1. 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.

2. Structure of a neuron

3. Signal transmission in salt water Problem of signal transmission in salt water Diffusion wouldn’t work: =2Dt, L=1 m, D~10 -9 m 2 /s, t~16 years! If we apply a potential difference V

5. 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

6. 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

7. 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.

8. 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.

9. 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.

10. 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

11. 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!).

12. 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.

13. 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)

14.  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

15. Potential energy profile for a K + ion in gramicidin A BD simulations – inverting data gives | MD simulations – Pot. mean force U w = 8 kT, U b = 5 kT, U w = 5 kT, U b = 22 kT 15

16. 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.

17. Electrostatic energy of a K + ion + 6 waters Bulk Gramicidin

18. Sampling problem in a simple vs complex system Test of Jarzynski’s Equation (J. Chem. Phys. 128:155104, 2008) Carbon nanotube Gramicidin A channel

19. 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 agreementComplete failure

20. 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.

21. 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)

22. Selectivity of S1 site Selectivity free energy  G(K +  Na + ) =  G S1 (K +  Na + )  G bulk (K +  Na + ) FEP calculations:  GCalc.Exp. Shaker-0.7> 2.1 + CMAP5.2> 2.1 KcsA1.8> 2.9 + CMAP8.4> 2.9 Units: kcal/mol

23. 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

24. 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

25. 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

26. 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 (B 12 ) transporter, 2002. Followed by many other transporter structures – ripe for simulations!

27. 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 B 12 importer (Locher et al. 2002)

28. Schematic picture of B 12 import

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

30. 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.

31. 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.

32. 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.)www.physics.usyd.edu.au/biophys

33. 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

34. 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.

35. 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.

36. 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 5 th 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 5 th ligand. (Question: Why isn’t the Na3 site seen in the crystal structure?)

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

38. IonHelix-residueCryst. str.Closed stateOpen state Na3TM3 – T89 (O)2.3 ± 0.1 TM3 – T92 (OH)2.4 ± 0.1 TM3 – S93 (OH)2.4 ± 0.12.3 ± 0.1 TM7 – N310 (OD)2.2 ± 0.1 TM7 – D312 (O 1 )2.1 ± 0.1 TM7 – D312 (O 2 )3.6 ± 0.23.5 ± 0.3 Na1TM7 – G306 (O)2.82.4 ± 0.2 TM7 – N310 (O)2.72.3 ± 0.12.4 ± 0.2 TM8 – N401 (O)2.72.4 ± 0.22.5 ± 0.2 TM8 – D405 (O 1 )3.02.2 ± 0.1 TM8 – D405 (O 2 )2.82.2 ± 0.12.3 ± 0.1 H2OH2O- Na2TM7 – T308 (O)2.62.3 ± 0.1 TM7 – T308 (OH)5.52.4 ± 0.1 HP2 – S349 (O)2.14.5 ± 0.3 HP2 – I350 (O)3.22.3 ± 0.1 HP2 – T352 (O)2.22.3 ± 0.1 Coord. of ions

39. 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.

40. Helix-residueAsp Cryst. strClosed stateOpen stateOpen (restr) HP1 – R276 (O)  N 2.43.0 ± 0.2 HP1 – S278 (N)  O 1 2.82.8 ± 0.1 HP  – S278 (OH)  O 2 3.82.7 ± 0.12.8 ± 0.22.8 ± 0.1 TM7– T314 (OH)  O 2 2.72.7 ± 0.12.8 ± 0.1 HP2 – V355 (O)  N 2.92.9 ± 0.211.9 ± 0.411.9 ± 0.3 HP2 – G359 (N)  O 2 2.83.1 ± 0.26.1 ± 0.46.3 ± 0.3 TM8 – D394(O 1 )  N 2.62.7 ± 0.1 TM8 – R397(N 1 )  O 2 4.64.2 ± 0.22.7 ± 0.1 TM8 – R397(N 2 )  O 1 2.52.9 ± 0.2 TM8 – T398(OH)  N 3.23.2 ± 0.23.0 ± 0.2 TM8 – N401(ND)  O 2 2.82.8 ± 0.13.0 ± 0.22.9 ± 0.2 GltPh residues coordinating Asp In the open state HP2 gate moves away from Asp but Asp remains bound

41. 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?

42. H-bond network that couples Na1 & Asp

43. Relase of Asp

44. 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.

45. 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.

46. 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 3 rd 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  G int  G tr GbGb Na3-23.34.6-18.7 Na3 -19.24.6-14.6 Na1-16.24.9-11.3 Na1 (Na3)-11.94.8-7.1 Ion  G int  G tr GbGb Na2-7.14.4-2.7 Na2 -1.74.4+2.7 (exp: -3.3)

47. The T92A and S93A mutations reduce the experimental sodium affinities significantly relative to wild type (K 0.5 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 typeT92AS93A 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

48. Asp binding energies (open structure) Contribution  G (kcal/mol) Notes Electrostatic-16.1-15.8 (FEP), -16.4 (TI) Lennard-Jones4.63.8 (bb) + 0.8 (sc) Translational3.3 Rotational3.9 Conform. restraints0.51.2 (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

49. 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.

50. 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)

51. 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.

52. 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.

53. 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.

54. 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

55. 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 +