Thanks to Aleksandra for Inviting me!

1. Thanks to Aleksandra for Inviting me! Particular Pleasure in Lausanne: Beaux Arts Claude Renoir by August Renoir

2. + ~30 Å Ion Channelsare theValves of CellsIon Channels are the Main Controllers of Biological Function Ions in Water* are the Selectivity Different Ions carry Different Signals Liquid of Life • *Pure H2O is toxic to cells & proteins 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

3. Ompf G119D A few atoms make a BIG Difference Glycine replaced by Aspartate Structure determined by Raimund Dutzler in Tilman Schirmer’s lab Current Voltage relation by John Tang in Bob Eisenberg’s Lab

4. Multi-Scale Issues are Always Presentin Atomic Scale Engineering Atomic & Macro Scales are both used by channels just because Channels are Nanovalves By definition: all valves use small structures to control large flows

5. How do a few atoms control (macroscopic) Biological Function? Answer, oversimplified: A few atoms control the electric field Much as they do in transistors

6. The Electric Field is Strong If you were standing at arm’s length from someone and each of you had  One percent more electrons than protons, the force would lift the Entire Earth! slight paraphrase of third paragraph, p. 1-1 of Feynman, Leighton, Sands (1963) ‘The Feynman Lectures on Physics, Mainly Electromagnetism and Matter’ also at http://www.feynmanlectures.caltech.edu/II_toc.html.

7. Channels are Devices Channels are (nano) valves Valves Control Flow Classical Theory & Simulations NOT designed for flow Thermodynamics, Statistical Mechanics do not allow flow Rate and Markov Models do not Conserve Current

8. Maxwell’s Equation A different talk! Maxwell Equations are aboutConservation of Current Details and PROOF at https://arxiv.org/abs/1609.09175

9. Maxwell Equations are aboutConservation of Current A different talk! ‘Current’ is whatever creates a magnetic field curl B in experiments J is defined by measurements of curl B and Electric Field takes on Whatever Value Conserves current, specifically Details and PROOF at https://arxiv.org/abs/1609.09175

10. A different talk! Electric Field takes on Whatever Value Conserves current, No matter what are the Properties of Matter and its Polarization. Theories of matter often treat electrodynamics cavalierly. Vacuum displacement current is usually ignored and so conservation of `current' is not enforced. Details and PROOF at https://arxiv.org/abs/1609.09175

11. Thermodynamics, Statistical Mechanics, Molecular Dynamics are UNSUITED for DEVICES Thermodynamics, Statistical Mechanics, Molecular Dynamicshave No inputs, outputs, flows, or power supplies or DEVICE EQUATIONSPower supply = spatially nonuniform inhomogeneous Dirichlet conditions Analysis of Devices must be NONEQUILIBRIUM with spatially non-uniform BOUNDARY CONDITIONS

12. Tremendous Opportunity For New Science Much more important than most Nobel Prizes THEORETICAL CHEMISTRY MUST BE REBUILT To deal with FLOW of CURRENT and NEW TECHNOLOGY

13. Where to start? Why not compute all the atoms?

14. Multiscale Issues Journal of Physical Chemistry C (2010 )114:20719 A different talk! Three Dimensional (106)3 Biological Scales Occur Together so must be Computed Together This may be impossible in simulations Physicists and Engineers rarely try

15. Multiscale Issues Journal of Physical Chemistry C (2010 )114:20719 Uncalibrated Simulations will not make devices that actually work Calibration is Hard Work particularly for Non-Ideal systems with Correlations, Finite Size effects, and Flows

16. Where to start? Mathematically ? Physically ?

17. . Reduced Models are Needed Reduced Models are Device Equations like Input Output Relations of Engineering Systems The device equation is the mathematical statement of how the system works Device Equations describe ‘Slow Variables’ found in some complicated systems How find a Reduced Model?

18. Biology is Easier than Physics Reduced Models Exist* for important biological functions or the Animal would not survive to reproduce *Evolution provides the existence theorems and uniqueness conditions so hard to find in theory of inverse problems. (Some biological systems  the human shoulder  are not robust, probably because they are incompletely evolved,i.e they are in a local minimum ‘in fitness landscape’ .I do not know how to analyze these. I can only describe them in the classical biological tradition.)

19. Reduced models exist because they are the adaptationcreated by evolution to perform a biological functionlike selectivity • Reduced Models • and its parameters • are found by Inverse Methodsof Reverse Engineering • Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67:960-989

20. Working Hypothesis: Crucial Biological Adaptation is Crowded Ions and Side Chains Wise to use the Biological Adaptation to make the reduced model! Reduced Models allow much easier Atomic Scale Engineering

21. 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

22. Crowded Active Sitesin 573 Enzymes Jimenez-Morales,Liang, Eisenberg

23. Don’t worry! Crowded Charge is GOOD It enables SIMPLIFICATION by exploiting a biological fact (an adaptation) Charges are Crowded where they are important!

24. Where do we begin? Crowded Charge enables Dimensional Reduction* to a Device Equation Inverse Problem! Essence of Engineering is knowing What Variables to Ignore! WC Randels in Warner IEEE Trans CT 48:2457 (2001) *Dimensional reduction = ignoring some variables

25. A Nonlocal Poisson-Fermi Model for Electrolyte Solutions Jinn Liang Liu 劉晉良 Jinn-Liang is first author on our papers J Comp Phys (2013) 247: 88 J Phys Chem B (2013) 117:12051J Chem Phys (2014) 141: 075102 J Chem Phys, (2014) 141: 22D532Physical Review E (2015) 92: 012711Chem Phys Letters (2015)637: 1J Phys Chem B (2016) 120: 2658

26. * *and in Boltzmann 1904 Berkeley Lectures (1964). Lectures on Gas Theory Does not Saturate Boltzmann distribution in PhysiologyBezanilla and Villalba-Galea J. Gen. Physiol. (2013) 142: 575–578 Saturates!

27. Three Channel Types RyR, CaV= EEEE, andNav= DEKA analyzed successfully* in a wide range of solutions by the ‘All Spheres’ Primitive Model Implicit solvent model of open channel ionsandproteinside chains are hard spheres in this model * Many methods have been used in more than 30 papers since Nonner and Eisenberg, 1998

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

29. Experiments have ‘engineered’ channels (5 papers) including Two Synthetic Calcium Channels MUTANT ─ Compound Calcium selective Unselective Natural ‘wild’ Type As density of permanent charge increases, channel becomes calcium selectiveErev ECa in0.1M1.0 M CaCl2 ; pH 8.0 built by Henk Miedema, Wim Meijberg of BioMade Corp. Groningen, Netherlands Miedema et al, Biophys J 87: 3137–3147 (2004); 90:1202-1211 (2006); 91:4392-4400 (2006) Mutants of ompF Porin Designed by Theory Glutathione derivatives Atomic Scale || Macro Scale

30. 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

31. Many methodsgive nearly identical results: Equilibrium MultiscaleMSA (mean spherical approximation) SPM (primitive solvent model) DFT (density functional theory of fluids), MC-loc(MC with localized side chains) Non-equilibrium Multiscale DFT-PNP (Poisson Nernst Planck) EnVarA (Energy Variational Approach) DMC Dynamic Monte Carlo NP-LEMC (Nernst Planck Local Equilibrium Monte Carlo) Steric PNP Poisson Fermi; etc.

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

33. Charge-Space Competition MonteCarloMethods Dezső Boda Doug Henderson Wolfgang Nonner DirkGillespie More than 35 papers are available at ftp://ftp.rush.edu/users/molebio/Bob_Eisenberg/reprints

34. Metropolis Monte Carlo Simulates Location of Ionsboth the mean and the variance MMC details • Start with Configuration A, with computed energy EA • Move an ion to location B, with computed energy EB • If spheres overlap, EB → ∞ and configuration is rejected • If spheres do not overlap, EB ≠0 and configuration may be accepted (4.1) If EB < EA: accept new configuration. (4.2) If EB > EA : accept new configuration with probability Key idea Instead of choosing configurations from uniform distribution, then weighting them with exp(−E/k BT), MMC chooses them with a Boltzmann probability and weights them evenly.

35. ‘All Spheres’ Model ofL-type Calcium ChannelCrowded with Charge Selectivity Filter O½ Nonner & Eisenberg + ++ ‘Side Chains’

36. 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

37. Signature of Cardiac Calcium Channel CaV1.n Anomalous* Mole Fraction (non-equilibrium) Na Channel Ca Channel *Anomalous because CALCIUM CHANNEL IS A SODIUM CHANNEL at [CaCl2] 10-3.4 Ca2+ is conducted for [Ca2+] > 10-3.4, but Na+ is conducted for [Ca2+] <10-3. Liu & Eisenberg (2015) Physical Review E 92: 012711

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

39. Sodium ChannelVoltage controlled channel responsible for signaling in nerve and coordination of muscle contraction

40. Challenge from channologists Walter Stühmer andStefan Heinemann GöttingenLeipzig Max Planck Institutes Can THEORY explain the MUTATION Calcium Channel into Sodium Channel? DEEA DEKA Calcium Channel Sodium Channel

41. 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 ParameterspH 8 Ca2+ 0 0 -6 -4 -2 0 0.05 0.1 log (Concentration/M) Concentration/MpH =8 EEEE has full biological selectivityin similar simulations Monte Carlo simulations of Boda, et al

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

43. 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

44. How?Usually Complex Unsatisfying Answers*How does a Channel Select Na+vs. K+ ?* Gillespie, D., Energetics of divalent selectivity in the ryanodine receptor. Biophys J (2008). 94: p. 1169-1184* Boda, et al, Analyzing free-energy by Widom's particle insertion method. J Chem Phys (2011) 134: p. 055102-14 Calculations and experiments done at pH 8

45. SimpleIndependent§ Control Variables*forDEKA Na+ channelbut only in a special caseand not for other channels Amazingly simple, not complex for the most important selectivity property of DEKA Na+ channels *Control variable = position of gas pedal or dimmer on light switch §Gas pedal and brake pedal are (hopefully) independent control variables OUTPUT of Calculations NOT Assumed or Manipulated Boda, et al

46. (1) Structure(Diameter) controls Selectivity(2) Dehydration/Re-solvationSolvation (dielectric) controls ContentsBoth emerge from calculations*Control variables emerge as outputsControl variables are not inputs Independent Control Variables* Dielectric constants Diameter

47. Structure(diameter) controls SelectivityControl Variable emerged as outputControl Variables are not inputsMonte Carlo calculations of the DEKA Na channel

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

49. Solvation(dielectric) controls ContentsControl Variable emerged as outputControl Variables are not inputsMonte Carlo calculations of the DEKA Na channel

50. DEKA Na Channel, 6 Å Na+ Occupancy 2.0 Å K+ 2.66Å Occupancy # Boda, et al Occupancy # Depends on Protein Dielectric ProteinDielectric ‘Amplifies’ Charge & Electrostatic effects Size Selectivity ratiodoes not depend on protein dielectric