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Size Selectivity in Ion channels
Roland RothDirk Gillespie
Model of Size Selectivity
• what is the simplest system that shows the effect of size selectivity?
• mixture of uncharged hard spheres that model e.g. water, Na and K• selectivity filter: protein confines water and ions by a soft and corrugated wall• effective attraction Uattr of ions into the selectivity filter• effective repulsion Vrep of water from the protein• hard-sphere diameter
H2O 0.28 nm
Na+ 0.20 nm
K+ 0.27 nm
Cs+ 0.34 nm
Bulk Approach to Size Selectivity
• system 1: bath
• fixed water concentration: H20
(55.5 M)
• fixed ion concentration: Na,K,, ... (100 mM)
• system 1: bath
• fixed water concentration: H20
(55.5 M)
• fixed ion concentration: Na,K,, ... (100 mM)
• system 2: filter
• attraction for ions into the filter Uattr > 0 (0...10 kB T)
• repulsion for water from the protein: Vrep > 0 (0,1,2,3 kB T)
water and ion concentrations in lter have to be calculated from (i= Na, K, H20)
iH20
2({i}) - Vrep
Na,K1({i}) = Na,K
2({i}) + Uattr
Ideal Gas Approximation
if ions are point particles no size selectivity possible
absorbance in the filter:
xNa,K = Na,K2 / Na,K
1
Selectivity:
S = xNa / xK
Binary Mixture of Water and one Ion Species
small ion selectivity
•binary mixture of water and Na (100 mM) or water and K (100 mM)Na / K = 0.74
absorbance in the filter xNa;Kselectivity S
Ternary Mixture of Water and two Ion Specii• ternary mixture of water, Na (100 mM) and K (100 mM)
absorbance in the filter xNa;K selectivity S
•small ion selectivity is enhanced through competition between Na and K•small ion selectivity is highly non-linear
Small Ion Selectivity• mechanism: electrostatic attraction of ions into the selectivity filter and competition for space• depends on ion concentration (50 mM, 100 mM and 150 mM)
•Na and K Density Proles
Na1 = K
1 = 100 mM ; Rpore = 3.5 A• the pore is soft and corrugated, protein can be penetrated by ions• Vattr =2, 6, 8, 10 kBT
Na density profiles K density profiles
Hydrophobic Channels
Uattr = 0, Vrep = 0,... ,3 kBTmodels hydrophobic repulsion of water from the proteinconsider Na and Cs in the bath; Na / Cs = 0.59; Na = Cs = 50 mM
absorbance in the filter xNa;Cs
selectivity: S = xCs / xNa
Na and Cs Density Proles
Na1 = Cs
1 = 50 mM; Rpore = 4.2 AUrep =0, 1, 2, 3 kBT
Na density profiles Cs density profiles
Large Ion Selectivity
• mechanism: water is repelled from the protein (the pore wall) and largest species lls free space
• is (almost) independent of ion concentration• is a surface effect
• -> best agreement between DFT and bulk approach for small channels
Mixed Channel
hydrophobic repulsion (Vrep = 3kBT) and electrostatic attraction (Uattr)
absorbance of Na and Cs SNa = xNa/xCs and SCs = xCs/xNa
crossover from large (Uattr small) to small ion selectivity (Uattr large)
Conclusions
• simple model allows to understand the mechanism for small and large ion selectivity
• selectivity filter provides an environment in which the small size difference of the ions get amplied
• entropy of ions is very important
• small ion selectivity: electrostatic attraction of ion into the selectivity filter and competition between ions for space (bulk effect)
• large ion selectivity: hydrophobic repulsion of water from the protein; large ions fill free space (surface effect)
• bulk approach is confirmed by DFT calculations
Outlook
• include electrostatics into bulk approach (MSA)
• attraction of ions into the channel will be generated by electrostatics
• additional species (e.g. Cl-) have to be included
• include nite channel geometry in DFT approach
• include electrostatics into DFT approach