Last Time 3/4/08

Increase (I) concentration increase slope intercept remains unchanged.

rS Vmax S

KM 1I

KI

S

Uncompetitive Inhibition

Inhibition only has affinity for enzyme-substrate complex

Developing the rate law

(1)

(2)  

E Sk1 k2

E Skcat P

IE Sk4 k5

I E S

rP rS kcat E S

rES 0 k1 E S k2 E S kcat E S k4 I E S k5 I E S

rIES 0

k4 I E S k5 I E S

Adding (1) and (2)

k1 E S k2 E S kcat E S 0

E S k1 E S k2 kcat

E S KM

I E S k4

k5

I E S I E S

KI

I E S KIKM

KI k5

k4

rp kcat E S kcat E S

KM

From (2)

Total enzyme

E t E E S I E S

E 1S

KM

I S

KIKM

rp kcatE t S

KM 1S

KM

I S

KIKM

rS rP Vmax S

KM S 1I

KI

rS rP Vmax S

KM S 1I

KI

1

rS

1

Vmax S KM S 1

I KI

KM

Vmax

1

S

1

Vmax

1I

KI

Slope remains the same but intercept changes as inhibitor concentration is increased

Lecture16 Thursday 3/6/08

Enzyme Kinetics

Noncompetive Inhibition

Bioreactors

Monod Equation

Yield Coeficients

Washout

Bioreactors

D=vo / V

Noncompetitive, Bioreactors

More uncompetitive inhibition

S

mI

I

S

I

ISm

SSP

CV

k

V

kC

r

kC

Ck

CVrr

11

1

1

maxmax

max

Only intercept changes

SC

1

Sr

1

Increasing I

No I

Lineweaver-Burk

Noncompetitive inhibition (Mixed)

Both slope and intercept change

SC

1

Sr

1

Increasing I

No I

E + S E·S P

E·I + S E·S·I

+I +I-I -I

I

I

S

m

I

I

S

I

ISm

SS

k

C

CV

k

k

C

Vr

kC

Ck

CVr

11

111

1

maxmax

max

Bioreactors

Cells + substrate → product + more cells

Cell growth can be modeled with enzyme equations since all cell reactors are enzyme catalyzed

Lag phase

Exponential growth phase

stationary phase Death

phase

Algorithm

1) Mass balance (later)

2) Rates

**

max

max

1

equation) monad(

P

n

P

POBS

OBSCSS

Sg

SS

SCg

CC

Ck

kCCk

Cr

Ck

CCr

sometimes

Product concentration at which all metabolism ceases (93 g/L for wine production, n = ½)

Substrate is used to form both products and cell maintenance

(rate of substrate disappearance for maintenanceCsm mCr

3) Stoichiometry – yield coefficients

CDD

CgCSSgCPP

CP

SCCSSC

Ckr

mCryrryr

y

yyy

//

/

///

formed cells new of mass

formedproduct of mass

1

consumed substrate mass

formed cells of mass

1) Mass balance

Parameters:

(product)

)(substrate

rate)(dilution 1

(cells) 0

0

000

0

0

PPP

SSSS

SSSS

dgCC

dgCC

rDCdt

dC

rCCDdt

dC

VrCvCvdt

dCV

V

vDrrDC

dt

dC

VrrCvdt

dCV

2) Rates

CDD

CgCSS

gCPP

n

P

POBS

OBSCSS

Sg

Ckr

mCryr

ryr

C

CK

KCCk

Cr

/

/

*

max

1

VDVvCvmCvm

CDmyykknC

PpC

SCPCSDSP

, , ,

, , , , , , , , ,

000

0//*

max