Size Selectivity in Ion channels Roland Roth Dirk 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 H2OH2O0.28 nm Na nm K+K nm Cs 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 U attr > 0 ( k B T) repulsion for water from the protein: V rep > 0 (0,1,2,3 k B T) water and ion concentrations in lter have to be calculated from (i= Na, K, H 2 0)     i  H20 2 ({  i }) - V rep  Na,K 1 ({  i }) =  Na,K 2 ({  i }) + U attr

Ideal Gas Approximation if ions are point particles no size selectivity possible absorbance in the filter: x Na,K =  Na,K 2 /  Na,K 1 Selectivity: S = x Na / x K

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 x Na;K selectivity S

Ternary Mixture of Water and two Ion Specii ternary mixture of water, Na (100 mM) and K (100 mM) absorbance in the filter x Na;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  Na 1 =  K 1 = 100 mM ; R pore = 3.5 A the pore is soft and corrugated, protein can be penetrated by ions V attr =2, 6, 8, 10 k B T Na density profiles K density profiles

Hydrophobic Channels U attr = 0, V rep = 0,...,3 k B T models hydrophobic repulsion of water from the protein consider Na and Cs in the bath;  Na /  Cs = 0.59;  Na =  Cs = 50 mM absorbance in the filter x Na;Cs selectivity: S = x Cs / x Na

Na and Cs Density Proles  Na 1 =  Cs 1 = 50 mM; R pore = 4.2 A U rep =0, 1, 2, 3 k B T 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 (V rep = 3k B T) and electrostatic attraction (U attr ) absorbance of Na and Cs S Na = x Na /x Cs and S Cs = x Cs /x Na crossover from large (U attr small) to small ion selectivity (U attr 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