study of kinetic parameters in a mechanistic model for enzymatic hydrolysis of sugarcane bagasse...

ORIGINAL PAPER

Study of kinetic parameters in a mechanistic model for enzymatichydrolysis of sugarcane bagasse subjected to differentpretreatments

Joao Moreira Neto • Daniella dos Reis Garcia •

Sandra Marcela Gomez Rueda • Aline Carvalho da Costa

Received: 18 October 2012 / Accepted: 12 February 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract The goal of this work is to evaluate the influ-

ence of different pretreatments in the kinetics of enzymatic

hydrolysis of sugarcane bagasse and to propose a reliable

methodology to easily perform sensitivity analysis and

updating kinetic parameters whenever necessary. A kinetic

model was modified to represent the experimental data of

the batch enzymatic hydrolysis of sugarcane bagasse pre-

treated with alkaline hydrogen peroxide. The simultaneous

estimation of kinetic parameters of the mathematical model

was performed using the Pikaia genetic algorithm using

batch hydrolysis experimental data obtained with different

enzymatic loads. Subsequently, Plackett–Burman designs

were used to identify the kinetic parameters with the higher

influence on the dynamic behavior of the process variables,

which were re-estimated to describe experimental data of

the hydrolysis of bagasse pretreated with phosphoric

acid ? sodium hydroxide. The methodology was accurate

and straightforward and can be used whenever there are

changes in pretreatment conditions and/or fluctuations in

biomass composition in different harvests.

Keywords Enzymatic hydrolysis � Sugarcane bagasse �Modeling � Parameter estimation � Sensitivity analysis

List of symbols

B Concentration of cellobiose (g/L)

C Concentration of cellulose (g/L)

enzc Cellulase activity concentration (FPU/L)

enzg b-Glucosidase activity concentration (CBU/L)

G Concentration of glucose (g/L)

k1 Maximum specific rate of cellulose hydrolysis to

cellobiose (h-1)

k2 Specific rate of cellobiose hydrolysis to glucose

(g/(CBU h))

K1 Lumped specific rate of cellulose hydrolysis to

cellobiose (h-1)

K2 Lumped specific rate of cellobiose hydrolysis to

glucose (g/(L h))

Keq Cellulase adsorption saturation constant (FPU/L)

KL Constant for b-glucosidase adsorption to lignin

(L/g)

Km Cellobiose saturation constant for b-glucosidase

(g/L)

K1B Inhibition constant of cellulase by cellobiose (g/L)

K1G Inhibition constant of cellulase by glucose (g/L)

K2G Inhibition constant of b-glucosidase by glucose

(g/L)

L Concentration of lignin (g/L)

r1 Volumetric rate of cellulose hydrolysis to

cellobiose (g/(L h))

r2 Volumetric rate of cellobiose hydrolysis to glucose

(g/(L h))

t Time (h)

k Rate of decrease in cellulose specific surface area

(h-1)

Introduction

The major steps involved in the production of ethanol from

lignocellulosic biomass are pretreatment, enzymatic hydro-

lysis, fermentation and distillation. Owing to the recalcitrant

J. M. Neto (&) � D. dos Reis Garcia �S. M. G. Rueda � A. C. da Costa

Laboratory of Fermentative and Enzymatic Process Engineering,

School of Chemical Engineering, University of Campinas,

Campinas, SP 13083-970, Brazil

e-mail: [email protected]

123

Bioprocess Biosyst Eng

DOI 10.1007/s00449-013-0930-6

structure of lignocellulosic materials, the pretreatment step is

essential to remove lignin and disorganize the crystalline

structure to release the polymer chains of cellulose, so that it

becomes more accessible to the enzymatic complex [1].

The pretreatment with alkaline hydrogen peroxide

occurs in mild conditions (temperature, pressure and

absence of acids) and is expected to cause less sugar

degradation than acid processes [2]. Hydrogen peroxide is

well known in the paper and cellulose industry, where it is

used as a bleach agent. It has also the great advantage of

not leaving residues in the biomass, as it decomposes into

oxygen and water [3]. It has been shown to result in a

material highly susceptible to enzymatic hydrolysis when

sugarcane bagasse is the biomass considered [4–6].

Diluted sulfuric acid pretreatment is one of the most

popular pretreatment methods for bioethanol production

from biomass [7], but there are many drawbacks associated

with this acid, such as the requirement for expensive reac-

tors that are resistant to corrosion and the formation of

degradation products that inhibit fermentation. Because

phosphoric acid is non-corrosive, nontoxic, safe to be used

and inexpensive compared to other mineral acids [8], it is a

good alternative to replace sulfuric acid in diluted acid

pretreatments, mainly because phosphate is a nutrient for

the microorganisms in the subsequent fermentation process.

However, diluted acid pretreatment of sugarcane bagasse

alone leads to unacceptably low conversions in the hydro-

lysis [9] and posterior delignification is necessary. Delig-

nification with sodium hydroxide is the most used [10].

The quantitative description of the enzymatic hydrolysis

using robust mathematical modeling is a powerful tool in

the evaluation of process alternatives. Modeling allows not

only the understanding of the mechanisms involved, but

also assist the various stages of implementing a process, as a

mathematical model can be used to design reactors, to

determine new control structures, for process optimization

and to simulate the impact of variables of interest such as

residence time and substrate on yield, conversion and pro-

ductivity. The models that aim to elucidate the enzymatic

hydrolysis of cellulosic and lignocellulosic biomass can be

divided into two main categories: mechanistic and empiri-

cal. The majority of the mechanistic models are based on

Michaelis–Menten models with inhibition [11, 12], step of

enzymatic adsorption [13–16], enzyme deactivation [17]

and adsorption of the enzyme to lignin [13, 15, 18]. The

empirical models have been used to correlate the hydrolysis

of substrates over time with structural properties [19, 20].

Unfortunately, no model can satisfactorily predict the

digestibility of various types of biomass due to the com-

plexity of the enzymes, the structural characteristics of

heterogeneous lignocellulosic biomass, observed changes

to adsorption of enzymes in biomass in time and enzyme

inhibition by hydrolysis products [21].

It is well known that biomass composition is influenced by

the method and operational conditions of pretreatment. In

addition, there are fluctuations in biomass compositions

depending on the kinds of soil, weather, etc., so that bio-

masses from different harvests have different compositions.

This fluctuations in composition influences the kinetics of

hydrolysis and should be taken into consideration in a robust

model, which should have its parameters re-estimated

always based on the raw materials (different harvests, dif-

ferent pretreatments) used. However, the re-estimation of

kinetic parameters is a difficult task, due to the nonlinearity

of the parameters and the interaction between them.

Plackett and Burman sensitivity analysis is a promising

screening technique that can aid in reducing the parameter

set, such that only the most significant parameters need to

be re-estimated, making the process of updating the

mathematical model much easier.

The objective of this work is to evaluate the modeling of

the enzymatic hydrolysis of sugarcane bagasse considering

two pretreatments: alkaline hydrogen peroxide and phos-

phoric acid ? NaOH delignification. The influence of the

pretreatment on the kinetics of enzymatic hydrolysis is

evaluated and a methodology to perform kinetic parameters

sensitivity analysis, including updating is proposed and

applied successfully to re-estimate the kinetic parameters

when a different pretreatment was considered.

Materials and methods

Substrate

The biomass used in all experiments was fresh sugarcane

bagasse (Saccharum officinarum) obtained from the sugar

plant ‘‘Usina da Pedra’’, located in Serrana, Sao Paulo,

Brazil. The bagasse was dried for 3 days, ground in a knife

mill (Wiley Mill Model 3) and a hammer mill (General

Electronic) for 10 min at each mill, to present greater

uniformity. It was subsequently sieved using Tyler 35 sieve

and stored in freezer in sealed plastic bags.

Pretreatments

The two pretreatments were performed in the optimal

conditions determined in previous works [9, 22] and using

bagasse from an only harvest.

Alkaline hydrogen peroxide

The pretreatment was performed using 8 % (w/v) of

bagasse, 11 % (v/v) of hydrogen peroxide and pH adjusted

to 11.5 with sodium hydroxide. The pretreatment solution


123

was incubated in an orbital shaker (Marconi, Piracicaba,

SP, Brazil, MA-832), agitated at 150 rpm, at 25 �C for 1 h.

Phosphoric acid ? sodium hydroxide

The pretreatment was performed using 10 % (w/v) of

bagasse and 0.5 % (w/v) of phosphoric acid in autoclave

for 2 h at 140 �C. Delignification was performed after acid

pretreatment, in autoclave with 1 % (w/v) of sodium

hydroxide for 1 h at 100 �C.

Enzymatic hydrolysis

The enzymatic hydrolysis was performed in 250 mL

erlenmeyer flasks, containing a 100 mL mixture of citrate

buffer (pH 4.8) and 3 % (w/v) of bagasse pretreated in the

optimal condition for the two pretreatments. The values of

enzymes concentrations (cellulase from Trichoderma

reesei, Sigma-Aldrich, Steinheim, Germany, ATCC 26

921, and b-glucosidase from Aspergillus niger, Novozym

188) were simultaneously varied from 1.7 to 30 FPU/g

dry bagasse (50–900 FPU/L) and from 7.3 to 50 CBU/g

dry bagasse (220–1,500 CBU/L) for cellulase and b-glu-

cosidase, respectively. The flasks were incubated in an

orbital shaker (Marconi MA-832) agitated at 100 rpm at

50 �C.

Chemical analysis of bagasse

Extractives, ash, structural carbohydrates and lignin were

analyzed in accordance with Sluiter et al. [23–25] and

Hyman et al. [26]. Sugar concentrations were determined

by high-performance liquid chromatography (HPLC;

Waters Corporation, Massachusetts, USA) equipped with a

refractive index detector. The separation was performed in

a Sugar-Pak I column (Waters Corporation) at 70 �C with a

flow rate of 0.5 mL/min, using filtered deionized water as

the mobile phase. The sample was centrifuged and filtered

through 0.2 lm (Acrodisc) and a volume of 10 lL was

injected. Acetyl content was determined using a Biorad

HPX87H column at 45 �C, eluted at 0.55 mL/min with

0.01 mol/L sulfuric acid. Acetyl groups were detected in a

65 �C temperature-controlled RI detector (Knauer, Berlin,

Germany, HPLC pump and detector). Sugar loss by acid

degradation was considered using the Sugar Recovery

Standards as suggested by the NREL method [25].

Enzymatic activities

Cellulase activity was determined as filter paper units per

milliliter (FPU/mL), as recommended by the International

Union of Pure and Applied Chemistry [27, 28]. b-glucosidase

activity was determined using a solution of cellobiose

15 mmol/L and expressed in units per milliliter (CBU/mL)

[29]. Enzyme activity was 64.1 FPU/mL for cellulase and

308.4 CBU/mL for b-glucosidase.

Kinetic model

In this work, the kinetic model of simultaneous sacchari-

fication and fermentation developed by Philippidis et al.

[30, 31] and Philippidis and Hatzis [13] was modified and

the step of fermentation was removed from the model. In

addition, parameters were re-estimated to describe the

different conditions of a hydrolysis separated from the

fermentation, including product inhibition. The objective is

to use the model to describe the kinetics of batch enzymatic

hydrolysis of sugarcane bagasse.

To develop the model the following considerations were

made:

1. Cellulose is converted to cellobiose and then to

glucose. Direct conversion of cellulose to glucose

was neglected. This assumption results in the reactions

in series shown in reaction R1.

C !r1

ðEG=CBHÞB !r2

ðBGÞG ðR1Þ

2. The cellulolytic complex (enzc) consists of endoglu-

canase and cellobiohydrolase, but there is no distinc-

tion between them.

3. It is considered that the rates of adsorption–desorption

of cellulase on the substrate surface remain in balance

at all times.

According to reaction R1, cellulose (C) is hydrolyzed to

cellobiose (B) in a heterogeneous reaction catalyzed by

endoglucanase (EG) and cellobiohydrolase (CBH). Cello-

biose is converted to two units of monomeric glucose

(G) in a homogeneous reaction catalyzed by b-glucosidase

(BG).

The mass balances of the enzymatic hydrolysis model

are given by Eqs. 1–3.

dC

dt¼ �r1 ð1Þ

dB

dt¼ 1:056 r1 � r2 ð2Þ

dG

dt¼ 1:053 r2 ð3Þ

where the concentration of (C), (B) and (G) are given in (g/

L), t is the time (h) and r1, r2 and r3 are the reaction rates


123

(g/(L h)). The hydrolysis reaction rates are given by

Eqs. 4–5.

r1 ¼K1 C e�kt

1þ BK1Bþ G

K1G

ð4Þ

r2 ¼K2 B

Km 1þ GK2G

h iþ B

ð5Þ

where K1 and K2 are lumped specific rate constants for

cellulose (h-1) and cellobiose (g/(L h)). K1B, K1G, and K2G

are inhibition constants (g/L) for noncompetitive inhibition

of cellulase by cellobiose and glucose and competitive

inhibition of b-glucosidase by glucose, respectively. Km is

the cellobiose saturation constant for b-glucosidase (g/L),

and k is a constant (h-1) that accounts for the rate of

decrease in cellulose specific surface area.

The lumped specific rate constant, K1, exhibit Michaelis–

Menten dependence on cellulase concentration according to

Eq. 6.

K1 ¼k1 � enzc

Keq þ enzcð6Þ

where enzc is the cellulase activity concentration (FPU/L),

k1 is the maximum specific rate of cellulose hydrolysis to

cellobiose (h-1) and Keq is the cellulase adsorption–

desorption equilibrium constant on the substrate (FPU/L).

The lumped specific rate constant, K2, of the homoge-

neous cellobiose hydrolysis is proportional to the b-glu-

cosidase concentration with reduction owing to irreversible

adsorption to lignin [13], and is described by the Eq. 7.

K2 ¼ k2 � enzg 1� KL Lð Þ ð7Þ

where enzg is the b-glucosidase activity concentration

(CBU/L), k2 is the specific rate of cellobiose hydrolysis to

glucose (g/(CBU h)), KL is the constant of irreversible

adsorption of b-glucosidase to lignin (L/g) and (L) is the

concentration of lignin (g/L).

Although the model proposed in this work considered 2

kinds of enzyme activities, enzc (whole activity of cellu-

lolytic enzymes) and enzg (b-glucosidase activity), this is a

simplification, since the enzymatic complex called cellu-

lase contains endoglucanase (EG), cellobiohydrolase

(CBH), b-glucosidase (BG) and other side activities that

may influence the hydrolysis reaction. This simplification

was the same used by other authors [14–16].

Another simplification of the model is that adsorption of

b-glucosidase to lignin is taken into account, but not the

adsorption of cellobiohydrolases or endo-glucanases to

cellulose or lignin. However, to describe these phenomena

in the model, further experiments involving enzyme

adsorptions and their description through isotherms (such

as Langmuir isotherms) are needed considering the same

raw material and pretreatments used in this work, which

will be addressed in future works. Despite this simplifica-

tion, the proposed model described accurately the experi-

mental data.

Estimation of kinetic parameters

Estimation of kinetic parameters for bagasse pretreated

with alkaline hydrogen peroxide

To estimate kinetic parameters, it is required to search

the values of these parameters for which the values of

glucose computed by the model are close to the measured

concentration of glucose within acceptable tolerance at all

times during the hydrolysis process. The kinetic param-

eters are estimated by minimizing an objective function.

Let h specify a kinetic parameters vector, which contains

all kinetic constants. The optimal kinetic parameter

vector is found out by minimizing the objective function

E(h):

EðhÞ ¼Xnp

i¼1

Xm

j¼1

Gi;j � Gei;j

� �2 ð8Þ

where np and m are the number of experimental sampling

points of the batch hydrolysis and the number of experi-

mental profiles, respectively; Gei,j is the measured con-

centration of glucose at the sampling time i for the profile j;

Gi,j is the concentration of glucose computed by the model

at the sampling time i for the profile j.

The modeling and parameter estimation was carried out

with the software COMPAQ VISUAL FORTRAN version

6.6. Model differential equations were solved using a

FORTRAN program with an integration algorithm based

on the fourth-order Runge–Kutta method (routine IVPRK

of the IMSL MATH LIBRARY FORTRAN-90) to obtain

values of C, B and G.

A genetic algorithm has been used to minimize the

objective function E(h) given by Eq. 8. The genetic algo-

rithm used in this work was PIKAIA, a general purpose

function optimization FORTRAN code subroutine devel-

oped by Charbonneau and Knapp [32]. More details about

the technique are available in the User’s Guide to PIKAIA

1.0 [32].

When compared with traditional optimization methods

based on the gradient of a function (Successive Quadratic

Programming—SQP), the GAs (Genetic Algorithm) have

as advantage the fact of they do not request much infor-

mation about the mathematical structure of the system and

they do not need initial guesses [33].


123

Sensitivity analysis of enzymatic hydrolysis model

parameters based on Plackett–Burman designs

Before the re-estimation of the kinetic parameters of the

model to describe the hydrolysis of H3PO4 ? NaOH pre-

treated bagasse, a methodology based on Plackett–Burman

(PB) designs was used to identify the parameters with the

strongest influence on the dynamic behavior of the process

variables.

The PB design is a fractional factorial design method

that allows the testing of multiple independent process

variables with only a small number of trials, instead of

using complete factorial designs. Plackett–Burman sensi-

tivity analysis (PBSA) presents several advantages over

one-at-a-time (OAAT) sensitivity analysis methods [34],

where all parameters significances are individually evalu-

ated. Among them, in PB designs the effect of parameters

on the model is calculated considering average variations

in the remaining parameters, instead of fixing them at given

values. Thus, all parameters are simultaneously investi-

gated, which makes this technique more efficient and

avoids loss of information [35]. OAAT method does not

uncover potentially important interactions between two

parameters where significant effects could occur due to the

synergism among parameters [36]. According to Beres

et al. [36] the rationale for PBSA includes: PBSA finds

2-way interactions; PBSA is applied to a wide range of

models, including both simulation and analytic models;

PBSA is prescriptive, using pre-determined designs; PBSA

designs for up to 100 parameters are readily available;

PBSA rankings are easy to compute; the range of the

parameters in PBSA does not need to be identically sized,

as occurs in OAAT analysis, but its range can be limited

and defined by the modeler, allowing a more suitable

choice subjected to intervals with physical meaning for

each particular parameter.

Andrade et al. [35, 37] used a similar procedure to re-

estimate kinetic parameters in an alcoholic fermentation

Fig. 1 General flowchart of the

methodology for selecting and

re-estimation of the most

significant parameters of the

kinetic model of hydrolysis of

sugarcane bagasse subjected to

different pretreatments. Where

np and m are the number of

experimental sampling points

and the number of experimental

profiles, respectively; Gei,j is the

measured concentration of

glucose at the sampling time

i for the profile j; Gi,j is the

concentration of glucose

computed by the model at the

sampling time i for the profile

j (adapted from Andrade et al.

[35])


123

process with fluctuations in the quality of raw material with

good results. In their work, however, analysis was per-

formed only at the end of the fermentation. In this work, as

some parameters can have different impacts at the begin-

ning, middle or at the end of the hydrolysis, a dynamic PB

design evaluation was proposed, where the influence of the

parameters was determined as a function of the hydrolysis

time.

The methodology of re-estimation of parameters

involves the steps described in Fig. 1 and explained below:

1. Estimate 9 kinetic parameters from the model adapted

from Philippidis et al. [30, 31] and Philippidis and

Hatzis [13];

2. Fix the i less significant parameters determined by PB

design in the estimation procedure;

3. Define the order of magnitude for each significant

parameter. As the literature data is scarce for sugar-

cane bagasse, the kinetic parameters estimated for

bagasse pretreated with alkaline hydrogen peroxide

were taken as reference;

4. Collect new experimental data for hydrolysis (glucose

profile) with change in bagasse pretreatment;

5. Estimate the significant parameters by genetic algo-

rithm, minimizing the objective function;

6. The procedure is repeated until a pre-set number of

generations is reached.

Results and discussion

Estimation of kinetic parameters for bagasse pretreated

with alkaline hydrogen peroxide

Data from 6 experimental runs of enzymatic hydrolysis of

alkaline hydrogen peroxide (AHP) pretreated sugarcane

bagasse with initial concentration of biomass at 30 g/L and

varying the cellulase and b-glucosidase loadings were used

for the determination of the kinetic parameters. Two

experiments performed using different enzymes loadings

(but inside the range used for modeling) were used for

validation. The initial concentrations of lignin, cellulose,

cellobiose and glucose used in the model simulation were

set at 2.96 g/L (bagasse with 9.87 % of lignin), 18.0 g/L

(bagasse with 60.09 % of cellulose), 0.0 and 0.0 g/L,

respectively.

The 9 parameters from the kinetic model estimated by

the genetic algorithm Pikaia are shown in Table 1. The set

of parameter values in Table 1 was used in the model to

simulate the enzymatic hydrolysis of sugarcane bagasse

pretreated with alkaline hydrogen peroxide. The resulting

model described the experimental data accurately. Figure 2

shows the results when the model was used to simulate the

assays not used in the parameter estimation procedure

(validation).

Table 1 Parameters estimated by Pikaia GA for hydrolysis of

bagasse pretreated with alkaline hydrogen peroxide and bagasse

pretreated with phosphoric acid ? sodium hydroxide

Parameter Bagasse pretreated

with H2O2

Bagasse pretreated with

H3PO4 ? NaOH

k1a 12.50 h-1 14.32 h-1

k2a 0.995 g/(CBU h) 1.065 g/(CBU h)

ka 0.046 h-1 0.088 h-1

Keqa 6,590.7 FPU/L 11,509.9 FPU/L

KL 0.033 g/L 0.033 g/L

Kma 96.34 g/L 96.28 g/L

K1Ga 2.11 g/L 0.87 g/L

K1B 23.25 g/L 23.25 g/L

K2Ga 0.43 g/L 3.57 g/L

a Parameters with re-estimation

Fig. 2 Validation of the model. Experimental data are for concen-

tration of glucose (filled square). Simulated curves in the concentra-

tions of cellobiose (dotted line), cellulose (dashed line) and glucose

(solid line). a Experimental and simulated data for enzymes loading

of 5.8 FPU/g dry bagasse (175 FPU/L) and 42.7 CBU/g dry bagasse

(1,280 CBU/L). b Experimental and simulated data for enzymes

loading of 15.8 FPU/g dry bagasse (475 FPU/L) and 50 CBU/g dry

bagasse (1,500 CBU/L)


123

The prediction quality of the model was characterized

using the residual standard deviation written as a percent-

age of the average of the experimental values �yi, RSD (%),

Eq. 9, which provides an indication of the prediction

accuracy, as suggested in the work of Atala et al. [38],

Andrade et al. [35] and Rivera et al. [5, 39].

RSD %ð Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1 yi � ypi

� �2

n

s� 100

�yið9Þ

in which yi is the experimental value, ypi is the value

predicted by the mathematical model, n is the number of

experimental points and �yi is the average of the

experimental values. Moreover, the prediction quality of

the model can be characterized using the correlation

coefficient (COR (%)) [40], Eq. 10.

COR %ð Þ ¼ 1� SEE

STT

� �� 100 ð10Þ

where SEE ¼Pn

i¼1 yi � ypi

� �2and STT ¼

Pni¼1 yi � �yið Þ2

Table 2 shows the values of RSD (%) for all experi-

mental assays performed. It can be seen that the values of

RSD (%) varied from 8.21 to 23.84 %, which are in the

range of errors found in the work of Atala et al. [38]. The

values of COR (%) were from 88.62 to 99.35 %, which

also shows that the model described the experimental data

with acceptable accuracy.

Plackett–Burman design for screening of significant

parameters

After estimation of the kinetic parameters for the hydrolysis

of bagasse pretreated with alkaline hydrogen peroxide,

Plackett–Burman (PB) design was used to study the influ-

ence of the 9 kinetic parameters on the time profiles of

cellulose (C), cellobiose (B) and glucose (G) concentrations.

The initial concentrations of C, B and G were set at 18.0, 0.0

and 0.0 g/L, respectively. The concentrations of cellulase

and b-glucosidase were 15.8 FPU/g dry bagasse (475 FPU/L)

and 25 CBU/g dry bagasse (750 CBU/L), respectively.

The PB design was performed by varying the values of

the parameters shown in Table 1 (for the hydrolysis of

bagasse pretreated with alkaline hydrogen peroxide) in

±10 % to define two different levels, low (-) and high

(?). A PB design with 20 trials was used and the model

was simulated with the combination of parameters values

defined for each trial. For each simulation the values of C,

B and G were obtained at times of 10, 20, 30, 40, 50 min, 1,

3, 6, 12, 24, 36, 48, 60, 72 h and used as responses in the

Plackett–Burman design. The data were analyzed using

the Software Statistica 7.0 (Statsoft) and the effects of the

parameters on the concentrations of cellulose (C), cello-

biose (B) and glucose (G) as a function of hydrolysis time

are plotted in Fig. 3.

The data presented in Fig. 3 show that the influence of

several kinetic parameters on the responses changes with

hydrolysis time. In Fig. 3c, it can be seen that parameter khas a small effect on glucose concentration at the beginning

of hydrolysis, but over time the influence of this parameter

becomes very significant. On the other hand, parameters

K2G and Km present some influence at the beginning of the

hydrolysis but practically no influence at the end. In

Fig. 3b, we can notice that the effects of all the kinetic

parameters on cellobiose concentration decrease with

hydrolysis time, so they have greater influence on this

response in the early hours of reaction. These results

indicate that if we perform the analysis only at the end of

hydrolysis as suggested in the work of Andrade et al. [34],

important parameters to describe the beginning of hydro-

lysis can be left out in the re-estimation step.

Table 3 shows the effects of kinetic parameters on the

concentrations of cellulose, cellobiose and glucose at the

beginning (up to 10 h) and at the middle end of hydrolysis

(10–72 h). In this table, the black area means that the

parameter has a strong influence on the response, the gray

area indicates that the parameter has a weak influence and

Table 2 Residual standard

deviation, RSD (%) used to

characterize the prediction

quality of kinetic model for

bagasse pretreated with alkaline

hydrogen peroxide and for

bagasse pretreated with

phosphoric acid ? sodium

hydroxide

Assays RSD (%) COR (%) RSD (%) RSD (%)

H2O2 H2O2 H3PO4 ? NaOH

Without re-estimation

H3PO4 ? NaOH

With re-estimation

5.8 FPU/g, 7.3 CBU/g 23.84 92.71 80.6 25.66

5.8 FPU/g, 42.7 CBU/g

(validation)

11.10 98.25 89.73 25.24

25.8 FPU/g, 7.3 CBU/g 23.00 88.62 43.58 11.16

25.8 FPU/g, 42.7 CBU/g 19.70 92.16 52.94 13.93

1.7 FPU/g, 25 CBU/g 16.59 96.76 195.7 25.95

30 FPU/g, 25 CBU/g 8.05 99.34 44.33 10.2

15.8 FPU/g, 50 CBU/g

(validation)

9.99 98.99 63.6 16.3

15.8 FPU/g, 25 CBU/g 8.21 99.35 88.22 14.44


123

the white area means that the influence of the parameters

on the response is negligible. At the beginning of hydro-

lysis, the most significant parameters for the concentration

of cellulose (black area) are: k1, Keq and K1G. The

parameters of minor influence (gray area) are: k2, k, Km and

K2G. The parameters KL and K1B (white area) had no

influence. For the concentration of cellobiose, the signifi-

cant parameters at the beginning of hydrolysis were k1, k2,

Keq, Km, K2G (black area) and K1G (gray area), while the

parameters k, KL and K1B had no influence. The influence

of the parameters on the concentration of glucose up to

10 h of hydrolysis shows the same behavior observed for

the concentration of cellulose, with the exception of

parameter k, that had weak influence on cellulose con-

centration and has no effect on glucose concentration.

From 10 h up to the end of hydrolysis (72 h) it can be

seen from Table 3 that the parameters k1, k, Keq and K1G

(black area) were significant for both the concentrations of

cellulose and glucose. For the concentration of cellobiose,

the effects of all parameters decreased gradually at the end

of the hydrolysis time. The parameters k2, K2G and Km

were considered significant (gray area) because they pre-

sented influence, although small, during a greater time

interval than the other parameters. An explanation for the

behavior shown in the effects analysis for the concentration

of cellobiose is that it is an intermediate in the hydrolysis

reaction, presenting a higher concentration at the beginning

of the reaction and being almost totally consumed for the

formation of glucose at the end.

In the procedure of re-estimation of parameters, the

influence of the parameters throughout the hydrolysis time

was taken into consideration. Thus, according to Table 3,

there are two non-significant parameters (KL and K1B) and

seven significant parameters (k1, k2, k, Keq, Km, K1G and

K2G).

Re-estimation of kinetic parameters for bagasse

pretreated with phosphoric acid ? sodium hydroxide

To evaluate the performance of the kinetic model with

changes in the pretreatment, experimental data from 8

enzymatic hydrolysis assays were used. The assays were

performed using phosphoric acid ? sodium hydroxide

pretreated bagasse at an initial concentration of 30 g/L and

varying the cellulase and b-glucosidase loadings. 6

experiments were used for parameters re-estimation and 2

were used to validate the model. The initial conditions of

lignin, cellulose, cellobiose and glucose used in the pro-

cedure of parameter estimation and model simulation were

set at 4.23 g/L (bagasse with 14.11 % of lignin), 15.26 g/L

(bagasse with 50.86 % of cellulose), 0.0 and 0.0 g/L,

respectively.

Table 1 presents the most significant parameters that

have been re-estimated by genetic algorithm and the non-

significant parameters that were fixed in the model

simulation for the hydrolysis of bagasse pretreated with

phosphoric acid ? sodium hydroxide. Figure 4 presents

the results of simulations performed to evaluate the

Fig. 3 Effect of the kinetic parameters in the process variables as a

function of hydrolysis time. a Effect of kinetic parameters in

the concentration of cellulose. b Effect of kinetic parameters in the

concentration of cellobiose. c Effect of kinetic parameters in the

concentration of glucose


123

predictive ability of the model to changes in the pretreat-

ment of sugarcane bagasse. Two cases were considered:

(a) prediction using the model without parameters updat-

ing, i.e., the parameters used in the model were that esti-

mated using data of hydrolysis of bagasse pretreated with

alkaline hydrogen peroxide (Fig. 4a, b). (b) Prediction with

the model with significant parameters re-estimation

(Fig. 4c, d). This figure shows the validation of the model,

as the data was not used in the re-estimation procedure. It

can be seen that without parameters updating the model

developed to describe the hydrolysis of bagasse pretreated

with alkaline hydrogen peroxide do not describe the

dynamic behavior when the biomass is subjected to a

different pretreatment. Pretreatment with alkaline hydrogen

peroxide results in a biomass that is more susceptible to

enzymatic hydrolysis and the model developed for this

biomass overestimates conversion when used to describe

data of H3PO4 ? NaOH pretreated biomass.

The residual standard deviation, RSD (%), described by

Eq. 9 was used to characterize the prediction quality of the

model with and without re-estimation of the most signifi-

cant parameters. From Table 2, it can be seen that in all

assays without re-estimation of parameters the values of

RSD (%) were unacceptably high, in the range of

52.90–195.70 %.

The assays with re-estimation of parameters had sig-

nificant improvement in the values of RSD (%) and the

model with updated parameters was able to describe the

dynamic behavior of the process accurately.

A comparison of the parameters estimated for the

hydrolysis of bagasse subjected to the two pretreatments

considered can be made. From Table 1, it can be seen that

the parameters with significant changes were:

k: practically doubled for the pretreatment is with

phosphoric acid ? NaOH.

Figure 3 shows that parameter k has a positive effect on

the concentration of cellulose and a negative effect on the

concentration of glucose. The exponential decay term in

Eq. 4, e-kt, takes into consideration the decline in the rate

of glucose production as a result of reduced enzyme

mobility caused by the decrease in cellulose-specific sur-

face area, so the higher the value of k, the faster is the

reduction in the surface area and the more difficult the

conversion of cellulose in glucose over time. The value of kis determined by the nature of the biomass and by the

pretreatment conditions used; promising conditions are

those that produce a highly digestible material by increasing

its specific surface area (small k). In the study of Philippidis

and Hatz [13], the impact of parameter k on the ethanol

yield in a simultaneous saccharification and fermentation

process was evaluated. When wastepaper without pretreat-

ment (k = 0.02 h-1) was used, an ethanol yield of 45.7 %

was achieved. Using a pretreatment process that reduced the

k value by half led to an ethanol yield of 59.5 %.

Table 4 shows the conversion of the assays of Table 2 for

the hydrolysis of bagasse subjected to the two pretreatments

considered. Hydrolysis conversion is defined by Eq. 11.

Conversion ð%Þ ¼ g of glucose at the end of hydrolysis

g of glucan in pretreated bagasse� 0:9� 100

ð11Þ

where 0.90 is the factor used to convert sugar monomers to

anhydromonomers.

It can be seen from Table 4 that the conversions

achieved with hydrogen peroxide pretreated bagasse were

much higher than those obtained with phosphoric

acid ? NaOH pretreated bagasse. Based on these data of

conversion and on the value of parameter k, which is

almost the double for bagasse pretreated with phosphoric

Table 3 Effect of kinetic parameters in the variables at the beginning (Up to 10 h) and from 10 to 72 h of hydrolysis. Black color is for

parameters with strong influence on the response, gray color is for parameters with weak influence on the response and white color is for

parameters with no influence on the response

Time of

hydrolysisVariables K1 K2 Keq KL Km K1G K1B K2G

up to 10h

Cellulose

Cellobiose

Glucose

10 to 72h

Cellulose

Cellobiose

Glucose


123

acid ? NaOH, it can be concluded that the rate of decrease

in specific surface area is lower when the bagasse is pre-

treated with alkaline hydrogen peroxide, so this pretreat-

ment is more efficient, enabling the hydrolysis reaction to

proceed more completely.

Keq: almost doubled for the pretreatment with phos-

phoric acid ? NaOH.

Just as parameter k, Keq has a positive effect on cellulose

and a negative effect on glucose concentration, as can be

seen in Fig. 3.

Keq is the equilibrium constant for cellulase adsorption

and is related to the enzyme affinity to the substrate binding

site. Hatz and Philippidis [13] estimated the impact of the

enzyme binding efficiency on the process of simultaneous

saccharification and fermentation and showed that the

smaller the equilibrium constant, the stronger the affinity

of the enzyme for the substrate and therefore, the efficiency

of binding. These authors considered a cellulase with Keq

of 1,000 FPU/L, which led to an ethanol yield of 27.5 %

and a cellulase with Keq of 500 FPU/L, which resulted in a

yield of 34 7 %. The value of Keq when bagasse was pre-

treated with alkaline hydrogen peroxide (6,590.7 FPU/L)

Fig. 4 Validation of the model. Experimental data are for concen-

tration of glucose (filled square). Simulated curves in the concentra-

tions of cellobiose (dotted line), cellulose (dashed line) and glucose

(solid line). a Experimental and simulated data for enzymes loading

of 5.8 FPU/g dry bagasse (175 FPU/L) and 42.7 CBU/g dry bagasse

(1,280 CBU/L) without parameters re-estimation. b Experimental and

simulated data for enzymes loading of 15.8 FPU/g dry bagasse

(475 FPU/L) and 50 CBU/g dry bagasse (1,500 CBU/L) without

parameters re-estimation. c Experimental and simulated data for

enzymes loading of 5.8 FPU/g dry bagasse (175 FPU/L) and 42.7

CBU/g dry bagasse (1,280 CBU/L) with parameters re-estimation.

d Experimental and simulated data for enzymes loading of 15.8 FPU/

g dry bagasse (475 FPU/L) and 50 CBU/g dry bagasse (1,500 CBU/L)

with parameters re-estimation

Table 4 Simulated glucose conversions in the conditions of the

experimental assays of Table 2

Assays Bagasse pretreated with

H2O2 (%)

Bagasse pretreated with

H3PO4 ? NaOH (%)

1 77.06 40.00

2 74.19 38.58

3 96.99 71.83

4 97.75 69.04

5 45.79 20.69

6 98.79 72.66

7 92.97 58.41

8 93.70 58.86


123

was almost half the value of Keq (11,509.9 FPU/L) when

bagasse was pretreated with phosphoric acid ? NaOH,

which indicates a greater affinity of the cellulolytic com-

plex for the bagasse pretreated with peroxide.

K1G: decreased to less than half for the pretreatment

with phosphoric acid ? NaOH.

According to Fig. 3, K1G has a positive effect on glucose

and a negative effect on cellulose concentration. K1G is the

inhibition constant of cellulase by glucose. The smaller the

value of K1G, the greater the inhibition of cellulase by

glucose.

K2G: increased more than 8 times for the pretreatment

with phosphoric acid ? NaOH.

From Fig. 3, K2G has a positive effect on glucose only in

the initial stage of hydrolysis, but has no significant effect on

cellulose. K2G is the inhibition constant of b-glucosidase by

glucose. The smaller value of K2G, the greater the inhibition.

We were unable to assign a physical meaning to justify

the change of values of K1G and K2G for the two pre-

treatments, as K1G and K2G are parameters that are more

related to the enzyme complex used than to the charac-

teristics of the substrate.

Conclusions

The methodology of parameters estimation using genetic

algorithms has been shown to present good performance

and the model was able to predict the data set of glucose

concentrations in low and high levels of enzyme loadings

with one set of parameters. The analysis of the estimated

parameters confirms that alkaline hydrogen peroxide pre-

treatment is more efficient than the pretreatment with

phosphoric acid followed by delignification with sodium

hydroxide. The kinetic parameters obtained for hydrolysis

of alkaline hydrogen peroxide pretreated bagasse differed

drastically of the obtained using phosphoric acid ? NaOH

delignification pretreated bagasse. Thus, the re-estimation

procedure was necessary to represent accurately experi-

mental data when there are changes in the pretreatments

conditions. The same methodology can be used to account

for fluctuations in the composition/structure of bagasse

from different harvests.

Acknowledgments The authors acknowledge Fundacao de Amparo

a Pesquisa do Estado de Sao Paulo (FAPESP) process number

2009/02424-7 and Conselho Nacional de Desenvolvimento Cientıfico

e Tecnologico (CNPq) for financial support.

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study of kinetic parameters in a mechanistic model for enzymatic hydrolysis of sugarcane bagasse...

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