1 Physical Models of Permeability And Selectivity We are working on gating

2 Poisson-Nernst-Planck (PNP) Lowest resolution theory that includes Electrostatics and Flux is Poisson-Drift-Diffusion, Gouy-Chapman, (nonlinear) Poisson-Boltzmann, Debye-Hückel, are fraternal twins or siblings with similar resolution

3 IV of porin 2 M KCl OmpF G119D Fit of 1D PNP Current-Voltage 2M KCl Duan Chen John Tang Rush Medical Center

4 Selectivity in Channels Wolfgang Nonner, Dirk Gillespie University of Miami and Rush Medical Center

5 Physical properties of the Highly Compressible Plasma of Ions determine the Key Chemical Properties of Ion Solutions NOT details of Hydration and Orbital delocalization Central Result of Physical Chemistry Learned from Doug Henderson, J.-P. Hansen, among others…Thanks!

6 Properties of Highly Compressible Plasma of Ions Similar Results are computed by many Different theories and Simulations MSA is only simplest. We (and others) have used MSA, SPM, MC, and DFT MSA : M ean S pherical A pproximation SPM: S olvent P rimitive M odel MC: M ont e C arlo Simulation DFT: D ensity F unctiona l T heory of Solutions Most Accurate Atomic Detail Inhomogeneous Systems

7 Best Result to Date with Atomic Detail Monte Carlo, including Dielectric Boundary Force Dezso Boda, Dirk Gillespie, Doug Henderson, Wolfgang Nonner Na + Ca ++

8 Test of DFT (Atomic resolution Mean Field) Gillespie, Nonner Eisenberg

9 Ionic Selectivity in Protein Channels Crowded Charge Mechanism Simplest Version: MSA How does Crowded Charge give Selectivity?

10 Selectivity Arises in a Crowded Space Biological case: 0.1 M NaCl and 1  M CaCl 2 in the baths As the volume is decreased, water is excluded from the filter by crowded charge effects Ca 2+ enters the filter and displaces Na + Biological Case Wolfgang Nonner Dirk Gillespie

11 Ionic Selectivity in Protein Channels Crowded Charge Mechanism 4 Negative Charges of glutamates of protein DEMAND 4 Positive Charges nearby either 4 Na + or 2 Ca ++

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13 Ionic Selectivity in Protein Channels Crowded Charge Mechanism Simplest Version: MSA 2 Ca ++ are LESS CROWDED than 4 Na +, Ca ++ SHIELDS BETTER than Na +, so Protein Prefers Calcium

14 What does the protein do? Selectivity arises from Electrostatics and Crowding of Charge Precise Arrangement of Atoms is not involved in the model, to first order. but Certain MEASURES of structure are Powerful DETERMINANTS of Function e.g., Volume, Dielectric Coefficient, etc.

15 Protein provides Mechanical Strength Volume of Pore Dielectric Coefficient/Boundary Permanent Charge Precise Arrangement of Atoms is not involved in the model, to first order. but Particular properties (‘measures’) of the protein are crucial! What does the protein do?

16 Selectivity apparently does not involve subtle physics e.g., orbital delocalization or chemical binding Learned from Doug Henderson, J.-P. Hansen, among others…Thanks!

17 Cl − Selective Channel Selective for Larger Anions The Dilute Channel Wolfgang Nonner Dirk Gillespie

18 Model gives small-ion selectivity. Result also applies to the calcium channel. Na + Channel Biological Region Wolfgang Nonner Dirk Gillespie