Detecting small charge movements in biological

membrane systems

Benoit RouxUniversity 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):897-903, 2005.

?

Voltage Gating 101…

OC

side II

side I

Vmp

++

+ ---

side II

side I

Vmp

++

+

---

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

Open Closed

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

• “Qd” 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):2189-98, 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):2189-98, 2010.

Na+/K+-pump overview

K+

K+

Na+

Na+

ADP + Pi

ATP

Extracellularmatrix

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

ForwardPump cycle

E1

E2

Na+/K+-pump overview

Extracellularmatrix

Cytoplasm

• “Alternating-access” pump cycle

Post, R. L. et al, J. Gen. Physiol. (1969) 54:306Gadsby, D. C. et al, Nat. Commun. (2012) 3:669

ForwardPump cycle

Na+/K+-pump overview• Crystal structures available

PDBID: 2ZXE2.4 Å

PDBID: 3WGV2.8 Å

Shinoda, T. et al, Nature (2009) 459:446Kanai, 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: 3WGVNa3

.E1.(ADP.Pi)

PDBID: 2ZXEE2(K2)

• Crystal structures available

ForwardPump cycle

??

Extracellular ion binding• Limited structural information on the P-E2 state

(Ca2) E1~P:ADP

Ca2 E2P:ATP

Ca2 E1:ATP

E2P

Hn E2P:ATP

(Hn) E2 ~P:ATP

Hn E2:ATP

• Modeling the P-E2 state based on Ca2+ SERCA pump

PDBID1VFP

PDBID1WPG

PDBID3B9B

Ca2+ SERCAPump cycle

Extracellular ion binding

Ca2 E1:ATP

E2P

(Hn) E2 ~P:ATP

• Modeling the P-E2 state based on Ca2+ SERCA pump

PDBID1VFP

PDBID1WPG

PDBID3B9B

Ca2+ SERCAPump cycle

Extracellular ion binding

• Models for outward facing, ion loaded Na+/K+ pump

P-E2.Na3 P-E2.K2

Extracellularmatrix

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 (ΔQD) from MD trajectories

A 82 Å

B 107 Å

C 155 Å

nAtom ~150K

nPOPC 213

nWater 32K

System information

Gating charge upon ion binding

Triple occupancy Double occupancy Single occupancy Empty sites

• MD systems involved in Na+ release

1/3

1/3

1/3

1/3

1/3

1/3

1 1

Gating charge upon ion binding

Empty sites Single occupancy Double occupancy

• MD systems involved in K+ binding

1/2

1/2

11

Na+ release from P-E2.Na3 K+ binding in P-E2.K2

Calc. 0.56 ± 0.10 0.39 ± 0.07 0.01 ± 0.1 0.49 ± 0.12 0.37 ± 0.20

Exp. 0.61-0.71* ~0.3* 0.46** 0.27**

• Models for outward facing, ion loaded Na+/K+ pumpModelP-E2.Na3

ModelP-E2.K2

Table. Gating charge of ion binding/release from P-E2.

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

αM4αM5

αM8αM6

αM9

αM4αM5

αM8αM6

αM9

IIIIII

III

PDBID: 3WGVNa3

.E1.(ADP.Pi)

PDBID: 2ZXEE2(K2)

RMSDsiteHA = 3.0 Å

Ion binding site protonation state

€

exp −ΔGab kT[ ] = dX exp[−Ub /kT]∫dX exp[−Ua /kT]∫

= dX exp[− Ub −Ua( ) /kT] exp[−Ua /kT]∫

dX exp[−Ua /kT]∫

= exp[− Ub −Ua( ) /kT](a)

Gb - Ga = − kT ln exp[− Ub −Ua( ) /kT](a)

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Free Energy Perturbation

Difference in Hydration Free Energy

€

GNa −GK = - kT ln exp[−UNa −UK( ) / kT ](K)

⎛ ⎝ ⎜

⎞ ⎠ ⎟

-17.2 kcal/mol

K+ Na+

FEP/MD simulations

Selectivity of the Na+/K+ Pump in state E2P

System Setup Site I Site 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.

Selectivity of the Na+/K+ Pump in the state E2P

System Setup Site I Site 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 environmentof the binding sites to shift the pKa values of the residuesso that it can achieve K+ selectivity at the E2P state.