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Week 4
MD simulations of ion channels and transporters
•
Lecture 7: Biophysics of a single neuron; propagation of action
potential and ion channels; neurotransmission at synapses and
transporters; MD simulations of gramicidin and potassium
channels.
•
Lecture 8: Primary and secondary active transporters; Na-K pump
and ABC transporters use energy from ATP; secondary active
transporters use the membrane potential; MD simulations of
glutamate transporters.
Structure of a neuron
Signal transmission in salt water
Problem of signal transmission in salt water
Diffusion wouldn’t work: <x2>=2Dt, L=1 m, D~10-9 m2/s, t~16 years!
If we apply
a potential
difference V
vd 
t
F


eV D eV D

 40 10 9 m/s for 1 eV  40 kT
L kT kT L
L
 2.5 107 s  1 year
vd
Propagation of the action potential
1. Change of membrane voltage opens the sodium channels.
2. Na+ ions flow into the cell, which collapses the membrane potential from
−60 mV to 0.
3. This triggers the opening of the potassium channels, while the sodium
channels shut down stochastically.
4. K+ ions flow outside the cell, restoring the membrane potential. The
potassium channels shut down, returning the system to (1).
5. This process is repeated along the axon, which propagates the action
potential (non-linear cable equations, Hodgkin & Huxley).
out
in
Crystal structure of potassium channel (MacKinnon, 1998; Nobel 2003).
Reveals the mechanisms of selectivity and voltage gating
The selectivity filter has the
right size to bind the
dehydrated K+ ions (r=1.3 Å)
but it is too large for the
smaller Na+ ions (r=0.9 Å).
Selectivity filter
Voltage-gated
ion channels are
life’s transistors.
Crystal structure of a sodium channel (Caterall, 2011)
Selectivity filter in Nav (yellow)
is wider than in Kv (blue), and
can accommodate a hydrated
Na+ ion.
Neurons communicate via neurotransmitters at synapses
Vesicles contain hundreds of neurotransmitters. They travel about 10 nm
across the cleft and bind to receptors, which starts another action potential.
Synaptic transmission
1. When the action potential reaches an axon bulb, it triggers opening of the
calcium channels and calcium ions move in.
2. The rise in calcium concentration causes synaptic vesicles containing
neurotransmitters to move towards the membrane.
3. Synaptic vesicles merge with the
neurotransmitters into the synaptic cleft.
membrane
and
release
4. Neurotransmitters diffuse across the synaptic cleft (~ nm) and bind to
receptor proteins on the postsynaptic membrane. Excitatory
neurotransmitters open sodium channels, and sodium ions move in.
5. If sufficient excitatory neurotransmitter binds to receptors, an action
potential is produced in the postsynaptic membrane and travels along
the axon of the second neuron.
6. To prevent continuous stimulation or inhibition of the postsynaptic
membrane, neurotransmitters are broken down by enzymes or are
reabsorbed through the presynaptic membrane by transporters.
Ion channels in the central nervous system
Voltage-gated ion channels in CNS
 sodium and potassium channels are involved in the propagation
of action potential
 calcium channels facilitate release of nerotransmitters at the
axon terminal.
Ligand-gated channels in synapses:
 glutamate receptor channels: glutamate is the major excitatory
neurotransmitter in CNS – its binding opens a sodium channel
 GABA (g aminobutyric acid) and glycine receptor channels:
inhibitory neurotransmitters
 NACh (nicotinic acetylcholine) receptor channels: neuromuscular
junctions
What did we know about ion channels a decade ago?
A lot about their function:
• I-V curves, conductance-concentration curves
• Selectivity sequences for ions
• Gating properties
But not much about structure:
Water filled holes in the membrane
that open and close in response
to voltage change, chemicals, etc.
Without structure, we cannot answer even the most basic questions
about how channels select ions and how the gates open and close.
Thus most work on ion channels before 1998 were done on gramicidin,
which is an antibacterial drug (NMR structure, 1971). After 1998, all the
work focused on potassium channels (and now on sodium channels!).
MD simulations of ion channels
What we can do with MD simulations at present:
• Conductance calculations require more than microsecond MD
simulations, so we cannot determine it directly from MD by counting
ions crossing the channel.
Compromise solution: determine the free energy profiles from MD or
continuum electrostatics and use them in BD simulations.
• Ion selectivity ratios can be determined from MD-free energy
perturbation calculations.
• Gating happens in ms time domain so cannot be accessed directly
with brute-force MD. However targeted MD simulations and coarsegrained models have been used to study gating.
• The recent entrance of ANTON – the special purpose MD machine –
to the field has allowed extension of these limits.
A prerequisite for MD simulation of an ion channel is the availability of the
crystal structure or a good homology model. Because MD is an atomistic
model, it does not forgive any errors in the molecular structure of a
channel model.
What is available:
•
Gramicidin: Antibacterial peptide, structure known since the 70’ties.
•
Potassium channels: KcsA (1998), followed by many others, including
voltage-gated potassium channels.
•
Sodium channels: The latest entry. However the initial rush has been
moderated by the difficulty of constructing homology models from
bacterial crystal structure.
•
Calcium channels: The hardest one to crack due to lack of symmetry.
But BD simulations has given a good account of the conductance data.
•
Chloride (bacterial transporter), mechanosensitive (large opening)
Gramicidin A as a model for ion channels
 Dimer formed by two righthanded β helices
 Each monomer consists of 16
amino acid residues
 Pore is 26 Å long, 4 Å in
diameter
 Structure is stabilized by
hydrogen bonds
 Occupied by a single-file water
chain (~7)
 Water dipoles are aligned with
the channel axis
 Conducts cations at diffusion
rates
14
Potential energy profile for a K+ ion in gramicidin A
BD simulations – inverting data gives | MD simulations – Pot. mean force
Uw = 8 kT, Ub = 5 kT,
Uw = 5 kT, Ub = 22 kT
15
Ab initio simulations of ion+water in
bulk water vs gramicidin
Distribution of water dipole moments
in bulk and in gramicidin.
In bulk water, presence of a K+ ion
causes a reduction in the dipole
moment of hydration waters relative to
bulk.
In gramicidin, presence of a K+ ion
increases the dipole moment of
neighbouring waters relative to apo
gramicidin.
Electrostatic energy of a K+ ion + 6 waters
Bulk
Gramicidin
Sampling problem in a simple vs complex system
Test of Jarzynski’s Equation (J. Chem. Phys. 128:155104, 2008)
Carbon nanotube
Gramicidin A channel
Comparison of PMFs obtained from umbrella sampling
and from Jarzynski’s equality using steered MD simulations
Carbon nanotube
Gramicidin A channel
v(A/ns)
19
Good agreement
Complete failure
MD simulations of potassium channels
•
Most of the MD simulations have been done for the KcsA channel,
which has two-transmembrane topology and very stable structure
(see for example work of B. Roux and M. Sansom).
•
K/Na selectivity has been confirmed from FEP calculations
•
Permeation involves recycling between 2 and 3 K ions in the filter.
Entry of a third ion makes the filter state semistable, which results in
ejection of the third ion in the direction of applied electric field
(confirmed by BD simulations).
•
Voltage-gated potassium channels have six-transmembrane topology
(four of them function as voltage sensors) and are less stable.
MD simulations in Kv1.2 have shown that inclusion CMAP correction
in the torsion potential is essential to preserve the integrity of the
selectivity filter.
Selectivity filter
S0
Permeation cycle
S1
S2
Waiting state: (S1-S3-C)
Trigger event:
(S1-S3-C)  (S0-S2-S4)
S3
S4
K in S0 is ejected, leaving
two ions in the filter
(S2-S4)  (S1-S3)
C
Selectivity of S1 site
Selectivity free energy
DDG(K+  Na+)
= DGS1(K+  Na+)
DGbulk(K+  Na+)
FEP calculations:
DDG
Calc.
Exp.
Shaker
-0.7
> 2.1
+ CMAP
5.2
> 2.1
KcsA
1.8
> 2.9
+ CMAP
8.4
> 2.9
Units: kcal/mol
Single-ion PMFs
Binding of a third K+ ion
to the S4 site in Kv1.2
Binding of a third K+ ion
to the S0 site in Kv1.2
Two-ion PMFs
Concerted motion of two
K+ ions in the filter of Kv1.2
(S2-S4)  (S1-S3)  (S0-S2)
easy
hard
Same PMF in KcsA
Three-ion PMFs
Concerted motion of three
K+ ions in the filter of Kv1.2
(S1-S3-C)  (S0-S2-S4)
hard
Same PMF in KcsA
25
MD simulations of transporters
Two major families of transporters:
•
Primary active transporters use the energy from ATP (e.g. Na-K
pump, ABC transporters)
•
Secondary active transporters exploit the concentration gradients
across the membrane, that is, they couple the Na+ and K+ ions to the
substrate to enable its transport (e.g. glutamate and other amino acid
transporters)
Transporters have larger structures and therefore are harder to crystallize
compared to ion channels.
First complete structure: ABC (B12) transporter, 2002.
Followed by many other transporter structures – ripe for simulations!
ABC transporters
ATP-Binding Cassette (ABC)
transporters are involved in transport
of diverse range of molecules from
vitamins to toxic substances.
Two classes:
• Importers
• Exporters
Exporters play a role in
multi-drug resistance, e.g., in
chemotherapy, they expel the anticancer drug before it can act.
Vitamin B12 importer
(Locher et al. 2002)
Schematic picture of B12 import
First structure of sodium-potassium pump
(Poul Nissen et al. Dec. 2007)
First structure of a glutamate transporter
Glutamate transporters exploit the ionic gradients to transport one Glu into
the cell together with 3 Na+ and 1 H+ ions. One K+ ion is countertransported. There is no selectivity between Asp and Glu in eukaryotes.
In bacteria/archaea, there is no co-transport of H+ and counter-transport of
K+. These are presumably introduced during evolution to speed up the
transport cycle.
First crystal structure of an
archaeal Asp transporter
GltPh (Gouaux et al. 2004)
Each monomer in the trimer
functions independently.
A second structure of GltPh with ligand binding sites
Boudker, Ryan et al. 2007
Binding sites for Asp and two Tl+
(Na+) ions are observed.
MD simulations of GltPh in the outward-facing state
Crystal structure of GltPh – illuminating but incomplete: closed structure
only, and the binding site for the third Na ion missing
MD simulations have revealed:
• Opening of the extracellular gate
• The binding site for the third Na ion
• Complete characterization of the binding sites for Na ions and Asp
• Binding order of ligands from binding free energy calculations for Na
ions and Asp
• Understanding Asp/Glu selectivity of GltPh from free energy
perturbation (FEP) calculations.
(see G. Heinzelmann’s papers at www.physics.usyd.edu.au/biophys for
details of glutamate transporter simulations.)
Closed and open states of Gltph
The crystal structure is in closed state. After the Na+ ions and Asp are
removed, the hairpin HP2 moves outward, exposing the binding sites.
Closed
Open
HP2
HP1
Initial MD simulations of GltPh with 2 Na ions and Asp
• In the crystal structure, Na1 is coordinated by D405 side chain (2
O’s) & carbonyls of G306, N310, N401
• After (long) equilibration in MD simulations, D312 side chain swings
5 A and starts coordinating Na1, displacing G306 which moves out
of the coordination shell.
This picture is in conflict with the crystal structure.
• Proper question to ask: what is holding D312 side chain in that
location in the crystal structure?
• The tip of the D312 side chain is the most likely site for Na3.
Movement of the D312 sidechain in MD simulations
Initially, D312 (O) is > 7 A from Na1. After about 35 ns, it swings to the
coordination shell of Na1, pushing away G306 (O) and also one of the
D405(O). This is conflict with the crystal structure.
Hunt for the Na3 site
(after the experiments with radioactive Na+ revealed its existence)
• Reject those sites that do not involve D312 in the coordination of
Na3 (Noskov et al, Kavanaugh et al.)
• Two prospective Na3 sites are found that involve D312 as well as
T92 and N310 sidechains
1. In MD simulations that use the closed structure, the 5th ligand is
water. (Tajkhorshid, 2010)
2. In the open structure, the N310 sidechain is flipped around,
which shifts the Na3 site, making the Y89 carbonyl as the 5th ligand.
(Question: Why isn’t the Na3 site seen in the crystal structure?)
Ion
Coord.
Na3
of ions
Na1
Helix-residue
Closed state
Open state
TM3 – T89 (O)
2.3 ± 0.1
2.3 ± 0.1
TM3 – T92 (OH)
2.4 ± 0.1
2.4 ± 0.1
TM3 – S93 (OH)
2.4 ± 0.1
2.3 ± 0.1
TM7 – N310 (OD)
2.2 ± 0.1
2.2 ± 0.1
TM7 – D312 (O1)
2.1 ± 0.1
2.1 ± 0.1
TM7 – D312 (O2)
3.6 ± 0.2
3.5 ± 0.3
TM7 – G306 (O)
2.8
2.4 ± 0.2
2.4 ± 0.2
TM7 – N310 (O)
2.7
2.3 ± 0.1
2.4 ± 0.2
TM8 – N401 (O)
2.7
2.4 ± 0.2
2.5 ± 0.2
TM8 – D405 (O1)
3.0
2.2 ± 0.1
2.2 ± 0.1
TM8 – D405 (O2)
2.8
2.2 ± 0.1
2.3 ± 0.1
-
2.3 ± 0.1
2.3 ± 0.1
TM7 – T308 (O)
2.6
2.3 ± 0.1
TM7 – T308 (OH)
5.5
2.4 ± 0.1
HP2 – S349 (O)
2.1
4.5 ± 0.3
HP2 – I350 (O)
3.2
2.3 ± 0.1
HP2 – T352 (O)
2.2
2.3 ± 0.1
H2O
Na2
Cryst. str.
Points to note on coord. of ions
• Tl+ ions are substituted for Na+ ions in the crystal structure because
they have six times more electrons and hence much easier to
observe. Because Tl+ ions are larger, the observed ion coordination
distances are in general larger than those predicted for the Na+ ions.
• For the same reason, some distortion of the binding sites can be
expected (e.g. Na2)
• The path to the Na3 site goes through the Na1 site and is very
narrow. Therefore Tl+ substitution works for Na1 and Na2 but not for
Na3. That is, the Na+ ion at the Na3 site cannot be substituted by
the Tl+ ion at the Na1 site due to lack of space. This explains why
the Na3 site is not observed in the crystal structure.
GltPh residues coordinating Asp
Helix-residue
Asp
Cryst. str
Closed state
Open state
Open (restr)
HP1 – R276 (O)
aN
2.4
3.0 ± 0.2
3.0 ± 0.2
3.0 ± 0.2
HP1 – S278 (N)
aO1
2.8
2.8 ± 0.1
2.8 ± 0.1
2.8 ± 0.1
HP1 – S278 (OH)
aO2
3.8
2.7 ± 0.1
2.8 ± 0.2
2.8 ± 0.1
TM7– T314 (OH)
bO2
2.7
2.7 ± 0.1
2.8 ± 0.1
2.8 ± 0.1
HP2 – V355 (O)
aN
2.9
2.9 ± 0.2
11.9 ± 0.4
11.9 ± 0.3
HP2 – G359 (N)
bO2
2.8
3.1 ± 0.2
6.1 ± 0.4
6.3 ± 0.3
TM8 – D394(O1)
aN
2.6
2.7 ± 0.1
2.7 ± 0.1
2.7 ± 0.1
TM8 – R397(N1)
bO2
4.6
4.2 ± 0.2
2.7 ± 0.1
2.7 ± 0.1
TM8 – R397(N2)
bO1
2.5
2.9 ± 0.2
2.9 ± 0.2
2.9 ± 0.2
TM8 – T398(OH)
aN
3.2
3.2 ± 0.2
3.0 ± 0.2
3.0 ± 0.2
TM8 – N401(ND)
aO2
2.8
2.8 ± 0.1
3.0 ± 0.2
2.9 ± 0.2
In the open state HP2 gate moves away from Asp but Asp remains bound
Points to note on coord. of Asp

In the closed structure, Asp is coordinated by 10 N & O atoms
(3 from HP1, 2 from HP2, 1 from TM7, 4 from TM8)

In the open structure, HP2 gate opens, leading to loss of 2 contacts
but another one is gained from TM8.

In both cases, there is a 1-1 match between Exp. and MD.

Asp stably binds to the open structure in the presence of Na3 and
Na1.

Removing Na1, destabilizes Asp which unbinds within a few ns.

Corollary: Asp binds only after Na3 and Na1.

Question: is there a coupling between Asp and Na1?
H-bond network that couples Na1 & Asp
Relase of Asp
Binding free energies for Na+ ions and Asp in GltPh
The crystal structure provides a snapshot of the ion and Asp bound
configuration of the transporter protein but it does not tell us anything about
the binding order and energies. We can answer these question by performing
free energy calculations. The specific questions are:
1. We expect a Na+ ion to bind first - does it occupy Na1 or Na3 site?
2. Does a second Na+ ion bind before Asp?
3. Are the binding energies consistent with experimental affinities?
4. Are the ion binding sites selective for Na+ ions?
5. Can we explain the observed selectivity for Asp over Glu (there is no such
selectivity in human Glu transporters)
Once we answer these questions successfully in GltPh, we can construct a
homology model for human Glu transporters and ask the same there.
Convergence of binding free energies in TI method
TI calculations of the
binding free energy of
Na+ ion to the bind. site 1
in Gltph.
Integration is done using
Gaussian quadrature with
7 points.
Thick lines show the
running averages, which
flatten out as the data
accumulate. Thin lines
show averages over 50 ps
blocks of data.
Na binding energies from free energy simulations
Translocation free energy is obtained using free energy perturbation or
thermodynamic integration. Free energy changes due to loss of translational
entropy are included in 3rd column. Binding free energies are (in kcal/mol):
Ion
DGint
DGtr
DGb
Na3
-23.3
4.6
-18.7
Na3
-19.2
4.6
-14.6
Na1
-16.2
4.9
-11.3
Na1 (Na3)
-11.9
4.8
-7.1
Closed
Ion
DGint
DGtr
DGb
structure
Na2
-7.1
4.4
-2.7
Na2
-1.7
4.4
+2.7
Open
structure
(exp: -3.3)
Note that Na2’ energy is positive, i.e. Na ion does not bind to Na2’
Confirmation of the Na3 site from mutation experiments
The T92A and S93A mutations reduce the experimental sodium affinities
significantly relative to wild type (K0.5 increases by x10).
The same mutations reduce the calculated binding free energies at Na3
but not at Na1. (All energies are in kcal/mol)
Wild type
T92A
S93A
Na3
-18.7 ± 1.2
-11.2 ± 1.4
-12.8 ± 1.2
Na1 (Na3)
-7.1 ± 1.3
-6.7 ± 1.2
-6.4 ± 1.4
Conclusion: T92 and S93 are involved in the coordination of the Na3 site
Asp binding energies (open structure)
DG (kcal/mol)
Notes
-16.1
-15.8 (FEP), -16.4 (TI)
Lennard-Jones
4.6
3.8 (bb) + 0.8 (sc)
Translational
3.3
Rotational
3.9
Conform. restraints
0.5
Total
-3.8
Contribution
Electrostatic

1.2 (bulk) - 0.7 (b.s.)
Forward and backward calculations agree within 1 kcal/mol
(that is, no hysteresis)

Convergence is checked from running averages

Exp. binding free energy (-12 kcal/mol) includes gating & Na2 energy
Binding order from binding free energies
• The Na3 site has the lowest binding free energy, therefore it will be
occupied first (-18.7 kcal/mol).
• Asp does not bind in the absence of Na1, hence Na1 will be occupied
next (-7.1 kcal/mol).
• Asp binds after Na3 and Na1 (-3.8 kcal/mol).
• The HP2 gate closes after Asp binds.
• Na2 binds last following the closure of gate (-2.7 kcal/mol)
Experiments confirm that a Na ion binds first and another one binds
last but do not tell whether Asp binds after one or two Na ions.
Presence of two Na ions obviously enhances binding of an Asp.
MD simulations of GltPh in the inward-facing state
Crystal structure of the inward-facing state was found in 2009 (Reyes et al)
MD simulations of this structure have revealed that:
• Opening of the intracellular gate is different than that of the extracellular
gate
• The binding sites for Na ions and Asp are very similar in the inward and
outward-facing sates
• Ditto binding free energies, hence unbinding order is the reverse of the
binding order, that is, Na2, (gate opens), Asp, Na1, Na3
• The rate limiting step in the transport cycle is the unbinding of Na3.
(Rate calculations using Kramer’s rate theory is consistent with exp,
giving ~3 minutes for the transport cycle)
MD simulations of a homology model of EAAT3
No crystal structures are available for the mammalian excitatory amino acid
transporters (EAATs) yet. So one has to construct homology models for
EAATs using GltPh as a template. Most functional data available for
EAAT3, so we consider that first. Model should explain the differences
between EAATs and GltPh, e.g.
• Location of the proton binding site.
• Location of the K+ binding site.
• Why EAATs have a much faster turn over rate than GltPh.
Residues involved in the coordination of the ligands
E374 is the only site in EAAT3 which could accommodate a proton without
affecting the transport. E374Q mutation in EAAT3 does not affect Glu
affinity but it abolishes the pH dependence of Glu transport.
Residues that are not conserved between GltPh and EAATs are indicated with red.
MD simulations of EAAT3 with a protonated vs deprotonated E734
(A) Glu substrate (in green) bound to EAAT3 in the closed outward state
with a protonated E374 side chain. Glu is stable for 20 ns.
(B) The same but with a deprotonated E374 side chain. Glu becomes
unstable, losing most of the contacts after 10 ns of simulations.
Binding sites for K+ ion in EAAT3
Three potential sites are tested for binding of a K+ ion.
A) Site 1 is obtained by placing K+ at the Na1 site and equilibrating.
B) Site 2 is obtained by placing K+ next to E374 and equilibrating.
C) Site 3 is obtained by placing K+ next to Glu and equilibrating.
To decide which site is more favorable, we calculate the binding free
energies of in each site as well as K+/Na+ selectivity free energies.
Binding free energies of K+
Site 1 has the largest affinity for K+ and is not selective for either ion.
But because K+ concentration is much higher inside the cell, a Na+ ion at this
site could be easily replaced by a K+ ion.
Thus the last Na+ ion need not unbind, which is the rate-limiting step in
GltPh. Instead it is exchanged by a K+ ion, which is a much faster process.
This could explain ~1000 times faster turn over rates in EAATs compared
the GlltPh.