Michaelis-Menten reaktionskinetik - Steen Toft Jørgensen
Michaelis-Menten reaktionskinetik - Steen Toft Jørgensen
Michaelis-Menten reaktionskinetik - Steen Toft Jørgensen
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<strong>Michaelis</strong>-<strong>Menten</strong> <strong>reaktionskinetik</strong><br />
><br />
http://en.wikipedia.org/wiki/<strong>Michaelis</strong>%E2%80%93<strong>Menten</strong>_kinetics#Derivation<br />
Differentialligningssystem:<br />
Differentialligningsystemet opskrives i Maple:<br />
><br />
><br />
><br />
><br />
Begyndelsesbetingelser:<br />
http://se.wtb.tue.nl/sewiki/biological_systems/de#michaelis-menten_kinetics<br />
(1)<br />
(2)<br />
(3)<br />
(4)
Forventet graf:<br />
http://se.wtb.tue.nl/sewiki/biological_systems/de#michaelis-menten_kinetics<br />
><br />
Numerisk løsning af differentialligninger:<br />
http://en.wikipedia.org/wiki/Numerical_ordinary_differential_equations<br />
(5)
http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_method<br />
Differentialligningssystemet løses numerisk (tilnærmet), da det ikke kan løses eksakt:<br />
><br />
><br />
>
S<br />
0<br />
0 10 20 30 40 50<br />
t
E<br />
0<br />
0 10 20 30 40 50<br />
t
ES<br />
0<br />
0 10 20 30 40 50<br />
t
P<br />
0<br />
0 10 20 30 40 50<br />
t
ECES<br />
0<br />
0 10 20 30 40 50<br />
t
Farver på den samlede graf:<br />
GRØN = [S]<br />
RØD = [P]<br />
CYAN = [ES]<br />
BLÅ = [E]<br />
SORT = [E] + [ES]<br />
0<br />
0 10 20 30 40 50<br />
t