41
Table 4.1. Sensitivity of the reduced model to the assumed KM.
------------------------------------------------------CORRECT K~ CORP CT % ERROR IN THE PREDICTED:
(mm mm ) (mm s ) k Vmax
------------------------------------------------------0.002 6.0 4.7 30.2 0.002 12.0 13.3 22.3 0.002 24.0 42.9 16.7
0.004 6.0 0.0 0.0 0.004 12.0 0.0 0.0 0.004 24.0 0.0 0.0 0.008 6.0 -10.5 -23.7 0.008 12.0 -34.3 -3.7 0.008 24.0 -36.3 -18.5
Percent error in k and Vmax estima es sing an assumed KM of 0.004 mm mm and fixed Vmax of 0.15 mm s
When the reduced model was used to predict k and Vmax from these simulated data sets the values of the predicted parameters were highly accurate when the correct KM was used. When the KM was not constant but
3 -3
varied from the assumed value of 0.004 mm mm the predicted nodule conductances, and maximum rates of ethylene production deviated by -36.3 to 42.9% from the correct values. Large errors can result from the use of this model to predict k and Vmax if the assumed KM is in error, or varies over the experimental treatments being used. This represents a serious limitation to the use of Equation 4.4 to predict nodule conductance.
Reduced Model with Fixed Vmax
In contrast to the approach of Denison and Sinclair (1985) who fixed the value of KM in Equation 4.4 and then solved for k and Vmax, Winship and Tjepkema (1983) measured ethylene production rates of Alnus