to Tai-Chia Lin for inviting me

1. Thanks! to Tai-Chia Lin for inviting me And his GREAT kindness through the years here and in the USA and Canada.

3. Electricity is Different Electricity hasVERY different Physics in different systems. Current ALWAYS follows Maxwell exactly, say ± 10-12 E changes to produce EXACT conservation of ‘Current’

4. How can we use mathematics to describe biological systems? I believe some biology isPhysics ‘as usual’‘Guess and Check’ But you have to know which biology!

5. Mathematics describes only a tiny part of life, But Mathematics* Creates our Standard of Living *e.g.,Electricity, Computers, Fluid Dynamics, Optics, Structural Mechanics, ….

6. + ~30 Å Ion Channelsare theValves of CellsIon Channels are the Main Controllers of Biological Function Ions in Waterare the One Ion trajectory 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

7. The Cell Defined by a Membrane Note: intra-cellular compartmentsare defined by their membranes Bob Eisenberg: beisenbe@rush.edu

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. OmpF Biochemist’s View Structure All Atoms View Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative Bob Eisenberg: beisenbe@rush.edu

10. How do a few atoms control MACROSCOPIC biology? A mathematical multiscale question More than anything else

11. OutputCurrent i(V,t) Inputs Forward Problem Inverse Problem Open Channeli(V) Concentrations in Baths Potentials in Baths V(t) Structure Structure of Charge Permanent Structure of Charge Polarization How does it work? PNPF Finite size ions i(t) Gating OutputCurrent i(V,t) Inputs

12. Semiconductor PNP EquationsFor Point Charges Poisson’s Equation Drift-diffusion & Continuity Equation Chemical Potential Diffusion Coefficient Permanent Charge of Protein Thermal Energy Cross sectional Area Flux Number Densities Dielectric Coefficient Valence Proton charge valence proton charge

13. Semiconductor Devices PNP equations describe many robust input output relations Amplifier Limiter Switch Multiplier Logarithmic convertor Exponential convertor These are SOLUTIONS of PNP for different boundary conditions with ONE SET of CONSTITUTIVE PARAMETERSPNP of POINTS is TRANSFERRABLEAnalytical - Numerical Analysis should be attempted using techniques of Weishi Liu University of KansasTai-Chia Lin National Taiwan University & Chun Liu PSU

14. Integrated Circuit Technology as of ~2014IBM Power8 Too small to see!

15. 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 Na+Cl− or K+Cl −Note: Biology occurs in different solutions from those used in most measurements

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

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

18. 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.

19. Maxwell Equations as written by Heaviside, NOT Maxwell, using Gibbs notation Electrostatics Magnetostatics Magnetodynamics Electrodynamics’

20. Maxwell’s Equations KEY IDEA ‘Current’ is Conserved PERFECTLYFor ANY Polarization

21. Maxwell’s Ampere’s Law soCurrent is ConservedFor ANY Property of Matter

22. Current is Conserved PERFECTLY Because the Electric Field Changes to accommodate ANY physics

23. Mathematics of Continuity in Maxwell equations canCreate New Kind of Physics, New Kind of Charge When we unplug a computer power supply, we often CREATE SPARKS, i.e., a PLASMA, a NEW KIND of current flow Pop!

24. Maxwell Equations are Special Continuity of Current is Exact even though Physics of Charge Flow Varies Profoundly Current is NOT the flow of charges

25. ‘Charge’ is an Abstraction withVERY different Physics in different systems Physics of Charge Flow Varies Profoundly Current is NOT the flow of charges Maxwell Equations Control ANY Physics of Current and flow of charges

26. Current is Abstract with Different Physics in Different SystemsNOT the Flux of Charges Hungarian Journal of Industry and Chemistry (2016) 44 1-28 arXiv:1502.07251 Hungarian Journal of Industry and Chemistry 44(1): 1-28 arXiv:1502.07251

27. Rate Models Fail (until amended)becauseCurrent-in does not equal Current-out!! (if rate constants are independent of potential)

28. Current-in Current-out implies Artifactual Charge SERIOUS CONSEQUENCESFeynmanOne percent more electrons than protons, would lift the Entire Earth! • Failed Models have Metastasis of States

29. Failed Models have Metastasis of States Zagotta, Hoshi, Dittman and Aldrich (1994) J Gen Physiol 103 279-319.

30. 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

31. 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 Na+Cl− or K+Cl −Note: Biology occurs in different solutions from those used in most measurements

32. QuestionWhat does this have to do with biology? Answer All biology involves electricity All biology occurs in solutions that conduct electricity A LOT All biology occurs in Ion Solutions K+ Ca++ Na+ 3 Å Sodium Na+ Potassium K+ Calcium Ca2+ Chloride Cl- Cl-

33. All of Biology occurs in Salt Solutions of definite composition and concentration and that matters! Salt Water is the Liquid of Life Pure H2O is toxic to cells and molecules! K+ Ca++ Na+ 3 Å Sodium Na+ Potassium K+ Calcium Ca2+ Chloride Cl- Cl-

34. All of Biology occurs in Salt Solutions of definite composition and concentration and that matters! Salt Water is the Liquid of Life Pure H2O is toxic to cells and molecules! Salt Water is a Complex Fluid Main Ions are Hard Spheres, close enough Sodium Na+ Potassium K+ Calcium Ca2+ Chloride Cl- K+ Ca++ Na+ 3 Å Cl-

35. Central Result of Physical Chemistry Ionsin a solutionare aHighly Compressible Plasma although the Solution is Incompressible Free energy of an ionic solution is mostly determined by the Number density of the ions. Density varies from 10-11 to 101M in typical biological system of proteins, nucleic acids, and channels. Learned from Doug Henderson, J.-P. Hansen, Stuart Rice, among others…Thanks!

36. Electrolytes are Complex Fluids‘Everything’ interacts with everything else Treating a Complex Fluid as if it were a Simple Fluid will produce Elusive Results because Every Ion Interacts with Everything After 690 pages and 2604 references, “Single-Ion Solvation …Elusive* ” Hünenberger & Reif, 2011* ‘elusive’ is in the title!

37. It is not surprising that Inconsistent Treatments of ionic solutions have been so Unsuccessful despite more than a century of work by fine scientists and mathematicians Werner Kunz: “It is still a fact that over the last decades, it was easier to fly to the moon than to describe the free energy of even the simplest salt solutions beyond a concentration of 0.1M or so.” Kunz, W. "Specific Ion Effects" World Scientific Singapore, 2009; p 11.

38. 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 Na+Cl− or K+Cl −Note: Biology occurs in different solutions from those used in most measurements

39. Shielding is a defining property of Complex Fluids Mobile Charges Define Semiconductors and Ionic Solutions Far Field (macroscopic) boundaries

40. When a charge is added to an ionic solution, the other charge rearrange to form an Ionic Atmosphere called Shielding or Screening

41. Main Qualitative Result Shielding Dominates Electric Properties of Channels, Proteins, as it does Ionic Solutions Shielding is ignored in traditional treatments of Ion Channels and of Active Sites of proteins Rate Constants Depend on Shielding and so Rate Constants Depend on Concentration and Charge

42. Main Qualitative ResultShielding in Gramicidin Hollerbach & Eisenberg

43. No shielding terms!

44. Reconciling Mass Action and ShieldingMaxwell/Kirchoff will no doubt be a Long Journey

45. “Journeyof a thousand miles starts with a single step” in the right direction, I beg to add to this Chinese saying

46. That direction needs to include the electric field, calculated and calibrated,global and localif the journey is ever to end,in my view.

47. Replacement of “Law of Mass Action” is Feasible for Ionic Solutions using theAll Spheres(primitive = implicit solvent model of ionic solutions)andTheory of Complex Fluids

48. Motivation and Assumption for Fermi-Poisson Largest Effect of Crowded Charge is Saturation Saturation cannot be described at all by classical Poisson Boltzmann approach Nonlocal Poisson-Fermi APPROXIMATE Models Jinn Liang Liu 劉晉良 J Comp Phys (2013) 247:88 J Phys Chem B (2013) 117:12051J Chem Phys (2014) 141: 075102 J Chem Phys, (2014) 141: 22D532 Physical Review E (2015) 92: 012711Chem Phys Letters (2015)637: 1J Phys Chem B (2016) 120: 2658 Jinn-Liang is first author on our papers

49. Variational Approach EnVarA ‘Law’ of Mass Action includingInteractions Conservative Dissipative From Bob Eisenberg p. 1-6, in this issue

50. Energetic Variational Approach allows ‘exact’ computation ofFlow and Interactions in Complex Fluids like Liquid Crystals Engineering needs Calibrated Theories and Simulations Engineering Devices almost always use flow Classical theories and Molecular Dynamicshave difficulties with flow, interactions, and complex fluids