Why Do it So Fast?

How does the cell know which proteins to degrade, and when?

Okay, so we have to degrade proteins in order to lower the steady-state concentrations, but why should that be a rapid process? It seems wasteful to try to maintain the concentration of a protein while it is simultaneously being degraded.

Consider the following scheme:
-------ks-------> [protein] --------kd--------->

ks is the rate of synthesis of the protein and is experimentally a zero-order rate, while kd is the rate of degradation of the protein and is experimentally a first-order rate. [E] is the concentration of E at any time and [Eo] is the steady-state concentration of protein.

Then:                  dE/dt = ks - kd [E]

At steady state:       dE/dt = 0

Therefore:             ks = kd[Eo] and [Eo] = ks/kd

Thus, it is obvious that the steady-state concentration depends on how fast the protein is synthesized (ie., mRNA levels, the transcriptional activity, etc.) and the rate at which it is degraded.

Now consider what would happen if we change the rates of synthesis and/or degradation in response to some external signal. The new rates of synthesis and degradation are given by ks' and kd' respectively.

A new steady state concentration is reached with E' = ks'/kd' The rate of approach to the new steady state can be determined by:

writing the eqn for E as f(t)       dE/dt = ks' - kd'[E]

substituting from steady state      ks'=kd'[Eo']

integrating and evaluating             [Eo'-E]/[Eo'-Eo]=e^-kd't
Thus, the rate of approach to the new steady-state is determined solely by the degradation rate of the protein. To respond quickly, one needs a rapid degradation rate.

Refering to the figure above and assuming only the rate of synthesis changes:

 Case  ks  kd  ks'  kd'
 a  4µM/min  4/min  8µM/min  4/min
 b  2µM/min  2/min  4µM/min  2/min
 c  1µM/min  1/min  2µM/min  1/min
Additional readings:

The role of mRNA and protein stability in gene expression. Hargrove JL; Schmidt FH. FASEB J 3: 2360-70 (1989).

Microcomputer-assisted kinetic modeling of mammalian gene expression. Hargrove, JL. FASEB J 7,1163-70 (1993)