Chapter Contents |
Previous |
Next |
The MODEL Procedure |
The following is a simplified reaction scheme for the competitive inhibitors with recombinant human renin (Morelock et al. 1995).
Figure 14.82: Competitive Inhibition of Recombinant Human Renin
In Figure 14.82, E= enzyme, D= probe, and I= inhibitor.
The differential equations describing this reaction scheme are
For this system, the initial values for the concentrations are derived from equilibrium considerations (as a function of parameters) or are provided as known values.
The experiment used to collect the data was carried out in two ways; pre-incubation (type='disassoc') and no pre-incubation (type='assoc'). The data also contain repeated measurements. The data contain values for fluorescence F, which is a function of concentration. Since there are no direct data for the concentrations, all the differential equations are simulated dynamically.
The SAS statements used to fit this model are
proc model data=fit; parameters qf = 2.1e8 qb = 4.0e9 k2f = 1.8e5 k2r = 2.1e-3 l = 0; k1f = 6.85e6; k1r = 3.43e-4; /* Initial values for concentrations */ control dt 5.0e-7 et 5.0e-8 it 8.05e-6; /* Association initial values --------------*/ if type = 'assoc' and time=0 then do; ed = 0; /* solve quadratic equation ----------*/ a = 1; b = -(&it+&et+(k2r/k2f)); c = &it*&et; ei = (-b-(((b**2)-(4*a*c))**.5))/(2*a); d = &dt-ed; i = &it-ei; e = &et-ed-ei; end; /* Disassociation initial values ----------*/ if type = 'disassoc' and time=0 then do; ei = 0; a = 1; b = -(&dt+&et+(&k1r/&k1f)); c = &dt*&et; ed = (-b-(((b**2)-(4*a*c))**.5))/(2*a); d = &dt-ed; i = &it-ei; e = &et-ed-ei; end; if time ne 0 then do; dert.d = k1r* ed - k1f *e *d; dert.ed = k1f* e *d - k1r*ed; dert.e = k1r* ed - k1f* e * d + k2r * ei - k2f * e *i; dert.ei = k2f* e *i - k2r * ei; dert.i = k2r * ei - k2f* e *i; end; /* L - offset between curves */ if type = 'disassoc' then F = (qf*(d-ed)) + (qb*ed) -L; else F = (qf*(d-ed)) + (qb*ed); Fit F / method=marquardt; run;
This estimation requires the repeated simulation of a system of 42 differential equations (5 base differential equations and 36 differential equations to compute the partials with respect to the parameters).
The results of the estimation are shown in Output 14.10.1.
Output 14.10.1: Kinetics Estimation
Chapter Contents |
Previous |
Next |
Top |
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.