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 +

*d*t) = P1(t)(1 - K1

*d*t) + P2(t)K2

*d*t

[p1(t +

*d*t) - p1]/dt = -P1K1 + P2K2

take the lim as

*d*t 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!