Biophysical chemistry II.
Enzyme Kinetics
Doc. RNDr. Zbyněk Prokop, Ph.D.
z b y n e k @ c h e m i . m u n i . c z
OUTLINE
 E N Z Y M E K I N E T I C S
 S T E A D Y- S TAT E v s . T R A N S I E N T K I N E T I C S
 M AT H E M AT I C S A N D S O F T WA R E S
 R A P I D M I X I N G T E C H N I Q U E S
 K I N E T I C M E C H A N I S M S
 K I N E T I C S I N P R O T E I N E N G I N E E R I N G
EN ZYME K IN ETIC S
 K I N E T I C S - s t u d y o f m o t i o n a n d i t s c a u s e s
EN ZYME K IN ETIC S
 K I N E T I C S - s t u d y o f m o t i o n a n d i t s c a u s e s
 ( B I O ) C H E M I C A L K I N E T I C S - r a t e o f r e a c t i o n s / i n t e r a c t i o n s
 c h e m i c a l k i n e t i c s
 e n z y m e k i n e t i c s
 b i n d i n g k i n e t i c s
 ( u n ) f o l d i n g k i n e t i c s
 p h a r m a c o k i n e t i c s
EN ZYME R EA C TION
STEA D Y- STATE vs. TR A N SIEN T
 A C T I V I T Y A N A LY S I S
 S T E A D Y- S TAT E K I N E T I C S
 T R A N S I E N T K I N E T I C S
STEA D Y- STATE K IN ETIC S
 A C T I V I T Y A N A LY S I S
 M I C H A E L I S - M E N T E N K I N E T I C S
 l i n e a r i z a t i o n
=
Km
[S]
1
v
1
Vlim
+
Vlim
.
1
v =
Km + [S]
kcat . [S]
STEA D Y- STATE K IN ETIC S
 l i n e a r i z a t i o n
=
Km
[S]
1
v
1
Vlim
+
Vlim
.
1
v =
Km + [S]
kcat . [S]
STEA D Y- STATE K IN ETIC S
 l i n e a r i z a t i o n
 n o n l i n e a r r e g r e s s i o n ( e . g . , S i g m a P l o t , O r i g i n , E n z F i t e r )
 n u m e r i c a l s i m u l a t i o n ( e . g . , G e p a s y, D y n a F i t , K i n t e k E x p l o r e r )
STEA D Y- STATE K IN ETIC S
= - k1.[E].[S] + k-1.[ES]
d[S]
dt
= k1.[E].[S] - k-1.[ES]
d[ES]
dt
= k2.[ES]
d[P]
dt
 M i c h a e l i s - M e n t e n c o n s t a n t , K m ( m o l . l - 1 )
 a p p a r e n t e q u i l i b r i u m c o n s t a n t
 d e t e r m i n e d b y t r u e b i n d i n g c o n s t a n t a n d r a t e s o f c a t a l y t i c s t e p s
 Tu r n o v e r n u m b e r, k c a t ( s - 1 )
 n u m b e r o f m o l e c u l e s c o n v e r t e d p e r s e c o n d
b y o n e e n z y m e m o l e c u l e u n d e r s a t u r a t i o n
 i n f l u e n c e d o n l y b y r a t e s o f c a t a l y t i c s t e p s ( l i m i t i n g s t e p )
 S p e c i f i c i t y c o n s t a n t , k c a t / K m ( m o l . l - 1 . s - 1 )
 a p p a r e n t s e c o n d o r d e r r a t e c o n s t a n t
STEA D Y- STATE K IN ETIC S
TR A N SIEN T K IN ETIC S
R A PID MIXIN G TEC H N IQU ES
S T O P E D - F L O W R A P I D Q U E N C H - F L O W
R A PID MIXIN G TEC H N IQU ES
S T O P E D - F L O W R A P I D Q U E N C H - F L O W
 d e h a l o g e n a s e ( E C 3 . 8 . 1 . 5 )
 g l o b u l a r p r o t e i n s
 m o n o m e r i c / o l i g o m e r i c
 n o c o f a c t o r r e q u i r e m e n t
 c l e a v a g e c a r b o n - h a l o g e n b o n d
K IN ETIC MEC H A N ISMS
M U L T I P L E T U R N O V E R K I N E T I C S I N H I B I T I O N A S S A Y
R E A C T I O N B U R S TS I N G L E T U R N O V E R K I N E T I C S
K IN ETIC MEC H A N ISMS
A = + k2.tA0.e-k.tA = + A2.e-k2.t
A1.e-k1.t
kobs =
k2.[S]
[S] + Ks
+ k-2 + k3
B I N D I N G K I N E T I C S
kobs = + k -4b
[P] . k 4b
K 4a + [P]
v =
[S].kcat
Km.(1 + [P]/Kp1) + [S].(1 + [P]/Kp2)
K s k 2 k -2 k 3 k 4 K m k cat
(mM) (s
-1
) (s
-1
) (s
-1
) (s
-1
) (mM) (s
-1
)
1-chlorohexane 240 117 0.4 3.2 - 16 2.6
LinB bromocyclohexane > 450 > 200 1.1 2.5 - 23 1.8
chlorocyclohexane > 500 > 40 12.5 0.075 - 221 0.1
Substrat
1,2-dibromeethane1
> 27 > 130 - 10 4 10 3
1,2-dichloroethane1
2 200 50 - 14 8 530 3.3
DhlA
DhaA 1,3-dibromopropane2
60 - 300 300 - 14.8 3.9 5 2.7
d i s t i n c t r a t e - l i m i t i n g s t e p s
f o r r e l a t i ve e n z y m e s
K IN ETIC MEC H A N ISMS
PR OTEIN EN GIN EER IN G
 c o n v e r s i o n o f 1 , 2 , 3 - t r i c h l o r o p r o p a n e
b y d e h a l o g e n a s e f r o m R h o d o c o c c u s s p .
 i m p o r t a n c e o f a c c e s s p a t h w a y s
C176
Y176
F176
PR OTEIN EN GIN EER IN G
 l i b r a r y o f 5 , 3 0 0 c l o n e s
 s t a d y - s t a t e k i n e t i c s
s t e a d y - s t a t e c a t a l y s i s
i m p r o ve d 2 6 x
Km (mM) kcat (s-1
) kcat/Km
DhaA wt 0.98 ± 0.17 0.035 ± 0.002 0.04
DhaA 31 1.19 ± 0.15 1.26 ± 0.05 1.06
PR OTEIN EN GIN EER IN G
DhaA wt DhaA 31
Chemical reaction Product release
 t r a n s i e n t k i n e t i c s
PR OTEIN EN GIN EER IN G
DhaA wt DhaA 31
PR OTEIN EN GIN EER IN G
Chemical reaction Product release
 t r a n s i e n t k i n e t i c s
PR OTEIN EN GIN EER IN G
c h e m i c a l s t e p i m p r o ve d 4 5 0 x