te , and the add i t ion o f f i l te r pape r to the we l l to p resen t

g rea te r su r face fo r absorp t ion o f the CO2 produ ced Dixon and E l l io t t , 1930)

was wi th ou t e f fec t . The pa r t i a l p ressure o f oxyg en was main ta ined we l l abov e

t h e c r i ti c a l v a l u e t h r o u g h o u t t h e e x p e r i m e n t T a n g , 1 9 3 3; T a n g a n d F r e n c h ,

1933 ; F rench , 1934) by f requen t ly open ing the vesse l s to the a i r , r emoving the

s i d e a r m s t o p p e r s , a n d d r a w i n g a i r t h r o u g h

c f .

French , 1934) . I t is p rob ab ly

sa fe to assume the c r i t i ca l pO, fo r th i s endogenous reac t ion to be a t l eas t a s low

as tha t fo r the resp i ra t ion o f add ed sugar . S t i e r 1935-36) shows tha t th is a s -

sumpt ion i s p robab ly jus t i f i ed . )

W e fe e l t h a t t h e d e c l i n e in r a t e o f r e s p i r a t i o n h a s r e a l s i g n if i c a n c e

a n d i s n o t d u e t o t h e d e a t h o f a n y s i g n i f i c a n t p e rc e n t a g e o f t h e c e l l s

o r t o t e c h n i c a l a r t i f a c t s .

T h e O r d e r o f t h e R e a c t i o n

T h e s h a p e s o f b o t h t h e d i f f e r e n t i a l a n d i n t e g r a l c u r v e s

cf.

Figs . 1

a n d 2 ) f o r t h e d e c l in i n g r a t e t y p e o f c u r v e w e r e r e g u l a r e n o u g h t o s u g -

g e s t k i n e t i c a n a l y s i s . W e a s s u m e t h a t a s i n g l e r e a c t i o n is i n v o l v e d ,

v /z . t h e d e c o m p o s i t i o n o f s o m e s u b s t r a t e , d e s i g n a t e d fo r t h e p r e s e n t a s

S . C f .

F re n c h , Ko h n , a n d T a n g , 1 9 3 4 -3 5 , fo r a n i l l u s t r a t i v e c a s e

w h e r e m o r e t h a n o n e r e a c t i o n i s i n v o l v e d. ) T h e t o t a l a m o u n t o f

O ~ c o n s u m e d o r o f C O2 p r o d u c e d w a s a s s u m e d a d i r e c t m e a s u r e o f t h e

a m o u n t o f i n t e rn a l l y s to r e d s u b s t r a t e u t i li z e d . S i n c e t h e R .Q . (C O, / O2 )

e q u a l s 1 t h r o u g h o u t t h e c o u r se o f t h e r e a c t i o n

cf.

F i g . 2 ) t h e p ro d u c t s

o f t h e r e a c t i o n a r e d e s i g n a t e d p r o v i s io n a l l y a s C O , a n d H 2 0 . W e m a y

t h e n w r i t e t h e d e c o m p o s i t io n o f S a s :

1) S Enzym es ~ CO, + HaO.

O*

T h i s p r e d i c t s t h a t t h e c o n c e n t r a t i o n o f s u b s t r a t e m i g h t l im i t t h e

r a t e o f 0 ,. c o n s u m p t i o n a n d o f C O s p r o d u c t i o n a n d t h a t t h e r e a c t i o n i s

f i r s t o rd e r w i t h r e s p e c t t o t i m e a s l o n g a s n e i t h e r t h e p a r t i a l p r e s s u re

o f 0 2 n o r t h e e n z y m e c o n c e n t r a t i o n i s l i m i ti n g . T h a t t h e r a t e o f

a u t o f e r m e n t a t i o n o f l i v i n g y e a s t i s l i m i t e d b y t h e c o n c e n t r a t i o n o f


7/17

T. J . I3. STIER AND J . N . STANNARD 46 7

s u b s t r a t e h a s b e e n s u g g e s t e d m a n y t i m e s H a r d e n a n d P a i ne , 1 9 12 ,

H a r d e n , 1 9 32 ) a n d m o s t r e c e n t l y b y B e l i t z e r 1 9 3 4 ). O u r e v i d e n c e

v e r i f i e s t h i s s u g g e s t i o n .

130 -

12

~

o

iO

9

70

4O

3

20 ~

f l

H ~. I 2 3 4 5 6 7 8 9 I0

T i m o

F IG . 2. I n t e g r a l c u r v e s h o w i n g t h e t o t a l a m o u n t s c .m m . ) o f O 2 c o n s u m e d a n d

CO~ prod uced as a func t ion o f t ime a t 23C. in ~ /1 5 KH~PO4. Th e open c i rc les

repres ent O~ con sum ptio n and th e sol id circles CO~ prod uctio n. Th e R.Q. ----

i th rou gho ut . S t ra in 4350 cu l tu red a t 25C.)

D a t a o b t a i n e d i n 1 5 e x p e r i m e n t s w e r e t e s t e d b y t h e f o l l o w in g

m e t h o d :

L e t

y - - c .mm . O~ consu med in a t ime , t

A = t o t a l c .m m . O ~ c o n s u m e d o r C O s p r o d u c e d ; i. e. , t h e a s y m p t o t i c v a l u e

a - o r ig ina l conce n t ra t ion o f subs t ra te , S

x - - a m o u n t o f s u b s t r a te c o n s u m e d in t m i n u t e s

k - - v e l o c it y c o n s t a n t f o r d e c o m p o s i t io n o f S

kI = v e l o c i t y c o n s t a n t f o r o x y g e n c o n s u m p t i o n a n d C O s p r o d u c t i o n

I f t h e p r o c e s s i s f i r st o r d e r ,

i . e .

p s e u d o - u n i m o l e c u l a r ,

2) d__x =

K a - - x )

d t

14


8/17

4 6 8

E N D O G E N O U S R E S P I R A T I O N O F B A K E R S Y E A S T

wh i c h g i v e s o n i n t e g ra t i o n t h e u s u a l e x p re s s i o n :

1 a

( 3 ) k

i

- l n

t ( a - x )

A t h e a s y m p t o t i c v a l u e f o r t h e 0 2 c o n s u m e d o r C O2 p r o d u c e d , o b -

t a i n e d f r o m t h e i n t e g r a l c ur v e s , m a y b e t a k e n a s p r o p o r t i o n a l t o t h e

t o t a l a m o u n t o f s u b s t r a t e S , a n d y t h e a m o u n t o f g a s e x c h a n g e d in t h e

t i m e t m a y b e t a k e n a s p r o p o r t i o n a l t o x . I n o t h e r w o r d s :

L e t

y ~ - - c x

~ca

T h e n :

( 4 ) d = k ( a - y ) = k ' ( A - - y ) ,

dt a

a n d

(5 ) y - -- - A ( 1 - - e - t ) ,

w h e n c e w e o b t a i n t h e e x p r e s s io n

6) I n I - ) = - Y r.

P l o t t in g I n ( l - A ) a g a i n s t t i m e s h o ul d t h e n g i v e a s t ra i g h t l in e w i t h

s lo p e - k . F i g . 3 i s a n e x a m p l e o f t h e fi t o b t a i n e d w h e n d a t a f o r t h e

e n d o g e n o u s r e s p i ra t i o n o f y o u n g ce l ls a r e p l o t te d i n th i s m a n n e r . T h e

v e l o c i t y c o n s t a n t - k w a s c a l c u l a t e d a s 2.3 03 t i m e s t h e s l o pe o f t h e

l i n e s i n c e l o g a r i t h m s t o t h e b a s e 1 0 we re u se d . T h e d a t a u s e d i n

p l o t t i n g F i g . 3 a r e s h o wn in T a b l e I . L o g r a t e a g a i n s t t i m e a ls o g i v e s

a l i n e a r re l a t io n , b u t w e p r e f e r r e d t h e m e t h o d s h o w n i n T a b l e I a n d

F i g . 3 i n o rd e r t o o b t a i n t h e f i r s t o rd e r v e l o c i t y c o n s t a n t .

A f u r t h e r t e s t f o r t h e f i r st o r d e r c h a r a c t e r o f s u c h r e a c ti o n s h a s b e e n

s u g g e s te d i n a n o t h e r c o n n e c t io n b y F r e n c h , K o h n , a n d T a n g ( 1 9 3 4 -

35) fo r Chlorella pyreno idosa viz . p l o t t i n g t h e r a t e a t a n y t i m e , dr

a g a i n s t t h e total a m o u n t o f o x y g e n c o n s u m e d i n a n y t o t a l t i m e , t.

T h i s m e t h o d m a k e s i t u n n e c e s s a r y in t h e c a se o f a s i ng l e r e a c t io n t o


9/17

T. J. B. STIER AND J. lq. STANNARD

469

determine the asymptotic value for y i . e . A), and is useful when

velocity constants are not desired as a quick test for the order of the

reaction. It ha~ further application when a cons tant basal rate ob-

scures the order of a superimposed reaction.

The validity of the assumption that the concentration of substrate S is the

rate-limiting concentration when oxygen consumption or CO2 production is meas-

ured has been subjected to further tests. It has been shown already that pO~

or concentration of oxygen in the cell is probably not rate-limiting. Following

the data presented by Rubner (1913) and discussed by Rahn (1932)5, showing

0 75

; d

A Kninetic Analysis of Endogenous Respiration of Bakers Yeast

Documents