Applications of relative free energy calculations

1. Relative free energies are useful in two contexts: 1. Calculation of the free energy of binding of a ligand relative to bulk. This is the most common application. The simplest examples are binding of ions. As the ligand gets more complex, it becomes less accurate. 2. Calculation of the free energy change when a bound ligand is mutated. This gives selectivity of a binding site against different ligands. Again ion selectivity is the simplest and most common example. Mutation of amino acids is a powerful method but it has been neglected. Applications of relative free energy calculations

2. The first crystal structure in 1998 (MacKinnon), followed by many others. 1. Free energy calculations in potassium channels

3. 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. Then (S2-S4)  (S1-S3) Aqvist et al. (2000) did the first FEP calculations where they progressively loaded the filter with K+ ions, confirming the above picture. S0 Selectivity filter S1 S2 S3 S4 Cavity

4. MD simulations of potassium channels • Most of the simulations have been done for the KcsA channel, which has two-transmembrane topology (similar to Kir channels) and very stable structure. (See e.g. work of Roux and 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. • Thus it is imperative to check that the results obtained in KcsA are transferable to Kv channels.

5. Comparison of the filter structures: Shaker Kv1.2 (top) KcsA (bottom)

6. Effect of the dihedral energy correction terms (CMAP) in selectivity of K+ channels Dihedral potential: Basic dihedral configurations trans cis Definition of the dihedral angle for 4 atoms A-B-C-D

7. Without CMAP Shaker Kv1.2 With CMAP

8. Without CMAP KcsA With CMAP

9. Selectivity of S1 site Selectivity free energy DDG(K+ Na+) = DGS1(K+ Na+) -DGbulk(K+ Na+) Units: kcal/mol

10. Transporters – the new frontier Transporters have larger structures, which are partly outside the membrane. Also they have no symmetries. Therefore they are harder to crystallize compared to ion channels. First complete transporter structure: ABC (ATP binding cassette) transporter, Locher et al. 2002. First glutamate (aspartate) transporter: GltPh from Pyrococcus horikoshii, Gouaux et al. 2004; 2007) First sodium-potassium pump structure: Nissen et al. Dec. 2007) Two major families: Primary active transporters use the energy from ATP (e.g., Na-K pump) Secondary active transporters harness the gradient of Na+ ions (membrane potential) (e.g., Glu and Leu transporters) 2. Free energy calculations in glutamate transporters

11. Structure of sodium-potassium pump (Nissen et al. Dec. 2007)

12. ATP binding casette (ABC) transporters Much interest because of multi-drug resistance in chemotherapy ABC drug exporter (Sav1866) (Dawson and Locher, 2006) Vitamin B12 importer (Locher et al. 2002)

13. Schematic picture of B12 import

14. Structure of GltPh from Pyrococcushorikoshii Boudker et al. 2007 Binding sites for Asp and two Na ions are revealed Q: why is it called glut. transporter?

15. 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

16. Opening of the extracellular gate HP2

17. Initial MD simulations of GltPh with 2 Na+ ions • In the crystal structure, Na1 is coordinated by the carbonyl oxygens of Gly306, Asn310, Asn401and two carboxyl oxygens of Asp405 • After (long) equilibration in MD simulations, Asp312 sidechain swings 5 A and coordinates Na1. Also Gly306 moves out of the coordination shell. This disagrees with the crystal structure. • Human Glu transporters use 3 Na+ ions in the transport. For the GltPh structure to be useful in homology modeling, it must also have 3 binding sites for the Na+ ions. • It is possible that the third b.s. is not seen. Clue: what is holding Asp312 sidechain in that location in the crystal structure?

18. Simulation system for GltPh It is important to obtain a minimal system to save from computation time Original system Minimized system (150,00 atoms) (87,000 atoms)

19. 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.

20. Hunt for the Na3 site after the experiments 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?)

21. Position of the Na3 binding site Na3’ coordination shell from the closed structure: T92, N310, D312 (2), H2O Na3’ coordination shell from the open structure: T92, S93, N310, D312 (1), Y89 (bb) Both remain stable in long MD simulations. Which one is correct? open closed

22. Tests for the Na3 site We need to find out which configuration of N310 is more likely. 1. In 5 ns MD simulations without the Na3 ion, the N310 sidechain remains stable in the open structure but flips after 0.2 ns. in the closed. 2. After MD simulations with the Na3 ion, N310 sidechain moves 2 A away from the crystal structure in the closed case, but not in the open. Free energy of binding for the Na3 site are - 23.3 kcal/mol (open) and - 19.3 kcal/mol (closed). Compare with Na1: - 16.2 kcal/mol. crystal MD open closed

23. 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.

24. TI calculation for binding of a Na+ ion to Na3 site Total simulation time is 1.4 ns; equilibration, 0.4 ns; production, 1 ns. Open structure with only one Na+ ion at Na3 site is used in the calcul.

25. TI calculation for binding of Asp Calculation is performed in the presence of Na+ ions at Na1 and Na3. Asp is replaced by 5 water molecules in the binding site.

26. Na+ binding free energies Energies are obtained for binding of Na+ ions to the empty transporter (i.e. Asp and ions are removed and the gate is open) • Single Na binding energies (kcal/mol): Na3(open) : -19.3 Na3(closed) : -23.3 Na1 : -16.2 Na3 binds first and Y89 coordination is preferred to that of water. • As Na2 binds last, we next calculate Na1 binding energy in the presence of Na3 : -11.9

27. Asp binding free energies (gate open) Asp is replaced with 5 water molecules. • Asp binding energies (kcal/mol): With Na3 present : -4.3 With Na3 and Na1 present : -12.3 • Na1 binds after Na3. • Asp binds after Na3 and Na1. • The order of binding: Na3 Na1 Asp Gate closes Na2 -23.3 -11.9 -12.3 -4.1

28. Binding energies (gate closed) All three Na ions and Asp are present Na3 : -14.6 kcal/mol Na1 : -28.7 Asp: +2.6 Na2 : -4.1 Asp becomes unstable after closing of the gate! This may be useful for quick release of Asp to the cell interior. What about the Asp/Glu selectivity? Free energy difference for Asp/Glu binding : ~2 kcal/mol Experiments indicate ~4 kcal/mol (1000-fold reduction in bind. const.)

29. Lessons from the free energy simulations • Correct reading of the crystal structure is essential: Respect the long and medium distance structure but be careful with the short distance. • Free energy simulations can help to resolve structural issues as well as providing an overall picture for binding processes.

30. Computational program for protein-ligand interactions Find the initial configuration for the bound complex using a docking algorithm (e.g. AutoDock, ZDOCK, HADDOCK, etc. ) Refine the initial complex via molecular dynamics (MD) simulations Calculate the potential of mean force for binding of the ligand along a reaction coordinate → binding constants and free energies Determine the key residues involved in the binding Consider mutations of the key residues on the ligand and calculate their binding energies (relative to the wild type) from free energy perturbation in MD simulations Those with higher affinity are candidates for new drug leads