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

2. 2 Ion Channels are the Valves of Cells Ion Channels are the Main Controllers of Biological Function Chemical Bonds are lines Surface is Electrical Potential Red is negative (acid) Blue is positive (basic) Selectivity Different Ions carry Different Signals Life occurs in ~130 mM salt solutions Figure of ompF porin by Raimund Dutzler ~ 30 Å Flow time scale is 0.1 msec to 1 min 0.7 nm = Channel Diameter + Averaging is in time, from 10 -16 atomic scale to 10 -4 biological scale! Averaging is in number over 10 12 water molecules needed to specify 10 -7 M concentrations and other ‘thermodynamic’ variables Multiscale 3 Å K+K+ Na + Ca ++ Hard Spheres

3. 3 Multiscale Issues more later Biological Scales Occur Together so must be Computed Together This may be impossible in simulations Physicists and Engineers have not tried Computational Scale Biological Scale Ratio Time 10 -15 sec10 -4 sec10 11 Space 10 -11 m10 -5 m10 6 Spatial Resolution10 18 Solute Concentration10 11 Three Dimensional (10 6 ) 3

4. 4 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 cells Ion 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 Ion Channels are Biological Devices ~30 Å K+K+

5. Thousands of Molecular Biologists Study Channels every day, One protein molecule at a time This number is not an exaggeration. We have sold >10,000 AxoPatch amplifiers 5 Ion Channel Monthly AxoPatch 200B

6. Channels are parts of Machines, e.g., Excitation-Contraction Coupling L type Ca Channel RyR ryanodine receptor L-type Ca Channel RyR Thanks for the figure to László Csernoch, Debrecen, Hungary Isabelle Marty, Grenoble, France

7. 7 Function of SINGLE isolated RyR Channels in Artificial Planar Lipid Bilayers AxoPatch Patch-Clamp Amplifier Experimental Chamber Planar Bilayer 80-100 µM Diameter Teflon Septa Fused Vesicle Ca Single Channel Current open closed Designed at Rush Slide from Mike Fill Thanks!

8. Gating is Time Behavior Selectivity, Permeation are Amplitude Gating and Permeation

9. 9 Open Duration /ms Open Amplitude, pA Lowpass Filter = 1 kHz Sample Rate = 20 kHz Ca 2+ Release Channel of Inositol Trisphosphate Receptor : slide and data from Josefina Ramos-Franco. Thanks! Typical Raw Single Channel Records Current vs. time Amplitude vs. Duration Channel Structure Does Not Change once the channel is open 5 pA 100 ms

10. 10 3 Å K+K+ Na + Ca ++ Channels are Selective Different Ions Carry Different Signals through Different Channels Figure of ompF porin by Raimund Dutzler ~30 Å Flow time scale is 0.1 msec to 1 min 0.7 nm = Channel Diameter + ompF porin

11. 11 Different Types of Channels use Different Types of Ions for Different Information Channels are Selective

12. Central Problem* How does the channel control selectivity? *an example of “Reverse Engineering” 12 For Modelers and Mathematicians: This is an inverse problem!

13. 13 Goal: Understand Selectivity well enough to Fit Large Amounts of Data* and to Make a Calcium Channel * from many non-ideal solutions Atomic Scale Macro Scale

14. 14 Mutants of ompF Porin Calcium selective Experiments have built Two Synthetic Calcium Channels As density of permanent charge increases, channel becomes calcium selective E rev  E Ca Unselective Wild Type built by Henk Miedema, Wim Meijberg of BioMade Corp.,Groningen, Netherlands Miedema et al, Biophys J 87: 3137–3147 (2004) MUTANT ─ Compound Glutathione derivatives Designed by Theory Atomic Scale Macro Scale

15. Central Problem* How does the channel control selectivity? “Reverse Engineering” 15 This is an inverse problem Closely related inverse problems have been solved by mathematics used to design blast furnaces Burger, Eisenberg, and Engl (2007) SIAM J Applied Mathematics 67:960-989

16. Selective Binding Curve L type Ca channel 16 Wolfgang Nonner

17. Inverse Problem for Selectivity Badly posed, simultaneously over and under determined with noise and systematic error has actually been solved using methods for the Inverse Problem of a Blast Furnace 17 Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67: 960-989 For Modelers and Mathematicians: This is reverse engineering!

18. 18 Channels are only Holes Why can’t we understand and build them? Helpful to know physical basis of function if we want to build one and improve it Where do we start? Not with Molecular Mythology Not with gas phase models of traditional channology Liquids are not Gases; biological solutions are not ideal Not with guesses about trajectories of structural biologists Counting, Statistics, and Averaging are Essential

19. 19 Why can’t we understand and build channels? Uncalibrated Simulations will not make devices that actually work Unpopular view because Calibration is Hard Work

20. 20 Multiscale Issues are the key if we want to actually build channels that work Computational ScaleBiological ScaleRatio Time 10 -15 sec10 -4 sec Action Potential 10 11 Space 10 -11 m10 -5 m Side Chains of Proteins 10 6 Spatial Resolution10 18 Solute Concentration 10 -11 to 20 Molar 10 12 Three Dimensional (10 6 ) 3

21. 21 Multiscale Issues Biological Scales Occur Together so scales must be CALIBRATED TOGETHER in real biological solutions that are MIXTURES OF IONS Computational ScaleBiological ScaleRatio Time 10 -15 sec10 -4 sec Action Potential 10 11 Space 10 -11 m10 -5 m Side Chains of Proteins10 6 Spatial Resolution10 18 Solute Concentration10 -11 to 20 Molar10 12 Three Dimensional (10 6 ) 3

22. 22 Multiscale Issues Calibrations of Molecular Dynamics in Real Solutions are just starting! Unpopular Reality: hard work It may not be possible to deal with scale ratios of 10 11, 10 6,10 18, 10 12 all at once

23. 23 Physicists and Engineers do not even try! It may not be possible to deal with Ratios of Scales of 10 11 10 6 10 18 10 12 all at once Multiscale Issues

24. 24 Channels are only Holes Why can’t we understand and build them? Where do we start? Science as Usual Guess and Check

25. 25 Working Hypothesis Biological Adaptation is Crowded Ions and Side Chains

26. Active Sites of Proteins are Very Charged 7 charges ~ 20 M net charge Selectivity Filters and Gates of Ion Channels are Active Sites = 1.2×10 22 cm -3 - + + + + + - - - 4 Å K+K+ Na + Ca 2+ Hard Spheres 26 Figure adapted from Tilman Schirmer Pure water is 55 M OmpF Porin Physical basis of function Induced Fit of Side Chains Ions are Crowded K+K+ Na +

27. 27 Working Hypothesis Biological Adaptation is Crowded Ions and Side Chains Everything interacts Classical Models and Force Fields of Molecular Dynamics assume no interactions with ion concentrations

28. 28 Finite Size Effects Working Hypothesis ‘Primitive Implicit Solvent Model’ learned from Doug Henderson, J.-P. Hansen, Stuart Rice, among others… Thanks! 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

29. 29 Ions in Water are the Liquid of Life. They are not ideal solutions Chemically Specific Properties of Ionic Solutions come from Interactions Molecular Dynamics Force Fields are Calibrated assuming no interactions with concentrations Force Fields must be REcalibrated in each Biological Solution

30. 30 Ions in Water are the Liquid of Life. They are not ideal solutions Chemically Specific Properties of Ionic Solutions come from Interactions Chun Liu’s Energetic Variational Principle deals with Interactions EnVarA

31. 31 Everything Interacts with Everything Ions in Water are the Liquid of Life They are not ideal solutions For Modelers and Mathematicians Tremendous Opportunity for Applied Mathematics Chun Liu’s Energetic Variational Principle EnVarA

32. 32 Ions in Water not ideal solutions Chemically Specific Properties Come from Interactions Variational Principles Deal with Multiple Scales and Interactions Consistently and Automatically Chun Liu’s Energetic Variational Principle deals with Interactions EnVarA

33. 33 Variational Principles Deal with Multiple Scales Consistently and Automatically New Component or Scale of Energy or Dissipation implies New Field Equations (Euler Lagrange) by Algebra Alone No new Assumptions EnVarA

34. Page 34 Energetic Variational Approach EnVarA Chun Liu, Yunkyong Hyon, and Bob Eisenberg Mathematicians and Modelers: two different ‘partial’ variations written in one framework, using a ‘pullback’ of the action integral Action Integral, after pullback Rayleigh Dissipation Function Field Theory of Ionic Solutions that allows boundary conditions and flow and deals with Interactions of Components self-consistently Composite Variational Principle Euler Lagrange Equations

35. Page 35 Energetic Variational Analysis EnVarA being developed by Chun Liu with creates a new Multiscale Field Theory of Interacting Components that allows boundary conditions and flow and deals with Ions in solutions self-consistently (1) Yunkyong Hyon, Bob Eisenberg. Ions in Channels (2) Rolf Ryham, Bob Eisenberg and Fred Cohen. Virus fusion to Cells (3) Yoichiro Mori and Bob Eisenberg. Water flow in Tissues Multiple Scales

36. Page 36 We have already established that the Implicit Solvent (“Primitive”) Model of Ionic Solutions Describes Calcium and Sodium Channels quite well at Equilibrium without Preformed Structure Structure is the Computed Consequence of the Model

37. 37 O½O½ Selectivity Filter Selectivity Filter Crowded with Charge Wolfgang Nonner + ++ L type Ca Channel “Side Chains”

38. 38 large mechanical forces

39. 39 Solved with Metropolis Monte Carlo MMC Simulates Location of Ions both the mean and the variance Produces Equilibrium Distribution of location of Ions and ‘Side Chains’ MMC yields Boltzmann Distribution with correct Energy, Entropy and Free Energy Other methods give nearly identical results: Equilibrium Multiscale MSA (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 Multiscale Analysis at Equilibrium

40. 40 Key idea MMC chooses configurations with a Boltzmann probability and weights them evenly instead of choosing them from uniform distribution and then weighting them with exp(−E/k B T) Metropolis Monte Carlo Simulates Location of Ions both the mean and the variance 1)Start with Configuration A, with computed energy E A 2) Move an ion to location B, with computed energy E B 3) If spheres overlap, E B → ∞ and configuration is rejected 4)If spheres do not overlap, E B → 0 and configuration is accepted 5) If E B < E A : accept new configuration. 6) If E B > E A : accept new configuration with probability Details:

41. 41 Ion Diameters ‘ Pauling’ Diameters Ca ++ 1.98 Å Na + 2.00 Å K + 2.66 Å ‘Side Chain’ Diameter Lysine K 3.00 Å D or E 2.80 Å Channel Diameter 6 Å Parameters are Fixed in all calculations in all solutions for all mutants Boda, Nonner, Valisko, Henderson, Eisenberg & Gillespie ‘Side Chains’ are Spheres Free to move inside channel Snap Shots of Contents Crowded Ions 6Å Radial Crowding is Severe Experiments and Calculations done at pH 8

42. 42 Na Channel Concentration/M Na + Ca 2+ 0.004 0 0.002 0.050.10 Charge -1e DEKADEKA Boda, et al EEEE has full biological selectivity in similar simulations Ca Channel log (Concentration/M) 0.5 -6-4-2 Na + 0 1 Ca 2+ Charge -3e Occupancy (number) EEEAEEEA Mutation Same Parameters

43. Na, K, Li, Ca, Ba Binding in Calcium Channel

44. Calcium Channel has been examined in ~35 papers, e.g., 44 Most of the papers are available at f tp://ftp.rush.edu/users/molebio/Bob_Eisenberg/Reprints http://www.phys.rush.edu/RSEisenberg/physioeis.html

45. 45 Next, the Sodium Channel Summary Simulation Paper (and target for new experiments!) in Experimental Journal Calcium Channel

46. 46 DEKA Sodium Channel 6 Å Next, the Sodium Channel specifically, the Aspartate D Acid Negative Glutamate E AcidNegative Lysine K Basic Positive Alanine A AliphaticNeutral

47. DEKA Sodium Channel has very different properties from Ca channel, e.g., ‘binding’ curve, Na + vs Ca ++ selectivity Na + vs K + selectivity 47

48. 48 Challenge from leading biophysicists Walter Stühmer and Stefan Heinemann Max Planck Institutes, Göttingen, Leipzig Can a physical theory explain the mutation DEEA into DEKA?

49. 49 Ca Channel log (Concentration/M) 0.5 -6-4-2 Na + 0 1 Ca 2+ Charge -3e Occupancy (number) EEEAEEEA Boda, et al Same Parameters Mutation Same Parameters Mutation EEEE has full biological selectivity in similar simulations Na Channel Concentration/M Na + Ca 2+ 0.004 0 0.002 0.050.10 Charge -1e DEKADEKA

50. Nothing was changed from the EEEA Ca channel except the amino acids 50 Calculations and experiments done at pH 8 Calculated DEKA Na Channel Selects Ca 2+ vs. Na + and also Na + vs. K +

51. How? How does the DEKA Na Channel Select Na + vs. K + ? 51 Calculations and experiments done at pH 8

52. 52 Size Selectivity is in the Depletion Zone Depletion Zone Boda, et al [NaCl] = 50 mM [KCl] = 50 mM pH 8 Channel Protein Na + vs. K + Occupancy of the DEKA Na Channel, 6 Å Concentration [Molar] K+K+ Na + Selectivity Filter Na Selectivity because 0 K + in Depletion Zone K+K+ Na + Binding Sites NOT SELECTIVE

53. 53 Selectivity Filter log C/C ref Binding Sites *Binding Sites are outputs of our INDUCED FIT Model of Selectivity, not structural inputs Boda, et al Ion Diameter Ca ++ 1.98 Å Na + 2.00 Å K + 2.66 Å ‘ Side Chain’ Diameter 3.00 Å pH 8 2.80 Å pH 8 Na Channel DEKA 6 Å Lys or K D or E [NaCl] = [KCl] = 50 mM Size Selectivity NOT selective BLACK = Depletion=0 Na vs K Size Selectivity is in Depletion Zone

54. Na, K, Li, Cs Binding in Sodium channel

55. Inverse Problem We discover Control Variables* in simulations of the Na channel, but not the Ca channel. *These emerge as outputs. They are not inputs. 55

56. Control Variables discovered in DEKA Na channel Selectivity Na + vs K + depends only on pore diameter Diameter controls Selectivity 56

57. 57 Na + vs K + (size) Selectivity (ratio) Depends on Channel Size, not Protein Dielectric Coefficient* Selectivity for small ion Na + 2.00 Å K+K+ 2.66 Å * in DEKA Na Channel K+K+ Na + Boda, et al Small Channel Diameter Large in Å 6 8 10

58. Selectivity Na + vs K + depends only on pore diameter Conductance* depends on protein polarization Protein Dielectric Coefficient controls Conductance 58 * Gillespie & Boda (2008) Biophysical Journal 95:2658 Control Variables discovered in DEKA Na channel

59. 59 Occupancy Boda, et al DEKA Na Channel, 6 Å Channel Contents occupancy Na + 2.0 Å K+K+ 2.66 Å Control Variable Channel Contents (occupancy) depends on Protein Polarization (dielectric)

60. 60 Selectivity comes from Electrostatic Interaction and Steric Competition for Space Repulsion Location and Strength of Binding Sites Depend on Ionic Concentration and Temperature, etc Rate Constants are Variables

61. Channel and Contents form a Self-Organized Structure with Side Chains at position of Minimum Free Energy Protein Fits the Substrate “Induced Fit Model of Selectivity” 61 What does the protein do?

62. 62 Certain MEASURES of structure are Powerful DETERMINANTS of Function e.g., Volume, Dielectric Coefficient, etc. Induced Fit Model of Selectivity Atomic Structure is not pre-formed Atomic Structure is an important output of the simulation Nonner and Eisenberg What does the protein do?

63. 63 Protein maintains Mechanical Forces* Volume of Pore Dielectric Coefficient/Boundary Permanent Charge What does the protein do? Nonner and Eisenberg * Driving force for conformation changes ??

64. Binding Sites* are outputs of our Calculations 64 *Selectivity is in the Depletion Zone, NOT IN THE BINDING SITE of the DEKA Na Channel Our model has no preformed structural binding sites but Selectivity is very Specific Induced Fit Model of Selectivity

65. We can actually compute the Structures that determine Selectivity 65

66. Can EnVarA actually compute the Function of these systems? 66

67. 67

68. 68 Vaccination against Traditional Models

69. 69 Traditional Biochemistry and Traditional Molecular Dynamics Assume Ideal Solutions Ions in Water are the Liquid of Life Life Occurs in ~130 mM salt solutions Ions in Water and Life are NOT ideal

70. 70 No gas phase models of traditional channel biochemistry Liquids are not Gases No discussions of individual trajectories of Structural Biologists Counting and Statistics are essential

71. 71 Selectivity comes from Electrostatic Attraction and Steric Competition for Space Repulsion Location and Strength of Binding Sites Depend on Ionic Concentration and Temperature, etc Rate Constants are Variables

72. 72 Conclusion Selectivity can be understood by Reduced Models K channels Benoît Roux Susan Rempe Na & Ca channels Nonner, et al, RyR channels Gillespie & Meissner Best Evidence

73. Induced Fit Model Selectivity depends on Induced Fit of Side Chains and Ions Induced Fit is the Self-Organized Structure with Minimal Free Energy 73 Energy and Entropy

74. 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 74 Energy and Entropy

75. 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 75

76. 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 76

77. 77 Miedema et al, Biophys J 87: 3137–3147 (2004) Calcium selective Unselective Wild Type MUTANT ─ Compound Remember We can build them (reasonably well)

78. 78

79. Page 79 Energetic Variational Analysis EnVarA being developed by Chun Liu Yunkyong 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

80. Page 80 Energetic Variational Analysis EnVarA Chun Liu, Yunkyong Hyon, and Bob Eisenberg Variational Principle Rayleigh Dissipation Function Field Theory of Ionic Solutions that allows boundary conditions and flow and deals with Interactions of Components Self-consistently

81. Page 81 EnVarA Generalization of Chemical Free Energy Eisenberg, Hyon, and Liu

82. Page 82 Ca 2+ and Na + Binding Curves DEEA Calcium Channel Eisenberg, Hyon, and Liu

83. 83 Eisenberg, Hyon, and Liu

84. Page 84 Energetic Variational Analysis EnVarA Chun Liu, Yunkyong Hyon and Bob Eisenberg New Interpretations likely to be Controversial but Quantitative and Testable

85. 85 Energetic Variational Approach EnVarA * if they define an energy and its variation : Energy defined by simulations or theories or experiments is OK. Full micro/macro treatment is needed for an Atomic Model, with closure. Eisenberg, Hyon, and Liu New mechanisms* can be added

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

87. 87 Selectivity Filter is 10 Å long and 8 Å in diameter confines four D4899 negative amino acids. Four E4900 positive amino acids are on lumenal side, overlapping D4899. Cytosolic distributed charge The Geometry D. Gillespie et al., J. Phys. Chem. 109, 15598 (2005). Protein CytoplasmLumen

88. 88 Nonner, Gillespie, Eisenberg DFT/PNP vs Monte Carlo Simulations Concentration Profiles Misfit

89. 89 Divalents KCl CaCl 2 CsCl CaCl 2 NaCl CaCl 2 KCl MgCl 2 Misfit Error < 0.1 kT/e 2 kT/e Gillespie, Meissner, Le Xu, et al

90. 90 KCl Misfit Error < 0.1 kT/e 4 kT/e Gillespie, Meissner, Le Xu, et al

91. Theory fits Mutation with Zero Charge No parameters adjusted Gillespie et al J Phys Chem 109 15598 (2005) Protein charge density wild type* 13 M Water is 55 M *some wild type curves not shown, ‘off the graph’  0 M in D4899 Theory Fits Mutant in K + Ca Theory Fits Mutant in K Error < 0.1 kT/e 1 kT/e

92. 92

93. 93