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1/8

Ap pl M icrobiol Biotech nol (1994) 42:508-515 Springer-Ve rlag 1994

O R I G I N A L P A P E R

J . A . d e H o l l a n d e r

otent ia l m etabol ic l im i tat ions in lys ine prod uct ion by o r y nebac t e r i um

g l u t am i c um s rev eale d by m etabol ic network analys is

Rece ived: 11 Ap ril 1994 / Ac cepted: 10 May 1994

bstract

A n a l y s i s o f t h e m e t a b o l i c n e t w o r k o f ly s in e -

p r o d u c i n g

Corynebacterium glutamicum

s h o w e d t h a t

l y s i n e y i e l d s a r e l i m i t e d b y t h e e x c e s s e n e rg y p ro d u c -

t i o n i n l y s i n e b i o s y n t h e s i s . Th e m o s t p ro b a b l e m a x i -

m u m y i e l d is 0. 47 m o l / m o l o n g l u c os e , w h e n p h o s p h o e -

nolpyruvate

c a rb o x y l a s e fu n c t i o n s i n a n a n a p l e ro t i c

r e a c t i o n . W h e n t h is f u n c t i o n i s fu l f i ll e d b y t h e g l y o x y -

l a t e p a t h w a y , a m a x i m u m y i e l d o f 0 . 38 m o l / m o l i s o b -

t a i n e d .

ntroduction

Corynebacterium glutamicum

a n d c l o s e l y r e l a t e d

Brevi

bacterium

s p e c i e s a r e t h e m o s t i m p o r t a n t o r g a n i s m s

u s e d fo r th e i n d u s t r i a l f e rm e n t a t i v e p ro d u c t i o n o f l y -

s i n e . A l t h o u g h w i l d - t y p e s t r a i n s d o n o t e x c re t e l y s i n e a t

a l l , c l a s s i c a l m u t a t i o n p ro g ra m s h a v e r e s u l t e d i n s t r a i n s

p ro d u c i n g a h ig h t i t e r , m a i n l y a s t h e r e s u l t o f a r e l ie f o f

f e e d - b a c k i n h i b it i o n o f t h e k e y e n z y m e a s p a r t a t e k i -

n a s e . Th e y i e l d s o n g l u c o s e a s t h e c a rb o n s o u rc e a r e

v e ry s u b s t a n t i a l: v a l u e s o f 4 0 % ( t o o l / to o l ) o r e v e n h i g h -

e r c a n b e fo u n d i n t h e l i t e r a t u r e (To s a k a e t a l . 1 9 8 3 ;

N a k a y a m a 1 9 8 5 ) . G e n e t i c e n g i n e e r i n g t e c h n i q u e s c a n

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

i n g e n z y m e s . S u c h a n a p p r o a c h w a s s h o w n t o b e s u c -

c e s s fu l w h e n a p p l i e d o n l o w -y i e l d s t r ai n s (C re m e r e t a l.

1 99 1 ). H o w e v e r , i n d ic a t i o n s fo r t h e a p p l i c a t i o n o f t h e s e

t e c h n i q u e s t o t h e p ro d u c t i o n o f h ig h e r -y i e l d i n g i n d u s -

t r i a l s t ra ins a re ha rd to f ind in the case o f ly s ine fe r -

m e n t a t i o n . T h e v e r y h ig h c o n v e r s i o n y i e l d o f t h o s e

s t r a in s i m p l i e s a s u b s t a n t i a l i m p a c t o f l y s in e p ro d u c t i o n

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

o n t h e l y s i n e -b i o s y n t h e s i s p a t h w a y i t s e l f , b u t a l s o o n

t h e p a t h w a y s o f t h e a u x i l i a ry m e t a b o l i s m . Th i s c o u l d

v e ry w e l l b e a r e a s o n fo r t h e l i m i t e d s u c c e s s o f d i r e c t e d

i m p r o v e m e n t o f p a t h w a y e n z y m e s : t h e r e a l b o t t l e n e c k

J. A. de H ollander

Gist-brocades, PO Box i, 2600 MA Delft, The N etherlands.

FAX: +31-15-792490

m i g h t r e s i d e e l s e w h e r e i n t h e m e t a b o l i s m . M e t a b o l i c

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

p o t e n t i a l m e t a b o l i c b o t t l e n e c k s i n c l u di n g t h o s e o u t s i d e

t h e b i o s y n t h e si s p a t h w a y o f t h e p r o d u c t ( S t e p h a n o p o u -

l o s a n d S i n s k e y 1 9 93 ). I n a d d i t i o n , n e t w o rk a n a l y s is c a n

b e e m p l o y e d t o d e c r e a s e t h e d e g r e e o f f r e e d o m o f a

f e r m e n t a t i o n s y s t e m a n d t o d e r i v e p r e d ic t i v e fe r m e n t a -

t i o n m o d e l s ( d e H o l l a n d e r 1 9 9 1 a , b ) . N e t w o r k a n a l y s i s

w a s u s e d b y V a l l i n o a n d S t e p h a n o p o u l o s (1 9 93 ) to l o -

c a t e c r i t i c a l b r a n c h p o i n t s ( r i g i d n o d e s ) i n t h e m e t a -

b o l i s m o f l y s i n e -p ro d u c i n g C. glutamicum. In th i s a r t i -

c l e b o t t l e n e c k s i n t h e Corynebacterium m e t a b o l i s m a r e

i d e n t i f ie d , r e s u l t i n g f ro m t h e i m p o s s i b i l it y o f n e g a t i v e

f l u x e s t h ro u g h s o m e i r r e v e r s i b l e p a t h w a y s .

Metabol ic network analysis

T h e m e t a b o l i s m o f l y s in e - p r o d u ci n g C o r y n e b a c t e r i u m

Th e m a j o r c h a ra c t e r i st i c s o f l y s i n e - r e l a t e d m e t a b o l i s m

in

C. glutarnicum

a n d r e l a t e d o rg a n i s m s s u c h a s

Brevi

bacterium

s p e c i e s a r e f a i r l y w e l l k n o w n (K i n o s h i t a

1 98 5 ; N a k a y a m a 1 9 8 5) . N e v e r t h e l e s s , a n u m b e r o f i m -

p o r t a n t a s p e c t s r e m a i n u n c e r t a i n . T h e m o s t i m p o r t a n t

u n c e r t a i n t i e s a r e r e l a t e d t o m e t a b o l i s m a u x i l i a ry t o t h e

l y si n e p a t h w a y , s u c h a s t h e g e n e r a t i o n o f N A D P H , t h e

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

ro t i c r e a c t i o n t h a t i s u s e d . Th e fo l l o w i n g s h o r t o v e rv i e w

o f l y s i n e m e t a b o l i s m w i l l s t r e s s t h e s e a s p e c t s . F i g u re 1

p re s e n t s a s i m p l i fi e d , s c h e m a t i c o v e rv i e w o f t h e c e l l u l a r

m e t a b o l i s m o f Corynebacterium w i t h e m p h a s i s o n t h e

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

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

g ra p h .

F ro m c o n t i n u o u s -c u l t u r e s t u d i e s (S h v i n k a e t a l .

1980 ; Micha l sk i e t a l . 1984 ; Hi rao e t a l . 1989 ; Kiss and

S t e p h a n o p o u l o s 1 9 9 2 ; O h a n d S e rn e t z 1 9 9 3 ) i t c a n b e

c o n c l u d e d t h a t l y s i n e p ro d u c t i o n i s c l o s e l y a s s o c i a t e d

w i t h b a c t e r i a l g ro w t h , i . e . th e s p e c i fi c l y s in e p ro d u c t i o n

ra t e t e n d s t o b e d i m i n i s h e d a t v e ry lo w g ro w t h r a t e s. A

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2/8

509

G L U O S E

T P

B I O M A S S ~ J ~ p

M [ H M P

j - co2

N M H ~

ATP V

P E P

~ - ~ T P

C 2

C 2

~

I C I T

= A o g '. . . . . 1 ) - -

S y s/ S ~ C A

ATP-~

L Y S I N E e

Fig. 1 Metabo l ic pa thway s in lys ine -produc ing Cory nebac te r ium

glu tamicum. EM E m b d e n -Me y e rh o f , HMP h e x o s e m o n o p h o s -

pha te ,

G6P

glucose 6 -phospha te ,

PEP phosphoenolpyruvate,

PYR

pyruva te ,

OAA

oxa loace ta te ,

ICIT

isocitrate ,

SUC

succi-

hate ,

SUCA

s u c c in y l -C o A

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

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

c o n s i d e r e d w i t h i n t h e c o n t e x t o f t h e o v e r a l l b a c t e r i a l

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

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

t i o n .

A r e c e n t s t u d y ( S o n n t a g e t al . 1 9 9 3) c o n f i r m e d t h a t

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

p a t h w a y e x i s t i n

Corynebacterium

w h i c h m a y b e a c t i v e

s i m u l t a n e o u s l y , d e p e n d i n g o n t h e c o n d i t i o n s . E n e r g e t i -

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

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

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

Corynebacterium ( N e i s h t a d t - A b r a m o v i c h e t a l . 1 9 9 0 ,

E r t a n 1 9 9 2) . B y a n a l o g y w i t h o t h e r o r g a n i s m s i t c a n b e

a s s u m e d t h a t t h e e n e r g y - r e q u i r i n g g l u t a m a t e s y n t h a s e

r e a c t i o n i s p r e f e r r e d a t l o w o r l i m i t i n g a m m o n i a c o n -

c e n t r a t i o n s , w h i l e a t h i g h e r a m m o n i a c o n c e n t r a t i o n s

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

c o n d i t i o n s o f l y si n e p r o d u c t i o n i t i s n o t u n r e a s o n a b l e t o

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

A p o i n t o f c o n t r o v e r s y i s t h e q u e s t i o n o f w h i c h ( a n a -

p l e r o t i c ) r e a c t i o n i s r e s p o n s i b l e f o r t h e f o r m a t i o n o f o x -

a l o a c e t a t e . T h e g l y o x y l a t e p a t h w a y i s s o m e t i m e s p r o -

p o s e d t o f u l f il l t h i s r o l e i n l y s i n e b i o s y n t h e s i s ( S h v i n k a

e t a l. 1 9 8 0 ); h o w e v e r , w h e n g l u c o s e is th e m a i n c a r b o n

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

i s o f t e n l o w ( V a l l i n o a n d S t e p h a n o p o u l o s 1 9 9 3 ) a n d i n

s o m e s p e c i e s t h e e n z y m e i s i n d u c e d o n l y i n t h e p r e s -

e n c e o f a c e t a t e ( R u k l i s h a e t a l. 1 9 78 ) . T h e m o s t p r o b a -

b l e a l t e r n a t i v e i s t h e phosphoenolpyruvate ( P - p y r u -

v a t e ) c a r b o x y l a s e r e a c t i o n , w h i c h i s f o u n d t o b e p r e s e n t

i n h i g h a c t i v i t y i n Corynebacterium. P - p y r u v a t e c a r -

b o x y l a s e h a s b e e n t h e t a r g e t i n a d i r e c t e d s t r a i n - i m -

p r o v e m e n t s t u d y ( S a n o e t a l . 1 9 8 7 ) . I t s r o l e i s n o t u n e -

q u i v o ca l ly p r o v e n , h o w e v e r , b e c a u s e d e l e t io n m u t a n t s

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

y i e l d ( P e t e r s - W e n d i s c h e t a l. 1 99 3 ). A n u m b e r o f o t h e r

a l t e rn a t i v e s c a n b e t h o u g h t o f , s u c h a s t h e r e a c t i o n s c a -

t a l y z e d b y p y r u v a t e c a r b o x y l a s e , P - p y r u v a t e c a r b o x y -

k i n a s e , o r m a l i c e n z y m e . I n t h e i r o v e r a l l s t o i c h i o m e t r y

t h e y a r e s i m i l a r t o t h e P - p y r u v a t e c a r b o x y l a s e r e a c t io n ,

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

s ion .

N A D P H i s u s e d i n s e v e r a l r e a c t i o n s o f l y s i n e b i o -

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

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

N A D P H . A n o b v i o u s p o s s ib i li ty is t h e h e x o s e m o n o -

p h o s p h a t e ( H M P ) p a t h w a y , s h o w n i n F ig . 1 a s a b r a n c h

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

t iv e f o r t h e E m b d e n - M e y e r h o f p a t h w a y . O n l y

1/6

o f t h e

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

N A D P H v i a t h is r o u te , h o w e v e r . M o r e e f f ic i en t w o u l d

b e t h e o p e r a t i o n o f th e c y c li c f o r m o f t h e H M P p a t h -

w a y , w h i c h g i v es 1 0 0 y i e ld o f r e d u c t i o n e q u i v a l e n t s i n

t h e f o r m o f N A D P H . F o r c y cl ic o p e r a t i o n o f t h e H M P

p a t h w a y t h e g l u c o n e o g e n i c e n z y m e f r u c t o se - l, 6 -b i s -

p h o s p h a t a s e i s r e q u i r e d . A c t i v i t y o f t h i s e n z y m e i s i n -

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

E m b d e n - M e y e r h o f p a t h w a y , a n d i s n o r m a l l y r e p r e s s e d

u n d e r c o n d i t io n s o f g r o w t h o n g l u co s e . A n o t h e r p o s si -

b l e m e t h o d o f N A D P H g e n e r a t i o n is t h e r e a c ti o n c a ta -

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

u s u a l l y c o n s i d e r e d t o b e N A D P - d e p e n d e n t i n Coryne-

bacterium.

T h e t w o m o s t i m p o r t a n t c e l lu l a r t r a n s p o r t p r o c e s s e s

i n l y s i n e f o r m a t i o n , g l u c o s e u p t a k e a n d l y s i n e e x c r e -

t i o n , a r e b o t h e n e r g y - d r i v e n . F o r g l u c o s e u p t a k e t h e

p h o s p h o t r a n s f e r a s e s y s t e m i s e m p l o y e d ( M o r i a n d

S h i i o 1 9 8 7 ; M a l i n a n d B o u r d 1 9 8 7 ) , w h i c h u t i l i z e s t h e

h i g h - e n e rg y p h o s p h a t e g r o u p f r o m P - p y r u v a t e . A l -

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

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

e r e d i n p h o s p h o r y l a t e d f o r m . T h e r e a c t i o n i s t h e r e f o r e

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

t o g l u c o s e 6 - p h o s p h a t e b y A T P , a s s h o w n i n F ig . 1 . I n

h i g h - p r o d u c i n g s t r a in s o f Corynebacterium l y s ine i s ex -

c r e te d th r o u g h a O H - s y m p o r t s y s te m ( B ro ~ r an d

K r i m e r 1 99 1; K r i m e r 1 9 9 4 ), w h i c h i m p l i e s t h a t , a ss o -

c i a t e d w i t h l y s i n e e x c r e t i o n , m e t a b o l i c e n e r g y ( A T P

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510

a b l e 1 Reactions of the metabolism of Corynebac ter ium g lu -

t a m i c u m as displayed in Fig. 1. Reactions are formulated in a sim-

plified manner, excluding the oxidized counterparts of the reduc-

tance carriers (NAD, NADP and FAD), and the de-energized

counterpart of ATP (ADP). A number of (alternative) reactions

are commented on in the text E M Embden-Meyerhof, H M P

hexose monophosphate, T C A tricarboxylic acid, Oaa oxaloace-

tate, P r y pyruvate, Suc succinate, Glc glucose. P P r v p h o s p h o e n o l -

pyruvate, iC i t isocitrate)

Lysine biosyntheis

Lysine excretion

Glucose uptake

EM pathway

Cyclic HMP pathway

HMP pathway

Pyruvate kinase

TCA pathway

n a p l e r o t i c r e a c t io n

O x i d a t iv e p h o s p h o r y l a t i o n

B i o m a s s f o r m a t i o n

Oaa + Pry + 2NH3 + Suc-CoA + ATP + 4 NADPH ~ Lys + Suc + CO2

Oaa + Pry + 2 NH3 + Suc-CoA + 3 ATP + 4NADPH --, Lys + Suc + CO2

Oaa + Pry + 2NH3 + ATP + 4NADPH --, Lys + CO2

Oaa + Pry + 2NH3 + 2 ATP + 4 NADPH ~ Lys + CO2

Lys + al ATP ~ Lysc

Glc + ATP --, Glc6P

Glc6P ~ 2 PPrv + ATP + 2 NADH

Glc6P --, 6 COz + 12 NADPH

Glc6P --, % PPrv + CO2 + ATP + 2NA DPH + % NADH

PPrv -~ Prv+ ATP

Prv + Oaa --* iCit + CO2 + NADH

iCit --, Suc-CoA + 2 CO2 + 2 NADH

iCit --, Suc-CoA + 2 CO2 + NADH + NADPH

Suc-CoA ~ Suc + ATP

Suc --, Oaa + NADH + FADH

PPrv + CO2 ---, Oaa

2 Prv ~ Oaa + 2 CO2 + 4N ADH + FADH

NADH + 02 ~ P/O ATP + H20

FADH + 02 --' 9/3 P/O ATP + H20

o-Glc + cnxNH3 + 6ax ATP ~ 6X + 6(o--1)CO2 + (12 o-- 3yx )NADH

l a a

lb

lc

ld

2

3

4a

4b

5

6

7

8a

8b

9

10

11a

11b

12

13

14

a Reaction equations wi th the same number but with different letters represent metabolic alternatives, of which only one can be

active

equivalents) is used for the restoration of the mem-

brane potential.

Although some energy is used in the biosynthesis of

lysine and its excretion, the overall balance within the

context of the cellular metabolism is positive if one in-

cludes the AT P generated during oxidation of NADH ,

which is produced in the reactions leading to formation

of the precursors of the lysine pathway. This energy-

generating property of lysine biosynthesis might pro-

vide an explanation for the apparent association of ly-

sine for mation with cell growth, because biosynthesis of

new cell material is the normal process in which ATP is

utilized. The efficiency of energy genera tion (oxidative

phosphorylation) and efficiency of growth are therefore

an important factors that determine, to a large extent,

the maximum possible conversion yields, as will be il-

lustrated later.

A stoichiometric model for bacterial growth and

lysine production

The lysine fermentation system is considered, in simpli-

fied form, to be a reaction producing biomass and ly-

sine from glucose and ammonia. Elemental mass bal-

ance considerations pr ovide restrictions for the flows of

reactants. The de gree o f free dom of the system is deter-

mined by the numbe r of reactants minus the number of

mass balance equations (Roels 1983). The reactions

constituting the cellular metabolism form a network.

Network relationships provide further restrictions for

the metabolism, which reduce the degree of freedom of

the system. In a previous publication (de Hollander

1991a) it was concluded that the best way to explore

these restrictions is by expressing the network as a ma-

trix equation and by employing basic linear algebra

methods, as has also been done by a number of other

authors. Following the methodology described earlier,

the macroscopic flows of the system are divided into

primary flows and secondar y flows, the latter following

from the former through elemental mass balance rela-

tionships. For the lysine fermentation system the flows

of glucose, biomass and lysine are defined as primary

flows; flows of oxygen, carbon dioxide and ammonia

follow from the carbon, nitrogen and degree of reduc-

tance balance. Metabolic net work restrictions, based on

a pseudo-steady-state assumption for all intermediates,

can be used to derive a balance equation for the prima-

ry external flows. The network expression is obtained

by filling the rows of a matrix Z with the stoichiometric

coefficients of the reactions displayed in Fig. 1. In prin-

ciple only equations for reactions between metabolic

branch points are included. In most cases these equa-

tions are lumped equations, involving a few or many

individual enzymatic steps. For a number of reactions

alternative expressions are formulated, because of the

uncertainties discussed earlier. Stoichiometric coeffi-

cients related to the cellular energy metabolism are not

known exactly; these coefficients (as well as a few oth-

ers) are included as parameters.

The reaction equations are summarized in Table 1.

A num ber of reactions represent alternatives for the

metabolism; they have been given the same number

with a letter for discrimination.

For lysine biosynthesis four possible equations are

consider ed. The reacti on in Eq. la in Table 1 is the

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o v e ra l l e q u a t i o n fo r t h e s u c c i n y l a s e v a r i a n t o f t h e d i a m -

i n o p i m e l a t e p a t h wa y , i n c l u d i n g t h e a m m o n i a a s s i m i l a -

t i o n r e a c t i o n . F o r t h e d e h y d ro g e n a s e v a r i a n t s , s u c c i n y l -

C o A a n d s u c c i n a t e m u s t b e o m i t t e d ( E q . l c , d ) . W h e n

a m m o n i a a s s im i l a ti o n o c c u r s v i a t h e e n e r g y - r e q u i r i n g

g l u t a m i n e s y n t h a s e r e a c ti o n , t h r e e o r t w o A T P i n s t e a d

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

h y d ro g e n a s e v a r i a n t s r e s p e c t i v e l y (E q . 1 , d ) . Ac c o rd i n g

t o t h e m e c h a n i s m p r o p o s e d b y B r o ~ r a n d K r ~im e r

( 1 9 9 4 ) t w o p r o t o n s m u s t b e t r a n s l o c a t e d f o r e v e r y l y -

s i n e m o l e c u l e t h a t i s e x c re t e d . A s t h e e f f i c i e n c y o f e le c -

t r o n - t r a n s p o r t- d r i v e n p r o t o n t r a n s l o c a ti o n i s n o t

k n o w n , a p a r a m e t e r a~ i s i n c l u d e d i n e q . 2 t o r e p re s e n t

t h e e n e r g y c o s t s . A s a d e f a u l t v a l u e a ~ = l w a s a d -

o p t e d .

T h e E m b d e n - M e y e r h o f p a t h w a y a n d t h e c y cl ic f o r m

o f t h e H M P p a t h w a y a r e c o n s i d e r e d t o b e m u t u a l l y e x -

c l us iv e . T h e l i n e ar H M P p a t h w a y i s c o n s i d e r e d t o c o v e r

t h e s e q u e n c e f r o m g l u c o s e 6 - p h o s p h a t e t o p h o s p h o e -

nolpyruvate.

B e c a u s e f o u r b r a n c h i n g p o i n t s a r e i d e n ti f -

i e d i n t h e t r i c a rb o x y l i c a c i d p a t h w a y ( s e e F i g . 1 ), t h e

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

A c o m p l e t e b u t b r a n c h e d r e s p i r a t o r y c h a in w i t h

m u l t i p l e o x i d a s e s wa s d e s c r i b e d fo r Brevibacterium fla-

ru m

(S h v i n k a e t a l . 1 97 9) . B e c a u s e o f th i s b r a n c h i n g ,

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

c e n t e r s , t h e o v e ra l l P / O r a t i o o f t h e o rg a n i s m i s u n c e r -

t a i n , b u t w i l l b e l e s s t h e n t h e m a x i m u m v a l u e fo r a

c o m p l e t e (m i t o c h o n d r i a l - t y p e ) r e s p i r a t o ry c h a i n , as i s

a l so a p p a r e n t f r o m a r e l a ti v e l y l o w H + / O r a t io f o u n d

fo r

Brevibacterium lactofermentum

(Ka wa h a ra e t a l .

1 98 8) . T h e P / O r a t io f o r N A D H o x i d a t io n i s t h e r e f o r e

i n c l u d e d as a p a r a m e t e r . T h e P / O r a t io f o r F A D H o x i-

d a t i o n w a s a s s u m e d t o b e 2/3 o f t h e P / O r a t i o fo r t h e

c o m p l e t e r e s p i r a t o r y c h a in .

B i o m a s s (X) i n e q . 1 4 o f T a b l e 1 i s e x p re s s e d i n C -

m o l u n i t s , t h e a m o u n t c o n t a i n i n g 1 m o l c a rb o n . T h e

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

s i s o f 1 m o l C b i o m a s s i s a x , a p a ra m e t e r r e l a t e d t o t h e

m o r e o f t e n u s e d y i e l d o n A T P : ax=Mx/YATp, w h e r e

M x i s t h e we i g h t o f a C -m o l b i o m a s s . T h e c o e f f i c i e n t o -

f o r t h e c a r b o n s o u r c e i n t h i s e q u a t i o n r e s u l t s f r o m t h e

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

a n a b o l i c r e a c t i o n s ( n o t t o b e c o n f u s e d w i t h c a t a b o l i c

C O 2 p r o d u c t i o n ) . T h e n u m e r i c a l v a l u e f o r g r o w t h o n

g l u c o s e i s a b o u t 1 . 1 (B a b e l a n d M t i l l e r 1 9 8 5 ; Go m m e rs

e t a l . 1 9 8 8 ) . B i o m a s s fo rm a t i o n f ro m g l u c o s e n o rm a l l y

r e s u l t s i n a s m a l l s u rp l u s o f r e d u c t i o n e q u i v a l e n t s , d e -

p e n d i n g o n o - a n d t h e d e g r e e o f re d u c t i o n o f b io m a s s

(rx).

I n t o t a l , 1 4 m e t a b o l i c r e a c t i o n s h a v e b e e n f o r m u -

l a t e d , i n v o l v i n g 12 k e y i n t e rm e d i a t e s a n d 3 m a c ro s c o p i c

s u b s t a n c e s (g l u c o s e , l y s i n e a n d b i o m a s s ) , e x c l u d i n g t h e

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

T h e m e t a b o l i c n e t w o r k e q u a t i o n i s f o r m u l a t e d a s :

Z T R m = R 1 )

wh e re t h e m u l t i p l e o f t h e t r a n s p o s e d (1 4 x 1 5 ) st o i -

c h i o m e t ry m a t r i x Z a n d t h e (1 4 1) v e c t o r R m wi t h m e -

t a b o l i c r e a c t i o n r a t e s fo rm s a (1 5 x 1 ) v e c t o r R w i t h

f l o ws o f e x t e rn a l s u b s t a n c e s a n d i n t e rm e d i a t e s . A s a

c o n s e q u e n c e o f th e p s e u d o s t e a d y s t a te h y p o t h e s i s ( c e l-

l u la r c o n c e n t r a t i o n s o f i n t e rm e d i a t e s a r e a p p r o x i m a t e l y

c o n s t a n t ) , t h e v e c t o r R c o n t a i n s a n u m b e r o f z e ro s ,

w h i c h a l l o w s t h e e v a l u a t i o n o f a m e t a b o l i c b a l a n c e

e q u a t i o n f o r t h e e x t e r n a l f l o w s. T h e m e t h o d u s e d f o r

t h i s b a l a n c e e v a l u a t i o n i s r e l a t e d b u t n o t i d e n t i c a l t o a

p r e v i o u s l y d e s c r i b e d m e t h o d ( d e H o l l a n d e r 1 9 9 1 a ) a n d

m e t h o d s p u b l i s h e d b y o t h e r s ( P a p o u t s a k i s a n d M e y e r

1 9 8 5 ; T s a i a n d L e e 1 9 8 8 ) . T h e l a t t e r a u t h o r s d i d n o t

e v a l u a t e a m e t a b o l i c b a l a n c e e q u a t i o n , h o w e v e r . H e r e

t h e p ro c e d u re i s d e s c r i b e d b r i e f l y i n g e n e ra l t e rm s . L e t

t h e d i m e n s i o n s o f t h e m e t a b o l i c s y s t e m b e a s f o l lo w s : m

re a c t i o n e q u a t i o n s w i t h n b i o c h e m i c a l s p e c i e s ; t h e n u m -

b e r o f c o n s e r v e d s p e c i es ( m e t a b o l i c k e y i n t e r m e d i a t e s )

i s k , wh ich leave s l = n - k n o n - c o n s e r v e d s p e c i e s o r m a -

c ro s c o p i c s u b s t a n c e s . T h e n t h e fo l l o wi n g p a r t i t i o n i n g o f

t h e n e t wo rk e q u a t i o n (E q . 1 ) i s p o s s i b l e :

Zl l Z12

l + n - m ) x l l + n - m ) x m - l )

Z21 Z22

(m - l) l (m - l) (m - l)

R m l

I x 1

Rm2

m - l ) x i

: :

2 )

w h i c h c a n b e w o r k e d o u t t o :

Z R m l = R 1 , w ith Z - - Z l l - Z 1 2 Z ~ l Z 2 1 3 )

C a r e s h o u l d b e t a k e n t h a t, b y a p p r o p r i a t e a r r a n g e-

m e n t o f ro ws a n d c o l u m n s , m a t r i x Z 2 2 i s n o n - s i n g u l a r ,

o t h e rw i s e t h e e v a l u a t i o n o f E q . 3 w i ll fa i l. W h e n n > m

( i. e. t h e m e t a b o l i c s y s t e m i s o v e r -d e t e r m i n e d ) , t h e v e c -

t o r R 1 s t i l l c o n t a i n s a t l e a s t o n e z e ro e l e m e n t , s o t h e

m a t r i x e q u a t i o n c a n a g a i n b e p a r t i t i o n e d :

Z l t m l = t e l 4 )

wh e re Z 1 is a l l s u b m a t r i x r e l a t e d t o e x t e rn a l f l o ws

o n l y , a n d R e 1 i s t h e v e c t o r w i t h p r i m a ry e x t e rn a l f l o ws .

T h e v e c t o r w i t h m e t a b o l i c r e a c t i o n r a t e s t m l c a n b e

e l i m i n a t e d f ro m t h i s e q u a t i o n , r e s u l t i n g i n a b a l a n c e

e q u a t i o n f o r t h e p r i m a r y e x t e r n a l f l ow s :

Z 3 R ~ I = 0 , w i th Z 3 = Z 2 Z ~ - 1 ( 5)

F o r t h e c a s e o f t h e ly s in e f e r m e n t a t i o n ( t h r e e p r i m a -

ry e x t e rn a l f l o ws ) , E q . 5 c a n a l s o b e wr i t t e n a s :

Z i R s b g 2 R x - l -. ~ 3 N p = O ,

o r Rs=l /YxsRx+l /YpsRp

(6)

wh i c h i s t h e f a m i l i a r l i n e a r e q u a t i o n r e l a t i n g t h e c a r -

b o n s o u r c e c o n s u m p t i o n r a t e ( R s) w i th t h e r a t e o f b i o -

m a s s f o r m a t i o n ( R x) a n d t h e r a t e o f p r o d u c t f o r m a t i o n

(Rp) .

T h e y i e ld p a r a m e t e r s f o l l o w f r o m t h e b a l a n c e

e q u a t i o n c o e f f i c i e n t s

as:

Y x s = - g l / g 2 a n d Y p s = - g l / Z 3 .

T h e p a r a m e t e r Yps i s t h e d i f f e r e n t i a l c a rb o n u t i li z a t i o n

e f f i c i e n c y o f l y s in e p ro d u c t i o n ( t h e n e t l y s i n e y i e l d ). I t

s h o u l d b e n o t e d , h o w e v e r , t h a t th i s p a r a m e t e r d o e s n o t

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

w h i c h c a n b e r e a c h e d w h e n n o b i o m a s s f o r m a t i o n t a k e s

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Table 2 Differential a nd maximum overall lysine yields for a numb er of variants of C glutamicum metabolism

An aplero tic reaction N AD PH generation Limiting Yps

pathway (mol/mol)

Linear Cyclic ICD H a

H M P H M P

Y ~

(mol/mol)

Phosphoenolpyruvate carboxylase

Glyoxylate pathway

+ - - EM 0.778 0.333

+ - + EM 0.777 0.468

+ + - TC A 0.774 0.727

+ - - EM 0.712 0.353

+ - + EM 0.706 0.382

+ + - TC A 0.709 0.412

a Isocitrate dehyd rogenase

p l a c e . I t w a s a r g u e d t h a t t h e m e t a b o l i c r e a c t i o n s i n -

v o l v e d i n l y si n e p r o d u c t i o n a r e i n t e r l i n k e d w i t h t h e

g e n e r a l m e t a b o l i s m a n d l y s in e p r o d u c t i o n c a n n o t t o t a l -

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

o t h e r w a y o f h y d r o l y z i n g o f A T P is in t r o d u c e d . C a l c u -

l a t e d v a l u e s f o r Y p s a r e i n c l u d e d i n T a b l e 2 .

C a l c u l a t i o n o f in t e r m e d i a r y r e a c t i o n r a t e s a n d

m a x i m u m l y s in e y ie l d s

T h e m e t a b o l i c n e t w o r k e q u a t i o n ( E q . 1 ) c a n b e s o l v e d

f o r t h e i n t e r n a l r e a c t i o n r a t e s v e c t o r w h e n v a l u e s f o r

t h e p r i m a r y e x t e r n a l f l ow s a r e k n o w n . A s t h e s y s t e m i s

o v e r - d e t e r m i n e d b y o n e e q u a t i o n , f l o w s f o r g lu c o s e

a n d l y s i n e a r e s u f f i c ie n t to d o t h is . T h e s y s t e m w a s

s o l v e d f o r a ra n g e o f v a lu e s f o r t h e a p p a r e n t ( o v e r a ll )

l y s i n e y i e l d c o e f f i c i e n t Y p s, w h i c h i s t h e f l u x r a t i o

R p /

R s. F o r t h e b i o e n e r g e t i c p a r a m e t e r s a s e t o f r e a s o n a b l e

v a l u e s w a s a s s u m e d : t h e e f f i c i e n c y o f o x i d a t i v e p h o s -

p h o r y l a t i o n ( P / O r a t i o ) i s 1 . 5 , t h e b i o e n e r g e t i c g r o w t h

y i e l d Y A T P = 1 0 g / m o 1 A T P , a n d t h e e n e r g y c o s t s o f l y -

s i ne e x c r e t i o n a l = 1 m o l A T P / m o l l y si n e . T h e s e v a l u e s

r e s u l t i n a b i o m a s s y i e l d o n g l u c o s e o f 0 .5 0 g / m o l w h e n

n o l y s i n e p r o d u c t i o n t a k e s p l a c e , w h i c h c o r r e s p o n d s t o

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

r y m i c r o o r g a n i s m . M e t a b o l i c f l u x e s as a f u n c t i o n o f

~ p s

w e r e c a l c u l a t e d f o r v a r i o u s s e t s o f a l t e r n a t i v e r e a c t i o n s

t a k e n f r o m T a b l e 1 . T h e b a s ic s e t o f e q u a t i o n s i n c l u d es

t h e a l te r n a t i v e s i n d i c a t e d w i t h t h e l e tt e r a a d d e d t o

t h e i r r e a c t i o n n u m b e r .

F i g u r e 2 s h o w s t h e r e s u l t o f t h e m e t a b o l i c f l u x c a l c u -

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

s e t o f e q u a t i o n s . F l u x e s a r e e x p r e s s e d i n m o l / h r e l a t i v e

t o t h e g l u c o s e f l u x , a n d a r e a l l l i n e a r f u n c t i o n s o f Y p s.

I t c a n b e s e e n th a t t h e f lu x t h r o u g h t h e H M P p a t h w a y

i n c r e a s e s w i t h t h e l y s i n e y i e l d , r e s p o n d i n g t o t h e i n -

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

N A D P H , w h i le s i m u l ta n e o u s ly t h e f lu x th r o u g h t h e

E m b d e n - M e y e r h o f p a t h w a y d e c r e as e s. T h i s c o r re l a t io n

b e t w e e n t h e f lu x t h r o u g h t h e H M P p a t h w a y a n d l y si n e

p r o d u c t i o n w a s s h o w n t o e x i s t e x p e r i m e n t a l l y b y Is h i n o

e t a l. ( 1 9 9 1) , u s in g a 1 3 C - N M R s t u d y . A t r e l a t i v e l y h i g h

v a l u e s o f

~ p s

t h e s t o i c h i o m e t r i c m o d e l e v e n p r e d i c t s a

X

k ~

1 ,5

1 .0

0 . 5

0 . 0

- 0 . 5

- 1 . 0

4

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7

L y s i n e y i e l d M o l / M o l )

F/g. 2 Me tabolic fluxes for a range of overall lysine yields, calcu-

lated for the basic set of reactions from Table 1. Fluxes are ex-

pressed in mo l/h, relative to the glucose flux. Th e dark area of the

bar indicates the region of physiologically possible f luxes. 1

Em bden-M eyerhof pathway, 2 hexose monophosphate pathway,

3 citrate synthase, 4 succinyl-CoA synthase. Further details: see

text

r e v e rs i o n o f t h e f lu x t h ro u g h t h e E m b d e n - M e y e r h o f

p a t h w a y ( i. e. g lu c o s e 6 - p h o s p h a t e is p r o d u c e d f r o m

P - p y r u v a t e ) . T h i s i s a s i t u a t i o n w h e r e m o r e A T P i s

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

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

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

i n t h e E m b d e n - M e y e r h o f p a t h w a y is i rr e ve r si b le . T h e

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

z e r o r e p r e s e n t s , t h e r e f o r e , t h e m a x i m u m p o s s i b l e o v e r -

a ll y i e l d fo r l y s in e f o r m a t i o n u n d e r t h e a s s u m p t i o n t h a t

t h e b a s i c s e t o f m e t a b o l i c r e a c t i o n e q u a t i o n s i s v a l id .

T h e m a x i m u m y i e ld ( 0. 33 m o l / m o l ) , m i g h t b e e v e n l o w -

e r in p r a c ti c e , b e c a u s e i n t h e m o d e l n o N A D P H u t il iz a -

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1.5

1.0

2

513

1 . 0

0 . 5

X

m

ll

~

0

r~

0 5 -

0 . 0

X

0

0 . 0

- 0 . 5

_ 1 . 0 1 1

0 . 0 0 .1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7

L y s i n e y i e l d M o l / / M o l )

Fig. 3 Variation on Fig. 2: isocitrate dehydrogenase s NADP-de-

pendent. 1 Embden-Meyerhofpathway,2 hexose monophosphate

pathway, 3 citrate synthase, 4 succinyl-CoAsynthase. Further de-

tails: see text

- 0 . 5

- 1 . 0

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7

L y s i n e y i e ld M o l / M o l )

Fig. 4 Variation on Fig. 2:glucose catabolism proceeds exclusive-

ly through the linear and cyclicvariants of the hexose monophos-

phate (HMP) pathway. 1 cyclic HMP pathway, 2 linear HMP

pathway, 3 citrate synthase,4 succinyl-CoAsynthase. Further de-

tails: see text

tion in biomass formation was assumed and, further-

more, it can be expected that metabolic problems will

occur when the flux through the Embden-Meyerhof

pathway is low but still not zero.

The dotted lines in Fig. 2 represent the flux through

the Embden- Meyerho f pathway calculated for two var-

iants of the basic set: the dehydrogenase variant of the

lysine biosynthesis pathway, which causes the line to

pass through zero at a lower value of

Y ps,

and the case

where ammonia is assimilated via the glutamine syn-

thase reaction, which shifts the limiting situation to a

higher Y ps value. Both variations on the basic set have

quantitatively irrelevant effects, and they will not be

discussed further.

The effect of cofactor preference of isocitrate dehy-

drogenase is shown in Fig. 3, which shows int ernal

fluxes assuming that isocitrate dehydrogenase exclu-

sively uses NAD P as cofactor. The general characteris-

tics remain the same, the critical yield being shifted to a

higher value. It can be seen that at low lysine yields

there is a surplus of NADPH formation, causing a re-

version of the HMP pathway, which is of course physi-

ologically impossible. It is also interesting to note the

reversion of the succinyl-CoA synthase reaction

at Y ps

values just below the maximum. Physiologically this

presents no problem because the reaction is reversible.

Finally, in Fig. 4 the hypothetica l occurrence of a cyclic

HMP pathway together with its linear variant is shown.

Only at high lysine yields is the NADPH requirement

large enough to cause a positive flux through the HMP

cycle. In this case the lysine yield will be limited by the

flux through the (irreversible) citrate synthase reaction,

which is calculated to become negative at very high

overall lysine yields.

Maximum possible overall yields for various meta-

bolic set-ups can be calculated by fixing the flux

through the critical reaction step (Embden-Meyerhof

pathway or citrate synthase) on a zero value, which de-

creases the degree of freedom of the system with one.

The matrix Z3 in the metabolic balance equation

(Eq. 5) then has the dimensions 2 x 3

n-m

= 2), which

allows the calculation of the fluxes R~ and

Rp

for a giv-

en value of Rs, resulting in fixed values for Y ps and

Y xs. Table 2 shows the results for a number of meta-

bolic variants. The table also contains values for the dif-

ferential yields corrected for glucose utilization for

growth (Yps

in Eq. 6).

The data in Table 2 are dependent on assumptions

about the bioenergetic parameters, Y TPand the P/O

ratio. It is therefore interesting to evaluate the effect of

variation of these parameters on the maximum possible

overall yield. This is done in Fig. 5 for the second meta-

bolic variant of Table 2. As could be expected, the fig-

ure shows that a low bioenergetic efficiency (either a

low P/O ratio or a low YATP s beneficial for the maxi-

mum possible overall lysine yield.

7/26/2019 art%3A10.1007%2FBF00173913

7/8

514

3 0 0

2 2 5

I 5 0

0

0 7 5

0 0 0

5 0

7 5 1 0 0 1 2 5 1 5 0

Y a t p

Fig. 5 Contour lines for maximum possible overall lysine yields

as function of the efficiencyof oxidative phosphorylation

P/O

ratio) and the efficiencyof gro~vth (YATe)

iscussion

The differential yield of lysine on glucose appears to be

hardly influenced by the type of metabolism that is

used (Table 2). On first sight this seems surprising:

when the lysine biosynthesis reaction is considered in

isolation from the cellular metabolism, a yield of 1.0 is

calculated when oxaloacetate is formed through car-

boxylation of P-pyruva te, in comparison with a theore-

tical yield of 0.67 when the glyoxylate pathway is used

for this purpose. However, this difference in yield be-

comes much less when proper account is taken of the

substrate used for NADPH generation and the ATP

formed in the oxidation of excess NADH, using a meta-

bolic network equation of the form of Eq. 1. The differ-

ential yield of 0.78 mol/mol, calculated in case of the

P-pyruvate carboxylase reaction, is higher than the val-

ue of 0.69 mol/mol ment ioned in a study by Shvinka et

al. (1980). The difference can be explained by the fact

that these authors did not address the net energy pro-

duction in lysine biosynthesis, resulting in a saving in

the amount of glucose used for catabolic purposes.

The maximum conversion yield of lysine production

from glucose (when the lysine biosynthesis pathway

genes are sufficiently expressed) is shown to be limited

by over-production of energy, which causes the flux

through the glucose catabolic pathway to become zero.

This finding illustrates the value of metabolic flux anal-

ysis, not only for the assessment of the requ ired in vivo

activities of auxiliary pathways, but also as a tool to

identify limitation by reaction sequences that can not

run in a reverse direction. The estimated maximum

yield for at least a number of the metabolic variants

that were studied is lower than the highest yields for

lysine formation as reported in the literature. Appar-

ently, industrial strains use other pathways, or escape

mechanisms have been introduced during the process

of strain improvement (haphazardly or purposely). The

maximum lysine yield is quite sensitive to the way the

organism generates NADPH. When the hexose mono-

phosphat e rou te is the only possibility, a low maximum

yield of 0.33 mol/mol is calculated. Isocitrate dehydro-

genase generally occurs in two forms, a NAD-depend-

ent form and a NADP-dependent form. Normally it is

assumed that the isocitrate dehydrogenase reaction

uses NADP as a cofactor. However, if this were the

case an over-production of NADPH would result at

low lysine yields (Y ps

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515

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