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