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!

year 1 s105.2

kT 40 eV 1for m/s1040

7

9

d

d

vL

t

LD

kTeV

kTD

LeVF

vIf we apply

a potential difference V

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).

Voltage-gated

ion channels are

life’s transistors.

Selectivity filter

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 membrane and release neurotransmitters into the synaptic cleft.

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 coarse-

grained 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)

Dimer formed by two right-

handed 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

Gramicidin A as a model for ion channels

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

S1

S2

S3

S4

C

Permeation cycle

Waiting state: (S1-S3-C)

Trigger event:

(S1-S3-C) (S0-S2-S4)

K in S0 is ejected, leaving

two ions in the filter

(S2-S4) (S1-S3)

Selectivity of S1 site

Selectivity free energy

G(K+ Na+)

=GS1(K+ Na+)

Gbulk(K+ Na+)

FEP calculations:G Calc. Exp.

Shaker -0.7 > 2.1

+ CMAP

5.2 > 2.1

KcsA 1.8 > 2.9

+ CMAP

8.4 > 2.9Units: 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 anti-

cancer 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 counter-

transported. 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.

HP2

HP1

OpenClosed

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 Helix-residue Cryst. str. Closed state Open state

Na3 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

Na1 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

H2O - 2.3 ± 0.1 2.3 ± 0.1

Na2 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

Coord.

of ions

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.

Helix-residue Asp Cryst. str Closed state Open state Open (restr)

HP1 – R276 (O) N 2.4 3.0 ± 0.2 3.0 ± 0.2 3.0 ± 0.2

HP1 – S278 (N) O1 2.8 2.8 ± 0.1 2.8 ± 0.1 2.8 ± 0.1

HP – S278 (OH) O2 3.8 2.7 ± 0.1 2.8 ± 0.2 2.8 ± 0.1

TM7– T314 (OH) O2 2.7 2.7 ± 0.1 2.8 ± 0.1 2.8 ± 0.1

HP2 – V355 (O) N 2.9 2.9 ± 0.2 11.9 ± 0.4 11.9 ± 0.3

HP2 – G359 (N) O2 2.8 3.1 ± 0.2 6.1 ± 0.4 6.3 ± 0.3

TM8 – D394(O1) N 2.6 2.7 ± 0.1 2.7 ± 0.1 2.7 ± 0.1

TM8 – R397(N1) O2 4.6 4.2 ± 0.2 2.7 ± 0.1 2.7 ± 0.1

TM8 – R397(N2) O1 2.5 2.9 ± 0.2 2.9 ± 0.2 2.9 ± 0.2

TM8 – T398(OH) N 3.2 3.2 ± 0.2 3.0 ± 0.2 3.0 ± 0.2

TM8 – N401(ND) O2 2.8 2.8 ± 0.1 3.0 ± 0.2 2.9 ± 0.2

GltPh residues coordinating Asp

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):

Open

structure

Closed

structure

Note that Na2’ energy is positive, i.e. Na ion does not bind to Na2’

Ion Gint Gtr Gb

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

Ion Gint Gtr Gb

Na2 -7.1 4.4 -2.7

Na2 -1.7 4.4 +2.7(exp: -3.3)

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)

Conclusion: T92 and S93 are involved in the coordination of the Na3 site

Confirmation of the Na3 site from mutation experiments

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

Asp binding energies (open structure)

Contribution G (kcal/mol) Notes

Electrostatic -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 1.2 (bulk) - 0.7 (b.s.)

Total -3.8

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.

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 involved in the coordination of the ligands

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.

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 sites for K+ ion in EAAT3

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.

Binding free energies of K+