There is evidence that a critical concentration of a trigger protein is needed f

ID: 774470 • Letter: T

Question

There is evidence that a critical concentration of a trigger protein is needed for cell

division. This unstable protein is continually being synthesized and degraded. The rate of protein

synthesis controls how long it takes for the trigger protein to build up to the concentration

necessary to start DNA synthesis and eventually to cause cell division. Let's choose a simple

mechanism to consider quantitatively. The trigger protein U is being synthesized by a zero-order

mechanism with rate constant k0. It is being degraded by a first-order mechanism with rate

constant k1.

(a) Write a differential equation consistent with the mechanism.

(b) The solution to the correct differential equation is:

[U](t)=(k0/k1) [1 - exp(-k1 t)]

if [U] is equal to zero at zero time. Show that your equation in part (a) is consistent with this.

and its half-life for

degradation is 0.500 h, calculate the maximum concentration that U will reach. How long will it

take to reach this concentration? Make a plot of [U] vs. time.

(d) If a concentration of U of 1.00 ?M is needed to trigger DNA synthesis and cell replication,

how long will it take to reach this concentration?

(e) If the rate of synthesis is cut in half (k0 = 0.500 nM s-1), how long will it take for U to reach

a concentration of 1.00 ?M?

wait I am posting it.

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