Detecting small charge movements in biological membrane systems Benoit Roux University of Chicago March 2015

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): , ?

Voltage Gating 101… OC side II side I V mp side II side I V mp

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…

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

V=0 V +

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

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

Application of the Q-route to the VSD of Kv1.2 Correlation time is about 10 ns RMS fluctuations are related to capacitance

Application of the Q-route to the VSD of Kv1.2 F. Khalili, V. Jogini, E. Tajkhorshid, K. Schulten, B. Roux VSD

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): , 2010.

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): , 2010.

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

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

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

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

Forward Pump cycle ?? Extracellular ion binding Limited structural information on the P-E 2 state

(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

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

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

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.

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

Gating charge upon ion binding Triple occupancyDouble occupancySingle occupancyEmpty sites MD systems involved in Na + release 1/3 1 1

Gating charge upon ion binding Empty sitesSingle occupancyDouble occupancy MD systems involved in K + binding 1/2 1 1

Na + release from P-E 2.Na 3 K + binding in P-E 2.K 2 Calc.0.56 ± ± ± ± ± 0.20 Exp * ~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)

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

Free Energy Perturbation

Difference in Hydration Free Energy kcal/mol K+K+ Na + FEP/MD simulations

Selectivity of the Na + /K + Pump in state E2P System SetupSite ISite II 2ZXE: 334,786,811, B8E: 327,779,804, 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): , 2011.

Selectivity of the Na + /K + Pump in the state E2P System SetupSite ISite II 2ZXE: 334+,786+,811, B8E: 327+,779+,804, ZXE: 334+,786+,811, ZXE: 334,786+,811, ZXE: 334,786,811, B8E: 327,779,804, 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.