Thread: 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. Help!

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. 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

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.