Ion Channels: Proteins with a Hole

1. Chemist’s View Ion ChannelsProteins with a Hole All Atoms View Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative ~30 Å Figure by Raimund Dutzler

2. ION CHANNELS: Proteins with a Hole Channels form a class of Biological Systemsthat can be analyzed with Physics as Usual Physics-Mathematics-Engineering are the proper language for Ion Channels in my opinion

3. Ion Channels can be analyzed with Physics as Usual along with Biology as Usual

4. Biology is first of all a Descriptive Science Biology Involves Many Objects. The Devices and Machines of Biology must be Named and Described Then they can be understood by Physics as Usual

5. Physics as Usual along with Biology as Usual “Why think? . . . Exhaustively experiment. Then, think” Claude Bernard Cited inThe Great Influenza, John M. Barry, Viking Penguin Group 2004

6. “Why think? . . . Exhaustively experiment. Then, think” Claude Bernard Trial and Error is inefficient and often does not work at all

7. Channels control flow in and out of cells ION CHANNELS as Biological Objects ~5 µm

8. Goal: Predict Function From Structure given Fundamental Physical Laws

9. But … What are the Fundamental Physical ‘Laws’?

10. Verbal Models Are Popular with Biologists but Inadequate

11. James Clerk Maxwell “I carefully abstain from asking molecules where they start… I only count them…., avoiding all personal enquiries which would only get me into trouble.” Royal Society of London, 1879, Archives no. 188 In Maxwell on Heat and Statistical Mechanics, Garber, Brush and Everitt, 1995

12. I fear Biologists use Verbal Models where Maxwell abstained

13. Verbal Models areVagueandDifficult to Test

14. Verbal Modelslead to Interminable Argument and Interminable Investigation

15. thus,to Interminable Funding

16. and so Verbal Models Are Popular

17. Can Molecular Simulationsserve as “Fundamental Physical Laws”? Only if they count correctly !

18. It is very difficult for Molecular Dynamics to count well enough to reproduce ConservationLaws(e.g., of energy) Concentration (i.e., number density) or activity Energy of Electric Field Ohm’s ‘law’(in simple situations) Fick’s ‘law’(in simple situations) Fluctuationsin number density (e.g., entropy)

19. Can simulations serve as fundamental physical laws? Direct Simulations are Problematic Even today Simulations so far cannot reproduce macroscopic variables and phenomena known to dominate biology

20. Simulations as fundamental physical laws (?) First Principle of Numerical Integration The larger the calculation, the more work done, the greater the error First Principle of Experimentation The more work done, the less the error

21. Simulations so faroften do not reproduce Concentration (i.e., number density)(or activity coefficient) Energy of Electric Field Ohm’s ‘law’(in simple situations) Fick’s ‘law’(in simple situations) ConservationLaws(e.g., of energy) Fluctuationsin number density

22. Simulations so faroften do not reproduce Concentration (i.e., number density)(or activity coefficient) Most enzymes and many proteins are controlled by special molecules present in tiny (micromolar to nanomolar) concentrations. Small changes in concentration of a control molecule has a large effect on function. (‘allosteric effectors’, cofactors, agonists, antagonists, coenzymes, vitamins, are different names for these control molecules)

23. water molecules. atoms Simulations so faroften do not reproduce Concentration (i.e., number density)(or activity coefficient) Simulation of 1 µM calcium (for example) requires (say) 500 calcium ions for reasonable statistical error. 500 calciums are dissolved in water in Simulation must include Not Feasible!!

24. Simulations so faroften do not reproduce Energy of Electric Field Method must include charges on boundaries including induced charges at dielectric boundaries in irregular domains. Many methods tried. Calibration: is Gauss’ law satisfied? In my opinion, only the P3M method of computational electronics and plasma physics is calibrated properly

25. Simulations so faroften do not reproduce Ohm’s ‘law’(in simple situations) Fick’s ‘law’(in simple situations) Calibrated non-equlibrium simulations including spatially nonuniform boundary conditions are not available. period.

26. Simulations so faroften do not reproduce ConservationLaws(e.g., of energy) are surprisingly difficult to verify in long time scale simulations. Even conservation of number of particles is difficult in a simulation of msec with time step of femtoseconds.

27. Simulations so faroften do not reproduce Fluctuationsin number density, electric potential, and energy are not reproduced correctly even in computational electronics. Systems are strongly nonlinear so failure in reproducing fluctations can QUALITATIVELY change MACROSCOPIC AVERAGED behavior. Phenomena like stochastic resonance cannot be simulated on an atomic scale (yet).

28. How do we include Macroscopic Variables in Atomic Detail Calculations? Another viable approachisHierarchy of Symplectic Simulations

29. Symplectic integrators are precise in ‘one’ variable at a time! It is not clear (at least to me) that symplectic integrators can be precise in all relevant variables at one time

30. Analysis of Simulations e.g., How do we include Macroscopic Variables Conservation lawsin Atomic Detail Calculations? Because mathematical answer is unknown, I use an Engineering Approach Hierarchy of Low Resolution Models

31. Why not simulate? Simulations produce too many numbers 106 trajectories each 10-6 sec long, with 109 samples in each trajectory, in background of 1022 atoms

32. Simulations need a theory that Estimates Parameters (e.g., averages) or IgnoresVariables Theories and Models are Unavoidable!(in my opinion)

33. Physics as Usual Calibrated combination of theory, simulations and experiments

34. Engineering as Usual Respect for Structure Goal is Device Equation

35. Can Molecular Simulations Serve as “Fundamental Physical Laws”? Simulations are Reliable Science when they are Calibrated Simulations are not Mathematics! (e.g., results depend on numerical procedures and round-off error)

36. Can Molecular Simulations serve as “Fundamental Physical Laws”? Only if Calibrated!

37. Can Molecular Simulations serve as “Fundamental Physical Laws”? What should be calibrated? I believe Thermodynamics of ions must be calibrated, i.e., activity = free energy per mole, which means the Pair Correlation Function according to classical Stat Mech

38. Calibrated Molecular Dynamics may be possible Pair Correlation Function in Bulk Solution • MD without Periodic Boundary Conditions─ HNC HyperNetted Chain Saraniti Lab, IIT: Aboud, Marreiro, Saraniti & Eisenberg

39. Calibrated Molecular Dynamics may be possible Pair Correlation Function in Bulk Solution • MD without Periodic Boundary Conditions BioMOCA─ Equilibrium Monte Carlo (ala physical chemistry) van der Straaten, Kathawala, Trellakis, Eisenberg & Ravaioli

40. Calibrated MD may be possible,even in aGramicidin channel 16 Na+ single channel currents Molecular Dynamics without Periodic Boundary Conditions BioMOCA Simulations 235ns to 300ns, totaling 4.3 μs.Mean I = 3.85 pA, 24 Na+ crossings per 1 μs van der Straaten, Kathawala, Trellakis, Eisenberg & Ravaioli

41. Until Mathematics of Simulations is availablewe take anEngineering Approach Essence of Engineering is knowing What Variables to Ignore! WC Randels quoted in Warner IEEE Trans CT 48:2457 (2001)

42. What variables should we ignore when we make low resolution models? How can we tell when a model is helpful? Use the scientific method Guess and Check! Intelligent Guesses are MUCH more efficient Sequence of unintelligent guesses may not converge! (e.g., Rate/State theory of channels/proteins)

43. Use the scientific method Guess and Check! When theory works, need few checks Computations (almost) equal experiments Structural Engineering Circuit Design Airplane Design Computer Design Can be done (almost) by theory,

44. Use Theory of Inverse Problems (Reverse Engineering) optimizes “Guess and Check” 1) Measure only what can be measured (e.g.,not two resistors in parallel). 2) Measure what determines important parameters 3) Use efficient estimators. 4) Use estimators with known bias 5) no matter what the theory, Guess Cleverly!

45. Channels are only Holes Why can’t we have a fully successful theory? Must know physical basis to make a good theory Physical Basis of Gating is not known Is the physical basis of permeation known?

46. Proteins Bristle with Charge Cohn (1920’s) & Edsall (1940’s) Ion Channels are no exception We start with Electrostaticsbecause of biology

47. Many atoms in a protein have Permanent Charge ~1e Permanent charge is the (partial) charge on the atom when the local electric field is zero. Active Sites in Proteins haveMany Charges in a Small Place

48. Atom Charge in Arginine Atom Charge (units /e) N −0.40 H 0.25 C_a 0.10 C_b 0.00 C_g 0.00 C_d 0.10 N_e −0.40 H_e 0.30 C_z 0.50 NH_1 −0.45 HH_11 0.35 HH_12 0.35 NH_2 −0.45 HH_21 0.35 HH_22 0.35 C 0.60 O −0.55 according toCHARMM Average Magnitude 0.32

49. Active Sites of Proteins are VeryCharged e.g. 7 charges ~ 20 M net charge = 1.2×1022 cm-3 1 nM Selectivity Filters and Gates of Ion Channels are Active Sites

50. Start with electrostatics because Small Charge in Small Places Large Potentials* Vat psec times;dielectric constant = 2 mVat µsec times; dielectric constant =80 1 charge gives in a Sphere of diameter 14 Å *Current varies 2.7× for 25 mV because thermal energy = 25 meV