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 - K1
dt) + P2(t)K2
dt
[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!