Chemical Bonds are lines Surface is Electrical Potential Red is negative = acid

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

2. 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

3. Ions in Water are theLiquid of Life Life Occurs in ~130 mM salt solutions Ionic Solutions are NOT ideal. Chemically Specific Properties of Ionic solution are their DEVIATION from IDEAL

4. K+ ~30 Å Ion Channels are Biological Devices Natural nano-valves* for atomic control of biological function Ion channels coordinate contraction in the heart, allowing the heart to function as a pump Ion channels coordinate contraction in skeletal muscle Ion channels control all electrical activity in cellsIon channels produce signals of the nervous system Ion channels are involved in secretion and absorption in all cells:kidney, intestine, liver, adrenal glands, etc. Ion channels are involved in thousands of diseases and many drugs act on channels Ion channels are proteins whose genes (blueprints) can be manipulated by molecular genetics Ion channels have structures shown by x-ray crystallography in favorable cases. *nearly pico-valves: diameter is 400900 pico-meters

5. Channels are parts of Machines, e.g., Excitation-Contraction Coupling L type Ca Channel RyR ryanodine receptor L-type Ca Channel RyR LászlóCsernoch, Debrecen, Hungary Isabelle Marty, Grenoble, France

6. Goal: Understand Selectivity Selectivity Differsin Different Types of Channels Wolfgang Nonner, Dirk Gillespie, Douglas Henderson, Dezső Boda

7. Selectivity of Different Channel Types Studied in Many Solutions 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 RyR model of Gillespie is best worked out for ~ 120 solutions Selectivity of K Channel is studied in ~1 solution at infinite dilution K channel of Roux has atomic detail but is studied at infinite dilutionQuantum /K of Rempe has atomic detail but is studied at infinite dilution Nonner, Gillespie, Henderson, Boda

8. “There is only one word that matters in biology and that isSpecificity ....” Aaron Klug quoted in the first sentence of H. Pearson, Nature (2008) 455:160-164

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

10. ExperimentTwo Synthetic Calcium ChannelsDesigned by Theory MUTANT ─ Compound Glutathione derivatives Calcium selective Unselective Wild Type As density of permanent charge 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) Mutants of ompF Porin

11. Channels are only Holes Why can’t we understand and build them? Must have high quality measurements Must know physical basis of function Where do we start?Not with gas phase models of traditional channology Liquids are not Gases Not with guesses about trajectories of structural biologistsCounting and Statistics are essential

12. Active Sites of Proteins are VeryCharged 7 charges ~ 20 M net charge = 1.2×1022 cm-3 Pure water is 55 M Induced Fit of Side Chains + + + 1 nM=10Å + - + K+ K+ - Induced Fit of Side Chains - - Selectivity Filters and Gates of Ion Channels are Active Sites OmpF Porin Ions are Crowded Figure adapted from Tilman Schirmer

13. Ions in Water are the Liquid of Life Life Occurs in ~130 mM salt solutions Ionic Solutions are NOT ideal Chemically Specific Properties of Ionic solution are their DEVIATION from IDEAL

14. Finite Size EffectsWorking Hypothesis Chemically Specific Properties of ions (e.g. activity = free energy per mole) come from their Diameter and Charge and dielectric ‘constant’ of ionic solution Learned from Doug Henderson, J.-P. Hansen, Stuart Rice, among others…Thanks!

15. Selective Binding Curve L type Ca Channel Wolfgang Nonner

16. Selectivity FilterCrowded with Charge Selectivity Filter O½ Wolfgang Nonner L type Ca Channel + ++ “Side Chains”

17. large mechanical forces

18. Crowded Ions Snap Shots of Contents Radial Crowding is Severe ‘Side Chains’are SpheresFree to move inside channel 6Å Parameters are Fixed in all calculations in all solutions for all mutants Experiments and Calculations done at pH 8 Boda, Nonner, Valisko, Henderson, Eisenberg & Gillespie

19. Selectivity Filter is aSelf-Organized Structure with Side Chains at position of Minimum Free Energy The Protein Fits the Substrate “Induced Fit Model of Selectivity”

20. Mutation • Na Channel • Ca Channel Same Parameters • E • E • E • A • D • E • K • A Charge -3e Charge -1e 1 0.004 Na+ Ca2+ Na+ Occupancy (number) 0.5 0.002 Ca2+ 0 0 -6 -4 -2 0 0.05 0.1 log (Concentration/M) Concentration/M EEEE has full biological selectivityin similar simulations Boda, et al

21. Calcium Channelhas been examined in ~32 papers, e.g., Most of the papers are available athttp://www2.phys.rush.edu/RSEisenberg/physioeis.html Now, the Sodium Channel

22. Next, the Sodium Channel specifically, the Aspartate DAcid Negative Glutamate EAcid Negative Lysine KBasicPositive Alanine A Aliphatic Neutral DEKASodium Channel 6 Å

23. DEKASodium Channel has very different properties from Ca channel,e.g., ‘binding’ curve,Na+ vs Ca++ selectivity Na+ vs K+ selectivity

24. Mutation • Na Channel • Ca Channel Same Parameters • E • E • E • A • D • E • K • A Charge -3e Charge -1e 1 0.004 Na+ Ca2+ Na+ Mutation Occupancy (number) 0.5 0.002 Same Parameters Ca2+ 0 0 -6 -4 -2 0 0.05 0.1 log (Concentration/M) Concentration/M EEEE has full biological selectivityin similar simulations Boda, et al

25. DEKA Na Channel SelectsNa+vs. K+Nothing was changedfrom the EEEA Ca channelexcept the amino acids Calculations and experiments done at pH 8

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

27. Binding SitesNa+ SelectivityNot in binding Na+ Na+ Selectivity Filter K+ K+ Na Selectivity because 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] Calculations and experiments done at pH 8 of the DEKA Na Channel, 6 Å Boda, et al

28. Control Variablesare obvious in simulations of the Na channel,but not the Ca channel

29. Control Variablesin DEKA Na channel • SelectivityNa+ vs K+ depends only on pore diameter Diameter controls Selectivity

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

31. Control Variables in DEKA Na channel • SelectivityNa+ vs K+ depends only on pore diameter • Conductance* depends on protein polarization Protein Dielectric Coefficient controls Conductance *Gillespie & Boda (2008) Biophysical Journal 95:2658

32. Na+  410-5 210-5 Control VariableOccupancy depends on Protein Dielectric Occupancy# (Na) 20 60 Dielectric Coefficient of Protein Boda, et al,

33. Selectivity comes from Electrostatic InteractionandSteric Competition for Space Repulsion Location and Strength of Binding Sites Depend on Ionic Concentration and Temperature, etc Rate Constants are Variables

34. Best Evidence is from the RyRReceptor Gillespie, Meissner, Le Xu, et al, not Bob Eisenberg  More than 120 combinations of solutions & mutants 7 mutants with significant effects fit successfully

35. The Geometry • Selectivity Filter • is 10 Å long and 8 Å in diameter • confines four D4899negative amino acids. • Four E4900 positive amino acids are on lumenal side, overlapping D4899. • Cytosolic distributed charge Protein Cytoplasm Lumen Protein D. Gillespie et al., J. Phys. Chem. 109, 15598 (2005).

36. DFT/PNPvsMonte Carlo Simulations Concentration Profiles Misfit Nonner, Gillespie, Eisenberg

37. Divalents Gillespie, Meissner, Le Xu, et al KCl CaCl2 NaCl CaCl2 Error < 0.1 kT/e Misfit 2 kT/e CsCl CaCl2 KCl MgCl2 Misfit

38. KCl Gillespie, Meissner, Le Xu, et al Error < 0.1 kT/e 4 kT/e Misfit

39. Theory fits Mutation with Zero ChargeNo parameters adjusted Theory Fits Mutant in K + Ca Theory Fits Mutant in K Error < 0.1 kT/e 1 kT/e Protein charge densitywild type* 13M Water is 55 M *some wild type curves not shown, ‘off the graph’ 0M in D4899  1 kT/e Gillespie et alJ Phys Chem 109 15598 (2005)

40. The model predicted an AMFE for Na+/Cs+ mixturesbefore it had been measured Error < 0.1 kT/e Bulk Solution Bulk Solution Channel 62 measurementsThanks to Le Xu! Note Break in Axis Gillespie, Meissner, Le Xu, et al

41. Selectivity comes from Electrostatic AttractionandSteric Competition for Space Repulsion Location and Strength of Binding Sites Depend on Ionic Concentration and Temperature, etc Rate Constants are Variables

42. What does the protein do? Certain MEASURES of structure are PowerfulDETERMINANTSof Functione.g., Volume, Dielectric Coefficient, etc. Induced Fit Model of SelectivityAtomic Structure is not pre-formedAtomic Structure is an important output of the simulation Nonner and Eisenberg

43. What does the protein do? Protein maintains Mechanical Forces*Volume of PoreDielectric Coefficient/BoundaryPermanent Charge Induced Fit Model of Selectivity * Driving force for conformation changes ?? Nonner and Eisenberg

44. 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

45. Induced Fit Model • Selectivity depends on Induced Fit of Side Chains and Ions • Induced Fit is the Self-Organized Structure withMinimal Free Energy Energy and Entropy

46. Induced Fit Model • Monte Carlo computes the Structure of Minimal Free Energy • Monte Carlo computes the Induced Structure ‘perfectly’* *but the model itself is far from perfect Energy and Entropy

47. Selectivity Depends Sensitively on Self-organized Structure and their Flexibility Induced Structure is Different in Different Solutions so Structure must be Computed! Rate constants are variables that change dramatically with conditions

48. Computation Starts From Crystal Structure when available but Crystal Structures cannot determine Selectivity because 1) Crystal Structures are measured in only one unphysiological solution 2) Crystal Structures are not accurate enough 3) Crystal Structures do not give entropy

49. Miracle We can actually compute the Structures that determine Selectivity

50. Specificity “There is only one word that matters in biology and that is specificity. The truth is in the details, not the broad sweeps.”* if the detail is computed with the correct broad sweeps of physics† †Bob Eisenberg’s opinion*Aaron Klug quoted in the first sentence of Pearson Nature (2008) 455:160–164