algorithm yielded, for these three parameters, the values: 
A = 0.153 h-l, ki = 0.034 h-', and ki = 12.98 g L-' 
h-'. The regression of this model to the data is demon-
strated in Figure 8. It seems that inclusion of the first-order 
enzyme deactivation term improves the fit during the first 
6 hours because the additional parameter, A, gives more 
flexibility (degrees of freedom) to the model. However, 
the modified model fails to correctly predict the long-
term profiles of cellulose and glucose by overestimating 
the loss of enzymatic activity (Fig. 8). As a result, the 
cellulose concentration is grossly overestimated and the 
glucose concentration is significantly underestimated be-
cause the availability of cellobiose diminishes according to 
the model. The good fit to the cellobiose profile is clearly 
superficial; the experimental data suggest that the low levels 
of cellobiose are due to the dynamically equal rates of 
cellobiose formation and disappearance, not to the cessation 
of cellulase activity, which is implied by Eq. (18) for the 
later times of the reaction. This failure of the modified 
model is a strong indication that additional information is 
needed about the physicochemical properties of the sub-
strate and the enzyme-substrate interaction before devel-
oping more accurate and reliable mathematical expressions 
for the enzymatic hydrolysis of cellulosic biomass. Cur-
rently, in the absence of further information regarding the 
time-dependent variation in properties of the biomass sub-
strate (surface area, reactivity, size distribution), a simple 
rate expression, such as Eq. (13), appears to provide a 
satisfactory description of the cellulose hydrolysis kinetics