Ion selectivity of a biological channel at
high concentration ratio:
insights on small ion diffusion and
binding
M. Lidón López, Marcel Aguilella-Arzo,
Vicente Aguilella and Antonio Alcaraz
University “Jaume I” Spain
Outline
• Introduction:
– Ion selectity
– OmpF porin
– Previous results in OmpF selectivity
• Reversal potential results
• Modelling
• Conclusions
Ionic selectivity
•Selectivity in ionic channels:
Partitioning:
equilibrium,
measures
ionic
exclusion.
Diffusion: non equilibrium, measures relative
mobility of different ions.
OmpF porin
Outer membrane protein F in
E. Coli
Reconstituted into planar lipid membranes
OmpF porin forms trimeric channels
Each monomer has hourglass-like shape, and
it is slightly cation selective at neutral pH
Ionic selectivity in OmpF I
-60
The selectivity
pH
-40
Erev(mV)
is not a number
but depends
on:
Cation selective
-20
0
Cis = 1M/ Trans = 0.1M
20
40
Anion selective
60
0
2
4
6
pH
8
10
12
A. Alcaraz, E.M. Nestorovich, M. Aguilella-Arzo, V.M. Aguilella and S. M.
Bezrukov, Biophys. J. 87 (2004) 943.
Ionic selectivity in OmpF II
The selectivity
is not a number
but depends
on:
Salt
concentration
and
concentration
gradient
A. Alcaraz, E.M. Nestorovich, M. Aguilella-Arzo, V.M. Aguilella and S. M.
Bezrukov, Biophys. J. 87 (2004) 943.
Ionic selectivity in OmpF III
40
The selectivity
Type of
electrolyte
anion selective
20
RP (mV)
is not a number
but depends
on:
30
MgCl2
CaCl2
10
C trans = 0.1 M
0
-10
cation selective
NaCl
-20
-30
KCl
-40
5
10
15
20
Ccis/Ctrans
A. Alcaraz, E. M. Nestorovich, M. L. López , E. García-Guiménez, S. M.
Bezrukov and V. M. Aguilella, Biophys. J. 96 (2009) 56.
Measuring reversal potentials I
Through Ion channel reconstitution in planar lipid bilayers
Ag/AgCl with salt bridges, 2M KCl
Trans: 0.03 M
I
Cis: 0.09 M – 6M
pH = 6
Electrolytes: LiCl, NaCl, KCl, CsCl
Reversal Potential Model I
Selectivity in channels:
Partitioning: equilibrium, measures ionic exclusion
Diffusion: non equilibrium, measures relative ionic mobility
RP = 2 Donnan +
diffusion
Cis solution
Ion channel
∆φexclusioncis
Trans solution
RP
∆φDiffusion
∆φExclusion-trans
Reversal Potential Model II
RP = 2 Donnan +
diffusion
Exclusion potential:
Donnan Potential
∆φexclusion = ∆φDonnan cis − ∆φDonnan trans
2
k BT ( − X / 2c trans ) + ( − X / 2c trans ) + 1
=
ln
e
( − X / 2ccis ) + ( − X / 2ccis )2 + 1
Diffusion potential: Electroneutrality Approximation
∆φDiffusion
k BT D− − D+
D+ ccis + D− ( ccis − X )
=
ln
e D− + D+ D+ ctrans + D− ( ctrans − X )
Reversal Potential (mV)
Exclusion and diffusion
20
Diffusion goes with ln r at high r
Slope information D+/D-
Diffusion D+ < D−
Diffusion D+ = D−
0
-20
Diffusion D+ > D−
-40
∆φDiffusion
D+
1
−
k T
D−
ln r
≈A+ B
e 1 + D+
D−
Exclusion
-60
Exclusion saturates at high r
1
10
Concentration Ratio (cis/trans)
100
• Why high concentration gradients?
– At high concentration exclusion is saturated
– We can separate different contributions
LiCl and NaCl RP results I
Reversal Potential (mV)
Cationic selectivity ⇒
Anionic selectivity
0
LiCl
-10
-20
-30
NaCl
-40
1
10
100
Concentration Ratio (cis/trans)
M.L. López , M. Aguilella-Arzo, V. Aguilella and A. Alcaraz, J. Phys. Chem. B 113 (2009) 8745.
Diffusion D+ < D−
20
Diffusion D+ = D−
0
-20
Diffusion D+ > D−
-40
Exclusion
-60
1
10
Concentration Ratio (cis/trans)
100
Reversal Potential (mV)
Reversal Potential (mV)
LiCl and NaCl RP results II
0
LiCl
-10
-20
-30
NaCl
-40
1
10
100
Concentration Ratio (cis/trans)
LiCl and NaCl D+ < D-
Exclusion + diffusion can explain the results
but…….. slopes 50% higher aprox.
CsCl and KCl RP results
D(cm2/s) 10-5 1.03
ion
Li+
1.33
Na+
1.96
K+
2.06
Cs+
2.03
Cl-
Diffusion D+ < D−
20
Diffusion D+ = D−
0
-20
CsCl
Diffusion D+ > D−
-40
Exclusion
Reversal Potential (mV)
Reversal Potential (mV)
-10
CsCl
-20
-30
KCl
-40
-60
1
10
100
Concentration Ratio (cis/trans)
Exclusion + diffusion cannot
explain the results
There is another phenomenon
involved
1
10
100
Concentration Ratio (cis/trans)
M.L. López , M. Aguilella-Arzo, V. Aguilella
and A. Alcaraz, J. Phys. Chem. B 113 (2009)
8745.
Binding could influence
selectivity??
Cation binding in OmpF I
Fluorescence exp,
Dissociation constant 3 mM
•Y. Kobayashi and T. Nakae, Eur. J. Biochem. 151(1985) 231.
• A. Suenaga, Y. Komeiji, M. Uebayasi,T. Meguro, M. Saito and I.
Yamato, Biosci. Rep. 18 (1998) 39.
MD: Asp113
•C. Danelon, A. Suenaga, M. Winterhalter and I. Yamato, Biophys.
Chem. 104 (2003) 591.
Free energy
calculations
•E. M. Nestorovich, T. K. Rostovtseva and S. M. Bezrukov, Biophys.
J. 85 (2003) 3718.
Noise: Glu117
Push- out mechanism slows down cation diffusion
Cation binding in OmpF II
MD : 10 nS
Asp113
Glu117
Binding: Glu117, Asp113
Push- out mechanism slows down cation diffusion
RP Results at high gradients
Linear behaviour with Ln r ⇒ diffusional behaviour
Electrolyte
( D+
D− ) eff
( D+
D− )bulk
CsCl
KCl
NaCl
LiCl
0.48 ± 0.06
0.50 ± 0.08
0.58 ± 0.01
0.56 ± 0.05
Diffusion is reduced in a common pattern (50%)
⇓
Binding slows down cation
Molecular model for binding I
Aim of the model: obtain fraction of unbound acid, x
Binding to two specific acids :
Glu117, Asp113
Statistical mechanics: Hill 1956
Binding of antibiotic to
OmpF
S. Mafé, P. Ramírez, and A. Alcaraz, J. Chem.
Phys. 119 (2003) 8097.
H+
H+
H+ H+
K+
Possible states in gran cannonical
ensemble of the two acids
K+
K+ K+
H+ K+
K+ H+
Molecular model for binding II
H+
K+
H+
K+ K+
H+ H+
H+ K+
K+
K+ H+
q grand partition function , zi partition f.
ion i, λi related activity ion i
q = exp ( − u k BT ) + 2 z H λH + 2 z K λK + 2 z H λH z K λK + z H 2 λH 2 + z K 2λK 2 =
(
) (
) (
)
= exp ( − u k BT ) + 2 10 pK a − pH + 2 10 pKc c + 2 10 pK a − pH10 pKc c + 102( pKa − pH ) + (10 pKc c) 2
x, fraction non bound acid
∂ ln q
1
1− x =
λK
2
∂λ K
Modelling the reversal potential I
Modelling reduced diffusion
If we assume at high c, x =0,
Deff = x D free + (1 − x ) Dbound
(Deff ) high concentration = Dbound
+
(Deff ) high concentration = Dbulk / 2
Dbound = Dbulk / 2
Modelling the reversal potential II
RP
Exclusion
Fixed charge
concentration= 0.3 M
Diffusion
Binding
Fluorescence exp. Dissociation constant = 3mM
(pKc= 2.5)
Dissociation constant = 0.3 M (pKc = 0.5)
0
Reversal Potential (mV)
M. Aguilella-Arzo, J. J.
García-Celma, J. Cervera,
A. Alcaraz and V. M.
Aguilella,
Bioelectrochemistry 77
(2007) 320.
-10
-20
D+ = 0.5 D+ bulk
-30
pK c → +∞
-40
pK c = 0.5
-50
D+ = D+ bulk
pK c → −∞
-60
-70
1
10
Concentration Ratio (cis/trans)
100
Theory versus experiments
Reversal Potential (mV)
RP = 2 Donnan
+ diffusion
0
-10
-20
-30
-40 a
LiCl
NaCl
0
-10
-20
-30
-40 b
1
CsCl
KCl
10
100
Concentration Ratio (cis/trans)
Conclusions
• RP
measurements
at
large
concentration
⇒
useful
information.
• At high concentration ratios diffusion is hampered.
• The reduction of the cation diffusion is the same for all the
electrolytes and is consistent with a cation binding site.
• The theoretical model explains qualitatively RP results.
Acknowledgments – Thanks to….
Department of Physics,
Biophysics Unit
UNIVERSITY JAUME I, CASTELLON
• Vicente Aguilella
•Antonio Alcaraz
•Marcel Aguilella-Arzo
• Elena García-Giménez
• Andreu Andrio