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enderson Dezso Boda 122 Biological Case Chloride Channel Selectivity depends Qualitatively on concentration Wolfgang Nonner Dirk Gillespie 123 The Dilute Channel: Anion Selective Channel protein creates a Pressure difference between bath and channel Large ions like Cl– are Pushed into the channel more than smaller ions like F– Wolfgang Nonner Dirk Gillespie 124 Key: Hydrophobic Residues Repel Water giving ? Largeion selectivity (in both anion and cation channels). ? Peculiar nonmonotonic conductance properties and IV curves observed in experiments Hydrophobic repulsion can give gating. ?Vacuum lock? model of gating (M. Green, D. Henderson。 Selectivity Filter Selectivity Filter Crowded with Charge Wolfgang Nonner 80 Understand Selectivity well enough to Make a Calcium Channel using techniques of molecular geics, sitedirected Mutagenesis Goal: Gee Robillard, Henk Mediema, Wim Meijberg 81 General Biological Theme (?adaptation?) Selectivity Arises in a Crowded Space Biological case: M NaCl and 1 ?M CaCl2 in the baths As the volume is decreased, water is excluded from the filter by crowded charge effects Ca2+ enters the filter and displaces Na+ Biological Case Wolfgang Nonner Dirk Gillespie 82 Sensitivity to Parameters Volume Dielectric Coefficient 83 Tradeoffs ?? adjustable parameters Volume Dielectric Coefficient 84 Binding Curves Sensitivity to Parameters nm3 volume nm3 volume 85 At Large Volumes Electrical Potential can Reverse nm3 volume nm3 volume 0 Potential 0 Potential Positive Negative Negative 86 Competition of Metal Ions vs. Ca++ in Ltype Ca Channel Nonner amp。 12%) Activity* of ionic solutions from Infinite dilution, to Saturated solutions, even in Ionic melts. *Free Energy per Mole Learned from Doug Henderson, . Hansen, among others…Thanks! 74 1 ( ) ( ) ( )i i i ikT D ??? ? ?J x x x} Concentrationindependent ? geometric restrictions ? solvation (Born) terms Ideal term ? electrochemical potential of point particles in the electrostatic meanfield ? includes Poisson equation Excess chemical potential ?Finite size effects ?Spatial correlations Chemical potential has three ponents 0 i d ex( ) ( ) ( )? ? ???i i ix x x75 Simplest Physical Theory MSA ? ?122 2 2 200Ele c tro c he m ic a l P o te nti a l o f spe c ie s ln 24 1 1 3iH S ESi i i iHS i i i iiiiiiz F RTe z z?? ? ? ? ??? ??? ????? ? ?? ? ? ? ??? ????? ? ? ? ??? ??? ? ? ????? Ideal Ex ces sElectrostatic Spheres Hard Spheres Ionic radii ?I are known values in bulk Learned from Lesser Blum amp。jjjddx A x e z xA x dx dx? ??????? ???? ?m o b i l e f i x e d0idJdx ?includes Fixed Charge on Protein ? ? ? ? ? ? ii i i dJ D x A x x dx????includes only Mobile Charge Electrochemical Potential ? ? ? ? ? ? ? ?ex*ln ii i iz e k T ?? ? ????? ? ?????xx x xS p e c i a l C h e m i s t r y53 The Problem ionic concentrations, electrostatic potential held constant far from channel membrane with ion channel ionic concentrations, electrostatic potential held constant far from channel 54 Bath Bath Membrane Boundary conditions are Crucial Flared Access to Channel Required in 1D 55 I V INPUT OUTPUT THEORY PNP STRUCTURE Length, diameter, Permanent Charge Dielectric Coefficient EXPERIMENTAL CONDITIONS Bath concentrations Bath Potential Difference PNP Forward Problem 56 Current Voltage Relation Gramicidin 3D PNP Uwe Hollerbach 57 V I PNP 1 Inverse Problem Input Output Theory EXPERIMENTAL CONDITIONS Bath Concentrations Bath Potential Difference EXPERIMENTS ELECTRICAL STRUCTURE Length, diameter, Permanent Charge Dielectric Coefficient PNP 1 Inverse Problem for Mathematicians What measurements best determine electrical structure? 58 Charge Mutation in Porin Ompf Structure determined by xray crystallography in Tilman Schirmer’s lab G119D 59 Fit of 1D PNP CurrentVoltage 100 mM KCl OmpF G119D Duan Chen John Tang Rush Medical Center 60 Net Charge Difference = ? = ? Duan Chen John Tang 61 Shielding Dominates Electric Properties of Channels, Proteins, as it does Ionic Solutions Shielding is ignored in traditional treatments of Ion Channels and of Active Sites of proteins Main Qualitative Result 62 Main Qualitative Result Shielding in Gramicidin Uwe Hollerbach Rush Medical Center 63 PNP misfits in some cases even with ?optimal? nonuniform D(x) Duan Chen John Tang Rush Medical Center 64 Shielding/PNP is not enough PNP includes Correlations only in the Mean Field PNP ignores ion ion correlations and discrete particle effects: Single Filing, Crowded Charge Dielectric Boundary Force 65 Neither Field Theory nor Statistical Mechanics easily acmodates Finite Size of Ions and Protein Sidechains How can that be changed? Learn from Mathematicians and/or Physical Chemists Learned from Doug Henderson, . Hansen, among others…Thanks! 66 Learning with Mathematicians Zeev Schuss, Boaz Nadler, Amit Singer Dept?s of Mathematics Tel Aviv University, Yale University Molecular Biophysics, Rush Medical College We extend usual chemical treatment to include flux and spatially nonuniform boundary conditions We have concrete results only in the uncorrelated case! We have learned how to derive PNP (by mathematics alone). Count trajectories not states 67 Counting Langevin T