IonChannels-Ricam：离子通道的ricam.ppt

Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative Chemists View Ion Channels Proteins with a Hole All Atoms View Figure by Raimund Dutzler 30 1 Channels form a class of Biological Systems that can be analyzed with Physics as Usual Physics-Mathematics-Engineering are the proper language for Ion Channels in my opinion ION CHANNELS: Proteins with a Hole 2 Physics as Usual along with Biology as Usual Ion Channels can be analyzed with “Why think? . . . Exhaustively experiment. Then, think” Claude Bernard Appropriate when nothing was known of Inverse Problems! Cited in The Great Influenza, John M. Barry, Viking Penguin Group 2004 3 Channels control flow in and out of cells ION CHANNELS as Biological Objects 5 m 4 30 Ion Channels are the Main Molecular Controllers “Valves” of Biological Function Figure by Raimund Dutzler 5 Channels control flow of Charged Spheres Channels have Simple Invariant Structure on the biological time scale. Why cant we predict the movement of Charged Spheres through a Hole? ION CHANNELS as Physical Devices 6 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 I-V characteristics and selectivity (and gating?) Ion channels allow Mutations that modify conductance, selectivity, and function. Ion channels are Device Elements that self-assemble into perfectly reproducible arrays. Ion channels form Templates for design of bio-devices and biosensors. 30 Figure by Raimund Dutzler 7 Channels Control Macroscopic Flow with Atomic Resolution ION CHANNELS as Technological Objects 8 Ion Channels are Important Enough to be Worth the Effort 9 Goal: Predict Function From Structure given Fundamental Physical Laws 10 Current in One Channel Molecule is a Random Telegraph Signal 11 Voltage Step Applied Here (+ 80 mV; 1M KCl) Gating: Opening of Porin Trimer John Tang Rush Medical Center 12 Single Channel Currents have little variance John Tang Rush Medical Center 13 Lipid Bilayer Setup Recordings from a Single Molecule Conflict of Interest 14 Patch clamp and Bilayer apparatus clamp ion concentrations in the baths and the voltage across membranes. Patch Clamp Setup Recordings from One Molecule 15 Voltage in baths Concentration in baths Fixed Charge on channel protein Current depends on John Tang Rush Medical Center OmpF KCl 1M 1M| G119D KCl 1M 1M | ompF KCl 0.05 M 0.05M | G119D KCl 0.05 M 0.05M| Bilayer Setup 16 Current depends on type of ion Selectivity John Tang Rush Medical Center OmpF KCl 1M 1M| OmpF CaCl2 1M 1M| Bilayer Setup 17 Goal: Predict Function From Structure given Fundamental Physical Laws 18 Structures Location of charges are known with atomic precision (0.1 ) in favorable cases. 19 Charge Mutation in Porin Ompf Structure determined by x-ray crystallography in Tilman Schirmers lab Figure by Raimund Dutzler G119D 20 Goal: Predict Function From Structure given Fundamental Physical Laws 21 But What are the Fundamental Physical Laws? 22 Verbal Models Are Popular with Biologists but Inadequate 23 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 24 I fear Biologists indulge themselves with verbal models of molecules where Maxwell abstained 25 Verbal Models are Vague and Difficult to Test 26 Verbal Models lead to Interminable Argument and Interminable Investigation 27 thus, to Interminable Funding 28 and so Verbal Models Are Popular 29 Can Molecular Simulations serve as “Fundamental Physical Laws”? Only if they count correctly ! 30 It is very difficult for Molecular Dynamics to count well enough to reproduce Conservation Laws (e.g., of number, energy) Concentration (i.e., number density) or activity Energy of Electric Field Ohms law (in simple situations) Ficks law (in simple situations) Fluctuations in number density (e.g., entropy) 31 Can Molecular Simulations serve as “Fundamental Physical Laws”? Only if Calibrated! 32 Calibrated Molecular Dynamics may be possible n MD without Periodic Boundary Conditions HNC HyperNetted Chain Pair Correlation Function in Bulk Solution Saraniti Lab, IIT: Aboud, Marreiro, Saraniti dielectric constant = 2 mV at sec times; dielectric constant = 80 45 We start without quantum chemistry* (only at first) * i.e., delocalization of orbitals of outer electrons 46 Although we start with electrostatics We will soon add Physical Models of Chemical Effects 47 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 email for the papers 48 Very Different from Traditional Structural Biology which, more or less, ignores Electrostatics 49 Poisson-Nernst-Planck (PNP) Lowest resolution theory that includes Electrostatics and Flux is (probably) PNP, Gouy-Chapman, (nonlinear) Poisson-Boltzmann, Debye-Hckel, are fraternal twins or siblings with similar resolution 50 ION CHANNEL MODELS Poissons Equation Continuity Equation J.-P. Hansen; Mark Sansom; Sergei Sukarev) Chloride Channel Wolfgang Nonner Dirk Gillespie 124 Conclusion Each channel type is a variation on a theme of Crowded Charge and Electrostatics, Each channel types uses particular physics as a variation. Wolfgang Nonner Dirk Gillespie 125 Function can be predicted From Structure given Fundamental Physical Laws (sometimes, in some cases). 126 More? DFT 127 Density Functional and Poisson Nernst Planck model of Ion Selectivity in Biological Ion Channels Dirk Gillespie Wolfgang Nonner Department of Physiology and Biophysics University of Miami School of Medicine Bob Eisenberg Department of Molecular Biophysics and Physiology Rush Medical College, Chicago 128 We (following many others) have used Many Theories of Ionic Solutions as Highly Compressible Plasma of Ions with similar results MSA, SPM, MC and DFT MSA: Mean Spherical Approximation SPM: Solvent Primitive Model MC: Monte Carlo Simulation DFT: Density Functional Theory of Solutions Most Accurate Atomic Detail Inhomogeneous Systems 129 Density Functional Theory HS excess chemical potential is from free energy functional Energy density depends on “non-local densities” Nonner, Gillespie, Eisenberg130 HS excess chemical potential is Free energy functional is due to Yasha Rosenfeld and is considered more than adequate by most physical chemists. The double convolution is hard to compute efficiently. Nonner, Gillespie, Eisenberg We have extended the functional to Charged Inhomogeneous Systems with a bootstrap perturbation method that fits MC simulations nearly perfectly. 131 Example of an Inhomogeneous Liquid A two-component hard- sphere fluid near a wall in equilibrium (a small and a large species). Near the wall there are excluded-volume effects that cause the particles to pack in layers. These effects are very nonlinear and are amplified in channels because of the high densities. small species large species 132 The Problem We are interested in computing the flux of ions between two baths of fixed ionic concentrations. Across the system an electrostatic potential is applied. Separating the two baths is a lipid membrane containing an ion channel. ionic concentrations and electrostatic potential held constant far from channel membrane with ion channel ionic concentrations and electrostatic potential held constant far from channel 133 Modeling Ion Flux The flux of ion species i is given by the constitutive relationship The flux follows the gradient of the total chemical potential. where Di is the diffusion coefficient i is the number density i is the total chemical potential of species i 134 concentration-independent geometric restrictions solvation (Born) terms ideal term electrochemical potential of point particles in the electrostatic mean-field includes Poisson equation excess chemical potential the “rest”: the difference between the “real” solution and the ideal solution The chemical potential has three components 135 When ions are charged, hard spheres the excess chemical potential is split into two parts Electrostatic Component describes the electrostatic effects of charging up the ions Hard-Sphere Component describes the effects of excluded volume the centers of two hard spheres of radius R cannot come closer than 2R 136 Density Functional Theory HS excess chemical potential is derived from free energy functional Energy density depends on “non-local densities” Nonner, Gillespie, Eisenberg137 HS excess chemical potential is Free energy functional is due to Yasha Rosenfeld and is considered more than adequate by most physical chemists. The double convolution is hard to compute efficiently. Nonner, Gillespie, Eisenberg We have extended the functional to Charged Inhomogeneous Systems with a bootstrap perturbation method that fits MC simulations nearly perfectly. 138 Density Functional Theory Energy density depends on “non-local densities”: Nonner, Gillespie, Eisenberg139 Nonner, Gillespie, Eisenberg The non-local densities ( = 0, 1, 2, 3, V1, V2) are averages of the local densities: where is the Dirac delta function, is the Heaviside step function, and Ri is the radius of species i. 140 We use Rosenfelds perturbation approach to compute the electrostatic component. Specifically, we assume that the local density i(x) is a perturbation of a reference density iref(x): The ES Excess Chemical Potential Density Functional Theory 141 The Reference Fluid In previous implementations, the reference fluid was chosen to be a bulk fluid. This was both appropriate for the problem being solved and made computing its ES excess chemical potential straight-forward. However, for channels a bulk reference fluid is not sufficient. The channel interior can be highly-charged and so 20+ molar ion concentrations can result. That is, the ion concentrations inside the channel can be several orders of magnitude larger than the bath concentrations. For this reason we developed a formulation of the ES functional that could account for such large concentration differences. 142 Test of ES Functional To test our ES functional, we considered an equilibrium problem designed to mimic a calcium channel. two compartments were equilibrated edge effects fully computed 24 M O-1/2 CaCl2 NaCl or KCl 0.1 M The dielectric constant was 78.4 throughout the system. 143 144 145 New Mathematics is Needed: Analysis of Simulations 146 Can Simulations serve as “Fundamental Physical Laws”? Direct Simulations are Problematic Even today 147 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 148 Simulations so far often do not reproduce Concentration (i.e., number density) (or activity coefficient) Energ