NLMOD Procedure

(View the complete code for this example.)

The Michaelis-Menten model of enzyme kinetics (Ratkowsky 1990, p. 59) relates a substrate’s concentration to its catalyzed reaction rate. You can analyze the Michaelis-Menten model by using a least squares estimation because it does not specify how the reaction rate is distributed around its predicted value. The relationship between reaction rate and substrate concentration is

where represents the concentration for n trials and is the reaction rate. The vector contains the rate parameters.

The input data must be a table on your CAS server, and a CAS session must be set up. For more information, see the sections Using CAS Sessions and CAS Engine Librefs and Loading a SAS Data Set onto a CAS Server in Chapter 2, Shared Concepts. The following DATA step creates the Enzyme data table, which consists of experimental measurements of reaction rate and concentration, in your CAS session:

data mylib.Enzyme;
   input conc rate @@;
   datalines;
0.26 124.7   0.30 126.9
0.48 135.9   0.50 137.6
0.54 139.6   0.68 141.1
0.82 142.8   1.14 147.6
1.28 149.8   1.38 149.4
1.80 153.9   2.30 152.5
2.44 154.5   2.48 154.7
;

These statements assume that your libref is named mylib, but you can substitute any appropriately defined libref.

The following SAS statements estimate the parameters and :

proc nlmod data=mylib.Enzyme;
   parms theta1=0 theta2=0;
   model rate ~ residual(theta1*conc / (theta2 + conc));
run;

The least squares estimation that PROC NLMOD performs for this enzyme kinetics problem produces the analysis of variance table in Figure 1. The table displays the degrees of freedom, sums of squares, and mean squares along with the model F test.

Finally, Figure 2 displays the parameter estimates, standard errors, t statistics, and 95% confidence intervals for and .

In the enzyme kinetics model, no information was supplied about the distribution of the reaction rate around the model’s mean value. Therefore, the residual model distribution was specified to perform a least squares parameter fit.