The Michaelis-Menten (M-M) model was used to describe the hydrolysis of Solka Floc and avicel [^10-13]. The hydrolysis of alkali-treated bagasse by Trichoderma reesei cellulase was evaluated using M-M kinetics with competitive inhibition [¹⁴]. The M-M model was used by Caminal et al. [¹⁵], but the authors could not distinguish between competitive and noncompetitive inhibition by cellobiose. The M-M model works on the assumption that the substrate concentration is much higher than the enzyme concentration and this may not always be the case. A mechanistic model similar to M-M kinetics was proposed and differential equations were solved for the different substrate components [⁷].

The shrinking-site hydrolysis model with a Langmuir-type adsorption isotherm was used in order to get three different rate equations for cellulose, cellobiose and glucose [¹⁶]. Recently, the shrinking-site model was extended to rice pollards, sawdust, wood particles and used paper [¹⁷].

The model has a similar mathematical form to M-M, except that an enzyme term appears in the denominator rather than a substrate term [¹⁸,¹⁹].

A mechanistic model proposed by Fan and Lee that describes the hydrolysis of cellulose and cellobiose, but does not include an adsorption step [²⁰].

This model was proposed by Huang when cellulose hydrolysis by T. viride cellulase was modelled using the M-M mechanism with competitive inhibition [²¹].

The HCH-1 model was proposed by Holtzapple et al. [²²], which is essentially the M-M mechanism with noncompetitive inhibition and a parameter to account for the number of reactive sites covered by the enzymes. A pseudo-steady state approximation for the HCH-1 model was developed [²³] and recently applied to lime pretreated corn stover [²⁴].

Most of the mechanistic models used to describe cellulose hydrolysis in the literature fit into the six mathematical forms presented in Table 1[⁹]. In some cases, the constants are interpreted differently. In other cases, the models are applied multiple times to each enzyme and substrate component. It is worthwhile to compare these models in order to determine their relative merits. To simplify the system, an initial rate data was generated from ammonia fiber explosion (AFEX)-treated wheat straw that was hydrolyzed with T. reesei cellulase. The data were fitted to the various models so they could be compared on an equal basis.

Using the AFEX process [³¹], moist wheat straw was contacted with liquid ammonia. After thorough mixing, ammonia (which disrupts hydrogen bonds in cellulose) was instantaneously released to the atmosphere. This sudden decrease in pressure caused the liquid ammonia trapped in the cellulose fibres to 'explode', which decreased the crystallinity of the cellulose and increased the surface area.

In order to pretreat the wheat straw used in this study, 1370 g of ground wheat straw (0.08 g water/g dry biomass) was mixed with 142 mL of water to bring the moisture content to 0.19 g water/g dry biomass. The wheat straw was placed in an airtight container in an incubator at 35?C for at least 15 min in order to distribute the moisture evenly throughout the straw. Batches of 150 - 250 g of moist wheat straw were treated with ammonia at a ratio of 1.2 g NH₃/g dry wheat straw in an AFEX apparatus [³²] at 220 psig (1.62 MPa) and 125?F (52?C) for 15 min.

After this first treatment, all of the batches were recombined and allowed to dry for 36 h. Prior to the next treatment, the wheat straw was mixed with water to bring the moisture content to 0.20 g water/g dry biomass and the AFEX process was repeated. This procedure was repeated again, so that the entire amount of wheat straw was AFEX-treated a total of three times.

After treatment, the final moisture content was 0.18 g water/g dry biomass. In order to prevent changes in cellulose structure during storage, the treated wheat straw was kept frozen until its use in the hydrolysis runs. Table 10 lists wheat straw composition as measured by the forage fibre analysis of Goering and Van Soest [³³], particle size analysis [³] and other physical properties.

The enzymatic hydrolysis experiments were conducted in an apparatus employing an Amicon ultra-filter membrane (Figure 8). In order to perform the hydrolysis, the AFEX-treated wheat straw was placed in the Amicon stirred cell (10,000 MW-cutoff membrane filter) with 0.05 M, pH 4.8 citric acid buffer. The stirred cell was completely filled with solution. The apparatus was wrapped by a heating tape and the temperature was manually regulated using a Variac. When the desired temperature was achieved, insulation (polyurethane) was placed around the holder in order to maintain the temperature. The temperature could be maintained to within 0.1?C of the desired setting by adjusting the Variac setting or moving the insulation. In order to initiate the reaction, cellulase was injected into the Amicon filter holder using a six-port Rheodyne model 7125 high-performance liquid chromatograph (HPLC) switching valve with a 5-mL sample loop. The 10,000 MW-cutoff filter (Millipore PTGC 076 10) retained the AFEX-treated wheat straw and cellulase but allowed product (cellobiose and glucose) to pass.

The enzymes used in this study were T. reesei cellulase (Genencor 300P) and ?-glucosidase (Novozyme 188). The Novozyme 188, with a reported activity of 250 cellobiose units per gram, was purchased in liquid form and was kept refrigerated until use. As purchased, the Novozyme 188 contained about 40 g/L of glucose.

In order to remove the glucose in the Novozyme 188 by dialysis, an Amicon filter unit with a 10,000 MW cut-off filter was used. Two grams of the dialyzed Novozyme 188 was diluted with 0.05 M, 4.80 pH citrate buffer solution to bring the total volume to 1L. It was preserved with 0.03 wt% NaN₃. This procedure reduced the glucose by 1000 times; the final diluted Novozyme 188 solution contained 0.04 g/L glucose. The ?-glucosidase was added to each sample to convert cellobiose to glucose. The standard procedure was to add 100 ?L of the diluted Novozyme 188 solution to the sample (0.5 - 1.0 mL) and incubate the sample at 50?C for 24 h. The concentrations of the glucose before and after ?-glucosidase was added, were determined with YSI Model 27 glucose analyser. The glucose concentration before and after ?-glucosidase addition was used to determine the cellobiose produced after hydrolysis.

The ultra-filter (UF) cell was partitioned into two parts. The first compartment had a volume of 440 mL, which is where the reaction occurred. The second compartment, with a volume of 2 mL, was the space below the membrane where the effluent collected and was directed into the tube exiting the reactor. The cell was modelled as two perfectly mixed vessels in series. The glucose produced 30 min after reaction initiation was assumed to be the initial rate. The sugars present (glucose and cellobiose) inhibit the reaction. Glucose and cellobiose inhibition parameters determined by Cognata [³⁴] and Holtzapple et al. [³⁵] were used to correct the initial rates. As the sugar concentrations were small, little correction was required.

The nonlinear regression procedure NLIN was used for the SAS programming. The Marquardt method was used for the iteration and the Hougaard option was used to determine the skewness. The analysis of variance tables provided information on the sum of squares, F values, model parameter estimates and skewness. Scatter plots indicated the goodness of fit. The best models for each temperature were determined and the kinetic parameters were fitted using Arrhenius/van't Hoff plots using the re-parameterized equations suggested by Kittrell [³⁶]. For the experiments at 35? and 42?C, a sequential design of experiments was used to decrease the number of experiments required to determine the parameters [³⁷].

* r_s = 0.00629 g/(L?min)

* r_s = 0.03479 g/(L?min)

* r_s = 0.02516 g/(L?min)

AFEX, ammonia fibre explosion

? = Model success.

X = Model failure.

* Parameter estimates fail when estimates were negative.