to Tai Chia Lin 林太家 for inviting me

1. Thanks! to Tai Chia Lin 林太家 for inviting me And GREAT kindness he has shown me through the years in Taiwan, USA and around the world

2. + ~3 x 10-9 meters Channels are Selective Molecular DevicesDifferent Ions Carry Different Signals through Different Channels ompF porin Ca++ Na+ K+ 300 x 10-12 meter 0.7 10-9 meter = Channel Diameter Diameter mattersIonic solutions are NOT ideal Classical Biochemistry assumes ideal solutions. K+& Na+ are identical only in Ideal Solutions. Flow time scale is 10-4 sec to 1 min Figure of ompF porin by Raimund Dutzler

3. Biology is made of Devicesand they are Multiscale

4. Entire Function of Nerve can be Calculated and (almost all) Understood in molecular detail Nerve Skeletal muscle

5. Biology is made of Devicesand they are MULTISCALE A different talk! Hodgkin’s Action Potential is the Ultimate Multiscale model from Atoms to Axons Ångstroms to Meters

6. All Spheres Models work well for Calcium and Sodium Channels Nerve Heart Muscle Cell Skeletal muscle

7. ‘Typical’ Cell

8. K+ ~30 x 10-9meter 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 Coordinate contraction in skeletal muscle Control all electrical activity in cells Produce signals of the nervous system Are involved in secretion and absorption in all cells:kidney, intestine, liver, adrenal glands, etc. Are involved in thousands of diseases and many drugs act on channels Are proteins whose genes (blueprints) can be manipulated by molecular genetics Have structures shown by x-ray crystallography in favorable cases Can be described by mathematics in some cases • *Device is a Specific Word, that exploits specific mathematics & science *nearly pico-valves: diameter is 400 – 900 x 10-12 meter; diameter of atom is ~200 x 10-12 meter

9. Ion Channels are DevicesValves that Control Flowas are FETs of our computers Classical Theory & Simulations NOT designed for flow Thermodynamics, Statistical Mechanics do not allow flow Rate Models are inconsistent with Maxwell’s Eqn (Kirchoff Law) (if rate constants are independent of potential)

10. Gain Vout Vin Power Supply 110 v Device Amplifier Converts an Input to an Output by a simple ‘law’ an algebraic equation

11. DEVICE IS USEFULbecause it is ROBUST and TRANSFERRABLE ggainis Constant!! Device converts an Input to an Output by a simple ‘law’

12. Gain Vout Vin Power Supply 110 v Device Amplifier Converts an Input to an Output CHALLENGE What is different about the Voltage on the input Vin And Voltage on the output Vin

13. Gain Vout Vin Power Supply 110 v HintLook at the currents at the input and output and their sensitivity to voltage, i.e., look at input and output impedances CHALLENGE What is different about the Voltage on the input Vin and Voltage on the output Vin

14. Devices are Built to Implement Equations in Engineering Devices are Evolved to Provide Functions in Biology

15. Inengineering we know the equation and seek to improve the device. In biology oftenwe have to discover the function, and how molecules perform the function. InverseProblem* Reverse Engineering *Actually solved for channel problemBurger, Eisenberg and Engl (2007) SIAM J Applied Math 67: 960-989

16. 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.)

17. 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.)

18. Engineers:this is reverse engineering For example, Find Charge Distribution in Channel from Current Voltage Relations Problem (with noise and systematic error) has actually been solvedbyTikhonov RegularizationBurger, Eisenberg, Engl (2007) SIAM J Applied Math 67: 960-989 using procedures developed by Engl to study Blast Furnaces and their Explosions Inverse Problems Given the OutputDetermine the Reduced Model

19. Inverse Problem for Selectivity Badly posed, simultaneously over and under determined with noise and systematic error has actually been solvedwith Robust Solution*using methods for the Inverse Problem of a Blast Furnace Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67: 960-989 *Key is lots of data from many conditions

20. New Problem Nobel Prize in My Opinion How can Inverse Methods be used to determine Reduced Models? Hint: start with known successes, like FET devices Move to SIMPLE ion channels

21. Ompf G119D A few atoms make a BIG Difference OmpF 1M/1M G119D 1M/1M OmpF0.05M/0.05M G119D 0.05M/0.05M Glycine replaced by Aspartate Structure determined by Raimund Dutzlerin Tilman Schirmer’s lab Current Voltage relation by John Tang in Bob Eisenberg’s Lab

22. How does it work? How do a few atoms control (macroscopic) Biological Function Mathematics of Molecular Biology is aboutSolving Specific Inverse Problems • Problem for Channels has actually been solvedBurger, Eisenberg, Engl (2007) SIAM J Applied Math 67: 960-989

23. Multi-Scale Issues are Always Presentin Atomic Scale Engineering A different talk Journal of Physical Chemistry C 114: 20719-20733 (2010). • Atomic & Macro Scales are both used by channels just because Channels are Nanovalves • By definition: all valves use small structures to control large flows

24. The Reduced Equationis How it works! Multiscale Reduced Equation Shows how a Few Atoms ControlBiological Function

25. Single Channel Recording

27. Gating is the process that opens and closes ion channels. Gating is widely thought to be a conformational change. Conformational change of what? Driven by whatphysics? How (physically) does conformation change function? Gating

28. New Problem: Gating Selectivity,Permeation are Amplitude Gating is Time Behavior

29. Conformational change of what? Driven by whatphysics? How (physically) does conformation change function? New Problem Gating Answers to these questions are needed if phrase ‘conformational change’ is to be more than vague description* *Opinion of Bob Eisenberg, not generally shared

30. New Problems? How can current be independent of time from 10-5 to 101when thermal motion is MANY atomic diameters in 10-5 sec? Thermal motion  speed of sound 103m/sec=1 atom diameter/10-12sec (!)

31. Does PNP-steric have unstable solutions? Coulomb blockade Can tiny changes to PNP produce unstable solutions?

32. A different talk! Where to start? Compute all atoms in a device?

33. Simulations produce too many numbers 106 trajectories each 10-6 sec long, with 109 samples in each trajectory, in background of 1022 atoms Estimators are Needed Estimators are a kind of Reduced Model

34. Multi-Scale Issues A different talk! Journal of Physical Chemistry C (2010 )114:20719 Three Dimensional (104)3 Atomic and Macro Scales are BOTH used by channels because they are nanovalves so atomic and macro scales must be Computed and CALIBRATED Together This may be impossible in all-atom simulations

35. Where to start? A different talk Compute all atoms in a device? Calibrated all-atom simulations are Barely Feasible if they must accurately compute biological function Macroscopic Time & Distance Scales Macroscopic Electric Fields & Gradients Power SuppliesPower Supply = spatially nonuniform inhomogeneous Dirichlet Boundary Conditions Flows, Non-ideal mixtures including [Ca2+]=[10-8↔101 M]

36. Where to start? Mathematically ? Physically ?

37. Here is where we do Science, not Mathematics Here we GUESS and CHECK

38. Guess 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

39. Density and Concentration Fields are Weak One percent  change in density does almost nothing The Electric Field is Strong One percent  change in charge lifts the Earth,

40. 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

41. Crowded Active Sitesin 573 Enzymes Jimenez-Morales, Jie Liang and B. Eisenberg (2012) European Biophysics J 41: 449-460

42. Everything Interacts with Everything Else by steric exclusioninside crowded active sites Everything interacts with macroscopic Boundary Conditions (and much else) through long range electric field ‘Law’ of mass action needs to be generalized

43. Where do we begin? • Crowded Charge • has • HUGE electric fields • Poisson Equation, i.e., Conservation of Charge • and • LARGE steric repulsionFermi distribution

44. Electrolytes are Complex Fluids Treating a Complex Fluid as if it were a Simple Fluid will produce Elusive Results

45. ‘Everything Interacts with Everything Else’ immediately implies the need for Variational Methods for those who understand. But I did not understand for some fifty years, chemists/biologists do not understand even now, so it is not obvious to all. I apologize to those who already understand!

46. Evidence for Reduced Model ‘Crowded Charge’

47. Na+ 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 ½ ½ ½ ½ ½ ½ ½ Na+ Na+ Na+ ionsandproteinside chains are hard spheres in this model * Many methods have been used in more than 30 papers since Nonner and Eisenberg, 1998 ½

48. 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

49. Solved by DFT-PNP (Poisson Nernst Planck) DFT-PNP gives location of Ions and ‘Side Chains’ as OUTPUT Other methodsgive nearly identical results DFT (Density Functional Theory of fluids, not electrons) MMC (Metropolis Monte Carlo)) SPM (Primitive Solvent Model) EnVarA (Energy Variational Approach) Non-equil MMC (Boda, Gillespie) several forms Steric PNP (simplified EnVarA) Poisson Fermi (replacing Boltzmann distribution)

50. DFT/PNPvsMonte Carlo Simulations Concentration Profiles Misfit Nonner, Gillespie, Eisenberg Different Methods give Same Results NO adjustable parameters