Comparison of mechanistic models in the initial rate enzymatic hydrolysis of AFEXtreated wheat straw
 Russell F Brown^{1},
 Frank K Agbogbo^{2}Email author and
 Mark T Holtzapple^{3}
DOI: 10.1186/1754683436
© Brown et al; licensee BioMed Central Ltd. 2010
Received: 6 August 2009
Accepted: 23 March 2010
Published: 23 March 2010
Abstract
Background
Different mechanistic models have been used in the literature to describe the enzymatic hydrolysis of pretreated biomass. Although these different models have been applied to different substrates, most of these mechanistic models fit into two and threeparameter mechanistic models. The purpose of this study is to compare the models and determine the activation energy and the enthalpy of adsorption of Trichoderma reesei enzymes on ammonia fibre explosion (AFEX)treated wheat straw. Experimental enzymatic hydrolysis data from AFEXtreated wheat straw were modelled with two and threeparameter mechanistic models from the literature. In order to discriminate between the models, initial rate data at 49°C were subjected to statistical analysis (analysis of variance and scatter plots).
Results
For threeparameter models, the HCH1 model best fitted the experimental data; for twoparameter models MichaelisMenten (MM) best fitted the experimental data. All the threeparameter models fitted the data better than the twoparameter models. The best three models at 49°C (HCH1, Huang and MM) were compared using initial rate data at three temperatures (35°, 42° and 49°C). The HCH1 model provided the best fit based on the F values, the scatter plot and the residual sum of squares. Also, its kinetic parameters were linear in Arrhenius/van't Hoff's plots, unlike the other models. The activation energy (Ea) is 47.6 kJ/mol and the enthalpy change of adsorption (ΔH) is 118 kJ/mol for T. reesei enzymes on AFEXtreated wheat straw.
Conclusion
Among the twoparameter models, MichaelisMenten model provided the best fit compared to models proposed by Humphrey and Wald. For the threeparameter models, HCH1 provided the best fit because the model includes a fractional coverage parameter (ϕ) which accounts for the number of reactive sites covered by the enzymes.
Background
Over the years, two kinds of cellulose hydrolysis models have been developed: empirical and mechanistic models. As empirical models lack a firm theoretical foundation, it is impossible to extend them beyond the range of data to which they were fit. Therefore, our attention was focused on mechanistic models that describe the reaction mechanism between lignocellulosic biomass and enzyme. In order to formulate an appropriate mechanistic model, we needed to know how enzymes hydrolyze lignocellulosic substrates.
The hydrolysis of lignocellulosic substrates depends on enzyme characteristics [1], including: (1) adsorption of enzyme onto lignocellulosic biomass prior to reaction; (2) endproduct inhibition which is competitive [2] or noncompetitive [3]; (3) synergy of the various enzyme components; and (4) mass transfer limitations affecting the transport of the enzyme to the substrate [1]. Enzymatic hydrolysis also depends on substrate characteristics including: (1) lignin distribution; (2) the presence of other components such as hemicellulose, proteins and fats; (3) particle size; and (4) crystallinity [4].
Incorporating all these factors into a single model is cumbersome and highly complicated. We, therefore, divided these factors into shortterm and longterm factors. For shortterm hydrolysis (initial rate), Fan and Lee [5] have shown that: (1) product inhibition is not important; (2) hydrolysis is least affected by mass transfer effects; (3) chemical pretreatment is important; and (4) the pseudosteady state assumption can be used [5]. For longterm hydrolysis, Fan and Lee [6] have indicated that: (1) rate is higher initially but changes later due to product inhibition; (2) pseudosteady state assumptions do not apply; and (3) changes occur in the crystallinity index and surface area. Literature models consider the above factors and, in some cases, differential equations were used to model both the shortterm and longterm hydrolysis process [7, 8]. The simplest forms consider a single substrate and a single enzyme system.
Summary of models.
Model 2A
The MichaelisMenten (MM) model was used to describe the hydrolysis of Solka Floc and avicel [10–13]. The hydrolysis of alkalitreated bagasse by Trichoderma reesei cellulase was evaluated using MM kinetics with competitive inhibition [14]. The MM model was used by Caminal et al. [15], but the authors could not distinguish between competitive and noncompetitive inhibition by cellobiose. The MM 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 MM kinetics was proposed and differential equations were solved for the different substrate components [7].
Model 2B
The shrinkingsite hydrolysis model with a Langmuirtype adsorption isotherm was used in order to get three different rate equations for cellulose, cellobiose and glucose [16]. Recently, the shrinkingsite model was extended to rice pollards, sawdust, wood particles and used paper [17].
Model 2C
The model has a similar mathematical form to MM, except that an enzyme term appears in the denominator rather than a substrate term [18, 19].
Model 3A
A mechanistic model proposed by Fan and Lee that describes the hydrolysis of cellulose and cellobiose, but does not include an adsorption step [20].
Model 3B
This model was proposed by Huang when cellulose hydrolysis by T. viride cellulase was modelled using the MM mechanism with competitive inhibition [21].
Model 3C
The HCH1 model was proposed by Holtzapple et al. [22], which is essentially the MM mechanism with noncompetitive inhibition and a parameter to account for the number of reactive sites covered by the enzymes. A pseudosteady state approximation for the HCH1 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.
Results and discussion
Initial velocity data for enzymatic hydrolysis of ammonia fibre explosion (AFEX)treated wheat straw at 49°C.
Experiment. No.  [S] (g/L)  [E] (g/L)  r_{s} × 100 (g/L·min) 

1  15.60  0.738  0.629* 
2  3.85  1.145  0.648 
3  1.93  0.736  0.194 
4  3.85  0.364  0.220 
5  7.90  0.365  0.197 
6  7.90  0.735  0.580 
7  47.77  0.739  0.792 
8  3.91  1.138  0.485 
9  7.86  1.138  0.739 
10  15.52  1.138  1.257 
11  15.49  0.365  0.297 
12  31.01  0.365  0.310 
13  15.47  0.187  0.215 
14  15.47  0.094  0.098 
15  15.50  0.364  0.323 
16  7.76  0.364  0.216 
17  15.43  1.712  1.460 
18  3.87  1.712  0.770 
19  15.41  1.141  1.044 
20  31.01  1.141  1.319 
21  7.76  0.730  0.616 
22  15.43  2.287  2.229 
23  3.89  2.287  0.979 
24  48.73  1.138  1.579 
25  3.97  4.559  1.358 
26  15.72  4.561  3.549 
27  48.34  4.561  6.241 
28  7.74  4.561  2.218 
29  3.93  3.412  1.237 
30  3.89  6.825  1.738 
31  15.50  6.825  5.014 
Initial velocity data for enzymatic hydrolysis of ammonia fibre explosion (AFEX)treated wheat straw at 42°C.
Experiment No.  [S] (g/L)  [E] (g/L)  r_{s} × 100 (g/L·min) 

1  48.34  3.412  3.479* 
2  15.50  1.142  1.063 
3  31.01  1.153  1.171 
4  3.93  1.153  0.483 
5  15.39  3.420  2.598 
6  48.15  4.562  4.795 
7  8.49  4.562  1.956 
8  7.74  1.152  0.666 
9  11.92  4.563  2.653 
10  11.90  2.548  1.927 
Initial velocity data for enzymatic hydrolysis of ammonia fibre explosion (AFEX)treated wheat straw at 35°C.
Experiment No.  [S] (g/L)  [E] (g/L)  r_{s} × 100 (g/L·min) 

1  48.34  3.412  2.516* 
2  15.50  1.144  0.668 
3  30.82  1.153  0.804 
4  3.89  1.153  0.357 
5  15.49  3.420  1.232 
6  48.15  4.562  2.998 
7  7.74  1.152  0.515 
8  25.42  4.563  2.117 
9  16.10  2.092  1.209 
Parameter estimates at 49°C.
Models  Parameter 1  Parameter 2  Parameter 3  F value  Residual sum of square 

2A  k = 0.0200 (g/(g·min))  K_{m} = 23.5237 (g/L)    1311.34  0.000117 
2B  K = 0.00042 (L/g)^{(1/3)}·min^{1}  α = 9.1015 (g/L)    60.26  0.00208 
2C  k = 8489674 (g/L)  α = 2.4E10 (g/(g·min))    245.34  0.00117 
3A  k = 0.00156 (g/(L·min))  κ = 0.0204 (g/(g·min))  α = 27.1162 (g/L)  1072.28  0.000076 
3B  κ = 0.0190 (g/(g·min))  α = 12.7035 (g/L)  ε = 1.7855 (g/g)  2219.86  0.000045 
3C  κ = 0.0168 (g/(g·min))  α = 10.2269 (g/L)  ε = 2.4631 (g/g)  2232.79  0.000045 
Parameter estimates at 42°C.
Models  Parameter 1  Parameter 2  Parameter 3  F value  Residual sum of square 

2A  k = 0.0137 (g/(g·min))  K_{m} = 14.7743 (g/L)    548.33  0.000043 
3B  κ = 0.0138 (g/(g·min))  α = 5.5471 (g/L)  ε = 2.4092 (g/g)  1044.74  0.000013 
3C  κ = 0.0115 (g/(g·min))  α = 3.5973 (g/L)  ε = 3.6250 (g/g)  3428.53  0.000004 
Parameter estimates at 35°C.
Models  Parameter 1  Parameter 2  Parameter 3  F value  Residual sum of squares 

2A  k = 0.00978 (g/(g·min))  K_{m} = 21.9288 g/L)    199.41  0.000042 
3B  κ = 0.0119 (g/(g·min))  α = 5.7541 (g/L)  ε = 7.4772 (g/g)  805.81  0.000006 
3C  κ = 0.00748 (g/(g·min))  α = 1.3730 (g/L)  ε = 8.2915 (g/g)  1196.19  0.000004 
For the twoparameter models at 49°C, Model 2A (MM) is clearly the best. The F values and the residual sum of squares (RSS) favour the MM mechanism. Model 2B (Humphrey) produced negative parameters, so it is clearly inadequate. The fit from Model 2C (Wald) is very poor from the scatter plots. Of the threeparameter models, Model 3C (HCH1) provided the best fit. The HCH1 model has the highest F value of 2232 and provided a better fit from the scatter plot. Model 3B (Huang) has an F value of 2219 and the scatter plots were very similar to HCH1. Therefore, Model 3B (Huang) is the closest competitor to the HCH1 model.
As the F value, RSS or the correlation coefficient (R^{2}) provide a comparison between models with the same number of parameters; they will be used to compare models with the same number of parameters [25–27]. Among the twoparameter models at 49°C, the F values and the RSS show that Model 2A is the best model. The two best models for the threeparameter models at 49°C are Model 3B and Model 3C based on the F values and the RSS. These three models (2A, 3B and 3C), were further tested at 35° and 42°C. Among the two threeparameter models tested at 35° and 42°C, the HCH1 model (Model 3C) provided the best fit based on the F values and the RSS.
Summary of cellulase activation energies and heats of adsorption.
Enzyme Source  Substrate  Ea (kJ/mol)  ΔH(kJ/mol)  Reference 

Trichoderma reesei  AFEXtreated wheat straw  47.6  118  This Work 
T. viride (endo)  Cotton fibres  54.6  16.5  Beltrame et al. [28] 
T. viride (endo)  Pulp  55.1  48.9  Beltrame et al. [28] 
T. viride (exo)  Cotton fibres  137.4  66.1  Beltrame et al. [28] 
T. viride (exo)  Pulp  137.4  76.9  Beltrame et al. [28] 
T. viride  Cellobiose  45.1  20.9  Beltrame et al. [28] 
Aspergillus niger  Cellobiose  46.1    Calsavara et al. [29] 
T. reesei  Avicel  29.8  148  Drissen et al. [30] 
Summary of model comparison results.
Model  F value  Parameter estimates*  Scatter plots  Arrhenius plots 

2A  √  √  √  X 
2B  X  X  X  
2C  X  √  X  
3A  X  √  √  
3B  √  √  √  X 
3C  √  √  √  √ 
Conclusions
Among the twoparameter models, Model 2A (MM) is the best, although it does not include an adsorption step prior to hydrolysis. Model 2B (Humphrey) introduced an adsorption parameter, a lumped constant which might be responsible for the negative parameters that were generated. Model 2C (Wald) and Model 3A (Fan and Lee) are based on a complex reaction system that did not adequately describe the data. Model 3B (Huang) assumed fast adsorption and slow reaction. It was good at a given temperature. However, there was more scatter in the Arrhenius plot compared to HCH1. Model 3C (HCH1) includes the fractional coverage parameter (ϕ) which accounts for the number of reactive sites covered by the enzyme. The inclusion of the coverage parameter gives HCH1 a better fit for the data. At a fixed temperature, Model 3C (HCH1) was comparable to Model 3B (Huang). However, Model 3C had much less scatter in the Arrhenius plot.
Methods
Pretreatment
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 NH_{3}/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 AFEXtreated a total of three times.
Physical properties of pretreated wheat straw.
No. of treatments  3 

Moisture content (g H_{2}O/g dry matter)  0.18 
Cellulose (%)  36.9 
Hemicellulose (%)  27.9 
Lignin (%)  10.7 
Cell solubles (%)  19.9 
Protein (%)  2.3 
Ash (%)  2.2 
Average length (mm)  2.9 ± 0.9 
Average width (mm)  0.8 ± 0.3 
Hydrolysis apparatus
Enzymes
The enzymes used in this study were T. reesei cellulase (Genencor 300P) and βglucosidase (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 cutoff 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% NaN_{3}. This procedure reduced the glucose by 1000 times; the final diluted Novozyme 188 solution contained 0.04 g/L glucose. The βglucosidase was added to each sample to convert cellobiose to glucose. The standard procedure was to add 100 μL 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 βglucosidase was added, were determined with YSI Model 27 glucose analyser. The glucose concentration before and after βglucosidase addition was used to determine the cellobiose produced after hydrolysis.
Data analysis
The ultrafilter (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.
Statistical analysis
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 reparameterized 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].
Abbreviations
 AFEX:

ammonia fibre explosion
 MM:

MichaelsMenten model
 RSSH:

residual sumofsquares under the null hypothesis for the lack of fit Ftest
 RSS:

residual sum of squares
 UF:

ultrafilter
 [E]:

cellulase concentration
 g/L:

k: rate constant
 g/(g·min):

K_{ m }: MichaelisMenten constant
 g/L:

n: total number of observations
 p :

difference in the number of parameters
 r _{ s } :

the rate of appearance of sugars
 [S]:

substrate concentration
 g/L:

V: rate of reaction
 g/(L·min):

α: lumped parameter
 g/L:

ε: coverage parameter
 g/g, κ:

rate constant; g/(g·min)
 ϕ:

ratio of free substrate to total substrate, dimensionless.
Declarations
Authors’ Affiliations
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