Life is Different. It is inherited Oberwolfach March 7-1 2018

1. Life is Different: it is inherited Oberwolfach Workshop, February 2018Bob Eisenberg Department of Applied MathematicsIllinois Institute of Technology Department of Physiology and BiophysicsRush University Chicago USA

2. Oberwolfach Workshop 1809 The Mathematics of Mechanobiology and Cell Signaling 25 February – 3 March 2018 Organizers: Davide Ambrosi, Milano Italy Chun Liu, State College PA USA Matthias Röger, Dortmund Germany Angela Stevens, Münster Germany at the MathematischesForschungsinstitutOberwolfach.

3. Thanks to Chun Liu柳 春 For a very special FriendshipandCollaboration!

4. Life is special because it is inherited from a tiny number of atoms And the central question of biology is How is this possible?

7. How can a few thousand atoms conceivably control 1025 atoms?

8. Ompf G119D Experimental Evidence: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

9. How can a few thousand atoms conceivably control 1025 atoms? Traditional Statistical Mechanics says this is impossible! where and specifies the radius of the small spherical volume over which the spatial average takes place.

10. How can a few thousand atoms conceivably control 1025 atoms? The thousand atoms of one gene occupy say 10-27 m3 The volume of a person might be 1m3 Volume of Canada, USAChina 1m high is 1013m3 Fraction of space of a gene is about 10-27 Fraction of Space of One Person in Canada is 10-13 1 m3 has no effect in Canada 1 gene should have no effect

11. How can a few thousand atoms conceivably control 1025 atoms? Biological Answer: Structure: a Hierarchy of Devices Physical Answer: Electrodynamics: Strong and Universalinside atoms to stars Another talk* another day! *Eisenberg, Oriols, and Ferry. 2017. Dynamics of Current, Charge, and Mass. Molecular Based Mathematical Biology 5:78-115 arXiv https://arxiv.org/abs/1708.07400.

12. Everyone knows Biology is made of Structures Working hypothesis: The Structures make Devicesthat span the scales What is a Device? How are they studied? A different talk!

13. Answer:Biology is made of Devicesand they span the scales Organelle 10-6m Organ10-1 m Molecule 10-8 m ATOM 10-10 m Cell 10-5m Tissue 10-3 m Cell 10-5m ORGANISM1 m

14. How can a few thousand atoms conceivably control 1025 atoms? ANSWER:by forming a HIERARCHY of DEVICES

15. Different Kind of Averaging in Device Precise stochastic definition • Definition of a DeviceOutput is Perfectly Correlated with Input • Averaging in a Device Creates a Perfectly Correlated* Replica of the Input Notequal *Coherence function of Device = 1.0 Coherence function in general == cross, self-powerspectral densityestimator of

16. Structural Complexity so characteristic of life, so daunting to mathematicians is the Hierarchy of Devices

17. Structural Complexityof Life is the Hierarchy of Devices Biology is made of Devicesand they are Multiscale

18. Structural Complexity of Life is the Hierarchy of Devices One Cell contains many Devices

19. Example: Real Biological System A Nerve Cell is a Hierarchy of DevicesCell Body,Dendrites,Axon,Terminals Andrew Huxley with his mentor Alan Hodgkin Bob, I would not put it that way…..

20. Nerve Signal is the propagating ‘Action Potential’, a waveform in x and t Purely Local Theory is Impossible because the phenomena involves centimeter scales, as well as Angstroms. All atom Molecular Dynamics is impossible because ~1023 atoms are involved Atomic Properties of the Voltage Sensor are coupled to the macroscopic electric field a centimeter away. The electric field controls the sensor; the sensor controls the electric field. That is how propagation works!

21. Channels are Source of Signal

23. Start with Voltage Sensor

24. Voltage Sensor Structure (NOT conduction channel) Emerging Consensus …. Vargas, E., Yarov-Yarovoy, V., Khalili-Araghi, F., Catterall, W. A., Klein, M. L., Tarek, M., Lindahl, E., Schulten, K., Perozo, E., Bezanilla, F. & Roux, B.An emerging consensus on voltage-dependent gating from computational modeling and molecular dynamics simulations. The Journal of General Physiology 140, 587-594 (2012).

25. Voltage Sensor Structure (NOT conduction channel) Emerging Consensus …. Vargas, E., Yarov-Yarovoy, V., Khalili-Araghi, F., Catterall, W. A., Klein, M. L., Tarek, M., Lindahl, E., Schulten, K., Perozo, E., Bezanilla, F. & Roux, B.An emerging consensus on voltage-dependent gating from computational modeling and molecular dynamics simulations. The Journal of General Physiology 140, 587-594 (2012).

27. Physiologists§ Mistakenly call a Saturating distribution ‘Boltzmann’ e.g., Bezanilla, Villalba-Galea J. Gen. Physiol (2013) 142: 575 Current to maintain test potential External Dissolved Ions Voltage Clamp =0 External Dissolved Ions Arginines Physicists: Saturation Fermi distribution Boltzmann* distribution does NOT saturate. Boltzmann is exponential, like. *Boltzmann (1904) Lectures on Gas Theory, Berkeley § p.503 of Hodgkin and Huxley. 1952. ‘Quantitative description ...’ J. Physiol. 117:500-544. Holding Potential Voltage Clamp = Test Potential Dissolved Ions Internal Dissolved Ions Fermi Distribution not Boltzmann Test Potentials Test Potentials Holding Potential Holding Potential Bezanilla. How membrane proteins sense voltage Nature Rev Mol Cell Biol (2008) 9, 323

28. Perhaps the firstConsistent Model of a Protein Machinemade by a conformation change Francisco Bezanilla Allen Tzyy-Leng Horng Chun Liu 柳 春 Bob Eisenberg 洪子倫

29. Voltage Sensor works by Charge Injection through a fluid dielectric of side chains, not yet fully known. More work needed! intracellular extracellular Figure 1. Geometric configuration of the reduced mechanical model. Voltage sensor works by charge injection through a fluid dielectric of side chains, attachments of arginines to the S4 segment.

31. Variational Formulation EnVarA because ‘Everything’ interacts with ‘Everything Else’through the electric field and often through steric interactions of Pauli exclusion principle 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.

32. Defining Laws Charge Creates Electric Field Transport of Mass + , Na, Cl, 1,2,3,4

33. 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:

35. Fitting Data Figure 9. (a) Time courses of subtracted gating current [A1]with voltage rising from -90mV to VmV at t=10, holds on till t=150, and drops back to -90mV, where V=-62, -50, … -8 mV. (b) τ2 versus V compared with experiment [7].

36. Fitting Data Figure 3. (a) QV curve and comparison with [7]. Steady-state distributions for Na, Cl and arginines at (b) V=-90mV, (c) V=-48mV, (d) V=-8mV.

37. Current is Conserved Conservation of Current is an Important Constraint. Rate Models of Chemical Kinetics;Molecular Dynamics do not conserve current A different talk INPUT Voltage Clamp Ions t Electric Field OUTPUTCurrent including

38. Nerve Signaling is a Hierarchy of Devices

39. Channels are Source of Signal

40. Classical cable theory of transmission lines, telegrapher’s equations, Kelvin, Hodgkin, Noble,including 3D-cable theory, ~10 papers, e.g.,Eisenberg and Johnson. 1970. Three dimensional electrical field problems in physiology. Prog. Biophys. Mol. Biol. 20:1-65 Barcilon, Cole, Eisenberg. 1971. Singular Perturbation … SIAM J. Appl. Math. 21:339-354. Another talk, another time! Channels + lipid capacitance Poisson Equation

41. How do ions move through channels? 75 papers since 1986

42. Working Hypothesis bio-speak: Crucial Biological Adaptation is Crowded Ions and Side Chains Biology occurs in concentrated >0.3 M mixtures of spherical charges NOT IDEAL AT ALL Poisson Boltzmann does NOT fit data!!Solutions are extraordinarily concentrated >10M where they are most important, near DNA, enzyme active sites, and channels and electrodes of batteries and electrochemical cells. Solid NaCl is 37M

43. Solutions are Extraordinarily Concentrated >10M Solid NaCl is 37Mwhere they are most important, DNA, enzyme active sites, channels and electrodes of batteries and electrochemical cells

44. 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

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

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

47. 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 Evidence RyR (start) Atomic Scale || Macro Scale

48. 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

49. 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 Evidence RyR (start) Atomic Scale || Macro Scale

50. Poisson Fermi Approach to Ion Channels . 劉晉良 Jinn-Liang Liu discovered role of SATURATIONBob Eisenberg helped with applications