Supporting Information
Section A: SAC Geometric Functions
The expression of xV ( λ) can be written as
xV ( λ)  BV  λ d A
(A.1)
where d A is the ablation dimension and BV is the molar volume prefactor. xV is dependent on λ
with a simple power law. The assumed power low behavior xV ( λ)  λ dA shows that the shape of
SAC will be preserved during hydrolysis (Zhou, Schuttler et al. 2009). To keep track of
monomer units exposed on the SAC surface, we have
xM ( λ)  xV ( λ)  xV ( λ  1)  ( λ  1)
(A.2a)
with
if λ  1
if 0  λ  1
1
( λ  1)  
0
(A.2b)
To represent the random distribution of SAC sizes., we use the parameter of SAC geometric
class, which is labeled by σ with σ=1, 2, ..., MMD, where MMD is the population size of SAC
geometric classes. So that x V,  , the total concentration of monomer units contained in class-σ
SACs, and xM, , the concentration of enzyme-accessible monomer units exposed on the surfaces
of class-σ SACs are given by
xV, ( λ )  BV,  λ
1
d A,
(A.3)
xM, ( λ )  xV, ( λ )  xV, ( λ  1)  ( λ  1)
(A.4a)
with
1
( λ  1)  
0
if λ  1
if 0  λ  1
(A.4b)
where BV,  is the molar volume prefactor for class-σ SACs, and d A, is the ablation dimension
factor for class-σ SACs. x V,  and xM, must obey the relationships written as
xV   xV, ( λ )
(A.5)
xM   xM, ( λ )
(A.6)


We use two parameters to describe the enzyme accessibility, which are FA , the overall
fraction of enzyme-accessible monomer units, and FA, , the fraction of enzyme-accessible
monomer units for the class-σ SACs. Their expressions are given by
FA, ( λ ) 
FA 
xM, ( λ )
xV, ( λ )
xM
    FA, ( λ )
xV

(A.7)
(A.8)
where   xV, / xV . The value of FA can be directly observed before enzymatic hydrolysis and
(0)
used as an initial input value, that is, FA , in the model, and decide the initial value of  . We
use the assumption of the Gaussian distribution for the total molar concentration of monomer
units per geometric class, and then have
2

   Avg

 wid
(0)  exp (

    Avg 2 
)2 / 2 /  exp  ( 
) / 2
 wid
 


(A.9)
By adjusting the two Gaussian distribution parameters  Avg and Wid , a proper initial distribution
of the molar monomer concentration per geometry class can be obtained to match the value of
FA(0) .
Section B: Derivation of Surface Layer Ablation Rate Equations
In order to derive the surface layer ablation rate equations, we first define  R , ,  0 as the loss
rate of type-μ sites belonging to type-ρ chains exposed on class-σ SAC surfaces, and  R  0 as
the total loss rate of monomer units exposed on class-σ SAC surfaces into solution. So that we
can obtain
R     R , , 
 ,
d
xV, ( λ (t ))   λ xV, ( λ )  λ
dt
(B.1)
where  λ is shorthand for the derivative  / λ . The removal of a small fraction of a layer during
)
a short time interval dt will result in a removal of  dxV,( fra
   λ xV,  dλ monomer units from
the SAC surface by chain fragmentation and then result in a change of SAC exposed surface area
( fra )
by dxM,
   λ xM, dλ monomer units. The net concentration of newly exposed monomer units at
the surface, resulting from the removal of overlaying monomer units and the change of surface
area, is thus
(exp)
( fra )
( fra )
dxM,
  dxV,  dxM,  ( λ xV,   λ xM, )dλ   R (1   λ xM, /  λ xV, )dt
Based on Eq. (B.2), the net concentration of newly exposed sites is given by
3
(B.2)
(exp)
dx(exp)
, ,  (dxM, ) M, , (  1)  g  ,  ,
(B.3)
where g  ,  , ( ) is the native site fraction functions representing the fraction of type-μ sites
contained in type-ρ chains in the interior of the class-σ SACs. g  ,  , ( ) can be treated as a
layer–independent parameter, which means g  ,  , ( )  g  ,  , ( )  g  ,  , . In addition, we
denote g E ,  , as the native L-end (or R-end) broken site fraction of type-ρ chains in class-σ
SACs, which has such relationship
g
i
LUi ,  ,
  i g RU ,  ,  g E ,  , and can be obtained from the
i
degree of polymerization of type-ρ chains DP .
Combining the surface exposure contribution dx(exp)
, , with the surface fragmentation
)
contribution dx( fra
, , , which is given by
)
dx( fra
, ,  R , ,  dt
(B.4)
)
(exp)
we can obtain the net increment of type-μ surface sites, that is, dx ,  ,  dx( fra
,  ,  dx ,  , , and the
rate function Equation (3a). Then from Eq. (B.1) we can immediately obtain the changing rate of
 , which is Equation (3b).
4
Section C: Enzyme Adsorption and Inhibition Equilibriums
The first step for an enzyme molecule to cut an intact bond is to form an enzyme–substrate (ES)
complex, that is, to adsorb a bond site exposed on SAC surfaces. The cutting rate for a intact
bond site of type μ in a chain belonging type ρ, having already adsorbed an enzyme molecule on
the surface of an SAC belonging class σ, is thus given by the product of rate coefficient and ES
complex concentration, written in the form   , μ ,   z κ , μ ,  ,σ , where κ represents the type of
enzymes; z κ , μ ,  ,σ represents the concentration of (κ , μ,  ) ES complexes on class-σ SAC
surfaces; and   , μ ,  represents the cutting rate coefficient (in the unit of cuts per second per ES
complex), which is identical for all the geometric classes. It is assumed that the ES complex
formation process is much faster than the bond cutting kinetics. Therefore, the enzyme
adsorption quasi-equilibrium is maintained at the SAC surfaces during hydrolysis and written as
z κ , μ ,  ,σ  Lκ , μ ,   vκ  y μ ,  ,σ
(C.1a)
where y μ ,  ,σ is the molar concentration of free type-μ sites contained in type-ρ chains on class-σ
SAC surfaces, vκ is the concentration of free type-κ enzymes and Lκ , μ ,  is the substrate
adsorption coefficient which is the inverse of the conventional desorption equilibrium
coefficient.
As hydrolysis proceeds, some enzyme molecules may also be inhibited by soluble oligomers
to form enzyme-oligomer (EO) complexes in solution. This type of enzyme adsorption
equilibrium in solution can be written as
zκ ,  (l )  I κ, (l )  vκ  yS ,  (l )
5
(C.2b)
with 1  l  lS , . Here, zκ ,  (l ) is the concentration of (κ ,  , l ) EO complexes in which each
oligomer contains l monomer units, I κ ,  (l ) is the oligomer adsorption coefficient; yS ,  (l ) is the
molar concentration of free oligomers contained l monomer units and dissolved from type-ρ
chains, and vκ is the same parameter as in Equation (C.1a). As described in Supporting
Information section B, zκ , μ ,  ,σ and zκ ,  (l ) can be calculated and expressed in terms of x ,  , and
xS ,  (l ) by solving enzyme adsorption and inhibition equations.
The construction of RS , (l ) describes the reactions between oligomers and beta-enzymes and
requires the solutions of the enzyme adsorption and inhibition equilibriums. In this model, the
reaction mechanism of beta-enzymes in solution is simplified as: a free oligomer which contains
l monomer units can adsorb and be hydrolyzed by its corresponding beta-enzymes into a
monomer unit and an oligomer containing l  1 monomer unit(s). So the expression of RS , (l )
can be written as
lS , 1

R
(1)


(2)

z
(2)

 S ,
2   , (l )  zκ , (l )
 ,
κ ,


 RS , (l )    , (l )  zκ ,  (l )    , (l  1)  zκ ,  (l  1)

 RS , (lS ,  1)    , (lS ,  1)  zκ ,  (lS ,  1)


l  lS ,  1
2  l  lS ,  2
l  lS ,  1
(C.3)
where   , (l ) is the oligomer cutting rate coefficient. Note that in this model, only beta-enzymes
could hydrolyze oligomers in solution after forming EO complexes with them in solution. So for
endo- and exo- enzymes, their corresponding values of   , (l ) are 0, which means they are
inhibited by forming EO complexes with oligomers. And for any monomer unit,   , (1) is also 0
6
which means all the enzymes will inevitably be inhibited by monomer units during hydrolysis.
Furthermore, both the cutting rate coefficient   , (l ) and the oligomer adsorption coefficient
I κ ,  (l ) have two dimensions representing the enzyme types and the chain types.
The free enzyme and surface site concentrations vκ and y μ ,  ,σ are related to their total
concentrations u κ and x μ ,  ,σ , respectively, by way of the total enzyme and total site balance
relations:
uκ  vκ 
z
μ ,  ,σ
κ , μ ,  ,σ
  zκ ,  (l )
(C.4)
 ,l
xS ,  (l )  yS ,  (l )   zκ ,  (l )
(C.5)

x μ ,  ,σ  y μ ,  ,σ   zκ , μ ,  ,σ 
κ

κ , μ ',  '
f μ ,  ,σ   κ  zκ , μ ',  ',σ
(C.6)
where f μ,  ,σ  xμ,  ,σ / xM ,σ . The last term in the Equation (C.6) arises from the fact that the
footprint area of a surface-adsorbed enzyme molecule is far greater than the average surface area
of a bond site. Hence, a type-κ enzyme molecule, bound to a type-μ' surface site, will in effect
cover up, and obstruct access to some number (  ) of other surface sites that are located in
spatial proximity to the type-μ' binding site. Due to the current lack of value of  for each type
enzymes discussed in this work, we simply use the value of cellulase, that is, 39, for all the
enzymes.
Equations. (C.1a), (C.2b), (C.4), (C.5) and (C.6) can then be solved simply by iteration in
order for vκ , y μ ,  ,σ , z κ , μ ,  ,σ and zκ ,  (l ) . Combining the mass action and balance relations, the
general form of enzyme adsorption and inhibition equilibrium can be shown as
7
vκ 
1

μ , ,σ
uκ
Lκ , μ ,   yμ ,  ,σ   I κ ,  (l )  yS ,  (l )
(C.7)
 ,l
yS ,  (l ) 
xS ,  (l )
1   I κ ,  (l )  vκ
(C.8)

y μ ,  ,σ 
xμ ,  ,σ
 μ ,  (1   μ ',  '  μ ',  ',  μ ',  ' )
 μ ,   1   L , μ,   v
(C.9)
(C.10)

 μ ,      L , μ ,   v
(C.11)

 μ ,  , 
xμ ,  ,
 μ ,   xM ,
(C.12)
To calculate vκ and y μ ,  ,σ , as functions of u κ and x μ ,  ,σ this system of coupled non-linear
equations can be solved iteratively, starting from the initial guess
v (init )  u

 
( init )
 yS ,  (l )  xS ,  (l )
 (init )
 y ,μ ,  x , μ , 
(C.13)
Section D: Site Number Increments and Chain Site Distribution Model
N  ',  , (k , k ' ) can be expressed as
N  ,  , (k , k ' )  N  ,  , (k )  N  ,  , (k ' )  N  ,  , (k  k ' )
8
(D.1)
where N  ,  , (k ) denotes the average number of type-μ sites per insoluble type-ρ chain of class-σ
SACs for k  lS ,  , with N  ,  , (k )  0 for k  lS ,  ,and N  ,  , (k , k ' ) is thus the difference of the
number of type-μ sites belonging to type-ρ chain caused by a cut.
The specific functional form of N  ,  , (k ) depends on the distribution of site types along a
type-ρ chain. So we construct the site distribution model based on the assumption that O-sites are
randomly distributed with a uniform probability φO ,  ,σ over all l  1 intact bonds within a type-ρ
chain. By straightforward site counting, we thus construct N  ,  , (l ) for any insoluble type-ρ chain
with l  lS ,   7
(l  1)  φ
O ,  ,σ

φUi , 

N  ,  , (l )  (1  φO ,  ,σ )  φUi ,   φU j , 

(l  3)  (1  φO ,  ,σ )  φUi ,   φU j , 
l  φ
 Ji , 
μO
μ  LUi or RUi
μ  X Uij or YUij
(D.2)
μ  NUij
μ  Ji
Here, φU i ,  is the average molar ratio of the type-i monomer units to all the monomer units
contained in the backbone of a type-ρ chain, and φJ i ,  is the average molar ratio of the type- J i
side groups to all the monomer units contained in the backbone of a type-ρ chain. Both of them
actually characterize the natural composition of the type-ρ chains which can be easily obtained
from literature and used in the model. Based on Equations (D.1) and (D.2),we can easily obtain
the detailed expression of N  ',  , (k , k ' ) .
9
Section E: Derivation of Chain Fragmentation Probabilities
This section shows the derivation of how to express P , (k , k ' |  , 1) in terms of P , (l ) and
P , ( μ | k , k ' ,1) . Here, P , (l ) is defined as the probability of a randomly selected insoluble
type-ρ chain, exposed on a class-σ SAC surface, to contain l
monomer units, and
P , ( μ | k , k ' ,1) is the probability for a randomly selected intact bond to be of site type μ on a
type-ρ chain, provided that the site is located k monomer units from the L-end and k' monomer
units from the R-end of the type-ρ chain. P , ( μ | k , k ' ,1) describes the distribution of different
site types along a type-ρ chain (relative to the chain ends).
In order to express P , (k , k ' |  , 1) in terms of P , (l ) and P , ( μ | k , k ' ,1) , first, let us
consider a random sample of type-ρ chains, with random chain lengths and a very large sample
size NL →∞. Let these NL type-ρ chains be concatenated, in random order, into a "super type-ρ
chain" where the R-end of each individual chain is connected to the L-end of its right neighbor
chain by a fictitious bond, referred to as a “−1-bond”, and the real internal bonds between
monomer units contained in each chain are referred to as “+1-bonds”. Hence, we are assigning to
each bond site on the “super type-ρ chain” a “bond integrity” variable ζ, with ζ = +1 for intact
bond site types NUij , X Uij , YUij , O and ζ = −1 for broken bond site types between adjacent chain
ends (i.e. for a pair of adjacent L,R-sites).
Then, let us consider the average chain length for type-ρ main chains l
 ,
, that is, the
average degree of polymerization (DP), for type-ρ chains exposed on class-σ SAC surfaces.
10
l
 ,
can be expressed in terms of the L-end broken site fraction of type-ρ chains f E ,  , , or the
concentration of type-ρ chain xE ,  , , which is written as

l
 ,
  l  P , (l ) 1/ f E,  ,  xM, , / xE, ,
(E.1)
l 1
In Equation (E.1), f E ,  , comes from the site type fractions f  ,  , , which is, for any site type
belonging to type-ρ chains on class-σ SAC surfaces, defined by
f  , , 
x , ,
(E.2)
xM , ,
Based on the "uniform segment exposure" assumption (Zhou, Schuttler et al. 2009), the
number of left chain ends must equal the number of right chain ends, which is
x
LUi ,  ,
i
  xRU ,  ,  xE ,  , . Also, because of the relationship between LU i and XUij site groups,
i
i
and between RU i and YUij site groups, we can get
f
i
f
i
RUi ,  ,
  fYU
f E ,  , 
i, j
x
i
ij
,  ,
i, j
ij
/ (1  φO ,  ,σ ) and
,  ,
/ (1  φO ,  ,σ ) , so that f E ,  , can be expressed as
LUi ,  ,
xM , ,
  f XU
LUi ,  ,
  f LU ,  , 
i
i
f
i, j
X Uij ,  ,
(1  φO ,  ,σ )

f
i, j
YUij ,  ,
(1  φO ,  ,σ )
  f RU ,  , 
i
i
x
i
RUi ,  ,
xM , ,
(E.3)
Next, we denote P ,  (k , k ' ,  ) as the probability that a bond randomly selected from the "super
type-ρ chain" is a ζ-bond, where ζ is either +1 or −1, and that this randomly selected ζ-bond will
be located k ≥ 1 monomer units from its nearest L-end and be located k' ≥ 1 monomer units from
its nearest R-end. The expression of P ,  (k , k ' ,  ) is given by:
11
 P , (k , k ', 1)  f E ,  ,  P , (k  k ')

 P , (k , k ', 1)  f E ,  ,  P , (k )  P , (k ')
(E.4)
This can be derived from the "super type-ρ chain" construction as follows: for ζ = +1,
P ,  (k , k ' ,1) is a joint probability for two conditions meeting at the same time: the first one is
that the bond located k monomer units to the left of the randomly selected ζ-bond should be a
“−1-bond”; the second one is that the adjacent k + k' monomer units to the right of that “−1bond” should form a single contiguous chain of length l  k  k ' . The probabilities for these two
conditions are f E , , and P , (k  k ' ) , respectively, hence the joint probability P ,  (k , k ' ,1) is
the product f E ,  ,  P , (k  k ') . For ζ = −1, P , (k , k ' ,1) can be derived by a similar way. And it
can be easily verified that  k ,k '1   1 P , (k , k ',  )  1 .
Next, we introduce the conditional site type probability, given the type-ρ chain fragments,
denoted by P , (  | k , k ' ,  ) which is the probability for a randomly selected "super type-ρ chain"
bond to be of site type μ, given that the randomly selected bond is a ζ-bond; and given that it is
located k and k' monomer units from its nearest −1-bond to the left and to the right, respectively.
Just like N  ,  , (k ) , the conditional type-ρ chain site probabilities P , (  | k , k ' ,  ) depend on the
distribution of type-μ sites along the type-ρ chains. In fact, for purposes of the fragmentation
kinetics P , (  | k , k ' ,  ) comprises the complete mathematical description of the chain site
distribution model. The values of P , (  | k , k ' ,1) and N  ,  , (k ) are not independent of each
other: for any type-ρ chain site distribution, P , (  | k , k ' ,  ) must be normalized to
  P  ( | k , k ',  )  1 , and P  ( | k , k ' ,1) and N    (k ) must obey the following general chain
,
,
, ,
site number counting relations for all intact bond site types:
12
l 1
N  ,  , (l )  (l  lS ,   1)   P , (  | k , l  k ,1)
(E.5a)
k 1
for   NUij , X Uij , YUij , O with
1 if l  0
(l )  
0 if l  0
(E.5b)
where P , (  | k , k ' ,1) completely determines N  ,  , (k ) for site groups NUij , X Uij , YUij , O .
Based on the chain site model N  ,  , (l ) , we thus assign the site groups NUij , X Uij , YUij , O of the
intact type-ρ chain bonds to the corresponding "super type-ρ chain" +1-bonds, while formally
LU i , RU i is randomly assigned to each "super type-ρ chain" −1-bond with probability φU i ,  ,σ / 2
corresponding to   1 / 2 for site groups LU and RU . Then P , (  | k , k ' ,  ) can be written as
i
i
  φ
  ,1 O ,  ,σ
  ,1  φUi ,  ,σ / 2

P , ( μ | k , k ',  )    ,1   k ,k X  (1  φO ,  ,σ )  φUi ,  ,σ  φU j ,  ,σ

  ,1   k ',kY  (1  φO ,  ,σ )  φUi ,  ,σ  φU j ,  ,σ
  (1  
k , k X ,  )  (1   k ', kY , )  (1  φO ,  , σ )  φU i ,  , σ  φU j ,  , σ
  ,1
μO
μ  LUi or RUi
μ  X Uij
(E.6)
μ  YUij
μ  NUij
Finally, we can construct the conditional type-ρ fragmentation probability, given the site type,
P , (k , k ' |  ,  ) , defined as the probability for a randomly selected bond in “super type-ρ chain”
to be located k and k' monomer units from its nearest “−1-bond” to the left and to the right,
respectively, given that the bond is a ζ-bond and that it is of site type μ. By Bayes’ theorem, we
have
P , (k , k ' |  ,  ) 
P , (  | k , k ',  )  P , (k , k ',  )
P , (  ,  )
13
(E.7)
where the unconditional site type probability P , (  ,  ) is given by:
P , (  ,  ) 

 ,1  f  ,  ,
P
(
k
,
k
',

,

)


  ,
k , k '1

 ,1  f  ,  , / 2
for  =NUij , X Uij , YUij , O
for  =LUi , RUi
(E.8)
P , (k , k ' |  ,  ) is defined only where P , (  ,  )  0 . The fragmentation probabilities are
normalized as k 1 k '1 P , (k , k ' |  ,  )  1 .Thus we obtain the expression of P , (k , k ' |  , 1)


in terms of P , (l ) and P , ( μ | k , k ' ,1) , given by
P , (k , k ' |  , 1) 
f E ,  ,
f  ,  ,
 P , (  | k , k ', 1)  P , ( k  k ')
(E.9)
By using Equation (E.9), the expression of NS , ,  , (k ) can be written as

(



N S ,  ,  , (k )  (


(


f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
)  Ui ,   U j ,   (1  O ,  , )    2   k ,k X ,   k ,kY ,  P , (k  k X ,  )  P , (k  kY ,  ) 
  NU
ij
)  Ui ,   U j ,   (1  O ,  , )    k ,k X ,  P , ( k  k X ,  ) 


  XU
)  Ui ,   U j ,   (1  O ,  , )    k ,kY ,  P , (k  kY ,  ) 
  YU
ij
ij
(E.10)
Section F: Detailed Expression of the Surface Sites Increment Factor N ', ,  ,
14


(


(


(



(


(



(


(




(


(



(



(


(



(



(


(


f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2    P ,  (lS ,  )  P ,  (lS ,   k X ,  -1) 


  XU ,  '  XU
)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2    P ,  (lS ,  )  P ,  (lS ,   k X ,  -1) 


  X U ,  '  YU
)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2    P ,  (lS ,  )  P ,  (lS ,   kY ,  -1) 


  YU ,  '  X U
)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2    P ,  (lS ,  )  P ,  (lS ,   kY ,  -1) 
  YU ,  '  YU

1
)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2    2lS ,  -1
 
f
E ,  ,


1
)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2    2lS ,  -1
 
f E ,  ,

ij
ij
i' j'
ij
ij
i' j'
i' j'
i' j'



  NU ,  '  X U



  NU ,  '  YU
ij
ij
i' j'
lS ,  k X , -1


)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2    k X ,    (l - k X ,  - 3) P ,  (l ) 


l  lS , 


  X U ,  '  NU
lS ,  kY , -1


)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2    kY ,    (l - kY ,  - 3) P ,  (l ) 
l  lS , 


  YU ,  '  NU
lS ,  k X , -1
lS ,  kY , -1
 3

)   -U i ,   U j ,   U i ' ,   U j ' ,   (1  O ,  , ) 2   
 lS ,  2 - 7lS ,   3 - k X ,  - kY ,    ( k X ,   3 - l ) P ,  (l )   ( kY ,   3 - l ) P ,  (l ) 

 f
l  lS , 
l  lS , 
 E ,  ,

  NU ,  '  NU
lS ,   k X ,  -1


)   -U i ,   U j ,   (1  O ,  , )  O ,  ,    k X ,    (l - k X ,  -1) P (l ) 
l  lS , 


  XU ,  '  O
lS ,   kY ,  -1


)   -U i ,   U j ,   (1  O ,  , )  O ,  ,    kY ,    (l - kY ,  -1) P (l ) 


l  lS , 


  YU ,  '  O
ij
ij
i' j'
i' j'
ij
ij
ij
lS ,  k X , -1
lS ,  kY , -1
 1

)   -U i ,   U j ,   (1  O ,  , )  O ,  ,   
 ls 2 - 3ls  1- k X ,  - kY ,    ( k X ,   1- l ) P (l )   ( kY ,   1- l ) P (l ) 

 f
l  ls
l  ls
 E ,  ,

lS ,   k X ,  -1


)   -U i ,   U j ,   (1  O ,  , )   Ji ,  ,    k X ,    (l - k X ,  ) P (l ) 
l  ls


  NU ,  '  O
ij
  XU ,  '  Ji
ij
lS ,   kY ,  -1


)   -U i ,   U j ,   (1  O ,  , )   J i ,  ,    kY ,    (l - kY ,  ) P (l ) 
l  ls


  YU ,  '  J i
lS ,  k X , -1
lS ,  kY , -1


)   -U i ,   U j ,   (1  O ,  , )   J i ,  ,   lS ,  2 - lS ,  - k X ,  - kY ,    ( k X ,  - l ) P (l )   ( kY ,  - l ) P (l ) 


l  ls
l  ls


  NU ,  '  J i
ij
15
ij
(F.1)
i' j'
i' j'
Section G: Derivation of Production Factor of Oligomer
As P , (k , k ' |  , 1) can be expressed in terms of P , (l ) and P , ( μ | k , k ' ,1) , we can obtain
N S , ,  , (k )  (
f E ,  ,
f  ,  ,
)


k '  ls ,   k
 P , (  | k , k ', 1)  P , (  | k ', k , 1)   P , (k ' k )
(G.1)
By using the "Chain End Decomposition" theory (Zhou, Schuttler et al. 2009) we can separate
the effects of the near-chain-end sites, which can be cut by both exo- and endo-enzymes, from
the chain interior sites, which can only be cut by endo-enzymes. P , (  | k , k ', 1) can then be
decomposed into left end (L), right end (R) and interior (I) contributions of the type-ρ main
chain, which can be written as
P , ( | k , k ', 1)  P(,I) ,  L,  (k )  P(,L), (k )  R,  (k ')  P(,R), (k ')
(G.2)
where  L ,  (k )  (lL ,   k ) and  R ,  (k ')  (lR ,   k ') are the cut-off factors dividing a type-ρ
chain into three parts with lL ,   k X ,   1 and lR ,   kY ,   1 . Notice that in the model,
k  k '  lLR ,   lL ,   lR ,   1 and P , ( | k , k ', 1)  P(,I) , is independent of k and k ' when there
are k  lL ,  and k '  lR ,  . Based on the functional form, we can obtain in detail the values of three
contributions for each hydrolysable intact bond site, shown as
 P(,I) ,  (1  φO ,  ,σ )φU ,  φU , 
i
j


(
L
)
 P ,  , (k )   k ,k (1  φO ,  ,σ )φU ,  φU , 
X ,
i
j

(
R
)
 P ,  , (k ')   k ',k (1  φO ,  ,σ )φU ,  φU , 
Y ,
i
j

(I )
( L)
 P ,  ,  0; P ,  , (k )   k ,k X , (1  φO ,  ,σ )φUi ,  φU j ,  ; P(,R), (k ')  0

 P(,I) ,  0; P(,L), (k )  0; P(,R), (k ')   k ',kY , (1  φO ,  ,σ )φU i ,  φU j , 


16
μ  NUij
μ  X Uij
μ  YU ij
(G.3)
which then can be used to obtain the detailed expressions of NS , ,  , (k ) .
Section H: Derivations of Chain Concentration Rate Equations and Rate
Equations Closure
In order to find the solution for P , (l ) with l  lC ,  , a new rate equation system is developed for
type-ρ chains concentration variables H  , (l ) by defining H  , (l )  P , (l )  xE ,  , , with
H  , (l )  0 for l  lS ,  . Here, xE ,  , is the concentration of insoluble type-ρ chains, as discussed
in Supporting Information section D. All the surface site concentration variables now could be
xM ,  ,   l l l H  , (l )

expressed
in
terms
of
H  , (l )
by
using
S ,
and
x ,  ,   l l N  ,  , (l ) H  , (l ) . Analogous to the site ablation rate equations, the rate equations

S ,
of H  , (l ) is given by
H  , (l )  RH ,  , (l )  R  ( )   M ,  , (  1)  Q , (l ,   1) /


j  lS , 
j Q , ( j,   1)
(H.1)
where RH , , (l ) is the changing rate of type-ρ chains of length l due to bonds cutting, and the
second term of the equation above gives the rate of exposure of new type-ρ chains due to the
removal of overlaying material. Q , (l , λ ) is the type-ρ chain length distribution of the native
substrate material in each layer of class-σ SACs, which obeys the delta-function native type-ρ
chain length distribution Q , (l , λ )  l , DP . Q , (l , λ ) has a close relationship with the native
site fraction g  ,  , , which is given by
17

g E ,  ,  1/   l l  Q , (l , λ ) 
 S ,

g  ,  , ( )  g E ,  ,   l N  ,  , (l )  Q , (l , λ )
(H.2a)

S ,
(H.2b)
As described in Supporting Information section G, RH ,  , ( k ) can be written by
RH , , (l )     ,  ,  z ,  ,  ,  N H ,  ,  , (k )
 ,
(H.3)
Then we can have



RH ,  , (l )    R , (l  k , k ')     R , ( j  k , l )  R , ( j  l , k ) 
k , k '1
k 1 j l 1
(H.4)
and
R , (l  k , k ')     ,  ,  z ,  ,  ,  P , (k , k ' |  , 1)   l , k  k '
 ,
(H.5)
R , (l  k , k ') is denoted as the rate at which surface-exposed type-ρ chains of length l on
class-σ SACs are being cut into two type-ρ chain fragments of length k and k ' , from the L-end
and R-end of the original type-ρ chains respectively. As P , (k , k ' |  , 1) can be expressed in
terms of P , (l ) and P , ( μ | k , k ' ,1) , we can rewrite RH ,  , ( k ) by
RH , , (l )     ,  ,  z ,  ,  ,  N H ,  ,  , (k )
 ,
(H.6)
By using the "Chain End Decomposition" (Zhou, Schuttler et al. 2009) theory
P , (  | k , k ', 1) , we can obtain
18
N H ,  ,  , (l )  (
f E ,  ,
f  ,  ,
)   AH ,  ,  , (l )  BH ,  ,  , (l )  DH , ,  , (l ) 
(H.7a)
where
AH ,  ,  , (l )   N  ,  , (l )  P , (l )
l
BH , ,  , (l )  2P(,I) ,  P(,L), (l )L, (l )  P(,R), (l )R, (l )   1   j 1 P , ( j ) 


 DH ,  ,  , (l )   l lE , P , (l )   P(,L), ( j  l ) L,  ( j  l )  P(,R), ( j  l ) R ,  ( j  l ) 


j l 1

lE ,   max(lL ,  , lR ,  )  1
(H.7b)
(H.7c)
(H.7d)
The detailed expression of N H , ,  , (l ) can be obtained by combining Equations (H.7a),
(H.7b), (H.7c), (H.7d) and (D.2), written as

(



N H ,  ,  , (l )  (


(


f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
f E ,  ,
f  ,  ,
l


)  Ui ,   U j ,   (1  O ,  , )    2  2 P , ( k )  (l  3)  P , (l )  P , (l  k X ,  )  P , (l  kY ,  ) 
k 1


  NU
ij
)  Ui ,   U j ,   (1  O ,  , )    P , (l  k X ,  )  P , (l ) 


  XU
)  Ui ,   U j ,   (1  O ,  , )    P , (l  kY ,  )  P , (l ) 
  YU
ij
(H.8)
To solve the chain concentration rate equations for H  , (l ) at short chain lengths from l to
the cut-off length lC ,  , it is necessary to use the value of P , ( j ) at chain lengths from l to
lC ,   lE ,  . Obviously, the length ranges of l are different for H  , (l ) and P , ( j ) , which will
make the equation system redundant. So in order to solve H  , (l ) with the length range of
lS ,   l  lC ,  by using P , (l ) with the same length range, the Local Poisson (LP) approximation
scheme (Zhou, Schuttler et al. 2009) is used here for P , (l ) , so that we have
19
ij
P , (l )
P , (lC ,  )  P , (lC ,  ) / P , (lC ,   1) 
( l lC , )
(H.9)
for lC ,   1  l  lC ,   lE ,  . By using Equation (H.9) with the relationship P , (l )  H  , (l ) / xE ,  , ,
a closed ordinary differential equation (ODE) system for the site concentration formalism is
completed.
Section I: Parameters
All parameters are categorized into four groups and showed in four tables respectively. The
(0)
 (0)
first group in Table I1 includes FA and M,Xyl , which describe the initial substrate morphology
i.e. the enzymatic accessibilities of the whole substrate and xylan, respectively. Based on the
values of these two parameters we can obtain the enzymatic accessibility of cellulose. We
believe that the values of these two parameters could be measured by using reliable experimental
techniques in the future. However, there are currently no values for these two parameters. So we
(0)

adjust the values for FA and M,Xyl based on the values of enzymatic accessibility of cellulose,
(0)
which is commonly measured in experiments. The values we used were from Zhu et al. (2009).
Based on the experiments by Zhu et al. (2009) the enzymatic accessibility of cellulose was 0.243
for DA-pretreated corn stover and 0.0238 for non-pretreated corn stover. Thus we believe that
the value of the enzymatic accessibility of cellulose for AFEX-pretreated corn stover, as well as
poplar, should range from 0.0238 to 0.243. The values of the enzymatic accessibility of cellulose
we used in the model were 0.0832, 0.0998 and 0.0753.
The second group is adsorption and kinetic parameters and shown in Table I2. The values of
L1, N ,Glu L1, X ,Glu L1,Y ,Glu L2, N ,Glu L2,Y ,Glu L2, X ,Glu L3, N ,Glu L3, X ,Glu
L
,
,
,
,
,
,
,
and 3,Y ,Glu , which describe the
20
adsorption equilibrium between cellulose-sites and cellulases, were adopted from Zhou et al.
(2009) with referenced experiments.
and
L3,Y , Xyl
L1, N , Xyl L1, X , Xyl L1,Y , Xyl L2, N , Xyl L2, X , Xyl L2,Y , Xyl L3, N , Xyl L3, X , Xyl
,
,
,
,
,
,
,
are parameters describing the adsorption equilibrium between xylan sites and
cellulases. The values for these parameters were all set to be 0 as we assume that if there is no
effective adsorption between enzyme molecule and bond site leading to bond cleavage, the
parameter of adsorption equilibrium would be set to 0. For the same reason,
L4, N ,Glu L4, X ,Glu
,
,
L4,Y ,Glu L5, N ,Glu L5, X ,Glu L5,Y ,Glu L5, N , Xyl L5,Y , Xyl L7,  , 
L
,
,
,
,
,
,
and 8,  ,  , which describe the adsorption
equilibrium between sites and enzymes having no adsorption relationships, were also set to be 0.
L4, N , Xyl L4, X , Xyl
L
,
and 4,Y , Xyl describe the adsorption equilibrium between Endo-acting xylanases and
xylan sites and the values of these parameters were from the experiments by Qing and Wyman
(2011). The values of kinetic parameters
 4,Y , Xyl
 1, N ,Glu  1, X ,Glu  1,Y ,Glu  2, X ,Glu  3,Y ,Glu  4, N , Xyl  4, X , Xyl
,
,
,
,
,
,
and
came from the experiments by Banerjee et al. (2010) which used AFEX-pretreated corn
stover as substrate. The relationship among these parameters was based on Zhang and Lynd
(2006) in which the activity ratio of EG:CBH2:CBH1 was 5:2:1. For ineffective adsorptions that
cannot lead to bond cleavage, the corresponding kinetic parameters would be 0. So the values of
 1, N , Xyl  1, X , Xyl  1,Y , Xyl  2, N ,Glu  2,Y ,Glu  2, N , Xyl  2, X , Xyl  2,Y , Xyl  3, N ,Glu  3, X ,Glu  3, N , Xyl  3, X , Xyl  3,Y , Xyl
,
,
,
,
,
,
,
,
,
,
,
,
,
 4, N ,Glu  4, X ,Glu

,
and 4,Y ,Glu were all set to be 0. Currently, there are no reliable values of the
adsorption and kinetic parameters of Exo-acting xylanases. So we assumed that values of
L5, N ,Glu
,
L5, X ,Glu L5,Y ,Glu L5, N , Xyl L5,Y , Xyl L5, X , Xyl L6, N ,Glu L6, X ,Glu L6,Y ,Glu L6, N , Xyl L6, X , Xyl
L
,
,
,
,
,
,
,
,
,
and 6,Y , Xyl were equal
to the values of corresponding parameters of Endo-acting xylanases. However, these parameters
21
did not affect the simulation results since it is assumed that commercial enzyme mixtures do not
contain significant amount of Exo-acting xylanases.
The third group is inhibition parameters and shown in Table I3.
I
(1)
I1,Glu (1) I 2,Glu (1)
,
and 3,Glu
are D-glucose (G1) inhibition parameters for EG, CBH2 and CBH1 respectively, and their values
were from Levine, Fox et al. (2010). Similarly,
I1,Glu (2) I 2,Glu (2)
I
(2)
,
and 3,Glu are cellobiose (G2)
inhibition parameters for EG, CBH2 and CBH1 respectively, and their values were from Jeffrey
et al. (1999). There are limited reported values for cello-oligomers (G3-G6) inhibition
parameters for cellulases. The values of
I1,Glu (3) I 2,Glu (3) I 3,Glu (3) I1,Glu (4) I 2,Glu (4) I 3,Glu (4)
,
,
,
,
,
,
I
(6)
I (2)
I1,Glu (5) I 2,Glu (5) I 3,Glu (5) I1,Glu (6) I 2,Glu (6)
,
,
,
,
and 3,Glu
were based on the values of 1,Glu
,
I 2,Glu (2)
and
I 3,Glu (2)
as well as the experiments by Lo Leggio and Pickersgill (1999) which
describe the relationship among cello-oligomers (G2-G6) inhibition parameters for cellulases.
Currently, there are no reliable values of the D-xylose (X1) inhibition parameters for EG, CBH2
and CBH1 respectively. So we assumed that values of
I
(1)
I1, Xyl (1) I 2, Xyl (1)
,
and 3, Xyl
were equal to
I
(1)
I1,Glu (1) I 2,Glu (1)
,
and 3,Glu respectively due to the similarity between the structures of these two
monomer units.
I (2)
I1, Xyl (2) I 2, Xyl (2)
,
and 3, Xyl
are xylobiose (X2) inhibition parameters for EG,
CBH2 and CBH1 respectively, and their values were from the work by Ntarima et al. (2000).
The values of
I1, Xyl (3) I 2, Xyl (3) I 3, Xyl (3) I1, Xyl (4) I 2, Xyl (4) I 3, Xyl (4) I1, Xyl (5) I 2, Xyl (5) I 3, Xyl (5)
,
,
,
,
,
,
,
,
,
I
(6)
I (2)
I1, Xyl (6) I 2, Xyl (6)
I (2) I
(2)
,
and 3, Xyl
were based on the values of 1, Xyl , 2, Xyl
and 3, Xyl as well as
the experiments by Lo Leggio and Pickersgill (1999) which also describe the relationship among
xylo-oligomers (X2-X6) inhibition parameters for cellulases.
22
I 4,Glu (1)
is D-glucose (G1)
inhibition parameter for Endo-acting xylanases which currently do not have too much reliable
values. So we assumed that value of
I 4,Glu (1)
was equal to
I1,Glu (1)
due to the same inhibitor. For
the same reason, the values of cello-oligomers (G2-G6) inhibition parameters for Endo-acting
xylanases, which are
I 4,Glu (2) I 4,Glu (3) I 4,Glu (4) I 4,Glu (5)
I
(6)
,
,
,
and 4,Glu
, were all determined. The
values of D-xylose (X1) and xylobiose (X2) inhibition parameters for Endo-acting xylanases
I 4, Xyl (1)
and
I 4, Xyl (2)
were based on the work by Ntarima et al. (2000). The values of
I 4, Xyl (3)
,
I
(6)
I 4, Xyl (4) I 4, Xyl (5)
I
(2)
,
and 4, Xyl
were based on the value of 4, Xyl
and the experiments by Lo
Leggio and Pickersgill (1999) which described the relationship among xylo-oligomers (X2-X6)
inhibition parameters for Endo-acting xylanases. Currently, there are no reliable values for the
inhibition parameters of Exo-acting xylanases. So we assumed that the values of inhibition
parameters of Exo-acting xylanases were equal to the values of
corresponding inhibition
parameters of Endo-acting xylanases. However, these parameters did not affect the simulation
results since we did not consider Exo-acting xylanases as enzyme species in any commercial
enzyme.
The fourth group is parameters about beta-enzymes and shown in Table I4.
I 7,Glu (2)
I 7,Glu (1)
and
are the D-glucose (G1) adsorption (or inhibition) parameter for beta-glucosidase (BG)
and the cellobiose (G2) adsorption parameter for BG respectively. The values of these
parameters were from the experiment by Chauve et al. (2010).
I 7,Glu (6)
I 7,Glu (3)
，
I 7,Glu (4)
，
I 7,Glu (5)
and
are cello-oligomers (G3-G6) adsorption parameters for BG. Their values were based on
the value of
I 7,Glu (2)
and the experiments by Yazaki et al. (1997) which described the
23
relationship among cello-oligomers (G2-G6) inhibition parameters for BG.
I 8, Xyl (1) I 8, Xyl (2)
,
,
I
(6)
I 8, Xyl (3) I 8, Xyl (4) I 8, Xyl (5)
,
,
and 8, Xyl
are D-xylose and xylo-oligomers (X2-X6) adsorption
parameters for beta-xylosidase (BX). Their values were from the work by Rasmussen, Sorensen
et al. (2006). Currently, there are no reliable values for the xylo-oligomers (X1-X6) adsorption
parameters for BG and cello-oligomers (G1-G6) inhibition parameters for BX. We only
considered the inhibitions of X1 for BG and G1 for BX and did not consider other "crossover"
oligomers adsorption for beta-enzymes in the model. We assumed that the values of
I 8,Glu (1)
were equal to
BG kinetic parameter
I 8, Xyl (1)
 7,Glu (2)
and
I 7,Glu (1)
I 7, Xyl (1)
and
respectively due to the same inhibitors. The value of
for cellobiose (G2) was from experiment by Chauve et al. (2010).
 7,Glu (3)  7,Glu (4)  7,Glu (5)

(6)
,
,
and 7,Glu
are BG kinetic parameters for cello-oligomers (G3-G6),
their values were based on the value of
 7,Glu (2)
and the experiments by Yazaki et al. (1997)
which described the relationship among BG kinetic parameters for cello-oligomers (G2-G6).
 8, Xyl (2)  8, Xyl (3)  8, Xyl (4)  8, Xyl (5)

(6)
,
,
,
and 8, Xyl
are BX kinetic parameters for xylo-oligomers
(X2-X6) and their values from the work by Rasmussen et al. (2006). As we did not consider
other "crossover" oligomers adsorption for beta-enzymes in the model, the corresponding kinetic
parameters were all set to be 0.
24
Table.I1 Key simulation parameters
Qing and Wyman 2011
Banerjee, Car et al. 2010
Kumar and Wyman 2009
Parameter
Value
Parameter
Value
Parameter
Value
FA(0)
0.1051
FA(0)
0.1431
FA(0)
0.1046
 (0)
M,Xyl
0.55
 (0)
M,Xyl
0.50
 (0)
M,Xyl
0.60
Table.I2 Adsorption and kinetic parameters
Parameter
Value
Ref.
Parameter
(1/mM)
L1, N ,Glu L1, X ,Glu L1,Y ,Glu
3
Value
Ref.
(1/min)
 1, N ,Glu  1, X ,Glu  1,Y ,Glu
(Zhou,
3317
(Zhang and
Hao et
Lynd 2006,
al. 2009)
Banerjee,
Car et al.
2010)
L1, N , Xyl L1, X , Xyl L1,Y , Xyl
 1, N , Xyl  1, X , Xyl  1,Y , Xyl
0
0
(Zhou, Hao
et al. 2009)
L2, N ,Glu L2,Y ,Glu
0
 2, N ,Glu  2,Y ,Glu
0
L2, X ,Glu
4
 2, X ,Glu
1399
(Zhang and
Lynd 2006,
Banerjee,
Car et al.
2010)
25
L2, N , Xyl L2, X , Xyl L2,Y , Xyl
 2, N , Xyl  2, X , Xyl  2,Y , Xyl
0
0
(Zhou, Hao
et al. 2009)
L3, N ,Glu L3, X ,Glu
0
 3, N ,Glu  3, X ,Glu
0
L3,Y ,Glu
3
 3,Y ,Glu
699.7
(Zhang and
Lynd 2006,
Banerjee,
Car et al.
2010)
L3, N , Xyl L3, X , Xyl L3,Y , Xyl
 3, N , Xyl  3, X , Xyl  3,Y , Xyl
0
0
(Zhou, Hao
et al. 2009)
L4, N ,Glu L4, X ,Glu L4,Y ,Glu
0
L4, N , Xyl L4, X , Xyl L4,Y , Xyl
0.574
(Zhang
 4, N ,Glu  4, X ,Glu  4,Y ,Glu
0
 4, N , Xyl  4, X , Xyl  4,Y , Xyl
50.12
(Zhang and
and
Lynd 2006,
Lynd
Banerjee,
2006,
Car et al.
Qing and
2010)
Wyman
2011)
 5, N ,Glu  5,Y ,Glu  5, X ,Glu
0
 5, N , Xyl  5,Y , Xyl
0
0.574
 5, X , Xyl
50.12
L6, N ,Glu L6, X ,Glu L6,Y ,Glu
0
 6, N ,Glu  6,Y ,Glu  6, X ,Glu
0
L6, N , Xyl L6, X , Xyl
0
 6, N , Xyl  6, X , Xyl
0
L6,Y , Xyl
0.574
 6,Y , Xyl
50.12
L7,  ,  L8,  , 
0
 7,  ,   8,  , 
0
L5, N ,Glu L5, X ,Glu L5,Y ,Glu
0
L5, N , Xyl L5,Y , Xyl
0
L5, X , Xyl
Assu
med
26
Assum
ed
Table.I3 Inhibition parameters
Parameter
Value
Reference
Parameter
(1/mM)
I1,Glu (1)
0.06
Value
(1/mM)
(Levine, Fox
I 2,Glu (1) I 3,Glu (1)
0.032
et al. 2010)
I1,Glu (2)
0.13
(Jeffrey
Tolan
0.3
S.
I 2,Glu (2) I 3,Glu (2)
0.13
and
(Jeffrey
Tolan
I1,Glu (4)
0.37
I1,Glu (5)
0.44
S.
Leggio
0.51
S.
and
Foody 1999)
I 2,Glu (3) I 3,Glu (3)
0.3
I 2,Glu (4) I 3,Glu (4)
0.37
I 2,Glu (5) I 3,Glu (5)
0.44
and
I1,Glu (6)
(Jeffrey
Tolan
and
Foody 1999,
Lo
(Levine, Fox et
al. 2010)
Foody 1999)
I1,Glu (3)
Reference
(Jeffrey
S.
Tolan
and
Foody
1999,
Lo Leggio and
Pickersgill
I 2,Glu (6) I 3,Glu (6)
0.51
Assumed
I 2, Xyl (1) I 3, Xyl (1)
0.032
(Lo
I 2, Xyl (2) I 3, Xyl (2)
2
Pickersgill
1999)
1999)
I1, Xyl (1)
0.06
I1, Xyl (2)
2
Leggio
and
I1, Xyl (3)
2
I1, Xyl (4)
4
10
Pickersgill
1999,
I1, Xyl (6)
11
I 4,Glu (1)
0.06
Nerinckx
(Lo Leggio and
Pickersgill
I 2, Xyl (3) I 3, Xyl (3)
2
I 2, Xyl (4) I 3, Xyl (4)
4
Ntarima,
I1, Xyl (5)
Assumed
1999, Ntarima,
Nerinckx et al.
2000)
et
I 2, Xyl (5) I 3, Xyl (5)
10
I 2, Xyl (6) I 3, Xyl (6)
11
I 5,Glu (1) I 6,Glu (1)
0.032
al. 2000)
Assumed
27
Assumed
I 4,Glu (2)
0.13
(Jeffrey
Tolan
I 4,Glu (3)
0.3
I 4,Glu (4)
0.37
S.
0.13
I 5,Glu (3) I 6,Glu (3)
0.3
I 5,Glu (4) I 6,Glu (4)
0.37
I 5,Glu (5) I 6,Glu (5)
0.44
I 5,Glu (6) I 6,Glu (6)
0.51
I 5, Xyl (1) I 6, Xyl (1)
0.4
I 5, Xyl (2) I 6, Xyl (2)
0.85
I 5, Xyl (3) I 6, Xyl (3)
1.5
I 5, Xyl (4) I 6, Xyl (4)
2
I 5, Xyl (5) I 6, Xyl (5)
4
I 5, Xyl (6) I 6, Xyl (6)
4.5
and
Foody 1999,
Lo
I 5,Glu (2) I 6,Glu (2)
Leggio
and
I 4,Glu (5)
0.44
I 4,Glu (6)
0.51
I 4, Xyl (1)
0.4
Pickersgill
1999)
(Ntarima,
Nerinckx
et
al. 2000)
I 4, Xyl (2)
0.85
I 4, Xyl (3)
1.5
(Lo
Leggio
and
Pickersgill
I 4, Xyl (4)
2
1999,
Ntarima,
I 4, Xyl (5)
4
I 4, Xyl (6)
4.5
Nerinckx
et
al. 2000)
Table.I4 Beta-enzymes parameters
Parameter
Value
Reference
Parameter
(1/mM)
I 7,Glu (1)
0.294
Value
Reference
(1/min)
(Chauve,
 7,Glu (1)
0
 7,Glu (2)
1897
Determined
Mathis et al.
2010)
I 7,Glu (2)
1.136
(Yazaki,
Ohnishi et al.
(Chauve,
Mathis et al.
28
1997,
I 7,Glu (3)
3.846
2010)
 7,Glu (3)
Chauve,
1738.9
Mathis et al.
I 7,Glu (4)
4.000
I 7,Glu (5)
2.174
2010)
(Yazaki,
Ohnishi et al.
 7,Glu (4)
1422.8
 7,Glu (5)
895.8
1997, Chauve,
Mathis et al.
2010)
I 7,Glu (6)
1.449
I 7, Xyl (1)
0.417
I 7, Xyl (2)
0
 7,Glu (6)
843.1
Assumed
 7, Xyl (1)
0
Not
 7, Xyl (2)
0
Determined
considered
I 7, Xyl (3)
0
 7, Xyl (3)
0
I 7, Xyl (4)
0
 7, Xyl (4)
0
I 7, Xyl (5)
0
 7, Xyl (5)
0
I 7, Xyl (6)
0
 7, Xyl (6)
0
I 8,Glu (1)
0.294
Assumed
 8,Glu (1)
0
I 8,Glu (2)
0
Not
 8,Glu (2)
0
considered
I 8,Glu (3)
0
 8,Glu (3)
0
I 8,Glu (4)
0
 8,Glu (4)
0
I 8,Glu (5)
0
 8,Glu (5)
0
I 8,Glu (6)
0
 8,Glu (6)
0
I 8, Xyl (1)
0.417
 8, Xyl (1)
0
 8, Xyl (2)
1897
(Rasmussen,
Sorensen
I 8, Xyl (2)
2.500
al. 2006)
et
29
(Rasmusse
I 8, Xyl (3)
5.000
 8, Xyl (3)
1250.3
n, Sorensen et
al. 2006)
I 8, Xyl (4)
6.250
 8, Xyl (4)
1164.1
I 8, Xyl (5)
10.000
 8, Xyl (5)
1293.4
I 8, Xyl (6)
12.500
 8, Xyl (6)
862.3
30