The Voltage Sensor Biophysics needs Physics

1. The Voltage Sensor Biophysics needs Physics Virtue of Necessity vs. Wages of Sin

2. Current to maintain test potential External Dissolved Ions Voltage Clamp =0 External Dissolved Ions Arginines Holding Potential Voltage Clamp Test Potential Dissolved Ions Internal Dissolved Ions Fermi Distribution not Boltzmann Test Potentials Holding Potential Holding Potential Bezanilla, F. How membrane proteins sense voltageNature Rev Mol Cell Biol 9, 323-332 VmTest Potentials

3. NECESSITY We need to know How can the movement of a small number of Arginines be detected in a sea of atoms? Answer requires the Virtue of Knowledge. The answer can only be found in Maxwell Equations of Electrodynamics

4. How can the movement 1.6×1010 out of 6×1021 of 2.7×10-10per cent have any effect? Scale of the Problem Area of the USA is 1013 m2 1 part in 1013 has little effect!

5. How can the movement of a small number of Arginines 1.6×1010 be detected in a ‘sea’ of 6×1021 atoms?? ‘Sea of Atoms’ is an experimental chamber of 50 cm3 containing 1/20 of a liter of 0.2 molar solution; 6 x 1023 atoms per mole = 6 x 1021 atoms

6. Number of Arginines Paraphrase of email from Francisco Bezanilla, “ … 16 Arginines move in a typical K channel. We measure currents from ~109 channels in a cut open oocyte preparation . So we measure the Movement of 1.6x1010 arginines. Best, Pancho ” ‘Sea of Atoms’ is an experimental chamber of 50 cm3 containing 1/20 of a liter of 0.2 molar solution; 6 x 1023 atoms per mole = 6 x 1021 atoms

7. How do a few atoms exert macroscopic effect? Answer, oversimplified: The Electric Field is Strong A few atoms control the electric field Much as they do in transistors

8. The Electric Field is Strong Coulomb’s Law in Chemical Units ∙= energy of diffusion

9. What do these numbers mean? Errors in Molecular Dynamics are variously quoted as between and Errors in best models of open channel (Gillespie) are much less because they get the electric field more or less right in my opinion

10. 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

11. The model predicted that AMFE disappears The Na+/Cs+ mole fraction experiment is repeated with varying amounts of KCl and LiCl present in addition to the NaCl and CsCl. The model predicted that the AMFE disappears when other cations are present. This was later confirmed by experiment. Error < 0.1 kT/e Prediction made without any adjustable parameters. Note Break in Axis Gillespie, Meissner, Le Xu, et al

12. Mixtures of THREE Ions Error < 0.1 kT/e The model reproduced the competition of cations for the pore without any adjustable parameters. Gillespie, Meissner, Le Xu, et al Li+& K+ & Cs+ Li+& Na+ & Cs+

13. 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, R. P., R. B. Leighton, and M. Sands. 1963. The Feynman: Lectures on Physics, Mainly Electromagnetism and Matter.New York: Addison-Wesley Publishing Co., also at http://www.feynmanlectures.caltech.edu/II_toc.html.

14. Conservation of Current and Conservation of Chargeare EXACTandUNIVERSAL

15. Maxwell’s Magnetism Current is Conserved PERFECTLY

16. Current has Very different Micro-physics in Different Systems butContinuity of Current is ExactNo matter what is the mechanism of current flow! Ag AgCl Ag AgCl D = permittivity  E

17. Continuity of Current is Exact Maxwell Equations are Special even though Physics of Charge Flow Varies Profoundly ‘Charge’ hasVERY different Physics in different systems

18. Continuity of Current is Exact How can that possibly be? even though Micro-physics of Charge Flow Varies Profoundly

19. How can that possibly be true? Continuity of Current is Exact One component of current flow is NOT governed by the Microphysics of charge movement

20. How can that possibly be true? Continuity of Current is Exact One component of current flow is governed by UNIVERSAL Electrodynamics ENTIRELY INDEPENDENT of the properties of matter

21. Universal Component of Current is the Displacement Current Displacement current is independent of the properties of matter except through E(r,t) given by Maxwell Equations. Displacement Current allows light to propagate through a vacuum.

22. Displacement Current is Differentin Different Devices because the Electric Field is Different in Different Devices Device 1 Device 2

23. Electric Field is Different in Different Devices so Displacement Current is Different in Different Devices Device 2 Device 1

24. differs in every devicebecause E(x,t) differs in every device by just enough so the TOTAL Current is exactly equal at every time in every location and every device Maxwell Miracle Device 1 Device 2 Total Current = Displacement Current + Device Current

25. Electric Field takes on Whatever Value Conserves TOTAL current, Specifically, E changes the displacement currentSo total current is always conserved • Details and PROOF at https://arxiv.org/abs/1708.07400 • including quantum mechanics

26. Original Sin of Chemical Kinetics Conservation of Current is not enforcedin Chemical Kinetics

27. Consequences of Ignoring Conservation of Current are Profound Wages of Sin* is the Death of Chemical Kinetics * Romans 6:23 of New Testament of Christian Bible

28. Rate Models FailbecauseCurrent-in does not equal Current-out!! (if rate constants are independent of potential) Rate Constants are INDEPENDENT parameters so

29. Rate Models FailbecauseCurrent-in does not equal Current-out!! (if rate constants are independent of potential)

30. ‘Current-in’ does not equal ‘Current-out’ in Rate Models if rate constants are independent and Currents are Uncorrelated

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

32. Cause of Frustration Biochemical Models are Rarely TRANSFERRABLEDo Not Fit Data even approximatelyin more than one solution* Title Chosen by Editors Editors: Charlie Brenner, Angela HoppAmerican Society for Biochemistry and Molecular Biology *i.e., in more than one concentration or type of salt, like or Note: Biology occurs in different solutions from those used in most measurements

33. Equations and Models of Electrical Engineering ARE Transferrable

34. Device is ROBUST and TRANSFERRABLE because it uses POWER and has complexity! Circuit Diagram of common 741 op-amp: Twenty transistors needed to make linear robust device Power Supply INPUTVin(t) OUTPUTVout(t) Power Supply Dirichlet Boundary Condition independent of time and everything else Device converts Input to Outputby a simple ‘law’ Dotted lines outline: current mirrors  (red);differential amplifiers (blue);class A gain stage (magenta); voltage level shifter (green);output stage (cyan).

35. Devices Must be Transferrable

36. Equations and Models of Chemistry are NOT Transferrable

37. What does this have to do with biology? LIPID METABOLISM is a big deal

38. What does this have to do with biology? METABOLISM is a big deal

39. Consequences of Ignoring Conservation of Current are Profound No Chemical Devices Wages of Sin Romans 6:23 of New Testament of Christian Bible

40. Consequences of Ignoring Conservation of Current are Profound Chemical Devices areNot Transferrable and Hardly Exist Wages of Sin Romans 6:23 of New Testament of Christian Bible

41. How can Chemical Kinetics be Fixed?

42. Continuity of Current enforces long range macroscopiccorrelationsthat cannot be described with ordinary differential equations in time

43. How can Chemical Kinetics be Fixed? Partial Differential Equations involving Space and Time must be used because conservation of current always involves space Definition of current involves space!

44. Any Questions?

45. Current to maintain test potential External Dissolved Ions Voltage Clamp =0 External Dissolved Ions Arginines Holding Potential Voltage Clamp Test Potential Dissolved Ions Internal Dissolved Ions Fermi Distribution not Boltzmann Test Potentials Holding Potential Holding Potential Bezanilla, F. How membrane proteins sense voltageNature Rev Mol Cell Biol 9, 323-332 VmTest Potentials

46. Perhaps the firstConsistent Model of a Protein Machine Francisco Bezanilla Allen Tzyy-Leng Horng Chun Liu Bob Eisenberg 春 柳 洪子倫

47. intracellular extracellular Figure 1. Geometric configuration of the reduced mechanical model including the attachments of arginines to the S4 segment.

48. Variational Formulation EnVarA because Everything interacts with Everything Else Poisson Equation and Transport equation are DERIVED, not assumed from variations like so cross terms are always consistent, i.e., satisfy all equations with one set of parameters.

49. Defining Laws Charge Creates Electric Field Transport of Mass

50. Conformation Change of Arginines is Described by an Elastic System where K is the spring constant, zi is the fixed anchoring position of the spring for each arginine cion S4, is the center-of-mass z position of S4 by treating S4 as a rigid body. follows the motion of equation based on spring-mass system: