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Mixing Effects on the Kinetics of Enzymatic Hydrolysis of Avicel for Batch Production of Cellulosic Ethanol Ashwin Gaikwad and Saikat Chakraborty* Department of Chemical Engineering, Indian Institute of Technology − Kharagpur, Kharagpur 721302, India ABSTRACT: This article presents a tightly coupled experimental and theoretical study to explore the effects of mixing and mass transfer on the kinetics and dynamics of cellulase-mediated cellulose (Avicel) hydrolysis for bioethanol production in batch reactors. The kinetic parameters (KM and VMax) for the three enzymes (endoglucanase, exoglucanase, β-glucosidase) that constitute cellulase are determined at various mixing speeds: 0 (no mixing), 40, 80, and 150 rpm (high mixing). The experimental values of KM and VMax are fitted to algebraic expressions that quantify them as functions of mixing speed, and that, in the asymptotic limit of complete mixing, give their purely kinetic values (without any mass transfer disguise). The glucose and reducing sugar yields as well as the degree of polymerization (DP) for Avicel are measured at all four mixing speeds for 45 h of incubation. Maximum yields of 76% for glucose and 87% for reducing sugar are obtained at no mixing condition (i.e., mass transfer controlled regime), and the DP was found to reduce from 300 to 41. An unsteady-state multistep three-enzyme kinetic model incorporating competitive and noncompetitive inhibition caused by the products glucose (monomer) and cellobiose (dimer) is simulated using the experimentally obtained KM and VMax values at various mixing speeds, and our model simulations are validated with our experiments. Our analysis shows that the KM and VMax for the three cellulase enzymes remain mass-transfer disguised kinetic parameters even at high mixing speeds, and we quantify the purely kinetic values they attain in the limit of perfect mixing. Our experiments and simulations show that lower mixing speeds increase glucose and reducing sugar yields and decrease DP by preventing the products glucose and cellobiose from coming in contact with the active sites of the cellulase, thus reducing product inhibition, an observation that may significantly reduce the energy costs for bioethanol production.

■

INTRODUCTION Cellulosic bioethanol has been gaining prominence in the recent past, primarily due to the abundance of cellulosic biomass such as woody crops, agricultural wastes, industrial wastes, etc. A typical lignocellulosic material consists of 40−45% cellulose, 15−25% hemicellulose, and the rest as lignin and extractives.1−3 Cellulose is a homopolysaccharide composed of β-D glucopyranose units linked together by 1−4 glycosidic bonds. Bundles of cellulose molecules are aggregated together to form a matrix of highly ordered crystalline regions that alternate with a less ordered amorphous region. The strong microfibrils structure, strong hydrogen bonds, and van der Waals interaction between the cellulose microfibrils make the cellulose highly tensile in strength and resistant to solubilization in most solvents.2 A particular bioethanol process consists of several steps starting from the collection of biomass feedstock to residue processing.3,4 After biomass collection, pretreatment of the biomass using acids, alkalis, steam, enzymes, or mechanical grinding reduces the rigidity of the crystalline fibers and increases its digestibility. Toxic compounds liberated at the end of pretreatment can be eliminated by employing detoxification/ neutralization techniques to make the reaction environment more favorable to the enzymes.3 The next step is the production of enzymes either from bacteria/fungi or from plants; however, enzymes obtained from bacteria are proved to be more efficient in converting cellulose to sugars. The separated and purified enzymes can then be utilized to catalyze cellulose hydrolysis to glucose and the fermentation of glucose to ethanol.4 The operation can be performed simultaneously, in which an engineered bacteria capable of secreting two different enzymes converts the cellulose to glucose and glucose to bioethanol.5 © 2013 American Chemical Society

Cellulase production from bacteria may be faster than that from fungi because of the higher growth rate of the former, for example, a new consortium of hyperthermophillic Archaea,6 but for now Trichoderma reesei enzymes are most used for lignocellulosic biomass hydrolysis. The most challenging step in the bioethanol production process is the cellulase-mediated enzymatic hydrolysis of cellulose. There are certain barriers in the process that can affect the functionality of the enzymes such as the prolonged time period required to break down the biomass, which, in turn, deactivates the enzymes by prolonged exposure to mechanical shaking, or thermal and chemical actions.7,8 During the chemical action, inhibitory compounds are released into the reaction environment, which negatively affects enzyme activity, thus slowing the reaction and reducing product yield. Furthermore, irreversible adsorption of cellulases on the nonpolysaccharide components of the biomass lowers enzyme activity. On the other hand, abundant and easy accessibility of cellulosic sites is also required for the enzymatic attack. For this, efficient, costeffective, and environment-friendly pretreatment processes are needed. Detailed knowledge of the multistep reaction scheme, inhibition agents, and optimum reaction conditions such as mixing speed, enzyme loading, temperature, pH, etc., is necessary for the design and construction of reactors for the enzymatic hydrolysis of cellulose.9,10 Received: Revised: Accepted: Published: 3988

October 24, 2011 February 9, 2013 February 20, 2013 February 20, 2013 dx.doi.org/10.1021/ie301234b | Ind. Eng. Chem. Res. 2013, 52, 3988−3999

Industrial & Engineering Chemistry Research

Article

and inert ends, and contribution of crystalline and amorphous regions in enzymatic hydrolysis of cellulose have been discussed in some of the existing models, most of the models were validated using the pure kinetic data (without accounting for mass transfer effects) available in the literature. However, as will be shown in this article, mass transfer plays an important role in influencing the reaction kinetics and the product yield. Sinitsyn and coworkers16 have studied enzymatic hydrolysis of cellulose in a stirred, batch reactor and discussed the modeling results based on the kinetic parameter obtained in the experiments, accounting for mass transfer effects. In our previous work, we have discussed through model simulations how mixing limitations can offset inhibition, and increase yield as well as the rate of formation of desired product when the cellulose hydrolysis is performed in CSTRs.32 We also suggested a novel reactor configuration of two CSTRs in series (with reasonable macromixing) with minimal local mixing/ micromixing in each tank and glucose removal at the exit of the first tank as the optimum reactor configuration for maximizing glucose yield.32 We also performed modeling studies on cellulase-mediated hydrolysis of cellulose in batch reactors, in which enzyme diffusivity, two-site binding of the substrate, both solid and the soluble part of the substrate, degree of synergy between the enzymes, etc., were considered.33 This article presents a tightly coupled experimental and theoretical study on the effect of mixing on Avicel hydrolysis in batch reactors. Following is the stepwise strategy we follow in this work: (i) We experimentally measured Michaelis−Menten kinetic parameters (KM and VMax) of endoglucanase, exoglucanase, and β-glucosidase, the three enzymes that constitute cellulase. We recognize that the parameters (KM and VMax) we measure are not pure kinetic parameters but mass transfer disguised kinetic parameters, which are influenced by the mixing speed. Therefore, we obtain the KM and VMax for the three enzymes (endoglucanase, exoglucanase, and β-glucosidase) at varying mixing speeds (0, 40, 80, 150 rpm). (ii) We fit our experimental data to obtain algebraic relations for KM and VMax as a function of mixing speed for each of the three enzymes. We use these relations to find the asymptotic values of KM and VMax in the limit of complete mixing where KM and VMax become pure kinetic parameters, unaffected by mass transfer. (iii) We present a three-enzyme kinetic model for predicting the dynamics of glucose yield, reducing sugar yield and degree of polymerization of the cellulose. We simulate this model to obtain the above-mentioned quantities as a function of time at various mixing speeds (0, 40, 80, 150 rpm). For this simulation, we use the KM and VMax (mass transfer disguised kinetic parameters) obtained in (i) at these respective rpms. We also simulate the effect of inhibition (competitive vs noncompetitive) on the yield of glucose, reducing sugar and DP. (d) We experimentally obtain the dynamics of glucose, reducing sugar yield and the degree of polymerization. We validate our model simulations with the help of our experimentally obtained data, and explore the reasons for the counterintuitive behavior of the system, which we observe. This article is organized as follows: a detailed presentation of the three-enzyme model is followed by the description of the

The process parameters, conditions, and interdependencies between the cellulose−cellulase systems have been investigated by several authors in great detail.11−14 Cellulosic hydrolysis can be done by using either acids or alkalis (chemical method) or enzymes. The enzymatic method is often preferred because it offers mild reaction conditions (temperature ≈ 50 °C and pH 4− 5), energy efficiency, and less hazardous environmental conditions.7,13−16 The process of hydrolysis depends significantly on the physical nature of the substrate, that is, substrates with lignin content (high or low), moisture content,17 particle size,18 crystallinity, etc. Furthermore, the process also depends on the enzyme purity, enzyme concentration, reaction time, degree of mixing, etc.19 Cellulosic substrates are made up of crystalline and amorphous regions of microfibrils, and the crystalline part severely affects the enzymatic hydrolysis.20 There is a rule given by Kyosov for the rate of enzymatic hydrolysis of crystalline cellulose: the better is the adsorption, the better is the catalysis.21 Thus, it is imperative that the adsorption of enzymes on the cellulosic surface plays an important role in the efficiency of enzymatic hydrolysis of cellulose. The crystallinity can be reduced by treating the substrate with phosphoric acid, ionic liquids, etc., or by treating it mechanically using ball mill or radiations. Recently, Kamiya and his co-workers22 have shown that there is a more than 2-fold increase in glucose yield when the substrate is treated with aqueous ionic liquid solution (IL to water ratio was taken as 1:4 (v/v)). Some of the authors have studied the reaction of cellulase on pure cellulosic substrates such as microcrystalline cellulose (Avicel PH-101, 102, 105), cotton, CMC, noncrystalline cellulose (NCC) to establish a relationship between the moisture content (4−10%), temperature (20−90 °C), and glucose yield.11,17,22 Mixing is an important process design factor that can influence cellulosic hydrolysis in several ways. Because of the heterogeneity of the hydrolysis reaction environment in which a liquid enzyme acts on a dissolved substrate, adequate mixing is required to ensure sufficient contact between the reactants, thus enhancing the mass transfer rates within the reaction vessel. However, it has been reported that excessive mixing can deactivate the enzyme and reduce the conversion and product yield, due to the shear generated by the mixer and the entrapment of air bubbles into the medium at the air−liquid surface.23,24 It has also been reported that excessively high mixing speeds (>200 rpm) lowered the extent of cellulose conversion for Avicel and paper pulp, while moderate mixing speeds (100−200 rpm) offer a good combination of fast initial hydrolysis rates and high glucose yield. It has been shown that while a mixing speed as high as 340 rpm enhanced the conversion of steam pretreated spruce wood, even higher mixing speeds (340−500 rpm) only increased the initial rate of hydrolysis and not the final conversion yield.25 Therefore, one way of improving the economy of the overall process is to determine the optimum level of mixing speed, so as to reduce the extent of shear induced enzyme deactivation and lower the mixing energy costs. Apart from shear effects, factors such as product inhibition, pH, and temperature also play significant roles in cellulose hydrolysis.26 Several models are available in the literature on cellulasecatalyzed cellulose hydrolysis,14,27−31 many of which are based on simplified representations of the cellulases and/or the substrate. The activities of the different cellulase enzymes are commonly lumped together and represented as a single enzyme concentration to reduce the complexity of the problem.31 While the cellulosic structure, soluble part and insoluble part, reactive 3989

dx.doi.org/10.1021/ie301234b | Ind. Eng. Chem. Res. 2013, 52, 3988−3999


Article k G1

experimental protocols used for measurement of kinetic data (KM and VMax) for endo-, exo-, and β-glucosidase, as well as those for measuring yields of glucose, reducing sugar and the degree of polymerization. Presentation and discussion of the results follow.

Eendo·Ci + C1 ← → (Eendo·C1·Ci)

■

k f1

Eendo·C1 + Ci ↔ (Eendo·C1·Ci)

k f1

k C1

Eendo·Ci + C2 ← → (Eendo·C2·Ci) k f1

Eendo·C2 + Ci ↔ (Eendo·C2·Ci)

k f2

Here, k1, kf1, kb1, kG1, kG2, kC1, and kC2 are the rate constants for Eendo and are independent of the degree of polymerization i. Cj and Ci−j are the end products with degree of polymerization i and (i − j), respectively. (Eendo·C i), (E endo·C 1), (Eendo·C 2), (Eendo·C1·Ci), and (Eendo·C2·Ci) are the end-product complexes. Applying continuity equation to species Ci for the above set of reactions 5−11 in a batch reactor, we get d[Ci] = −k f1(i − 1)[Eendo]f [Ci] + k b1[Eendo·Ci] dt ∞ [Eendo·Cj] − k f1(i − 1)[Eendo·C1][Ci] + 2k1 ∑ j = i + 1 (j − 1) + k b1[Eendo·C1·Ci] − k f1(i − 1)[Eendo·C2][Ci] + k b1[Eendo·C2·Ci]

(1)

∞

[Eendo] = [Eendo]f +

k f1

i=1

+

(2)

k C2

k G2

(11)

d[Eendo·Ci] = k f1(i − 1)[Eendo]f [Ci] − (k b1 + k1) dt [Eendo·Ci] =0

(3)

d[Eendo·C1] = k G1[Eendo]f [C1] − k G2[Eendo·C1] = 0 dt

(12)

(13)

(4)

d[Eendo·C2] = k C1[Eendo]f [C2] − k C2[Eendo·C2] = 0 dt

k G1

Eendo + C1 ← → (Eendo·C1)

i=3

Assuming quasi-steady state for intermediate species, we can write

k C1

Eendo + C2 ← → (Eendo·C2)

∞

∑ [Eendo·C1·Ci] + ∑ [Eendo·C2·Ci] i=3

k1

k b1

∑ [Eendo·Ci]

∞

where kf2 and kb2 are the forward and backward rate constants, respectively, for the formation of the enzyme−substrate complex, k2 is the rate constant for exoglucanase (Eexo), and CP2 is the product of hydrolysis. Noncompetitive Inhibition. For noncompetitive inhibition, the proposed reaction mechanism is given as Eendo + Ci ↔ (Eendo·Ci) → Eendo + Cj + Ci − j

(10)

where [Eendo]f denotes the free endoglucanase concentration. Note that [Ci] ≫ [Eendo]. The factor 2/(j − 1) on the right-hand side denotes the equal probability of chain of length j to break into particular smaller fraction i. The factor 2 accounts for two cases: (i) when i is broken down into the same fraction j and (i − j), and (ii) when the fractions are (i − j) and j. (i − 1) denotes the number of bonds that are available for breakage in cellulose chain of size i. Therefore, it is assumed that the rate and probability of breaking of a chain into smaller chains of particular size are equal to any other size. Because the total amount of enzyme is conserved, we have

k2

k b2

(9)

k b1

where kf1 and kb1 are the forward and backward rate constants, respectively, for the formation of the enzyme−substrate complex, k1 is the rate constant for endoglucanase (Eendo), and CP1 is the product of hydrolysis. Action of Exoglucanase (Eexo). Eexo reacts with cellulose as Ci + Eexo ↔ Eexo·Ci → Eexo + CP2

(8)

k C2

k1

k b1

(7)

k b1

MATHEMATICAL MODEL Three-Enzyme Kinetic Model for Cellulose Hydrolysis in Batch Reactors. Cellulases from fungal origin are best suited for enzymatic hydrolysis of cellulose. Among these, Trichoderma reesei, Trichoderma viride, Trichoderma koningii, and Sporotrichum pulverulentum are the major contributors of cellulase. Trichoderma viride produces a multicomponent enzyme system, including the 1,4-β-D-glucan glucanohydrolase (endo I; II; III; IV; V; VII), 1,4-β-D-glucan cellobiohydrolase (exo I; II; III), and β-D-glucoside glucohydrolase (β-glucosidase). A combination of these three types of enzymes is necessary for complete hydrolysis of crystalline cellulose. Endoglucanase and exoglucanase are known to act synergistically in hydrolyzing cellulose, while βglucosidase converts cellobiose, a strong inhibitor of both endoglucanase and exoglucanase.8 In cellulose hydrolysis, endoglucanase cuts the cellulosic chains randomly at rapid rate, while exoglucanase attacks at both the reducing and the nonreducing ends of the cellulosic chains to liberate cellobiose (dimer). At the end, β-glucosidase reacts with cellobiose to split it into two glucose molecules. It is important to note that the products of hydrolysis are mainly glucose and cellobiose, both of which inhibit the system either competitively or noncompetitively.9,14,33 Action of Endoglucanase (Eendo). Eendo reacts with substrate (Ci) and forms enzyme−substrate complex.14,27 The depolymerization of cellulosic substrate changes its degree of polymerization, DPi (i.e., a cellulose of chain length i) to fragments of cellulosic chain (lesser in chain length than the original, i.e., i′ and i″) DPi′ and DPi″ (where DPi = DPi′ + DPi″), and then exoglucanase (Eexo) randomly breaks glucosidic bonds to give cellobiose (dimer) and finally glucose (C1). The reaction is given as Ci + Eendo ↔ Eendo·Ci → Eendo + CP1

(6)

k G2

(5)

(14) 3990



Article ∞

d[Eendo·C1·Ci] = {k G1[Eendo·Ci][C1] − k G2[Eendo·C1·Ci]} dt

V1Max(2 ∑ j = i + 1 Cj − (i − 1)Ci) d[Ci] = C ∞ dt (KM1 + ∑i = 2 (i − 1)Ci) 1 + K 1 +

(

+ {k f1(i − 1)[Eendo·C1][Ci] − k b1[Eendo·C1·Ci]} = 0 (15)

C1

(KM2 +

,

∞ ∑i = 2

(

G2

(

)

,

∞

(

(19)

d[Ci] = dt

(21)

+

Applying continuity equation for the reactions in eqs 19−21 and solving for C2, we get

(

G3

)

C2 K C1

)

C1 K G2

+

)

C2 K C2

C1 K G3

)

(25)

∞

(K (1 +

C1 K G1

+

C2 K C1

)+∑

∞ i=2

V2Max(Ci + 2 − Ci)

( (

KM2 1 +

C1 K G2

+

C2 K C2

)

∞

+ ∑i = 2 Ci

)

(i − 1)Ci ,

)

i>2 (26)

where

i≤2 (22)

KM1 =

where KM3 =

G1

V1Max(2 ∑ j = i + 1 Cj − (i − 1)Ci) M1

,

(24)

Competitive Inhibition. For the case of competitive inhibition, we consider that only C1 and C2 inhibit the enzyme, and no enzyme−inhibitor−substrate complex is formed. Therefore, only eqs 3, 4, 5, and 10 are considered for derivation, and eqs 6−9 are not considered for endo- and exo- expressions, whereas for β-glucosidase only eqs 19 and 20 have been considered. Following a procedure similar to the case of noncompetitive inhibition, we obtain

k G3

k 3[Eβ‐G](C2) d[Ci] = C dt (KM3 + C2) 1 + K 1

(

(KM3 + C2) 1 +

(20)

k ′G3

)

V3Max C2

k G3

Eβ‐G·C2 + C1 ←→ (Eβ‐GC2·C1)

)

C2 K C2

V2Max(C4 − C2)

−

k3

k ′G3

C1 K G3

(KM2 + ∑i = 2 Ci) 1 +

i>2

For β-glucosidase, we assume the reaction mechanism to be

Eβ‐G + C1 ←→ (Eβ‐G·C1)

+

(

k + k1 k k k = b2 , K 2dis = b2 , K G2 = G2 , K C2 = C2 k f2 k f2 k G1 k C1

k ′G3

)

∞

where KM2 is the Michealis−Menten constant of exoglucanase and is given by

k G3

C1 K G2

V1Max(2 ∑ j = i + 1 Cj) d[C2] = C ∞ dt (KM1 + ∑i = 2 (i − 1)Ci) 1 + K 1 + +

Eβ‐G + C2 ←→ (Eβ‐G·C2) → 2C1 + Eβ‐G

C2 K C1

For cellobiose (dimer, i.e., i = 2):

(18)

KM2

(

Ci) 1 +

(KM3 + C2) 1 +

For exoglucanase, considering eq 2 in place of eq 1 and replacing Eendo by Eexo in eqs 3−9 and following the procedure similar to that of endoglucanase, we obtain C2 K C2

G1

V3Max C2

+

k b1 + k1 k k , K G1 = G2 , K C1 = C2 k f1 k G1 k C1

k 2[Eexo](Ci + 2 − Ci) d[Ci] = C ∞ dt (KM2 + ∑i = 2 Ci) 1 + K 1 +

(23)

V2Max C3

+

where KM1 =

i>2

,

(

(17)

i>2

)

C2 K C2

V1Max(2 ∑ j = i + 1 Cj) d[C1] = C ∞ dt (KM1 + ∑i = 2 (i − 1)Ci) 1 + K 1 +

∞

G1

+

)

∞

It may be mentioned that because each of the reversible reactions above (eqs 4−9) attains equilibrium, the terms inside each of the curly brackets in eqs 15 and 16 equal zero. From eqs 10−16, we get

)

C1 K G2

C2 K C1

where V1Max = k1[Eendo], V2Max = k2[Eexo], and V3Max = k3[Eβ‑G]. For glucose (i.e., i = 1):

(16)

(

(

∞

(KM2 + ∑i = 2 Ci) 1 +

+ {k f1(i − 1)[Eendo·C2][Ci] − k b1[Eendo·C2·Ci]} = 0

k1[Eendo](2 ∑ j = i + 1 Cj − (i − 1)Ci) d[Ci] = C C ∞ dt (KM1 + ∑i = 2 (i − 1)Ci) 1 + K 1 + K 2

V2Max(Ci + 2 − Ci)

+

d[Eendo·C2·Ci] = {k C1[Eendo·Ci][C2] − k C2[Eendo·C2·Ci]} dt

G1

k 3 + k′G3 k′ , K G3 = G3 k G3 k G3

=

k b1 + k1 k + k2 k , KM2 = b2 , K G1 = G2 , K C1 k f1 kf 2 k G1

k C2 k C1

and V1Max, V2Max, and V3Max are the same as in eq 23. For glucose (i.e., i = 1):

Combining all three expressions in eqs 17, 18, and 22 for endo-, exo-, and β-glucosidase, we can write 3991


Industrial & Engineering Chemistry Research ∞

(K (1 +

C1 K G1

M1

+

C2 K C1

)+∑

∞ i=2

(i − 1)Ci

)

N0

V2Max C3

( (

KM2 1 +

+

and, for the case of competitive inhibition, is given as

V1Max(2 ∑ j = i + 1 Cj)

d[C1] = dt +

Article

C1 K G2

+

C2 K C2

)

∞

+ ∑i = 2 Ci

)

+

(

) + C ⎞⎠

C1 K G3

2

(27) ∞

V1Max(2 ∑ j = i + 1 Cj)

(K (1 +

C1 K G1

M1

+

C2 K C1

)+∑

∞ i=2

(i − 1)Ci

)

V2Max(C4 − C2)

(K (1 + M2

−

+

C1 K G2

+

C2 K C2

)+∑

∞ i=2

Ci

)

V3Max C2

⎛ ⎜K 1+ ⎝ M3

(

C1 K G3

) + C ⎞⎠ 2

⎟

(28)

Degree of Polymerization. The degree of polymerization (DP) of the cellulose can be represented as number−average (DPn), weight-average (DPw), or viscosity-average (DPv). The number-average degree of polymerization (DPn) can be defined as the number average molecular weight of total monomers to the molecular weight of single monomer (i.e., 162 for anhydroglucose). Thus, DPn can be given as ∞

DPn =

∑i = 1 (i[Ci]) ∞ ∑i = 1 [Ci]

=

N0 ∞ ∑i = 1 [Ci]

(29)

∑i=1∞(i[Ci])

where N0 = = constant. Assuming that each association of cellulases with the cellulose fragments is the same, the rate of change of number average degree of polymerization for the case of noncompetitive inhibition is given as N0

d⎛ 1 ⎞ d d ⎟ = (∑ [Ci]) = (∑ {(i − 1)[Ci]}) ⎜ dt ⎝ DPn ⎠ dt i = 1 dt i = 1 =

k1[Eendo]S W k 2[Eexo]SM + (KM1 + S W )Ih1 (KM2 + SM)Ih2 k 3[Eβ‐G][C2] + (KM3 + [C2])Ih3 (30)

where ∞

SW =

∑ {(i − 1)[Ci]} i=3 ∞

SM =

∑ [Ci] i=3

Ih1 = (1 + [C1]/K G1 + [C2]/K C1) Ih2 = (1 + [C1]/K G2 + [C2]/K C2) Ih3 = (1 + [C1]/K G3)

(KM3 × Ih3 + C2)

(32)

EXPERIMENTAL ANALYSIS Substrate (Cellulose). Commercially available purified microcrystalline cellulose (MCC), Avicel PH-101 with average particle size of 50 μm and particle density of 0.600 g/cm3, purchased from Sigma Aldrich Co., U.S., was used for quantitative analysis of glucose and total reducing sugar. Enzyme. Dry solid purified cellulase enzyme with the activity of 1 U/mg of solid was purchased from HIMEDIA Laboratories, Mumbai, India, for the enzymatic saccharification of Avicel. This enzyme works with maximum activity in a pH range of 4.0−5.0 and a temperature of 40−50 °C against most cellulosic materials. The purified enzyme from Trichoderma viride contains all three components, that is, endoglucanase, exoglucanase, and βglucosidase. The activities of endo-1,4-β-D-glucanase, exo-1,4β-D-glucanase, and β-glucosidase were determined separately by hydrolysis of Avicel PH-101 at 0, 40, 80, and 150 rpm. The activities were calculated on the basis of the amount of enzyme that splits 1 μmol of D-glucoside linkages per minute during the initial period of reaction with Avicel concentration varying from 2 to 10 mg/mL at a pH of 4.8 using 50 mM sodium acetate buffer at 50 °C. Enzyme Kinetics. Experiments were performed at 0 (no mixing), 40, 80, and 150 rpm (high mixing), to determine the effects of mixing and mass transfer on the Michaelis−Menten kinetic constant (KM) and maximum reaction rate (VMax) for three cellulase components, endoglucanase, exoglucanase, and βglucosidase. Endoglucanase−Exoglucanase. This analysis assumes that there is no synergy between the enzymes and that in the first 30 min time span over which the enzyme kinetics was studied, not enough glucose and cellobiose were formed to inhibit the reaction. The kinetic constants KM and VMax were determined by using varying concentration of Avicel (0.5−1%) in 50 mM sodium acetate buffer (pH 4.8). 0.28 mL of enzyme solution (0.01%) was then added to it, and the resulting solution was incubated at 50 °C under the sterile condition. 12,34,35 Dinitrosalicylic acid (DNS) reagent was added to terminate the reaction, and the reducing sugar was measured at 540 nm.37 Samples were taken out of the reaction mixture after the first 10 min, the reaction (in the samples) was terminated by adding DNS solution, and the absorbance was measured. The rest of the reaction mixture was further incubated at 50 °C for another 20 min (i.e., 30 min from the start of the experiment), after which it was terminated using DNS. Endoglucanase first reacts with the cellulose molecules and breaks the long-chain polymer into two chain lengths, which is thus responsible for decreasing degree of polymerization of the cellulosic substrate, thereby generating new cellulosic chain ends susceptible to the exoglucanase action.38 The exoglucanases (CBH I and II) perform hydrolysis endwise in a processive manner.39−41 This processive action, including “pulling” of cellulosic chain away from the surrounding chain ends and simultaneous multiple hydrolysis reaction without dissociating from substrate, is a more difficult task than a bond hydrolysis by

⎟

For cellobiose (dimer, i.e., i = 2): d[C2] = dt

k 3[Eβ‐G]C2

■

V3Max C2

⎛ ⎜K 1+ ⎝ M3

k1[Eendo]Sw k 2[Eexo]SM d⎛ 1 ⎞ + ⎜ ⎟= dt ⎝ DPn ⎠ (KM1 × Ih1 + Sw ) (KM2 × Ih2 + SM)

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endoglucanase.42 A study of the three-dimensional structure of cellulase43 shows that the active site of exoglucanase is located at the carboxyl-terminal end of a parallel β barrel, in an enclosed tunnel through which the cellulose threads. On the basis of these observations, we assume that endoglucanase alone can act on the substrate for the first 10 min because the enclosed active site tunnel of exoglucanase is rendered practically inaccessible to the longer chain cellulose molecules until endoglucanase hydrolyzes them into smaller chains. Therefore, the reaction rate obtained in the first 10 min of incubation is from the action of endoglucanase alone, while that obtained in the following 20 min of incubation is due to the action of both endo- and exoglucanase. We measure the reaction rates (=amount of sugar obtained/ time) as a function of substrate (Avicel) concentration for the action of the endoglucanase alone (first 10 min of incubation) as well as for the combined action of endo- and exoglucanases (30 min of incubation). Using these two measurements, we obtain the reaction rate due to the action of exoglucanase alone by subtracting the reaction rate due to the action of endoglucanase alone from the reaction rate due to the combined action of endoand exoglucanases. We plot the inverse of the two reaction rates, one due to the action of endoglucanase alone, and the other due to the action of exoglucanase alone, against the inverse of substrate concentration, and the kinetic parameters VMax and KM for endoglucanase and exoglucanase were determined from the intercepts and slopes, respectively, of the corresponding plots for the two enzymes. The experiments were repeated at the four different mixing speeds mentioned above: 0 (no mixing), 40, 80, and 150 rpm (high mixing), and KM and VMax for the two enzymes were calculated at each speed to quantify the effects of mixing and mass transfer on the kinetic parameters. β-Glucosidase. Cellobiose solutions of eight different concentrations were prepared in 50 mM sodium acetate (pH 4.8) buffer, and 0.28 mL of enzyme solution (0.001%) was then added to the mixture and incubated for 30 min at 50 °C. Dinitrosalicylic acid (DNS) was then added to the incubated solution, and the reducing sugar was measured. The experiments were repeated thrice, and a plot of the inverse of reaction rate versus the inverse of substrate concentration was used to obtain the KM and VMax values at the same four mixing speeds (0, 40, 80, 150 rpm) as in the case of endo- and exoglucanases. Enzymatic Hydrolysis. For enzymatic hydrolysis, Avicel solution of 20 mg/mL was prepared in 0.1 M sodium acetate buffer (pH 5.0) and premixed in an incubator for 1 h under the sterile condition. Ten milligrams of cellulase was then added to start the reaction, and a pH of 5.0 and a temperature of 50 °C were maintained throughout the reaction for 48 h.13,16,25,36 In this experimental work, a reaction carried out in a 50 mL conical flask was considered as a batch reactor. The reaction volume of 10 mL in a 50 mL flask was kept at 0, 40, 80, and 150 rpm to examine the effects of mixing on product formation. Samples were taken out at different time intervals and analyzed by UV spectrophotometer to determine the glucose and reducing sugar yield. Reducing Sugar Activity (RSA). Samples of reaction mixture were collected at different time intervals, and 2 mL of DNS reagent was added immediately to terminate the reaction. The reducing sugar activity was measured by the procedure described in the literature.12,36,37 The samples were kept for boiling for 30 min at 100 °C, and absorbance was taken at 540 nm to determine the reducing sugar activity. Glucose Estimation. Glucose estimation was performed by glucose oxidase (GOD) and peroxidase (POD) method. In this

method, glucose oxidase converts glucose to gluconic acid along with hydrogen peroxide. In the presence of peroxidase, hydrogen peroxide oxidatively couples with 4-aminoantipyrine and phenol to produce red quinoneimine dye. The intensity of the colored complex is directly proportional to the glucose concentration in the solution. The reactions are given as GOD

β‐D glucose + O2 + H 2O ⎯⎯⎯⎯→ gluconic acid + H 2O2 (33) POD

H 2O2 + 4‐aminoantipyrine + phenol ⎯⎯⎯⎯→ red dye + H 2O (34)

Determination of Degree of Polymerization. The estimation of the degree of polymerization (DP) of cellulosic substrate is important in determining the extent of depolymerization that takes place during the course of enzymatic reaction. It also gives an idea of the relative abundance of terminal and interior β-glucosidic bonds and of substrates for endoacting and exoacting enzymes.44 The DP can be determined using different experimental techniques such as membrane osmometry, vapor pressure oscomometry, cryoscopy, ebullioscopy, size-exclusion chromatography, and reducing end concentration.27,44,45 The techniques used for DP measurement other than reducing end concentration method take a long time for sample preparation and larger volume of sample, proper drying and subsequent dissolution of volatile and corrosive chemicals, specialized instruments, and skilled manpower.44 In our experiments, we quantify the change of DP by reducing end concentration method. In this method, the total number of glycosyl monomers determined by the phenol−sulphuric acid method is divided by the total number of reducing chain ends determined by the modified 2−2′ bicinchoninate (BCA) method. Reducing End Determination by BCA Method. The BCA working solution was prepared by mixing solution A and solution B in 1:1 ratio (by volume). For solution A, 0.971 g of disodium 2,2′-bicinchoninate, 27.14 g of Na2CO3, and 12.1 g of NaHCO3 were dissolved in 500 mL of distilled water, whereas for solution B, 0.624 g of CuSO4·5H2O and 0.631 g of L-serine were dissolved in 500 mL of distilled water. Both reagents were stored at 4 °C, kept separately, and can be used for at least a month. The samples taken at various intervals of time during the enzymatic hydrolysis of Avicel are mixed with BCA working solution in equal amount and incubated at 75 °C for 30 min in moderate shaking condition to avoid the precipitation of the cellulose. After the tubes were cooled to room temperature, the absorbance was measured at 560 nm, and the glucose concentration was measured using a glucose standard plot prepared in the range 0−10 mM. Glucosyl Monomer Determination by Phenol−Sulphuric Acid Method. This method was developed for the determination of glucosyl monomer concentration for both soluble and insoluble glucan substrate.7 A suitably diluted sample of 1 mL was taken into the 5 mL vial. One milliliter of phenol reagent (5% v/v) was then added to the vial followed by 3 mL of concentrated sulphuric acid. The solution was then mixed and incubated for 5 min at 90 °C in a static water bath. The resulting solution was cooled to room temperature, and the absorbance was measured at 490 nm. A standard plot of glucose with concentration ranging from 0 to 10 mM was made for determining the final concentration of glucosyl monomer. 3993



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RESULTS AND DISCUSSION Enzyme Kinetics. Figures 1−4 show the method of determination of V Max and K M for endoglucanase and

Figure 3. Plot of inverse of reaction rate versus inverse of substrate concentration at 80 rpm for estimation of kinetic parameters of endoand exoglucanase. Figure 1. Plot of inverse of reaction rate versus inverse of substrate concentration for no mixing (0 rpm) for estimation of kinetic parameters of endo- and exoglucanase.

Figure 4. Plot of inverse of reaction rate versus inverse of substrate concentration at 150 rpm (high mixing) for estimation of kinetic parameters of endo- and exoglucanase. Figure 2. Plot of inverse of reaction rate versus inverse of substrate concentration at 40 rpm for estimation of kinetic parameters of endoand exoglucanase.

exoglucanase at the mixing speeds of 0, 40, 80, and 150 rpm using the method outlined in the Experimental Analysis section, that is, by plotting the inverse of the reaction rate against the inverse of Avicel concentration. As may be observed from each of these figures, the measured reaction rate under the combined action of endo- and exoglucanase is quite higher than that measured under the action of endoglucanase alone; this validates our initial assumption that endoglucanase alone acts on Avicel upon the initiation of the reaction (because there are very few broken chains at the start of the reaction for exoglucanase to act upon), while both endo- and exoglucanases act on the substrate as the reaction progresses. Figure 5 shows the plot of the inverse of rate against the inverse of Avicel concentration under the action of β-glucosidase alone at the mixing speeds of 0, 40, 80, and 150 rpm. The VMax and KM for the respective enzymes at the corresponding mixing speeds are obtained from the intercepts

Figure 5. Plot of inverse of reaction rate versus inverse of substrate concentration for estimation of kinetic parameters of β-glucosidase.

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Table 1. Experimental Values of Kinetic Constants (KM and VMax) for Endoglucanase, Exoglucanase, and β-Glucosidase at Different rpm’s endoglucanase

β-glucosidase

exoglucanase

rpm

KM (mg/mL)

VMax (μg/mL/min)

KM (mg/mL)

VMax (μg/mL/min)

KM (mg/mL)

VMax (μg/mL/min)

0 40 80 150

16.94 15.08 13.15 11.39

14.59 7.98 6.60 4.42

60.00 42.80 33.60 18.86

162.00 50.00 28.57 18.18

0.44 0.32 0.24 0.22

6.38 4.47 3.39 2.62

and slopes, respectively, in Figures 1−5. The values of these constants are presented in Table 1. The experimental values of VMax and KM at four different rpm’s (0, 40, 80, 150) were plotted against the rpm, as can be seen from Figure 6 for endoglucanase, and algebraic expressions were

Figure 7. Effective reaction rate constant at different mixing speeds (in rpm) for endoglucanase, exoglucanase, and β-glucosidase (inset).

can be seen at 350 rpm. As shown in Figure 7, in the limit of complete mixing (>700 rpm), all of the kinetic parameters of the system attain their respective asymptotic limits, which are their pure kinetic values in the absence of any mass transfer influence/ disguise. The asymptotic values of keff in the limit of perfect mixing (i.e., pure kinetically controlled regime) for the three enzymes have been listed in Table 2. Experiment−Model Comparison of the Dynamics of Cellulose Hydrolysis. Experiments were conducted in a batch reactor of 50 mL volume at four different mixing speeds (0, 40, 80, 150 rpm) to study the effect of mixing on the dynamics of cellulose hydrolysis. Figure 8 shows the dynamics of glucose yield for the Avicel−cellulase system at the four different mixing speeds, and Figures 9 and 10 present the dynamics of reducing sugar production for the same system. These figures also compare our experimental results (points) with our model predictions (solid lines). It may be mentioned that while the experimental results were obtained by measuring the increase of glucose and reducing sugar concentration with time using the protocols described above, the model predictions were obtained by simulating our three-enzyme kinetic model (eqs 10−27) using the VMax and KM values for the three enzymes measured at different mixing speeds, as shown in Figures 1−5. The inhibition constants were taken to be KG1 = KG2 = 2KG3 = 1.6 mmol/mL and KC1 = KC2 = 1.2 mmol/mL for competitive inhibition, and KG1 = KG2 = 2KG3 = 2.5 mmol/mL and KC1= KC2 = 2.0 mmol/mL for noncompetitive inhibition, which are of the same order of magnitude as those experimentally reported in the literature for similar enzyme−substrate pairs.41−43 Figures 8−10 show the effect of mixing on glucose and reducing sugar yields, obtained by varying the speeds of agitation (R) from 0 to 150 rpm. As may be noticed from Figure 8, the conversion of Avicel to glucose was found to increase from 56%

Figure 6. Exponential decay of KM and VMax with RPM for endoglucanase.

developed for all three enzymes to quantify the effect of mixing on the kinetic parameters. Table 2 shows the three different Table 2. Expressions for Evaluating Kinetic Parameters for Endoglucanase, Exoglucanase, and β-Glucosidase and Limiting Values of the Effective Rate Constant, keff (VMax/KM) V

enzyme

VMax (μg/mL/min)

KM (mg/mL)

endo-

4.4 + 10.11*exp(−R/ 42.98) 19 + 143*exp(−R/ 27)

8.01 + 8.98*exp(−R/ 151.41) 3.17 + 56.38*exp(−R/ 119.75) 0.2 + 0.54*exp(−R/ 51.60)

exoβ-G

2.19 + 4.18*exp(−R/ 64.82)

keff = Kmax limiting M (min)−1 0.549 × 10−3 5.99 × 10−3 10.95 × 10−3

expressions for endo-, exo-, and β-glucosidase for both VMax and KM as a function of the mixing speed “R” (in rpm). These algebraic expressions were then used to calculate the effective kinetic constant keff (=VMax/KM). Figure 7 shows how the effective kinetic constant keff increases with increasing mixing speed. As the mixing speed increases, mass transfer/mixing limitations in the system decrease, resulting in an increase of the mass transfer disguised effective kinetic constant keff. At an rpm of 700, a point is reached where the slope of the curve is almost negligible and becomes saturated for endoglucanase and exoglucanase, whereas for β-glucosidase the saturation value 3995



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Figure 8. Comparison of experimental and model simulation (for competitive inhibition) results for glucose production in enzymatic hydrolysis of Avicel.

Figure 10. Comparison of experimental and model simulation (for noncompetitive inhibition) results for reducing sugar activity (RSA) in enzymatic hydrolysis of Avicel.

rpm) giving the highest yield. This may be attributed to the fact that higher mixing resistance increases product yield by preventing the two inhibitors, glucose and cellobiose,46 from coming in molecular contact with the enzymes and the substrates and by reducing inhibition. In other words, the more is the local mixing in the reactor, the easier it is for the inhibitor to diffuse and bind to the active sites of the enzymes, forming enzyme− inhibitor/enzyme−inhibitor−substrate complexes (depending on whether the inhibition is competitive or noncompetitive) that, in turn, decelerate the reaction rate by leaving fewer cellulase active sites available to the cellulose (substrate) molecules to bind. Close inspection of Figures 9 and 10 reveals that the inhibition effects start dominating the overall reaction after 3 h of reaction time, following which the rate of product formation reduced significantly. The change of the degree of polymerization (DP) with the progress of the reaction (45 h) was also studied for Avicel PH101 (concn 20 mg/mL) with an initial DP of 300. Figure 11 shows the decrease in DP with time for competitive inhibition, obtained through simulation and experimental results obtained at 0, 40, 80, and 150 rpm. For 45 h of incubation of Avicel at 50 °C, DP reaches 41, 44, 46, and 50 for 0, 40, 80, and 150 rpm, respectively. Thus, the trend discussed above continues here: lower mixing facilitates the depolymerization process by reducing the inhibition, and the degradation of C-300 polymer was found to be higher at lower rpm, which also indicates that a larger number of glucosidic bonds were broken into smaller fragments at lower mixing rate. Effect of Inhibition Type. As mentioned before, both of the products glucose and cellobiose inhibit the cellulose hydrolysis process.47 Expressions for both competitive and noncompetitive inhibition have been derived (eqs 10−25), and simulated results in Figures 12 and 13 compare the mixing effects on inhibition type (competitive vs noncompetitive) for reducing sugar production and DP, respectively. As may be observed from each of the figures, the mixing effects are more significant for noncompetitive inhibition than for competitive inhibition. It may be noted from eqs 23 and 26 (for RSA) and eqs 30 and 32 (for

Figure 9. Comparison of experimental and model simulation (for competitive inhibition) results for reducing sugar activity (RSA) in enzymatic hydrolysis of Avicel.

at high mixing (150 rpm) to 76% at no mixing (0 rpm). The reducing sugar activity (RSA) was measured as a mixture of sugar (C1, C2...C6), and Figure 9 shows that RSA was found to decrease from 17.5 mg/mL at no mixing to 10.7 mg/mL at high mixing after 45 h of reaction. As may be observed from Figures 9 and 10, at high mixing speed, the initial rate of reaction was high (3.844 × 10−4 mmol/min for RSA) because of the large number of empty sites available for the enzymes at the start of the reaction. As may be observed from Figures 8−10, our model simulations (solid lines) match reasonably well with our experiments (points), both qualitatively as well quantitatively. It may be noted that our experiments as well as our model simulations for competitive and noncompetitive inhibition consistently show the same trend: as mixing limitations increase (i.e., mixing speed decreases), both glucose and reducing sugar yields increase, thus no mixing (0 3996



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Figure 13. Comparison of model simulations for temporal change of degree of polymerization (DP) of C-300 polymer (Avicel) for competitive and noncompetitive inhibition. Figure 11. Comparison of experimental and model simulation (for competitive inhibition) results of temporal change of degree of polymerization DP for C-300 polymer (Avicel).

Figure 13 shows the monotonic decrease in DP for both competitive and noncompetitive inhibition. In case of Avicel PH101, the initial DP was 300, which then decreased approximately up to 40 for competitive inhibition and 66 for noncompetitive inhibition at no mixing (0 rpm), and to 64 for competitive inhibition and 156 for noncompetitive inhibition at high mixing (150 rpm), after 50 h of reaction. This reiterates our previous observation that more sugar was formed from the degradation of C-300 polymer after 50 h of reaction for competitive inhibition as compared to that for noncompetitive inhibition. Further reduction in DP and hence higher conversion and yield can be achieved through pretreatment of the substrate, which opens the fibers for enzymatic attack.48

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CONCLUSION This work helps us understand how local mixing affects the kinetics and dynamics of cellulase-catalyzed cellulose hydrolysis in batch reactors. We show that under most practical circumstances, the Michaelis−Menten constants VMax and KM of each of the three cellulase enzymes, endoglucanase, exoglucanase, and β-glucosidase, are mixing-disguised kinetic parameters that attain their pure kinetic values only in the asymptotic limit of complete mixing. As may be intuited, the effective kinetic constant keff (=VMax/KM) increases monotonically as the mixing speed in the reactor increases and saturates to a pure kinetic asymptote (unaffected by mass transfer limitations) in the limit of perfect mixing. The effects of mixing on the yields of glucose and reducing sugar and on the temporal change of the degree of polymerization (DP) of the cellulose polymer are, however, interestingly counterintuitive: as mixing speed decreases, product yield increases and DP decreases. Increased mixing resistances in the reactor increase product yield by preventing the two inhibitors, glucose and cellobiose, from diffusing and binding to the active sites of the enzymes, forming enzyme−inhibitor/enzyme−inhibitor−substrate complexes, thus reducing product inhibition and accelerating the reaction. Hence, we find that the cellulase-catalyzed hydrolysis of Avicel gives maximum product yield when performed with no local mixing (at 0 rpm) in the reactor, an observation that when validated in large-scale reactors will significantly reduce the energy costs for cellulosic ethanol production via enzymatic routes.

Figure 12. Comparison of model simulations for reducing sugar activity (RSA) for competitive and noncompetitive inhibition in enzymatic hydrolysis of Avicel.

DP) that the denominator in each of the terms for the case of noncompetitive inhibition is larger than their respective counterparts in competitive inhibition. In other words, noncompetitive inhibition involves the formation of the enzyme− inhibitor as well as the enzyme−inhibitor−substrate complexes as opposed to competitive inhibition that involves the formation of enzyme−inhibitor complexes alone. It may be noted that lower mixing prevents both the enzymes and the substrates from coming in molecular contact with the inhibitors, thus reducing the formation of both the enzyme−inhibitor as well as the enzyme−inhibitor−substrate complexes. Therefore, noncompetitive inhibition appears to be more sensitive to local mixing than competitive inhibition. The addition of extra substrate will help reduce the inhibition (particularly for competitive inhibition) and increase the sugar production rate. 3997



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It may be mentioned that the cellulase kinetics observed here with Avicel as a substrate may not be quantitatively the same when applied to a complex lignocellulosic biomass, which has traces of lignin and hemicellulose or xylooligosaccharydes, depending on the pretreatment. Higher solid loading49,50 may also influence the quantitative nature that the effect mixing has on the enzyme kinetics. However, the qualitative relationship between enzyme kinetics and reactor mixing is expected to remain the same, irrespective of the composition or the loading of the substrate. This work hopes to provide a tightly coupled theoretical and experimental framework for unfolding the complex interlocked dynamics between enzyme kinetics and reactor mixing that may be used for both cellulosic and lignocellulosic substrates over a range of reaction conditions to increase product yield and decrease production cost.

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Sw = amount of bound mole concentration as substrate (=∑3(i − 1)[Ci]) (mmol/L) V1Max, V2Max, V3Max = maximum reaction rate for Eendo, Eexo, and Eβ‑G (mmol/mL/min)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +91-32222-83930. Fax: +91-32222-82250. E-mail: dr.s. [email protected]. Notes

The authors declare no competing financial interest.

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NOMENCLATURE [C1] = concentration of glucose (mmol/L) [C2] = concentration of cellobiose (mmol/L) [Ci] = concentration of cellulose fragment of degree of polymerization i (mmol/L) CMC = carboxymethylcellulose DP = degree of polymerization of cellulose DPn = number-average degree of polymerization Eendo = total concentration of endoglucanase (mg of protein/ mL) Eexo = total concentration of exoglucanase (mg of protein/ mL) Eβ‑G = total concentration of β-glucosidase (mg of protein/ mL) Ih1 = inhibition term of endoglucanase (=1 + C1/KG1 + C2/ KC1) Ih2 = inhibition term of exoglucanase (=1 + C1/KG2 + C2/KC2) Ih3 = inhibition term of β-glucosidase (=1 + C1/KG3) k1, k2 = rate constant of Eendo and Eexo, respectively (h−1) k f1 , k b1 = forward and backward rate constant for endoglucanase (h−1) kf2, kb2 = forward and backward rate constant for exoglucanase (h−1) kG3, k′G3 = forward and backward rate constant for βglucosidase (h−1) KM1, KM2, KM3 = Michaelis−Menten constant of Eendo, Eexo, and Eβ‑G, respectively (mmol/L) KG1, KG2, KG3 = inhibition constant of Eendo, Eexo, and Eβ‑G by glucose, respectively (mmol/L) KC1, KC2 = inhibition constant of Eendo and Eexo by cellobiose, respectively (mmol/L) N0 = total concentration of molecular unit (=∑1{i[Ci]} = constant) (unit mmol/L) RSA = reducing sugar activity as glucose/mL/h or (mmol/ mL) SM = amount of mole concentration as substrate (=∑3[Ci]) (mmol/L) S0 = initial weight concentration of cellulose (mmol/mL) 3998



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