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Kinetics of hydrolysis of insoluble cellulose by cellulase

  • Yong-Hyun Lee
  • L. T. Fan
  • Liang-Shih Fan
Conference paper
Part of the Advances in Biochemical Engineering book series (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.

Keywords

Crystalline Cellulose Product Inhibition Cellulose Hydrolysis Amorphous Cellulose Insoluble Substrate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Symbols

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

EAA

enzyme fraction active on amorphous cellulose, ML−3

EAC

enzyme fraction active on crystalline cellulose, ML−3

EAd

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

(Eo)

initial enzyme concentration, ML−3

Et

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

EG*

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

[G2]

cellobiose in polymerized form [Eq. (10)]

[G2]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, (So), [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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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Yong-Hyun Lee
    • 1
  • L. T. Fan
    • 1
  • Liang-Shih Fan
    • 1
  1. 1.Department of Chemical EngineeringManhattan, Kansas State UniversityKansesU.S.A.

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