Structure and function of transporters

from molecular dynamics simulations

Serdar Kuyucak

University of Sydney

Transporter families

Two major families:

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

They play a role in multi-drug

resistance. Vitamin B12 importer

(Locher et al. 2002)

Schematic picture of B12 import

First structure of sodium-potassium pump

(Poul Nissen et al. Dec. 2007)

Glutamate transporters and neuronal communication

Neurons communicate via neurotransmitters such as glutamate,

aspartate, acetylcholine, ...

First structure of a glutamate transporter

Glutamate is the major excitatory neurotransmitter in the central nervous system. Its extracellular concentration needs to be tightly controlled, which is achieved by glutamate transporters. They exploit the ionic gradients to transport 1 Glu into the cell together with 3 Na+ and 1 H+ ions. There is no selectivity between Asp and Glu in eukaryotes.

Structure of a bacterialaspartate transporter GltPh (Gouaux et al. 2004)Each monomer in the trimer functions independently.No H+ transport is observed.

A second structure of GltPh from Pyrococcus horikoshii

Boudker, Ryan et al. 2007

Binding sites for Asp and two

Na ions are observed.

MD simulations of the Asp transporter GltPh

Crystal structure of GltPh – illuminating but incomplete

MD simulations of GltPh reveal the binding site for the third

Na ion, which was not observed in the crystal structure

Complete characterization of the binding sites for the Na ions

and Asp

Binding free energy calculations for Na ions and Asp

determine the binding order

Understanding Asp/Glu selectivity of GltPh from free energy

perturbation (FEP) calculations.

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

Opening of the extracellular gate HP2

Binding sites for the two Na+ ions & Asp

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 (TBOA bound) structure 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?)

Comparison of Na3 sites from closed & open structures

Na3’ (closed structure) Na3 (open structure)

D312 (2), N310, T92, H2O D312 (1), N310, T92, S93, Y89

(Huang and Tajkhorshid, 2010) (Our results)

Comparison of N310 side chain config’s with MD simulations

Na3’ (closed structure) Na3 (open structure)

Crystal structure (dark shade), MD simulations (light shade)

Coordination of the Na2 site

Na2’ (crystal structure) Na2 (MD simulations)

T308, S349, I350 , T352 T308 (bb+sc), I350 , T352, H2O

Residues involved in the coordination of Na1

(Pair distribution functions for the Na—O distances)

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

Points to note

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.

Coordination 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?

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 it remains bound

H-bond network that couples Na1 & 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.

Absolute binding free energies from free energy perturbation

(FEP)

or thermodynamic integration (TI)

The total binding free energy can be expressed as

The various sigma’s are the translational and rotational rmsd’s of ligand

The last term is the interaction energy calculated from FEP or TI

27

siteres

bulkresres

rot

zyxtr

intresrottrb

GGG

ekTG

VV

ekTG

GGGGG

2321

2/3

30

0

2/3

8

)2(ln

1660,)2(

ln

Free energy perturbation (FEP)

Zwanzig’s perturbation formula for the free energy difference

between two states A and B:

To obtain accurate results with the perturbation formula, the

energy difference between the states should be ~ 2 kT, which is

not satisfied for most biomolecular processes. To deal with this

problem, one introduces a hybrid Hamiltonian

and performs the transformation from A to B gradually by

changing the parameter from 0 to 1 in small steps.

A

kTHHAB

ABkTGGBAG /)(expln)(

28

BA HHH )1()(

That is, one divides [0,1] into n subintervals with {i, i = 0, n}, and

for each i value, calculates the free energy difference from the

ensemble average

The total free energy change is then obtained by summing the

contributions from each subinterval

The number of subintervals is chosen such that the free energy

change at each step is < 2 kT, otherwise the method may lose its

validity. 29

ikTHHkTG iiii /))]()((exp[ln)( 11

1

01)()10(

n

iiiGG

1

0

)(

d

HG

Thermodynamic integration (TI)

Another way to obtain the free energy difference is to integrate

the derivative of the hybrid Hamiltonian H(:

This integral is evaluated most efficiently using a Gaussian

quadrature.

In typical calculations for ions, 7-point quadrature is sufficient.

(But check that 9-point quadrature gives the same result for

others)

The advantage of TI over FEP is that the production run can be

extended as long as necessary and the convergence of the free

energy can be monitored (when the cumulative G flattens, it has

converged).

30

H

dpdqe

dpdqeH

d

dGkTH

kTH

/

/

Na+ binding energy in glutamate transporter with FEP

Window G(Na+; b.s. bulk)

40 eq. 22.9

60 eq. 26.3

65 exp. 27.1

Free energy change G at each step of FEP calculation

Exponential versus equal spacing for

The interval [0, 0.5] is mapped to an exponential for 40 windows.

(Fold it over to get the interval [0.5, 1] )

exp.

equal

Convergence of binding free energies in TI method

TI calculation of the

binding free energy of

Na+ ion to the binding

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 losses due to transl. and rotat.

entropy are included (3rd column). Binding free energies (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

Convergence of Asp binding free energy in TI method

TI calculation of the

binding free energy of

Asp to the binding site

in Gltph.

Asp is substituted with

5 water molecules.

First 400 ps data

account for

equilibration and the 1

ns of data are used in

the production.

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.

Asp/Glu selectivity of GltPh (Open state)

The Glu side chain does not fit the binding site as well as Asp.

In the open state, R397 and T314 contacts with -carboxyl are lost.

G(Asp Glu)

= 5.2 kcal/mol

Asp/Glu selectivity of GltPh (Closed state)

In the closed state, the Glu side chain is in a higher energy conformation

and HP2 gate is not optimal. This may explain why Glu is not transported

by GltPh.

G(Asp Glu)

= 5.4 kcal/mol

(exp: 6.6)

Lessons from the free energy simulations

Correct reading of the crystal structure is essential:

Respect the long and medium distance structure (e.g. the D312

side chain is correct).

But be careful with short distance assignments of side chains

(e.g. the N310 side chain has the wrong conformation in the

closed structure).

Free energy simulations can:

help to resolve structural issues

provide an overall picture for the binding processes

confirm the reliability of the model via comparison with

experimental binding free energies.

Conclusions

MD simulations provide a unique tool for analysis and interpretation of structure-function relations in membrane proteins.

A reliable structure from either a crystal structure or a close homolog is essential for performing MD simulations.

Free energy calculations of ligand binding is important for checking the validity of the model.

MD simulations of transporters are still at the beginning stage. This problem is much more challenging than ion channels, and so far we don’t have a complete understanding of how a transporter works. More work needs to be done.

New developments: First crystal structure of a sodium channel has been determined last year. Sodium channels will dominate the ion channel field in near future.