Ion Channels are the Valves of Cells Ion Channels are the Main Controllers of Biological Function

1. + ~30 Å Ion Channelsare theValves of CellsIon Channels are the Main Controllers of Biological Function Ions in Waterare the Selectivity Different Ions carry Different Signals Liquid of Life Na+ Hard Spheres Ca++ Chemical Bonds are lines Surface is Electrical Potential Redis negative (acid) Blueis positive (basic) K+ 3 Å 0.7 nm = Channel Diameter Figure of ompF porin by Raimund Dutzler

2. K+ ~30 Å Ion Channels are Biological Devices Natural nano-valves* for atomic control of biological function Ion channels coordinate contraction of cardiac muscle, 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 picometers

3. + ~30 Å Channels are SelectiveDifferent Ions Carry Different Signals through Different Channels ompF porin Na+ Ca++ K+ 0.7 nm = Channel Diameter 3 Å Flow time scale is 0.1 msec to 1 min Figure of ompF porin by Raimund Dutzler

4. Goal: Understand Selectivity well enough toFit Large Amounts of Data*and to Make a Calcium Channel Atomic Scale Macro Scale *from many non-ideal solutions

5. Experiments have builtTwo Synthetic Calcium Channels MUTANT ─ Compound Calcium selective Unselective Wild Type As density of permanent charge increases, channel becomes calcium selectiveErev ECa in0.1M1.0 M CaCl2 built by Henk Miedema, Wim Meijberg of BioMade Corp.,Groningen, Netherlands Miedema et al, Biophys J 87: 3137–3147 (2004) Mutants of ompF Porin Designed by Theory Glutathione derivatives Atomic Scale || Macro Scale

6. Where do we start? with the Biological Adaptation! Working Hypothesis Biological Adaptation is Crowded Ions and Side Chains

7. Active Sites of Proteins are Very Charged 7 charges ~ 20M net charge = 1.2×1022 cm-3 liquidWater is 55 Msolid NaCl is 37 M + + + + + - - - - Selectivity Filters and Gates of Ion Channels are Active Sites Physical basis of function OmpF Porin Hard Spheres Na+ Ions are Crowded K+ Ca2+ Na+ Induced Fit of Side Chains K+ 4 Å Figure adapted from Tilman Schirmer

8. Implicit Solvent (“Primitive”) Model Chemically Specific Properties of ions (e.g. activity = free energy per mole) come from interactions of their Diameter and Charge and dielectric ‘constant’ of ionic solution Atomic Detail ‘Primitive Implicit Solvent Model’ learned from Doug Henderson, J.-P. Hansen, Stuart Rice, among others…Thanks!

9. 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

10. large mechanical forces

11. Multiscale Analysis at Equilibrium Solved with Metropolis Monte Carlo MMC Simulates Location of Ionsboth the mean and the variance ProducesEquilibrium Distribution of location of Ions and ‘Side Chains’ MMC yields Boltzmann Distribution with correct Energy, Entropy and Free Energy Other methodsgive nearly identical results: Equilibrium MultiscaleMSA (mean spherical approximation SPM (primitive solvent model) DFT (density functional theory of fluids), Non-equilibrium Multiscale DFT-PNP (Poisson Nernst Planck) EnVarA…. (Energy Variational Approach) etc

12. 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

13. Calcium Channelhas been examined in ~35 papers, e.g., Most of the papers are available at ftp://ftp.rush.edu/users/molebio/Bob_Eisenberg/Reprints http://www.phys.rush.edu/RSEisenberg/physioeis.html

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

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

16. 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

17. Nothing was changedfrom the EEEA Ca channelexcept the amino acids Calculated DEKA Na Channel SelectsCa 2+vs.Na + and also Na+vs. K+ Calculations and experiments done at pH 8

18. How?How does the DEKA Na Channel Select Na+vs. K+ ? Calculations and experiments done at pH 8

19. Binding SitesNOT SELECTIVE 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 mMpH 8 Concentration [Molar] of the DEKA Na Channel, 6 Å Boda, et al

20. What does the protein do? Channel and Contents form aSelf-Organized Structure with Side Chains at position of Minimum Free Energy Protein Fits the Substrate “Induced Fit Model of Selectivity”

21. Implicit Solvent (“Primitive”) Model ofIonic Solutions Describes Calcium and Sodium Channels quite well at EquilibriumwithoutPreformed Structure Structure is the Computed Consequence of the Model

22. Binding Sites* are outputsof our Calculations Induced Fit Model of Selectivity 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

23. Challenge Extend to Nonequilibrium need a Field Theory of Ionic Solutions Energy Variational Analysis EnVarA

24. Energetic Variational Analysis EnVarAbeing developed by Chun LiuYunkyong Hyon and Bob Eisenberg creates a Field Theory of Ionic Solutions that allows boundary conditions and flow and deals with Interactions of Components Self-consistently

25. Energetic Variational ApproachEnVarAChun Liu, Yunkyong Hyon, and Bob Eisenberg Mathematicians and Modelers: two different ‘partial’ variations written in one framework, using a ‘pullback’ of the action integral CompositeVariational Principle Action Integral, after pullback Rayleigh Dissipation Function Euler Lagrange Equations Field Theory of Ionic Solutions that allows boundary conditions and flow and deals with Interactions of Components self-consistently

26. Field Equations with Lennard Jones Spheres Non-equilibriium variational field theory EnVarA Nernst Planck Diffusion Equation for negative ions, positive ions is analogous Poisson Equation Eisenberg, Hyon, and Liu

27. Nonequilibrium Computations with Variational Field Theory EnVarA Current Voltage Time Curves Binding Curves

28. Miracle We can Actually Compute important properties of Ion Channels and We can build them

31. 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

32. 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).

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

34. 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

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

36. 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)