of 12
1
Supporting Information
Food polyelectrolytes compress the colonic mucus
hydrogel by a Donnan mechanism
Asher Preska Steinberg
1
, Zhen
-
Gang Wang
1
, and Rustem F. Ismagilov
1,2
*
1
Division of Chemistry and Chemical Engineering
2
Division of Biology and
Biological Engineering
California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, United States
2
Derivation of the ionic contribution to osmotic pressure due to Donnan partitioning.
We
imagine a negatively charged polyelectroly
t
e so
lution with added salt to be in contact with the
mucus layer. We take the volume of the polyelectrolyte solution
(
#
)
to be much larger than that
of the mucus layer
(
%
)
, which is true in our
ex vivo
set
-
up. In our
ex vivo
experiments, the
polyelectrolyte solution volume is
#
~
200
휇퐿
, and we can estimate
%
using the average
thickness of colonic mucus measured in ref.
1
(
~
70
휇푚
) and the
xy
dimensions of the explants
(~1 by 1
cm
), which gives
%
~
7
휇퐿
.
Therefore,
/
0
/
1
~
30
, and we can assume that the salt and
polyelectrolyte concentrations in the polyelectrolyte solution are unaffected by any partitioning
of ions into the mucus layer.
The total concentration of salt cations in the polyel
ectrolyte solution from the condition
of electroneutrality is simply (assuming the counterion of the polyelectrolyte is the same as the
cation from salt, which is the case in our system):
4
5
=
7
+
(S
1
)
Where
4
5
is the to
tal concentration of salt cations in the polyelectrolyte solution phase,
7
is the
salt concentration, and
is the charge concentration from the polyelectrolyte backbones. The
concentration of the salt anions (
:
5
) is just:
:
5
=
7
(S
2
)
This gives an osmotic pressure due to the small ions in the polyelectrolyte solution phase as:
3
Π
<=>
#
=
푅푇
(
2
7
+
)
(S
3
)
where
=
BC=
is the gas constant.
Now consider the small ion concentrations
in the mucus layer. The mucus network
contributes a fixed polyelectrolyte charge density of
m
. Electroneutrality then dictates:
4
E
=
:
E
+
(S
4
)
where
4
E
and
:
E
are the small cation and small anion concentrations, respectively. Let
be the
potential difference between the mucus layer and the polyelectrolyte solution, then equality of
electrochemical potential for the small ions entails:
2
푒휓
+
푅푇푙푛
4
E
=
푅푇푙푛
4
5
(S
5
)
푒휓
+
푅푇푙푛
:
E
=
푅푇푙푛
:
5
(S
6
)
Eq
S5 and S6
can be combined to give:
4
E
:
E
=
4
5
:
5
(S
7
)
4
Combining eq
S1, S2, S4, and S7
then gives:
4
E
=
1
2
L
M
N
+
4
7
(
7
+
)
+
P
(S
8
)
and:
:
E
=
1
2
L
M
N
+
4
7
(
7
+
)
P
(S
9
)
The osmotic pressure from the small ions in the mucus layer is thus:
Π
<=>
E
=
푅푇
M
N
+
4
7
(
7
+
)
(S
10
)
The osmotic
pressure difference between the polyelectrolyte solution and the mucus layer due to
ions (
Δ
Π
<=>
) is obtained by subtracting eq
S10 from eq S3:
Δ
Π
<=>
=
푅푇
L
2
7
+
M
N
+
4
7
(
7
+
)
P
(S
11
)
In the limit of
7
, the expression
simplifies to:
Δ
Π
<=>
=
푅푇
L
2
7
+
2
M
7
(
7
+
)
P
(S
12
)
5
Estimation of
the compression modulus
for the colonic mucus hydrogel.
The simplest model
for uniaxial deformations of a polymer network can be derived from the “affine netwo
rk model”,
which assumes affine deformation of the polymer network. The driving physics behind
deformations in this model is the entropic elasticity of the chains.
3
This model gives the classical
stress
-
elongation relation as (also eq
8
in main text):
T>U
=
(
1
N
)
(S
13
)
Where
T>U
is the engineering stress or the applied stress on the network (which in this case we
took to be
ΔΠ
),
G
is the
compression modulus
of the network (in
Pa
), and
is the deformation
factor. The negative sign in front of
G
is due to the fact that we are applying a compressive stress.
In this model,
G
can be written as:
=
휌푅푇
Z
(S
14
)
where
is the mass concentration of network strands (
푘푔
/
]
) and
Z
is the MW of a network
strand (in
푘퐷푎
). If we take the MW of a MUC2 network strand to be the MW of the polymer
between network cross
-
links (often
referred to as a “MUC2 monomer” in the biology literature),
we can estimate
Z
~
400
600
푘퐷푎
.
4,5
There are not existing literature values for the mass
concentration of the murine colonic mucus hydrogel, but for porcine gastrointestinal mucus it is:
6
~
19
30
푚푔
/
푚퐿
.
6,7
Taking the arithmetic mean of these values and inserting them into eq
S14
yields
~
120
푃푎
.
We speculate that eq
S14
may be lower than the value for
G
obtain
ed by
the curve fitting done in Figure 3 because eq
S14
assumes that the network strands are non
-
interacting.
References
(1)
Datta, S. S.; Preska Steinberg, A.; Ismagilov, R. F. Polymers in the Gut Compress the
Colonic Mucus Hydrogel.
Proc. Natl. Acad. Sci. U. S. A.
2016
,
113
(26), 7041
7046.
https://doi.org/10.1073/pnas.1602789113.
(2)
Overbeek, J. T. G. The Donnan Equilibrium.
Prog. Biophys. Biophys. Chem.
1956
,
6
, 58
64.
(3)
Rubinstein, M.; Colby, R. H.
Polymer Physics
; OUP Oxford: New York, 2003.
(4)
Ambort, D.; Johansson, M. E. V.
; Gustafsson, J. K.; Nilsson, H. E.; Ermund, a.; Johansson,
B. R.; Koeck, P. J. B.; Hebert, H.; Hansson, G. C. Calcium and PH
-
Dependent Packing and
Release of the Gel
-
Forming MUC2 Mucin.
Proc. Natl. Acad. Sci.
2012
,
109
(15), 5645
5650. https://doi.org/10
.1073/pnas.1120269109.
(5)
Axelsson, M. A. B.; Asker, N.; Hansson, G. C. O
-
Glycosylated MUC2 Monomer and Dimer
from LS 174T Cells Are Water
-
Soluble, Whereas Larger MUC2 Species Formed Early
during Biosynthesis Are Insoluble and Contain Nonreducible Inter
molecular Bonds.
J. Biol.
Chem.
1998
,
273
(30), 18864
18870. https://doi.org/10.1074/jbc.273.30.18864.
(6)
Sellers, L.
A
.; Allen, A.; Morris, E. R.; Ross
-
Murphy, S. B. The Rheology of Pig Small
7
Intestinal and Colonic Mucus: Weakening of Gel Structure by N
on
-
Mucin Components.
BBA
-
Gen. Subj.
1991
,
1115
(2), 174
179. https://doi.org/10.1016/0304
-
4165(91)90027
-
E.
(7)
Georgiades, P.; Pudney, P. D.; Thornton, D. J.; Waigh, T. A. Particle Tracking
Microrheology of Purified Gastrointestinal Mucins.
Biopolymers
2014
,
101
(4), 366
377.
https://doi.org/10.1002/bip.22372.
(8)
Hoogendam, C. W.; De Keizer, A.; Cohen Stuart, M. A.; Bijsterbosch, B. H.; Smit, J. A.
M.; Van Dijk, J. A. P. P.; Van Der Horst, P. M.; Batelaan, J. G. Persistence Length of
Carboxymethyl Cell
ulose as Evaluated from Size Exclusion Chromatography and
Potentiometric
Titrations.
Macromolecules
1998
,
31
(18),
6297
6309.
https://doi.org/10.1021/ma971032i.
(9)
Sj
ö
holm, E. Size Exclusion Chromatography of Cellulose and Cellulose Derivatives.
In
Handb
ook of
S
ize
Exclusio
n Chromatography and Related Techniques;
Mar
ce
l Dekker:
2004
,
331
352.
8
Figure S
1
.
Description of image processing for side
-
views presented in Figure 2.
(A
-
B) False
-
colored
confocal fluorescence (
A
) and confocal reflectance (
B
) xz side
-
views presented in Figure
2B. Brightness and contrast was not enhanced from the original images in either panel. (C) The
confocal fluorescence image in
A
but with enhanced brightness and contra
st. (D) The confocal
reflectance image in (
B
) but with enhanced brightness and contrast. (E) The confocal reflectance
image from
D
but with the top part of the image, above the dashed line, removed. Because the
particles also scatter light, we split the im
age below the position of the particles, which were
located in the fluorescence image (shown in
C
) for clarity. The dashed line in
C, D,
and
E
are at
the exact same z
-
position (right below the particles). (F) Combination of
C
and
E
presented in
Figure 2B.
Scale bars are 30
μ
m.
9
Figure S2.
Compression with carboxymethyl cellulose (CMC) is reversible.
Plot of mucus
thickness over time before and after adding CMC with a degree of substitution of 0.7 to a murine
colonic explant. The following time
-
points were
taken: Before adding CMC (time = 0 min), 10
and 25 min after adding CMC (time = 10 and 25 min), and then 10 min to an hour after washing
the explant three times with 1 mL of ice
-
cold 1x PBS to remove the CMC from the explant (time
= 35 to 85 min). Mucus t
hickness was measured using the “microparticle method” (see
Materials
and Methods)
and each data point represents the average thickness measured at 5 points on the
explant. Error bars are SEM with n = 5.
10
Figure S3.
Gel permeation chromatography (GPC)
measurements of charged and uncharged
polymers.
Chromatograms of polymers used in the study. Method of detection is right
-
angle light
scattering which is plotted on the vertical axis (unitless). CMC DS 0.9 = carboxymethyl cellulose
with a degree of substi
tution of 0.9, USP CMC = U.S.P. grade carboxymethyl cellulose fed to mice
in Figure 1, CMC DS 0.7 = carboxymethyl cellulose with a degree of substitution of 0.7, HEC =
hydroxyethyl cellulose.
11
Figure S4.
Polymer contribution and ionic contribution to th
e osmotic pressure.
The contributions
to the osmotic pressure (eq 4
)
from ionic effects (i.e. Donnan partitioning) which is given by eq 5
and from the polymer osmotic pressure which is given by eq 6. The polymer osmotic pressure
(black) is equal for all po
lymers (both carboxymethyl cellulose [CMC] derivatives and
hydroxyethyl cellulose [HEC]). There is no ionic contribution for HEC as it is uncharged. Dashed
line indicates the polymer overlap concentration (
), where
=
0
.
19
%
/
. “Ionic for CMC
DS
0.7” is the ionic contribution to the osmotic pressure for carboxymethyl cellulose with a degree
of substitution of 0.7. “Ionic for CMC DS 0.9” is the ionic contribution to the osmotic pressure for
CMC with a degree of substitution of 0.9.
12
Table S1:
Gel
permeation chromatography of polymers in phosphate
-
buffered saline.
Sample
HEC
USP
CMC
CMC DS 0.9
CMC DS 0.7
M
w
(kDa)
152
148
150
146
M
w
/M
n
3.17
2.19
2.25
2.10
R
h
(nm)
18.8
20.6
22.2
19.9
Carboxymethyl cellulose derivatives were analyzed using a
refractive index increment (dn/dc) of
h>
hi
=
0
.
163
.
8
Hydroxyethyl cellulose was analyzed using
h>
hi
=
0
.
150
.
9
HEC = hydroxyethyl
cellulose, USP CMC = U.S.P. grade carboxy
methyl cellulose (fed to mice in Figure 1), CMC DS
0.9 = carboxymethyl cellulose with a degree of substitution of 0.9, CMC DS 0.7 = carboxymethyl
cellulose with a degree of substitution of 0.7. M
w
= weight
-
average molecular weight; M
w
/M
n
=
the dispersity;
R
h
= hydrodynamic radius.