Supplementary Information (SI)
Concentrating membrane proteins using ultrafiltration without concentrating detergents
Hasin Feroz1, Craig Vandervelden1,2, Bon Ikwuagwu1,3, Bryan Ferlez4, Carol Baker4, Daniel J.
Lugar4, Mariusz Grzelakowski5, John Golbeck4,6, Andrew Zydney1 and Manish Kumar1*
1
Department of Chemical Engineering, The Pennsylvania State University, Pennsylvania, USA
2
3
Current address: Department of Chemical Engineering, University of Kansas, Kansas, USA
Current address: Department of Chemical Engineering, University of Pittsburgh, Pennsylvania,
USA
4
Department of Biochemistry and Molecular Biology, The Pennsylvania State University, USA
5
4
Applied Biomimetic Inc., Cinncinati, Ohio, USA
Department of Chemistry, The Pennsylvania State University, USA
*Corresponding Author, Department of Chemical Engineering, Pennsylvania State University,
155 Fenske Laboratory, University Park, PA 16802, USA. Phone: +1 814 865 7519. Email:
[email protected]
Page
Membrane protein purification
2
Determination of detergent and MP concentration
3
Stirred-cell Ultrafiltration experiments
4
Pressure in stirred cell
4
Mass transfer coefficient in stirred cell
5
Shear in stirred cell
5
Pressure in centrifugal filter
6
Cumulative filtrate volume versus time in centrifugal filter 7
Mass transfer coefficient in centrifugal filter
8
Shear in centrifugal filter
10
Stirred cell experiment for OG
11
Detergent transmission through 10 kDa
11
Analysis of detergent transmission
12
Membrane protein purification
Halorhodopsin
Expression and purification of HR was adapted from the protocol of Sato, et al (Sato et al. 2002).
We expressed Natronomonas pharaonis HR by cloning an E. coli codon optimized gene with a
C- terminal 6x histidine tag (1MAETLP......TPADD291LEHHHHHH]). Using the T7
polymerase/pCDF Duet-1 enhanced co-expression system for E. coli BL21 (DE3) (Novagen), we
obtained high expression of HR-LE-his from plasmid pCB8a. Cell culture and harvesting was
carried out in the Shared Fermentation Facility of the Huck Institute of Life Sciences at
Pennsylvania State University. A 25 ml inoculum in 2 x YT medium with 50μg/ml Spectinomycin
(Gold Biotechnology) was first grown overnight at 37 ˚C with shaking at 150 rpm and then
diluted 100 fold into 2 x YT medium in a baffled Fernbach flask to prepare the seed culture for
fermentation. This seed culture was grown overnight at 37 ˚C and transferred to 20 L of 2 x YT
medium supplemented with 50 µg/ml Spectinomycin at 1:20 fold dilution and initial OD600 of
0.335. On reaching an OD600 of 0.72, 2.5 µg/ml of all-trans-retinal was added and cells harvested
using a Sharples supercentrifuge after 4 hours. The final OD of the culture was around 4.09 and
a yield of ~ 153g cells(wet)/20 L was obtained. These cells were harvested, frozen and stored at
-80˚C. For purification, the cell pellet was resuspended in lysis buffer (50 mM Tris-HCl, pH 8.0,
5 mM MgCl2) and lysed by three passes through an M-110EH-30 microfluidizer processor
(Microfluidics). Cell debris was removed via low speed centrifugation (2000  g) and the
resulting supernatant was spun at 208,000 x g for 1 h at 4oC to pellet the plasma membranes. The
membrane pellets were suspended in 50mM MES, pH 6, 300 mM NaCl, 1.5 % decyl-β-D
maltoside (DM) (Affymetrix, California, USA) and solubilized overnight at 4oC. Unsolubilized
membranes were removed by ultracentrifugation at 208,000 x g for 1 hour at 4oC. The supernatant
fraction was passed over a HisPur Cobalt Resin (Thermo Fisher Scienctific) previously
equilibrated with 50 mM MES, pH 6.0, 300 mM NaCl, 5 mM imidazole, 0.2 % DM. Unbound
protein was removed by washing the column with 50 mM MES, pH 6, 300 mM NaCl, 45 mM
imidazole, 0.2 % DM. The protein was eluted [50 mM Tris-HCl, pH 7.6, 300 mM NaCl, 1 M
imidazole, 0.1% DM] and then dialyzed overnight against 0.4 % DM, 10 mM MES, 40 mM KCl,
pH 6.0 before filtration experiments.
Aquaporin
The RsAqpZ gene was cloned into the pET28b vector with the addition of a C-terminal 10
Histidine tag. A large-scale fermentation run was conducted to obtain cell pellets from which
protein was purified as described subsequently. This large scale fermentation run was carried out
at the Shared Fermenation Facility of the Huck Institute of Life Sciences at Pennsylvania State
University. A 12.5 ml inoculum in LB medium with 50 g/ml Kanamycin wat first grown
overnight at 37 ˚C with shaking at 200 rpm resulting in an OD600 of ~ 2 and then diluted 100
times in a 3 L baffled Fernbach flask to prepare the seed culture for fermentation. This seed
culture was grown overnight at 28 ˚C and 250 rpm and 600 ml of culture (OD ~ 2.4) was
inoculated into 60L of sterilized LB medium with 5ml Antiform 204 (Sigma Aldrich) with 25 mg
filter sterilized Kanamycin per liter of LB medium. This large-scale fermentation was carried out
overnight at 20˚C at 250 rpm agitation with air sparging. After the OD reached ~ 2.2, the culture
was induced with 0.1 mM (final concentration) IPTG for 2.5 hours and the cells harvested using
a Sharples supercentrifuge. The final OD of the culture was around 1.85 and a yield of ~ 400g
cells(wet)/60 L was obtained. These cells were frozen and stored at -80˚C. Cell lysis and
purification of C-terminally his-tagged RsAqpZ was conducted using the same Co-NTA resin as
for halorhodopsin and using the procedures described for RaAqpZ previously (ref Erbakan et al
2012). The final protein was dialyzed overnight against 2% OG, 100 mM KH2PO4, 100 mM NaCl,
pH 7.4 before filtration experiments.
Determination of detergent and MP
concentration
OG
and
determined
refractive
DM
concentrations
from
standard
index
(RI)
were
curves
versus
of
known
concentrations of detergent in respective
buffer solutions. Refractive index can be
used to quantify detergent over a wide range
of concentrations including those below the
cmc (Strop and Brunger 2005). It can also
Figure 1. Refractive index based concentration
determination of detergents, OG (100mM NaCl,
100mM K2HPO4, pH7.4) and DM (40 mM KCl,
10mM MES pH 6.0)
be used to quantify the detergent in a MP/detergent system due to minimal interference from
protein to the measured values of RI.
HR and RsAqpZ concentrations were determined from a standard calibration curve developed for
BSA using the Bradford assay (Grimsley and Pace 2003). Additionally, a correction factor of
1.684 was applied to Bradford assay-based HR concentrations, as obtained from amino acid
residue analysis (Molecular Structural Facility, UC Davis).
Stirred-cell Ultrafiltration experiments
All membranes were soaked in isopropyl alcohol for about 45 minutes and then washed with at
least 100 mL of water in the stirred cell to remove residues and ensure thorough wetting of the
pores. All filtration experiments were conducted using a 10 mL (effective membrane area of 4.1
cm2) Amicon stirred cell (Millipore) placed on a magnetic stir plate and connected to a gaspressurized polycarbonate reservoir filled with the appropriate solution. The membranes were
then soaked overnight in the solution to be filtered (detergent or protein/detergent mixture) to
ensure that observed results were not affected by the transient adsorption of molecules onto
membranes. The hydraulic permeability (Lp) of the membrane was measured over the same
pressure range (7 to 170 kPa = 1- 24 psi) before soaking in filtered solution and again after
filtration experiments to study the extent of adsorption of detergent/protein and irreversible
fouling of the membrane. All samples were stored at 4C till the time of experiment.
Sieving coefficient determination
6 ml of solution was filtered at each pressure with measurement of flux using a digital balance
(Mettler Toledo, Columbus, OH). 500 μl of permeate samples were collected at the 2nd, 4th and
6th ml for determination of average detergent and/or protein concentrations before depressurizing
the system. The respective concentrations in the feed/stirred cell were determined immediately
before and after filtration at each pressure and averaged to calculate So.
Equivalency between centrifugal filter and stirred cell filter operation
Pressure in stirred cell
For the stirred cell, the transmembrane pressure (TMP) is read directly off the pressure gauge and
can be set to match the calculated TMP of the centrifugal filter.
Mass transfer coefficient in stirred cell
Mass transfer coefficients for the micellar detergent can be determined from Colton-Smith
empirical correlation
Sh = 0.285 Re0.567 Sc 0.33 for 8 × 103 < Re ≤ 3.2 × 104
Sh = 0.0443 Re0.746 Sc 0.33 for 3.2 × 104 ≤ Re < 8.2 × 104
where Re =
T
ρω( )2
2
μ
μ
, Schmidt number, Sc =ρD and Sherwood number, Sh =
T
2
<k>( )
D
with ρ, ω, μ, D
and T being density, rotation speed (in radians per s), viscosity, diffusivity and stirred cell
diameter respectively (Colton and Smith 1972; Koutsou and Karabelas 2012). Since, shear rate,

γ = μ and ∝ 𝜔 (as demonstrated by Kosvintsef et al, in a stirred cell set-up), the mass transfer
coefficient is related to shear rate raised to the power 0.567 for laminar flow and 0.746 for
turbulent flow. Empirical correlations of the form, Sh = a Reb Sc c for mass transfer in narrow
channels indicate similar dependence of k on shear rates (Koutsou and Karabelas 2012).
Shear in stirred cell
The shear rates in the stirred cell at different rpm were calculated according to Kosvintsev et al
(Kosvintsev et al. 2005). The shear stress,  associated with the stirred cell is a function of the
rotation rate and was quantified by assuming Bodewadt flow according to Kosvintsev et al
(Kosvintsev et al. 2005). The shear stress is thus a function of the radial position in the stirred
cell, r, with the centrifugal force being balanced by the pressure gradient. The stirrer, in this case
a flat blade impeller with blade height, b, diameter, d and number of blades, n𝑏 = 2, thus divides
the shear field into two regimes- (a) forced vortex, r<r𝑐 (constant angular velocity induced by
rotating motion of stirrer) (b) free vortex, r>r𝑐 (constant angular momentum arising from vortices
generated by the stirrer). The critical radius, r𝑐 , marking the transition between the two regions,
is about 20 to 25 % of the stirred cell diameter for our experimental conditions and increases with
Reynolds number (Kosvintsev et al. 2005).
2d
Re( T )2
d
d b 0.036 0.116
rc = 1.23 (0.57 + 0.35 ) ( )
nb
(
)
2d
2
T T
1000 + 1.43Re( T )2
where Re =
T
ρω( )2
2
μ
, with 𝜌, 𝜔, μ, b, d and T are density, angular velocity (in radians), viscosity,
stirrer blade height, stirrer diameter and stirred cell diameter respectively. The shear stress,  is
thus
1
 = 0.825 ηωr δ , r<r𝑐
𝑟
1
 = 0.825 𝜂𝜔𝑟𝑐 ( 𝑟𝑐)0.6 𝛿 , r>r𝑐
where from the Landau-Lifshitz equation, the momentum boundary layer thickness is,
μ
δ=√
ρω
r
1
r
𝑐
𝑟
1
∫0 𝑐 0.825 ηωrδ 2 πr dr+∫r 0.825 ηω𝑟𝑐 ( 𝑟𝑐 )0.6 𝛿 2 πr dr
The area average shear,Avg =
Avg =0.825
𝜇𝜔 2 𝑟𝑐 3
𝛿
[
𝑟2
3
+
𝑟𝑐 1.6
1.4
r
∫0 2 πr dr
thus becomes
(𝑟 1.4 − 𝑟𝑐 1.4 )]
Pressure in centrifugal filter unit
The pressure head developed in the centrifuge can be calculated based on the liquid height, h and
the distance R from the center of a swinging bucket rotor, where the tubes swing to the horizontal
position during operation. The pressure at the bottom of the liquid is thus given as
ΔP=𝛒𝛚𝟐 (𝐑 𝐡 −
𝐡𝟐
𝟐
) (Borujeni and Zydney 2012). The vertical design of the centrifugal filter, i.e.,
rectangular filter plates tilted at an angle,  to the centerline leads to a more complicated behavior
since there is also a tangential flow along the surface of the filter (Figure 2).
For an incompressible fluid, ignoring shear in the direction of filtration, i.e., perpendicular to
membrane, and assuming that the centrifugal body force acting in the z-direction, i.e., the sin 
component, is g z = ω2 r sin where r=l-h and z = hsin, we can compute the local pressure using
the Navier Stokes equation in the z-direction
𝜕𝑣𝑧
𝜕𝑣𝑧
𝜕𝑣𝑧
𝜕𝑣𝑧
𝜕𝑃
𝜕 2 𝑣𝑧 𝜕 2 𝑣𝑧 𝜕 2 𝑣𝑧
𝜌[
+ 𝑣𝑥
+ 𝑣𝑦
+ 𝑣𝑧
] = 𝜌𝑔𝑧 −
+ 𝜇[ 2 +
+
]
𝜕𝑡
𝜕𝑥
𝜕𝑦
𝜕𝑧
𝜕𝑧
𝜕𝑥
𝜕𝑦 2
𝜕𝑧 2
ρω2 r sin −
∂P
=0
∂z
Substituting 𝑑𝑧 = 𝑑ℎ𝑠𝑖𝑛
ρω2 r sin −
∂P
=0
∂h sin
dP
= ρω2 (l − h)(sin)2
dh
ΔP = P − Patm = ρω2 (lh −
h2
2
)(sin)2
z=hsin
x=hcos
Figure 2. Determination of transmembrane pressure developed in centrifugal filter
Cumulative filtrate volume versus time in centrifugal filter
The cumulative volume of water filtered with time for different centrifugal speeds was calculated
and was in good agreement with experimental data (Figure 3). The theoretical permeate volume
was calculated from transmembrane pressure, ΔP and hydraulic permeability, LP of the 30 kDa
membrane,
ρ
dV
= ΔP LP AMem ρ
dt
Where
V=volume of water at any time, t in filter= 𝑏 ℎ2 tan 
AMem = area of membrane in contact with water = 2b
h
cos 
LP = hydraulic permeability of 30kDa membrane
Lmh
= 21.5
psi
= 8.6 × 10−7 m/s/kPa
Substituting
ΔP ,V and AMem into
above
equation,
ρ
d(b h2 tan )
h
= ΔP LP (2b
)ρ
dt
cos 
2h tan  ρ
dh
= ρ ω2 (lh
dt
h2
h
− ) (sin)2 LP (2b
)ρ
2
cos 
Figure 3. Volume of water filtered in a spin filter
at different rpms was modelled based on
hydraulic permeability of membrane (solid lines)
and show excellent agreement with experimental
data as represented by the symbols.
dh
h2
= ρ ω2 (lh − )sin LP
dt
2
h
L − h/2
ln ( ) − ln (
) = ρ ω2 sin LP t
ho
L − ho /2
Solving h as a function of time numerically, V was obtained and subtracted from initial
water volume at t=0s to obtain permeate volume at any time,t. The results are plotted as
solid lines and show good agreement with experimental data (Figure 3).
Mass transfer coefficient in centrifugal filter
Due to the high speeds used during centrifugal ultrafiltration, significant natural convection
(buoyancy induced flow) arises from the density gradient in the boundary layer near the
membrane, i.e., from the feed side to the membrane surface. This natural/free convection current
minimizes concentration polarization in the centrifugal system. The relative importance of
buoyancy forces arising from the concentration difference versus those due to forced convection,
can be evaluated from the ratio of the Grashof number (Gr) to the square of Reynolds number
(Re) as discussed by Youm et al. (Youm et al. 1996),
Gr =
(ω2 r cos  )αβ(x)4
υ2
Dh vx
Re=
ʋ
where
z = h sin 
x=h cos 
1 𝜕𝜌
α=𝜌 𝜕𝐶 = 0.225 g/cm3 (Somasundaran 2004;
Zhang and Somasundaran 2004)
1 ∂C
β=ρ ∂z =1×
CW −CB
ΔX
CB ≈
CPermeate
S0
CW ≈
CPermeate
Sa
CW −CB
= Average(x
before, xafter)
Figure 4. Filtration of 1 % DM and water over in
spin filter at 4000 rpm over different duration of
spins. Filtration velocity/flux can be calculated
from the polynomial fit h = -0.0079t3 + 0.1091t2 0.6122t + 2.5136
SO = observed sieiving coefficient ≈0.39
Sa = actual sieiving coefficient which was evaluated from the stirred cell UF data based on the
plot of sieving function versus flux≈ 0.12 (Table II)
Area
2h tan b
Dh , equivalent hydrodynamic diameter = 4 × Wetted perimeter = 4 × (4h tan+2 b)
𝑣𝑥 =
𝑑ℎ
𝑑𝑡
𝑐𝑜𝑠 , where
𝑑ℎ
𝑑𝑡
, i. e. , rate of change of liquid height is the velocity along membrane
obtained from retentate volume collected over different spin times divided by the area of
membrane in contact with retentate at each time (Figure 4).
The Sherwood number for the forced (ShF ) and mixed, i.e., free and forced (ShM ) convection
were determined(Youm et al. 1996)
ShF = 0.303Re0.465 Sc1/3
ShM
Gr
= [1 + 1.24 × ( 0.143 2 )3/4 ]1/3
ShF
Sc
Re
Mass transfer coefficient was determined from the correlation above,
Sh =
k Dh
D
Thus, Gr = 7.98 × 109 , vx =
Gr
Re2
=2.64× 1010 . Thus
Gr
Re2
dx
|
dt t=60s
= 6.697 × 10−5 m/s , Re=0.55 and
is far greater than the minimum value of 3 in stirred cell for free
convection to become important (Youm et al. 1996). This indicates significant role of free
convection in generating vortices on the membrane surface. Thus
kM
kF
=308 where k M =
15 μm/s (over 1.5 fold higher than that in stirred cell) and k F = 0.049 μm/s.
Shear in centrifugal filter
The shear stress can be calculated from Sherwood number using the correlation developed by
Reiss and Hanratty (Langsholt et al. 1997; Reiss and Hanratty 1963; Wang et al. 2002; Yan et al.
2012)
 = 1.9
μD
ShM 3
Dh
Thus  = 9.4 Pa = 1.4 psi and shear rate, γ=9.4× 103 s −1 which is significantly higher than
shear rates obtained in the stirred cell system.
Thus, for a flux or linear velocity, vz of 19.1 μm/s at average TMP of 20 psi, the sieving coefficient
for 1% DM, So is 0.35. This So is significantly lower than the sieving coefficients obtained in the
stirred cell system, due to the high shear rate of γ = 9.4 × 103 s −1 compared to that in the stirred
cell (Figure 4B in paper).
Stirred cell experiment for OG
Figure 5. Stirred cell experiments for OG also indicates concentration polarization dependence
of detergent transmission. A. Observed sieving coefficient transmission increases with increasing
flux and decreasing shear. B. The linear relation of sieving function with flux indicates
dependence of sieving on concentration polarization for all three stirring speeds.
Detergent transmission through 10 kDa
The
observed
significantly
sieving
lower
for
coefficient
the
10
is
kDa
membrane compared to the 30 kDa one with
no change for different shear rates.
So decreases further with increasing flux for
all three stirring speeds. This may be due to
greater increase in retentate concentration as
more solution is filtered at higher flux with
little or no change in permeate concentration
(Figure 6).
Figure 6. Observed sieving coefficient for
ultrafiltration of 1% DM solution through 10kDa
Ultracel membrane shows very little transmission
for smaller pore size membrane.
Analysis of detergent transmission
The observed sieving coefficient is due to the transport of both the unimeric and micellar
detergent through the membrane. The measured sieving coefficient can be expressed in terms of
the filtrate and bulk concentrations, Cf and Cb , for the two species as:.
So =
Cf,unimer + Cf,micelle
Cb,unimer + Cb,micelle
For experiments performed at concentrations above the CMC, the concentration of the unimer at
the membrane surface should be the same as that in the bulk solution, thus:
Cf,unimer = Sa,unimer Cb,unimer
In contrast, the micelle concentration at the membrane surface will be greater than that in the bulk
solution due to concentration polarization, thus:
Cf,micelle = Sa,micelle βCb,micelle
where β is the degree of concentration polarization (β = Cw,micelle/Cb,micelle) and is a function of the
ratio of the filtrate flux to the mass transfer coefficient. Substituting gives:
So =
Sa,unimer Cb,unimer +Sa,micelle βCb,micelle
Cb,unimer +Cb,micelle
Above equation can be rewritten in terms of the total bulk detergent concentration (Cb) as
So =
Sa,unimer Cb,unimer + Sa,micelle β(Cb − Cb,unimer )
Cb
So = fSa,unimer + (1 − f)Sa,micelle β
where f is the fraction of the feed in the form of the unimer (which is known for any given feed
concentration). The product of Sa,micelleβ is just the observed sieving coefficient of the micelle.
This could be evaluated from above equation as
Sa,micelle β =
𝐒𝐨 −fSa,unimer
1−f
≈
𝐒𝐨 −f
1−f
where the final expression is developed assuming that the sieving coefficient of the small unimer
is approximately unity.
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