Size Selectivity in Ion channels Roland Roth Dirk Gillespie

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