Experimental data are from the author's laboratory, showing the kinetics of HIV-1 protease. For experimental details see the reference below.
Experimental data and postulated reaction mechanism:
Least squares fit and optimized rate constants:
Reaction Mechanism
The chemical system analyzed in here is described by
the following reaction mechanism:
Differential Equations
The changes in concentrations of chemical species over time
are computed by solving and initial value problem described
by the following system of differential equations:
| d[M]/dt | = | -km[M]-km[M]+kd[E]+kd[E] |
| d[E]/dt | = | +km[M][M]-kd[E]-ka[E][S]+kr[ES] |
| d[S]/dt | = | -ka[E][S] |
| d[ES]/dt | = | +ka[E][S]-kr[ES] |
| d[P]/dt | = | +kr[ES] |
Importantly, the investigator does not need specify these fitting equations in the mathematical form. Instead, the theoretical model is entered in a symbolic format as follows:
[mechanism]
M + M <==> E : km kd
E + S --> ES : ka
ES --> E + P : kr
[constants]
km = 0.92, kd = 0.0019
ka = 10 ?, kr = 10 ?
The computer automaticaly derives the fitting equations from the text above. Rate constants identified with the question mark are optimized to achieve best least-squares fit.
Reference:
"Mechanical effects on the kinetics of the HIV proteinase deactivation."
Kuzmic, P.; Peranteau, A.G.; Garcia-Echeverria, G.; and Rich, D.H. (1996) Biochem. Biophys. Res. Commun. 221, 313-7.
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