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Detecting small charge movements in biological membrane systems Benoit Roux University of Chicago March 2015
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Sliding helix Paddle Transporter-like Large movement Small movement Long, Campbell & Mackinnon. Crystal structure of a mammalian voltage-dependent Shaker family K+ channel. Science. 309(5736):897- 903, 2005. ?
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Voltage Gating 101… OC side II side I V mp + + + - - - side II side I V mp + + + - - -
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t t+ t t+2 t t+3 t ……. Molecular Dynamics Simulations “The molecular dynamics or MD approach consists in, having represented the microscopic forces between the atoms with some potential function, generating a step-by-step trajectory of the atoms by numerically integrating the classical equation of motion of Newton, F=MA.” From position and velocity at some time, we calculate the position and velocity at a short time step later In fact, the widely used Verlet algorithm is slightly more complicated than this…
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F. Khalili, V. Jogini, V. Yarov, E. Tajkhorshid, B. Roux, K. Schulten MD of Full-length Kv1.2 in bilayer in open and closed state OpenClosed
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V=0 V +
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Define the excess free energy (or PMF) for the system at X arising from the applied membrane voltage V and averaged over all solvent degrees of freedom Y
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The constant field in PBC Displacement charge There are 3 routes that can be exploited: “ W” PMF with & without voltage “Q d ” Average displacement charge (with or without voltage) “G” Free energy of charging with & without voltage
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Application of the Q-route to the VSD of Kv1.2 Correlation time is about 10 ns RMS fluctuations are related to capacitance
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Application of the Q-route to the VSD of Kv1.2 F. Khalili, V. Jogini, E. Tajkhorshid, K. Schulten, B. Roux VSD
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Application of the Q-route to the Kv1.2 channel Khalili-Araghi et al. Calculation of the gating charge for the Kv1.2 voltage-activated potassium channel. Biophys J. 98(10):2189-98, 2010.
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Application of the G-route to the Kv1.2 channel Khalili-Araghi et al. Calculation of the gating charge for the Kv1.2 voltage-activated potassium channel. Biophys J. 98(10):2189-98, 2010.
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Na + /K + -pump overview K+K+ K+K+ Na + ADP + Pi ATP Extracellular matrix Cytoplasm Membrane transporter P-type ATPase Actively export 3Na + and import 2K + per pump cycle. Maintain healthy ion concentration gradients across cell membrane. Indispensible for excitable cells such as neurons. Skou, J. C., Biochim. Biophys. Acta. (1957) 23:394
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Forward Pump cycle E1 E2 Na + /K + -pump overview Extracellular matrix Cytoplasm “Alternating-access” pump cycle Post, R. L. et al, J. Gen. Physiol. (1969) 54:306 Gadsby, D. C. et al, Nat. Commun. (2012) 3:669
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Forward Pump cycle Na + /K + -pump overview Crystal structures available PDBID: 2ZXE 2.4 Å PDBID: 3WGV 2.8 Å Shinoda, T. et al, Nature (2009) 459:446 Kanai, R. et al, Nature (2013) 502:201
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Na + /K + -pump overview Extracellular matrix Cytoplasm β α β α A P N A P N PDBID: 3WGV Na 3. E 1. (ADP. Pi) PDBID: 2ZXE E 2 (K 2 ) Crystal structures available
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Forward Pump cycle ?? Extracellular ion binding Limited structural information on the P-E 2 state
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(Ca 2 ) E 1 ~P:ADP Ca 2 E 2 P:ATP Ca 2 E 1 :ATP E2PE2P H n E 2 P:ATP (H n ) E 2 ~P:ATP H n E 2 :ATP Modeling the P-E 2 state based on Ca 2+ SERCA pump PDBID 1VFP PDBID 1WPG PDBID 3B9B Ca 2+ SERCA Pump cycle Extracellular ion binding
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Ca 2 E 1 :ATP E2PE2P (H n ) E 2 ~P:ATP Modeling the P-E 2 state based on Ca 2+ SERCA pump PDBID 1VFP PDBID 1WPG PDBID 3B9B Ca 2+ SERCA Pump cycle Extracellular ion binding
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Models for outward facing, ion loaded Na + /K + pump P-E 2.Na 3 P-E 2.K 2 Extracellular matrix Cytoplasm Extracellular ion binding Water filled pathway leading to the binding site
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Simultaneous rebinding of ions from the extracellular side Extracellular ion binding Na + rebinding happens at 30- ns time mark in a 120-ns MD simulation.
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Gating charge upon ion binding Instantaneous displacement charge: Average displacement charge of a trajectory: Gating charge: Estimating gating charge (ΔQ D ) from MD trajectories A82 Å B107 Å C155 Å n Atom ~150K n POPC 213 n Water 32K System information
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Gating charge upon ion binding Triple occupancyDouble occupancySingle occupancyEmpty sites MD systems involved in Na + release 1/3 1 1
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Gating charge upon ion binding Empty sitesSingle occupancyDouble occupancy MD systems involved in K + binding 1/2 1 1
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Na + release from P-E 2.Na 3 K + binding in P-E 2.K 2 Calc.0.56 ± 0.100.39 ± 0.070.01 ± 0.10.49 ± 0.120.37 ± 0.20 Exp.0.61-0.71 * ~0.3 * 0.46 ** 0.27 ** Models for outward facing, ion loaded Na + /K + pump Model P-E 2.Na 3 Model P-E 2.K 2 Table. Gating charge of ion binding/release from P-E 2. Gating charge upon ion binding * Holmgren, M. et al, Nature (2000) 403:898 **Castillo, J. P. et al, Nat. Commun. (under review)
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Titratable residues at crystal structure ion binding sites αM4 αM5 αM8 αM6 αM9 αM4 αM5 αM8 αM6 αM9 I II III I II PDBID: 3WGV Na 3. E 1. (ADP. Pi) PDBID: 2ZXE E 2 (K 2 ) RMSD siteHA = 3.0 Å Ion binding site protonation state
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Free Energy Perturbation
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Difference in Hydration Free Energy -17.2 kcal/mol K+K+ Na + FEP/MD simulations
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Selectivity of the Na + /K + Pump in state E2P System SetupSite ISite II 2ZXE: 334,786,811,815 -2.5-2.7 3B8E: 327,779,804,808 -1.7-4.5 The sites are selective for Na + over K + ?????!!!!!!! Yu H, Ratheal IM, Artigas P, Roux B. Protonation of key acidic residues is critical for the K⁺-selectivity of the Na/K pump. Nat Struct Mol Biol. 18(10):1159-63, 2011.
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Selectivity of the Na + /K + Pump in the state E2P System SetupSite ISite II 2ZXE: 334+,786+,811,815+ +4.0+4.6 3B8E: 327+,779+,804,808+ +3.0+1.7 2ZXE: 334+,786+,811,815 -0.4+3.5 2ZXE: 334,786+,811,815+ -0.8-7.7 2ZXE: 334,786,811,815 -2.5-2.7 3B8E: 327,779,804,808 -1.7-4.5 Na + /K + pump can modulate the local electrostatic environment of the binding sites to shift the pKa values of the residues so that it can achieve K + selectivity at the E2P state.
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