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Continuum and Atomistic Modeling of Ion Transport Through Biological Channels

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## Continuum and Atomistic Modeling of Ion Transport Through Biological Channels

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**Continuum and Atomistic Modeling of Ion Transport Through**Biological Channels Xiaolin Cheng UT/ORNL Center for Molecular Biophysics September 16th, 2009 Beijing, China**Overview and Background**From Molecular Biology of the Cell. 4th ed. New York: Garland Publishing; 2002. Synaptic Transmission**Cryo-EM structure of nAChR from Torpedo marmorata, Unwin N**2005 ELIC (closed) Dutzler R 2008 GLIC(open) Dutzler R & Corringer J 2009**Ligand Gated Ion Channel**Channel Gating Ligand Binding Ion Permeation**Outstanding Ion Permeation Questions**What is the conduction mechanism at the atomic level? Where is the gate (ion binding site) located? What’s the nature of the gate? What’s the origin of the charge selectivity? Can we predict and provide microscopic explanations for macroscopic observations, such as channel conductance, current-voltage relationship, current-concentration relationship (saturation), conductance-charge/valence relationship…? multiple approaches at various levels of details**Multi-scale Modeling of Ion Permeation**Atomistic Modeling Molecular Dynamics timescale limitation, force filed issues Brownian Dynamics Continuum Modeling Poisson-Boltzmann Poisson-Nernst-Planck rigid channel structure, structureless dielectric solvent and mean-field ion-ion**MD Simulation of nAChR**120 Å 120 Å 5 subunits, 1835 residues ~290 POPC ~60600 TIP3P water molecules ~86 Na+, and 26 Cl- Ionic strength: 100 mM Total atoms ~260,000 NAMD2.6 CHARMM27 force field NPNST ensemble r-RESPA method (4 fs, 2 fs, 1 fs ) SPME electrostatics 20-100 ns production run 180 Å**Covariance Analysis**residues that form a physically connected network of van der Waals interactions within the protein core that may connect the binding site with the distant gating site**F135**L273 Single Channel Experiments Gint = (Gwm + Gmw) – Gmm = 1.06 kcal/mol**Water Dynamics inside the Channel**composition, size and membrane potential on-off transitions of single channel currents Eisenberg RE BJ 2008 fast (burst) phase on-off transition may be related to water dynamics**Barriers to Ion Translocation**Potential of Mean Force (PMF) the relative thermodynamic stability of states along channel axis z**A**FABF= - <F x> x x The PMF Calculation H = H0 + V(Q) Umbrella Sampling Adaptive Biasing Force**The PMF Calculation**A. Laio and M. Parrinello, PNAS, 2002 non-ergodic effect, not converge properly increase local roughness slow diffusion In complex systems: Metadynamics**Barriers to ion translocation**E20’ (-2 kcal/mol) Hydrophobic restriction 9 kcal/mol 5 kcal/mol E-1’ (-2 kcal/mol) D27’ (-2 kcal/mol) PMF for translocation of Na+ and Cl- within the nAChR pore**Snapshots from individual windows**D27’ E20’ V13’ L9’ Translocation of Na+ ion in the pore of nAChR. Snapshots from window 2, 4 and 6 of the ABF simulations.**Water around a sodium ion**partial desolvation within the narrowest (hydrophobic) region of the pore**Barriers to Ion Translocation**Hydrophobic restriction Electrostatic effect PMF for translocation of Na+ and Cl- within the GLIC channel with improved metadynamics in LAMMPS**Ion Translocation under Membrane Potentials**cation pausing periods in the extracellular domain - these charged rings along the ion translocation pathway concentrate ions, giving rise to charge selectivity. 1. co-crystallization of acetylcholine binding protein with sulfate ions; 2. Charge reversal mutation decreases conductance by up to 80%.**Multi-ion Channels**ion-ion interaction inside the channel the bacterial KcsA potassium channel Gramicidin A channel**PMFs for Ion Permeation**intracellular I I Harmonic Fourier beads method Khavrutskii IV JCP, 2006 The reactant state: E(C1); S0(W1); S1(C2); S2(W2); S3(C3); S4(W3) The product state: S1(C1); S2(W1); S3(C2); S4(W2); I(C3); I(W3) Reaction coordinate space includes all three cations, the oxygen atoms of the three water molecules in the single file and some protein degrees of freedom except the backbone of residues 67 to 74 and 80 to 82 during transition path optimization. E extracellular**Continuum Modeling of Ion Permeation**What is missing from the atomistic simulation? insufficient sampling – direct observation of ion conduction inadequacy in force fields - polarization Brownian Dynamics Poisson-Boltzmann long duration of time – kinetics, flux simulation scale can be much greater simple – gain fundamental insights Poisson-Nernst-Planck**Electrostatics Potentials across the Channels**Poisson-Boltzmann electrostatics for the TM domains of nAChR and GlyR. Electrostatic potentials along the z coordinate are shown below.**Protein Flexibility Affects Ion Conduction**Wang HL et al. PLoS Comput. Biol. 2007**Pore Size Fluctuations and Ion Conduction**Average pore sizes in different simulation windows (unpublished results)**Protein Flexibility Affects PB Calculations**Left: 10 representative snapshots taken from an unbiased simulation with only water in the channel; Right: 10 representative snapshots are taken from each umbrella window. (unpublished results) Note: GLIC channel is narrower than the nAChR channel.**BioMOCA Simulation**BioMOCA - A Transport Monte Carlo approach to Ion Channel Simulation that simulates ion transport in electrolytes by computing trajectories of ions moving in a continuum dielectric background that represents water. Brownian dynamics Ion-water interactions are accounted for by randomly interrupting the trajectories using a scattering rate. The local electric field is obtained by solving Poisson’s equation over the entire domain, which provides a simple way to include an applied bias and the effects of image charges induced at dielectric boundaries. The finite ion size is addressed here by including a pairwise Lennard-Jones potential.**BioMOCA Simulation**Time-averaged ion distributions in pre-TMD (left) and post-TMD (right) models Note: cation density increases in the narrow region of the channel. Wang et al. BJ 2008**BioMOCA Simulation**Current-voltage relationships. Wang et al. BJ 2008 Inward current rectification - the reduced conductance at positive potentials the conductance is 69 pS at negative potentials, while the conductance is 32 pS at positive potentials.**Poisson Nernst Planck Equation**Average ion fluxes in terms of density and potential gradients where, Electrostatic potential arises from the Poisson equation 3D PNP solver: Kurnikova MG, BJ 1999; Zhou Y et al. JPCB 2008 “Good agreement with experimental measurements is obtained (current-voltage characteristics)” in the study of ion transport through gramicidin A dimer. Kurnikova MG, BJ 1999 “In simple cylindrical channels, considerable differences are found between the two theories (PNP vs. BD) with regard to the concentration profiles in the channel and its conductance properties. These tests unequivocally demonstrate that the mean-field approximation in the Poisson-Nernst-Planck theory breaks down in narrow ion channels that have radii smaller than the Debye length.” Corry B BJ 2009**Continuum Modeling of Ion Channels**Continuum model: size - local heterogeneity PB: 1. effective dielectric constant inside the channel; 2. protein flexibility; 3. microscopic structure: solvation structure, van der Waals interactions, hydrogen bonding, … PNP: rigid channel structure, continuum electrostatics, and mean-field ion-ion interactions, diffusion coefficient inside the channel, … how to include these effects in the continuum models?**Continuum Modeling of Ion Channels**How is water dynamics related to channel gating? Water occupancy in the pore Nw vs time t. Dzubiella J and Hansen JP J. Chem. Phys. 2005 Probability Popen of a channel as a function of dcyl. Roth R. et al. BJ 2008**Acknowledgements**Prof. J. Andrew McCammon (UCSD) Dr. Benzhuo Lu Dr. Ivaylo Ivanov Dr. Ilja V. Khavrutskii Prof. Steven M Sine (Mayo Clinic) Dr. Hailong Wang (Mayo Clinic) Sebastian Fritsch (Heidelberg University/ORNL) Corinne Wacker (Heidelberg University/ORNL)