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Kinetics of hydrolysis of insoluble cellulose by cellulase

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Advances in Biochemical Engineering, Volume 17

Part of the book series: Advances in Biochemical Engineering ((ABE,volume 17))

Abstract

The article covers the literature on the kinetic aspects of the cellulose-cellulase system. The kinetic characteristics of this heterogeneous enzyme reaction are described first and then the kinetic expressions for the hydrolysis of insoluble cellulose by cellulase. In addition, the kinetics of the reactions of cellulases with soluble cellooligosaccharides is discussed.

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Abbreviations

a:

radius of enzyme, cm

As :

surface area of the substrate, L2

b:

constant, dimensionless

C:

concentration of the product [Eqs. (47) or (51)], ML−3

CA :

concentration of amorphous cellulose, ML−3

CC :

concentration of crystalline cellulose, ML−3

CE :

concentration of enzyme in the particle, mol cm−3

CEt :

total enzyme concentration, ML−3

Ci :

cellulose concentration of component i [Eq. (6)], ML−3

Ci :

substrate fragments of chain length i, mol cm−3

Cs :

concentration of substrate in the particle, mol cm−3

CsL :

concentration of substrate in the bulk solution, mol cm−3

CI, CII :

concentrations in each phase [Eq. (21)], ML−3

D:

diffusion constant, cm2 s−1

D:

inactivated form of enzyme-substrate complex [Eq. (18)], ML−3

Ds :

average restricted diffusion coefficient of soluble substrate fragments, cm2 s−1

DSF :

average free diffusion coefficient of the fragments, m2 s −1

e:

enzyme concentration (Eq. (3)], ML−3

E:

enzyme

E*:

enzyme-substrate complex concentration, ML−3

Ea :

enzyme adsorbed on the surface [Eq. (22)], mol

E AA :

enzyme fraction active on amorphous cellulose, ML−3

E CA :

enzyme fraction active on crystalline cellulose, ML−3

E dA :

deactivated form of enzyme

Eads :

adsorbed protein, (mg protein) (mg cellulose−1)

Eads, m :

maximum adsorbed protein, (mg protein) (mg cellulose−1)

El :

number of moles of enzyme on the surface, mol

Eo :

protein concentration in the supernatant, mgrnl−1

(E o ):

initial enzyme concentration, ML−3

Et :

enzyme concentration (exo-glucanase) [Eq. (10)], ML−3

E *G :

enzyme-substrate-product complex, ML−3

ES:

enzyme-substrate complex

EP:

enzyme-product complex

f:

fraction of amorphous cellulose in the total cellulose, dimensionless

G:

glucose concentration, ML−3

G2 :

cellobiose concentration

[G 2]:

cellobiose in polymerized form [Eq. (10)]

[G 2]0 :

initial cellobiose concentration in polymerized form, mol−3

G1, G2, G3, G4 :

glucose, cellobiose, cellotriose, cellotetraose concentration, ML−3

Gx :

reducing sugar concentration, ML−3

GG:

cellobiose concentration, ML−3

[I]:

inhibitor concentration, ML−3

k:

rate constant, T−1

k′, k″:

rate constants, T−1

K:

Michaelis constant [Eqs. (47) ∼ (51)]

K:

partition coefficient [Eq. (21)]

ki :

rate constant associated with cellulose component i, T−1

Ki :

dissociation constant for the EP complex [Eq. (13)], ML−3

K′i :

modified equilibrium constant between enzyme and products [Eq. (9)]

Km :

Michaelis constant, ML−3

K′m :

modified Michaelis constant, g l−1

Kp :

constant [Eq. (1)], ml mg−1

Kp :

equilibrium constant between enzyme and products

Ks :

dissociation constant for the ES complex [Eq. (13)]

\(\bar k\) :

overall mass transfer coefficient of the substrate, cm s−1

k1, k−1, k2, k3, k4, ks, k−5 :

rate constants, T−1

Kt :

constant, dimensionless

K3 :

constant, dimensionless

K5 :

constant, dimensionless

k2, k3, k4 :

rate constants for cellobiose, cellotriose and cellotetraose

k2:2, k3:l :

rate constants

m:

constant, dimensionless

M:

mass taken up at the boundary [Eq. (51)], ML−2

n:

constant, dimensionless

n:

number of particles [Eq. (60)]

P:

product (cellobiose) concentration [Eq. (13)], mol

P, (P):

product concentration, ML−3

r:

radial position within particles, cm

R:

particle radius, cm

S:

cellulose concentration, ML−3

(S), [S]:

cellulose concentration, ML−3

[S]a :

effective substrate concentration [Eq. (7)], g I−1

Sa :

amorphous cellulose concentration, ML−3

Sc :

crystalline cellulose concentration, ML−3

[S]i :

substrate concentration at time i [Eqs. (8) and (9)], g I−1

[S]t :

total substrate concentration [Eq. (7)], g I−1

[S]i+tr :

substrate concentration at time i + t r [Eq. (8)], g I−1

S0, (S)o, (S o ), [S]0:

initial cellulose concentration, g I−1 or mol I−1

t:

time, T

tr :

time required for reducing the cellulose concentration from [S]i to [S] i+tr , T

v:

rate of reaction, ML−3 T−

V:

maximum rate of reaction, ML−3 T−1

V′:

modified maximum rate of reaction [Eqs. (8) and (9)], g l−1 h−1

vi :

initial reaction rate, ML−3 T−1

VL :

volume of the liquid phase, cm3

VI :

volume of phase I at equilibrium, L3

x:

distance normal to the surface of reaction, L

X:

extent of hydrolysis, %

XA, Xc :

enzyme-substrate complex

X1, X2, X3 :

enzyme-substrate-product complex

X1m :

maximum value of X1, [Eq. (25)]

X2 :

enzyme-substrate complex [Eq. (25)]

X1 :

enzyme-substrate complex [Eq. (25)]

X1 :

enzyme-crystalline cellulose complex [Eq. (31)]

X2 :

enzyme-amorphous cellulose complex [Eq. (32)]

X3 :

enzyme-product complex [Eq. (33)]

YA, Yc :

enzyme-substrate-product complexes

α:

constant, dimensionless

γ:

pore radius of particle, cm

η:

correction factor pertaining to diffusional restriction, dimension-less

φ:

constant [Eq. (57)], dimensionless

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  1. Department of Chemical Engineering, Manhattan, Kansas State University, 66506, Kanses, U.S.A.

    Yong-Hyun Lee, L. T. Fan & Liang-Shih Fan

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  1. Yong-Hyun Lee
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  2. L. T. Fan
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Lee, YH., Fan, L.T., Fan, LS. (1980). Kinetics of hydrolysis of insoluble cellulose by cellulase. In: Advances in Biochemical Engineering, Volume 17. Advances in Biochemical Engineering, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09955-7_10

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  • DOI: https://doi.org/10.1007/3-540-09955-7_10

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