【正文】 f Charge (several partial charges in nm3) Selectivity Filter contains hydrophobic groups ? these are modeled to (slightly) repel water ? this results in largeion selectivity Conducts only anions at low concentrations ? Conducts both anions and cations at high concentration Current depends on anion type and concentration Wolfgang Nonner Dirk Gillespie Doug Henderson Dezso Boda 122 Biological Case Chloride Channel Selectivity depends Qualitatively on concentration Wolfgang Nonner Dirk Gillespie 123 The Dilute Channel: Anion Selective Channel protein creates a Pressure difference between bath and channel Large ions like Cl– are Pushed into the channel more than smaller ions like F– Wolfgang Nonner Dirk Gillespie 124 Key: Hydrophobic Residues Repel Water giving ? Largeion selectivity (in both anion and cation channels). ? Peculiar nonmonotonic conductance properties and IV curves observed in experiments Hydrophobic repulsion can give gating. ?Vacuum lock? model of gating (M. Green, D. Henderson。 12%) Activity* of ionic solutions from Infinite dilution, to Saturated solutions, even in Ionic melts. *Free Energy per Mole Learned from Doug Henderson, . Hansen, among others…Thanks! 74 1 ( ) ( ) ( )i i i ikT D ??? ? ?J x x x} Concentrationindependent ? geometric restrictions ? solvation (Born) terms Ideal term ? electrochemical potential of point particles in the electrostatic meanfield ? includes Poisson equation Excess chemical potential ?Finite size effects ?Spatial correlations Chemical potential has three ponents 0 i d ex( ) ( ) ( )? ? ???i i ix x x75 Simplest Physical Theory MSA ? ?122 2 2 200Ele c tro c he m ic a l P o te nti a l o f spe c ie s ln 24 1 1 3iH S ESi i i iHS i i i iiiiiiz F RTe z z?? ? ? ? ??? ??? ????? ? ?? ? ? ? ??? ????? ? ? ? ??? ??? ? ? ????? Ideal Ex ces sElectrostatic Spheres Hard Spheres Ionic radii ?I are known values in bulk Learned from Lesser Blum amp。? ? ?JxElectrochemical Potential ? ? ? ? ? ? ? ?ex*ln ii i iz e k T ?? ? ????? ? ?????xx x xS p e c i a l C h e m i s t r yincludes Fixed Charge on Protein includes only Mobile Charge 52 One Dimensional PNP Poisson?s Equation DriftDiffusion amp。ckel, are fraternal twins or siblings with similar resolution 51 ION CHANNEL MODELS Poisson?s Equation Continuity Equation amp。 1 charge gives ???1V at psec times。 Ravaioli 0 . 00 . 51 . 0g++(r)0 . 00 . 51 . 0g(r)E M CB i o M O C A 024g+(r)0 . 0 5 . 0 1 5 . 0 2 0 . 0r ( ? )1 0 . 035 Calibrated MD may be possible, even in a Gramicidin channel Molecular Dynamics without Periodic Boundary Conditions BioMOCA van der Straaten, Kathawala, Trellakis, Eisenberg amp。 Figure by Raimund Dutzler 8 Channels Control Macroscopic Flow with Atomic Resolution ION CHANNELS as Technological Objects 9 Ion Channels are Important Enough to be Worth the Effort 10 Goal: Predict Function From Structure given Fundamental Physical Laws 11 Current in One Channel Molecule is a Random Telegraph Signal Voltage Step Applied Here (+ 80 mV。1 Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative Chemist?s View Ion Channels Proteins with a Hole All Atoms View Figure by Raimund Dutzler ~30 197。 Ion Channels are the Main Molecular Controllers “Valves” of Biological Function Figure by Raimund Dutzler 6 Channels control flow of Charged Spheres Channels have Simple Invariant Structure on the biological time scale. Why can?t we predict the movement of Charged Spheres through a Hole? ION CHANNELS as Physical Devices 7 Physical Characteristics of Ion Channels Natural Nanodevices Ion channels have Selectivity. K channel selects K+ over Na+ by ~104. Ion channels Gate/Switch in response to pH, voltage, chemical species and mechanical force from conducting to nonconducting state. Ion channels have VERY Large Charge Densities critical to IV characteristics and selectivity (and gating?) Ion channels allow Mutations that modify conductance, selectivity, and function. Ion channels are Device Elements that selfassemble into perfectly reproducible arrays. Ion channels form Templates for design of biodevices and biosensors. ~30197。 Eisenberg 34 Calibrated Molecular Dynamics may be possible ? MD without Periodic Boundary Conditions BioMOCA ─ Equilibrium Monte Carlo (ala physical chemistry) Pair Correlation Function in Bulk Solution van der Straaten, Kathawala, Trellakis, Eisenberg amp。volt has significant effect on IV curve in a Sphere of diameter 14 197。 dielectric constant = 80 46 We start without quantum chemistry* (only at first) * ., delocalization of orbitals of outer electrons 47 Although we start with electrostatics We will soon add Physical Models of Chemical Effects 48 It is appropriate to be skeptical of analysis in which the only chemistry is physical But give me a chance, ask I will be in Linz for a week! (thanks to Heinz!) Or for the papers 49 Very Different from Traditional Structural Biology which, more or less, ignores Electrostatics 50 PoissonNernstPlanck (PNP) Lowest resolution theory that includes Electrostatics and Flux is (probably) PNP, GouyChapman, (nonlinear) PoissonBoltzmann, DebyeH252。i i i iD kT??? ? ?J x x x x? ? 0。 Rush Medical Center Dielectric Boundary Force DBF ? ? ? ? ? ?004qq??