Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative

1. Chemist’s View Ion ChannelsProteins with a Hole All Atoms View Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative ~30 Å Figure by Raimund Dutzler

2. Ion Channels can be analyzed with Physics as Usual along with Biology as Usual Biology has been a descriptive science, necessarily

3. Ion Channels are Biological Devices,the Valves* of Cells Main Controllers of Biological Function K+ Flow time scale is 0.1 msec to min ~30 Å Chemical Bonds are lines Surface is Electrical Potential Redis negative (acid) Blueis positive (basic) *Pun: Valve=VacuumTube≈PNPTransistor≈FET Transistor BritSpeak Figure of ompF porin by Raimund Dutzler

4. We start with Electrostaticsbecause of biology Proteins Bristle with Charge Cohn (1920’s) & Edsall (1940’s)

5. We start with Electrostaticsbecause of biology and we addFinite Size Effects because of Chemistry

6. Finite Size Effects FundamentalChemically Specific Properties of ions (e.g. activity= free energy per mole) come from their Diameter and Charge not vaguely defined hydration shells or ‘chemical’ bonds Main Result of Modern Physical Chemistry Established by Regensburg School, Josef Barthel leader, Learned from Doug Henderson, J.-P. Hansen, Stuart Rice, among others…Thanks!

7. Active Sites of Proteins are VeryCharged e.g. 7 charges ~ 20 M net charge = 1.2×1022 cm-3 + + + 1 nM=10Å + - + K+ K+ - - - Selectivity Filters and Gates of Ion Channels are Active Sites OmpF Porin Ions are Crowded Figure adapted from Tilman Schirmer

8. Selectivity Differsin Different Types of Channels Wolfgang Nonner, Dirk Gillespie, Douglas Henderson, Dezso Boda

9. Selectivity of Different Channel Types Studied in Many Solutions RyR model of Gillespie is best worked out, most dataK channel model of Benoit Roux is Similar Quantum Water/K+ Model of Susan Rempe is Similar, but Neither K model has yet been computed in a range of solutions Nonner, Gillespie, Henderson, Boda RyR Channel CalciumChannel Sodium Channel Synthetic Ca Channel Selectivity filter DDDD 4− charges Selectivity filter EEEE 4− charges Selectivity filter DEKA 2−, 1+ charge Selectivity filter Variousmany - charges PNP/DFT PNP/DFT Monte Carlo Monte Carlo PNP/DFT

10. Goal: Understand Selectivity well enough toFit Large Amounts of Data and to Make a Calcium Channel

11. Divalents in RyR: fits with a few parameters:Gillespie, Meissner, Le Xu, not Bob Eisenberg Error < 0.1 kT KCl CaCl2 NaCl CaCl2 Misfit CsCl CaCl2 KCl MgCl2 Misfit

12. ExperimentTwo Synthetic Calcium ChannelsDesigned by Theory MUTANT ─ Compound Calcium selective Unselective Wild Type As charge density increases, channel becomes calcium selectiveErev ECa built by Henk Miedema, Wim Meijberg of BioMade Corp.,Groningen, Netherlands Miedema et al, Biophys J 87: 3137–3147 (2004) Glutathione derivatives

13. Hole in Plastic: Synthetic Nanopore NO PROTEIN 5 nm diameter 0.1 mM CaCl2 1.0 mM KCl 10 mM KCl 10 mM CaC2 Polyethylene terephthalate pA pA Ca2+ selectivity K+ selectivity mV mV Ca2+ selectivity pA 12 µm 1.0 mM KCl 10 mM KCl 10 mM CaCl2 0.1 mM CaCl2 200 nm mV Vr ~ 10 mV Zuzanna Siwy & Yan He, UC Irvine

14. Goal: Understand Selectivitywith Reduced Models Kchannels*Benoit Roux; Susan Rempe/Sameer Varma *K+ channels in only one solution so farNa & Ca channels§Nonner,et al, RyR channels§†Gillespie & Meissner §Wide range of solutions†Wide range of electrical potentials

15. Binding Curve Wolfgang Nonner

16. Selectivity FilterCrowded with Charge Selectivity Filter O½ Wolfgang Nonner + ++

18. Crowded Ions Snap Shots of Contents ‘Side Chains’are SpheresFree to move inside channel Radial Crowding is Severe 6Å Parameters are Fixed in all calculations in all solutions for all mutants Boda, Nonner, Valisko, Henderson, Eisenberg & Gillespie

19. AspartateE acid (negative) Lysine K basic (positive)

20. Na+ 2.0 Å Ca++ 1.98 Å 6 8 10 Small Size  Greater Charge Selectivity Charge SelectivityNa+vs Ca++Depends on Dielectric Dielectric Boundary Force = DBF Small Size andLargeDielectricBoundaryForce DEKA Na Channel, 6 Å Dielectric is a Charge Amplifier 25 15 LargeDielectric Boundary Force Selectivity #Na+/#Ca++ 5 ZeroDielectric Boundary Force Diameter/Å Boda et al

21. Size SelectivityNa+vs K+inthe DEKA Na ChannelNothing was changed in the model

22. Na+ Na+ Selectivity Filter K+ K+ 0 K+in Depletion Zone Depletion Zone Size Selectivity is in the Depletion Zone Na+vs. K+ Occupancy Channel Protein [NaCl] = 50 mM[KCl] = 50 mM Concentration [Molar] of the DEKA Na Channel, 6 Å Boda, et al

23. Size Selectivity Size Selectivity log C/Cref Selectivity Filter Binding Sites* *Binding Sites are outputs of our model, not structural inputs Selectivity Filter Selectivity Filter Selectivity Filter Selectivity Filter Selectivity Filter Selectivity Filter Lys or K Selectivity Filter D or E BLACK=Depletion=0 [NaCl] = [KCl] = 50 mM Na vs K Size Selectivity is in Depletion Zone Boda, et al

24. Na+ 2.00 Å K+ Na+ K+ 2.66 Å 6 8 10 Small Channel Diameter Largein Å Boda, et al Size Selectivity (ratio)Depends on Channel Size,not ProteinDielectric Coefficient Selectivity for small ion inDEKA6Å Na Channel

25. DEKANa Channel,6 Å Na+ Occupancy 2.0 Å K+ 2.66Å Occupancy # = Dielectric Coefficient =of Protein Boda, et al Size Selectivityratiodoes not depend on protein dielectricOccupancy # Depends on Protein Dielectric ProteinDielectric ‘Amplifies’ Charge & Electrostatic effects

26. Binding Sites* are OUTPUTSof our Calculations Our model has no preformedstructural binding sites but Selectivity is very Specific *Selectivity is in the Depletion Zone,NOT IN THE BINDING SITEof the DEKA Na Channel

27. Binding Sites Electrostatic AttractionSteric Competition for Space Repulsion Location and Strength of Binding Sites Depend on Ionic Concentration and Temperature (etc)

28. What does the protein do? Selectivity arises from Electrostatics and Crowding of Charge Certain MEASURES of structure are PowerfulDETERMINANTSof Functione.g., Volume, Dielectric Coefficient, etc. Precise Arrangement of Atoms is not involved in the model, to first order. Nonner and Eisenberg

29. What does the protein do? Protein maintains Mechanical Forces*Volume of PoreDielectric Coefficient/BoundaryPermanent ChargePrecise Arrangement of Atoms is not involved in the model, to first order. butParticular properties (‘measures’) of the protein are crucial! *?? Driving force for conformation changes ?? Nonner and Eisenberg

30. Other Properties of Ion Channels are likely to involve more subtle physics including orbital delocalization and chemical binding Selectivity apparently does not! Nonner, Henderson, Gillespie, Boda and Eisenberg

31. Selectivity can be understood by Reduced Models KchannelsBenoit Roux Susan Rempe Na & Ca channelsNonner,et al, RyRchannelsGillespie & Meissner Best Evidence Conclusion