# algebra/differential equations

• May 6th 2006, 08:38 AM
KAF33
algebra/differential equations
I am trying to work through a model describing enzyme kinetics of development and I am stuck. Previous steps have been worked out to the following answers, which are from a published article and I worked them out myself as well:

dP1(t)/dt = -K1P1(t)+K2P2(t)
dP2(t)/dt = K1P1(t)-(K2+K3)P2(t)+K4P3(t)
dP3(t)/dt = K3P2(t)-K4P3(t)

Each of the three differential equations were created the following way:
p1(t + dt) = P1(t)(1 - K1dt) + P2(t)K2dt
[p1(t + dt) - p1]/dt = -P1K1 + P2K2
take the lim as dt goes to 0
dP1(t)/dt = -K1P1(t) + K2P2(t)

If you solve for steady state conditions (i.e. dPi(t)/dt = 0)you should get:
P2 = 1/(1 + k2/k1 + k3/k4)

but I'm stuck and can't get there. I have tried rearranging and substituting for each of the variables and cannot figure out the steps to get there. :confused: Help!
• May 6th 2006, 08:54 AM
CaptainBlack
Quote:

Originally Posted by KAF33
I am trying to work through a model describing enzyme kinetics of development and I am stuck. Previous steps have been worked out to the following answers, which are from a published article and I worked them out myself as well:

dP1(t)/dt = -K1P1(t)+K2P2(t)
dP2(t)/dt = K1P1(t)-(K2+K3)P2(t)+K4P3(t)
dP3(t)/dt = K3P2(t)-K4P3(t)

Each of the three differential equations were created the following way:
p1(t + dt) = P1(t)(1 - K1dt) + P2(t)K2dt
[p1(t + dt) - p1]/dt = -P1K1 + P2K2
take the lim as dt goes to 0
dP1(t)/dt = -K1P1(t) + K2P2(t)

If you solve for steady state conditions (i.e. dPi(t)/dt = 0)you should get:
P2 = 1/(1 + k2/k1 + k3/k4)

but I'm stuck and can't get there. I have tried rearranging and substituting for each of the variables and cannot figure out the steps to get there. :confused: Help!

There is no unique solution as your system in underdetermined in the steady
state, you will need another condition to obtain a unique solution.

RonL
• May 6th 2006, 09:17 AM
KAF33
Thanks anyway. I am trying to follow the logic to work through a model for a presentation and am completely stumped. Unfortunately, none of the literature tells you how they got to that step. Everything else has worked out fine, before and after this point, I just can't figure this step out. :mad: