1. Structure and function of transporters from molecular dynamics simulations Serdar Kuyucak
University of Sydney

2. 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!

3. 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)

4. Schematic picture of B12 import

5. First structure of sodium-potassium pump (Poul Nissen et al. Dec. 2007)

6. Glutamate transporters and neuronal communication
Neurons communicate via neurotransmitters such as glutamate,
aspartate, acetylcholine, ...

7. 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 bacterial
aspartate transporter GltPh
(Gouaux et al. 2004)
Each monomer in the trimer functions independently.
No H+ transport is observed.

8. A second structure of GltPh from Pyrococcus horikoshii
Boudker, Ryan et al. 2007
Binding sites for Asp and two Na ions are observed.

9. 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.

10. 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

11. Opening of the extracellular gate HP2

12. Binding sites for the two Na+ ions & Asp

13. 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.

14. 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.

15. 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?)

16. 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)

17. Comparison of N310 side chain config’s with MD simulations
Na3’ (closed structure) Na3 (open structure)
Crystal structure (dark shade), MD simulations (light shade)

18. Coordination of the Na2 site
Na2’ (crystal structure) Na2 (MD simulations)
T308, S349, I350 , T T308 (bb+sc), I350 , T352, H2O

19. Residues involved in the coordination of Na1
(Pair distribution functions for the Na—O distances)

20. Ion
Helix-residue
Cryst. str.
Closed state
Open state
Na3
TM3 – T89 (O)
2.3 ± 0.1
TM3 – T92 (OH)
2.4 ± 0.1
TM3 – S93 (OH)
TM7 – N310 (OD)
2.2 ± 0.1
TM7 – D312 (O1)
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
TM7 – N310 (O)
2.7
TM8 – N401 (O)
2.5 ± 0.2
TM8 – D405 (O1)
3.0
TM8 – D405 (O2)
H2O -
Na2
TM7 – T308 (O)
2.6
TM7 – T308 (OH)
5.5
HP2 – S349 (O)
2.1
4.5 ± 0.3
HP2 – I350 (O)
3.2
HP2 – T352 (O)
2.2

21. 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.

22. 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?

23. 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
HP1 – S278 (N)
a-O1
2.8
2.8 ± 0.1
HP1 – S278 (OH)
a-O2
3.8
2.7 ± 0.1
2.8 ± 0.2
TM7– T314 (OH)
b-O2
2.7
HP2 – V355 (O)
2.9
2.9 ± 0.2
11.9 ± 0.4
11.9 ± 0.3
HP2 – G359 (N)
3.1 ± 0.2
6.1 ± 0.4
6.3 ± 0.3
TM8 – D394(O1)
2.6
TM8 – R397(N1)
4.6
4.2 ± 0.2
TM8 – R397(N2)
b-O1
2.5
TM8 – T398(OH)
3.2
3.2 ± 0.2
TM8 – N401(ND)
In the open state HP2 gate moves away from Asp but it remains bound

24. H-bond network that couples Na1 & Asp

26. 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:
We expect a Na+ ion to bind first - does it occupy Na1 or Na3 site?
Does a second Na+ ion bind before Asp?
Are the binding energies consistent with experimental affinities?
Are the ion binding sites selective for Na+ ions?
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.

27. 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

28. 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 l from 0 to 1 in small steps.

29. That is, one divides [0,1] into n subintervals with {li, i = 0, n}, and for each li 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.

30. Thermodynamic integration (TI)
Another way to obtain the free energy difference is to integrate the derivative of the hybrid Hamiltonian H(l):
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 DG flattens, it has converged).

31. Na+ binding energy in glutamate transporter with FEP
Window DG(Na+; b.s. bulk)
40 eq
60 eq
65 exp. 27.1

32. Free energy change DG at each step of FEP calculation

33. Exponential versus equal spacing for Dl
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

34. 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.

35. 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 Note that Na2’ energy is positive, i.e. Na ion does not bind to Na2’
Ion
DGint
DGtr
DGb
Na3
-23.3
4.6
-18.7
Na3’
-19.2
-14.6
Na1
-16.2
4.9
-11.3
Na1 (Na3)
-11.9
4.8
-7.1
Ion
DGint
DGtr
DGb
Na2
-7.1
4.4
-2.7
Na2’
-1.7
+2.7
(exp: -3.3)

36. 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)
Conclusion: T92 and S93 are involved in the coordination of the Na3 site
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

37. 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.

38. Asp binding energies (open structure)
Contribution
DG (kcal/mol)
Notes
Electrostatic
-16.1
-15.8 (FEP), (TI)
Lennard-Jones
4.6
3.8 (bb) (sc)
Translational
3.3
Rotational
3.9
Conform. restraints
0.5
1.2 (bulk) (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

39. 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.

40. 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 b-carboxyl are lost.
DDG(Asp  Glu)
= 5.2 kcal/mol

41. 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.
DDG(Asp  Glu)
= 5.4 kcal/mol
(exp: 6.6)

42. 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.

43. 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.