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Cdk5 Targets Active Src for Ubiquitin-dependent Degradation by Phosphorylating Src(S75)
Q. Pan, F. Qiao, C. Gao, B. Norman, L. Optican, and P. Zelenka*,
Laboratory of Molecular and Developmental Biology, National Eye Institute, National Institutes
of Health, Bethesda, MD 20892
Supplement:
The simple kinetic model usually employed to determine the half-life of a protein by
radioactive pulse-chase can be expressed by the equation:
dz/dt = S – kz(t)
where z is the amount of radiolabeled protein, S is its rate of synthesis, and k is the decay
constant. This equation has the solution
z = (C/k)*exp(-kt) + S/k
When S = 0, as during a radioactive pulse-chase experiment,
ln(z) = ln[C/k] -kt
which yields a straight line with slope –k when plotted as a log-linear graph.
However, this model is not sufficient to describe the equilibrium between the inactive and
active forms of Src, coupled with the ubiquitin-dependent degradation of the active form:
S
k1
k3
->[inactive Src] <-> [active Src] -> degradation
k2
This case is described by the set of first order linear differential equations:
dx/dt = S - k1*x(t) + k2*y(t)
dy/dt = k1*x(t) – k2*y(t) – k3*y(t)
z=x+y
where x is the amount of inactive Src, y is the amount of active Src, z is the total Src, S is
the rate of synthesis, and k1, k2, and k3 represent the rate constants of the indicated
reactions. Using the symbolic toolbox of Matlab (Mathworks, Inc., Natick, MA) to solve
the above equations (function dsolve), we found that a closed form solution of these
equations exists, but it is not compact. Neither x (inactive Src) nor y, (active Src)
undergoes simple exponential decay. Thus, their sum z (total Src) also does not undergo
simple exponential decay and the log-linear plot of z(t) deviates from a straight line. The
slope of this curve (dz/dt) approaches zero with increasing time, indicating that the
turnover of total Src is slower than predicted by the initial slope.
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