Enzymatic Reactor with Product Inhibition

inlet enzyme flow rate

1

inlet substrate flow rate

1

substrate

product

enzyme

set-up figure

A reaction,

S→2P

, catalyzed by an enzyme,

E

, takes place in a constant-volume well-mixed reactor, as can be seen from the set-up figure. The governing equations are:

F

1

=

F

E

+

F

S

,

V

d

S

1

dt

=

F

S

0

-

F

1

S

1

+

r

S

V

,

V

d

P

1

dt

=-

F

1

P

1

+

r

P

V

,

V

d

E

1

dt

=

F

E

0

-

F

1

E

1

,

where

r

P

=-2

r

S

and

r

S

=-

E

1

K

2

S

1

K

m

+

S

1

+

P

1

K

I

.

F

1

,

F

E

,

F

S

are the exit flow rate and the enzyme and substrate inlet flow rates, respectively;

V

is the reactor volume.

S

0

and

E

0

are the inlet concentration of substrate and enzyme, respectively;

S

1

,

E

1

and

P

1

are the substrate, enzyme, and product concentrations in the reactor, respectively; and finally,

K

m

is the saturation constant,

K

I

is the product inhibition constant, and

K

2

is a rate constant.

This Demonstration presents the dynamic behavior of this enzymatic reactor with product inhibition. The plotted curves correspond to the substrate, product, and enzyme concentrations versus time.