Simulating Membrane Channels, E. Tajkhorshid, Part 2

A Recipe for Membrane Protein Simulations
•  Continue to constrain the protein (heavy atoms), but release
everything else; minimize/simulate using a short “constant-
pressure” MD (NPT) to “pack” lipids and water against the protein
and fill the gaps introduced after removal of protein-overlapping
lipids.
•  Watch water molecules; They normally stay out of the hydrophobic
cleft. If necessary apply constraints to prevent them from
penetrating into the open cleft between the lipids and the protein.
•  Monitor the volume of your simulation box until the steep phase of
the volume change is complete (.xst and .xsc files). Do not run the
system for too long during this phase (over-shrinking; sometimes
difficult to judge).
•  Now release the protein, minimize the whole system, and start
another short NPT simulation of the whole system.
•  Switch to an NPnAT or an NVT simulation, when the system
reaches a stable volume. Using the new CHARMM force field, you
can stay with NPT.

Lipid-Protein Packing During the
Initial NpT Simulation

Adjustment of Membrane Thickness to
the Protein Hydrophobic Surface

Description of full conduction pathway

Complete description of the conduction pathway
Constriction region

Selectivity
filter

Channel Hydrogen Bonding Sites

…
{set frame 0}{frame < 100}{incr frame}{
animate goto $frame
set donor [atomselect top
“name O N and within 2 of
(resname GCL and name HO)”]
lappend [$donor get index] list1
set acceptor [atomselect top
“resname GCL and name O and
within 2 of (protein and name HN HO)”]
lappend [$acceptor get index] list2
}
…

Channel Hydrogen Bonding Sites
GLN 41 OE1 NE2 LEU 197 O
TRP 48 O NE1 THR 198 O
GLY 64 O GLY 199 O
ALA 65 O PHE 200 O
HIS 66 O ND1 ALA 201 O
LEU 67 O ASN 203 ND2
ASN 68 ND2
ASP 130 OD1 LYS 33 HZ1 HZ3
GLY 133 O GLN 41 HE21
SER 136 O TRP 48 HE1
TYR 138 O HIS 66 HD1
PRO 139 ON ASN 68 HD22
ASN 140 OD1 ND2 TYR 138 HN
HIS 142 ND1 ASN 140 HN HD21 HD22
THR 167 OG1 HIS 142 HD1
GLY 195 O GLY 199 HN
PRO 196 O ASN 203 HN HD21HD22
ARG 206 HE HH21HH22

The Substrate Pathway
is formed by C=O groups

The Substrate Pathway
is formed by C=O groups

Non-helical motifs
are stabilized by
two glutamate
residues.

N E NPA E NPAR C

Conservation of Glutamate Residue in
Human Aquaporins

Glycerol – water competition for hydrogen
bonding sites

Revealing the Functional Role of
Reentrant Loops

Potassium channel

AqpZ vs. GlpF
•  Both from E. coli
•  AqpZ is a pure water channel
•  GlpF is a glycerol channel
•  We have high resolution structures for both channels

Steered Molecular Dynamics is a
non-equilibrium method by nature
•  A wide variety of events that are inaccessible to
conventional molecular dynamics simulations can
be probed.

•  The system will be driven, however, away from
equilibrium, resulting in problems in describing the
energy landscape associated with the event of
interest.

Second law of thermodynamics W ≥ ΔG

Jarzynski’s Equality
ΔG W
Transition between two equilibrium states
e-βWp(W) W ≥ ΔG
T T
λ = λ(t)
λ = λi λ = λf
work W
heat Q

p(W)
ΔG = G f − Gi

C. Jarzynski, Phys. Rev. Lett., 78, 2690 (1997)
C. Jarzynski, Phys. Rev. E, 56, 5018 (1997)
e − βW
=e − βΔG

β= 1
k BT
In principle, it is possible to obtain free
energy surfaces from repeated non-
equilibrium experiments.

Steered Molecular Dynamics
constant force constant velocity
(250 pN) (30 Å/ns)

SMD Simulation of Glycerol Passage

Trajectory of glycerol pulled by constant force

Constructing the Potential of Mean Force

4 trajectories
v = 0.03, 0.015 Å/ps
k = 150 pN/Å

f (t ) = − k[ z (t ) − z0 − vt ]

t
W (t ) = ∫ dt ʹ′ vf (t ʹ′)
0

Features of the Potential of Mean Force

•  Captures major features of the channel
•  The largest barrier ≈ 7.3 kcal/mol; exp.: 9.6±1.5 kcal/mol
Jensen et al., PNAS, 99:6731-6736, 2002.

Features of the Potential
of Mean Force

Cytoplasm
Periplasm

Asymmetric Profile in the Vestibules
Jensen et al., PNAS, 99:6731-6736, 2002.

Artificial induction of glycerol
conduction through AqpZ

Y. Wang, K. Schulten, and E. Tajkhorshid Structure 13, 1107 (2005)

Three fold higher barriers

periplasm cytoplasm SF

NPA

AqpZ 22.8 kcal/mol
GlpF 7.3 kcal/mol


Could it be simply the size?


It is probably just the size that
matters!


Water permeation
5 nanosecond
Simulation

18 water conducted 7-8 water
In 4 monomers in 4 ns molecules in each
1.125 water/monomer/ns channel
Exp. = ~ 1-2 /ns

Correlated Motion of Water in the Channel
Water pair correlation

The single file of
water molecules is
maintained.

Diffusion of Water in the channel

One dimensional diffusion: 2 Dt = ( zt − z0 ) 2

Experimental value for AQP1: 0.4-0.8 e-5

Diffusion of Water in the channel
2 Dt = ( zt − z0 ) 2

0 1 2 3 4
Time (ns)

Improvement of statistics

Water Bipolar Configuration in Aquaporins

R E M E M B E R:

One of the most useful advantages of
simulations over experiments is that you
can modify the system as you wish: You
can do modifications that are not even
possible at all in reality!

This is a powerful technique to test
hypotheses developed during your
simulations. Use it!

Electrostatic Stabilization of
Water Bipolar Arrangement

Proton transfer through water
H+
H+ H+
H O H O H O H+
H+

H H H
H+
H+ O H O H O H H+ H+
H+
H H H
H+
H O H O H O H+ H+
H+
H H H

Cl- channel

K+ channel Aquaporins

A Complex Electrostatic Interaction

SF

NPA

“Surprising and clearly not a hydrophobic channel”
M. Jensen, E. Tajkhorshid, K. Schulten, Biophys. J. 85, 2884 (2003)

A Repulsive Electrostatic Force at
the Center of the Channel

QM/MM MD of the behavior
of an excessive proton

Simulating Membrane Channels, E. Tajkhorshid, Part 2

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