A Recipe for Membrane Protein Simulations•  Continue to constrain the protein (heavy atoms), but release   everything else...
Lipid-Protein Packing During the     Initial NpT Simulation
Adjustment of Membrane Thickness to  the Protein Hydrophobic Surface
Glycerol-Saturated GlpF
Description of full conduction pathway
Complete description of the conduction pathwayConstriction region                                    Selectivity          ...
Channel Hydrogen Bonding Sites…{set frame 0}{frame < 100}{incr frame}{    animate goto $frame    set donor [atomselect top...
Channel Hydrogen Bonding SitesGLN    41   OE1 NE2   LEU   197   OTRP    48   O NE1     THR   198   OGLY    64   O         ...
Channel Hydrogen Bonding SitesGLN    41   OE1 NE2   LEU   197   OTRP    48   O NE1     THR   198   OGLY    64   O         ...
The Substrate Pathwayis formed by C=O groups
The Substrate Pathway     is formed by C=O groupsNon-helical motifsare stabilized bytwo glutamateresidues.N    E   NPA    ...
Conservation of Glutamate Residue in         Human Aquaporins
Glycerol – water competition for hydrogen              bonding sites
Revealing the Functional Role of        Reentrant Loops                       Potassium channel
AqpZ vs. GlpF•    Both from E. coli•    AqpZ is a pure water channel•    GlpF is a glycerol channel•    We have high resol...
Steered Molecular Dynamics is anon-equilibrium method by nature   •  A wide variety of events that are inaccessible to    ...
Jarzynski’s Equality                                                           ΔG     WTransition between two equilibrium ...
Steered Molecular Dynamicsconstant force          constant velocity   (250 pN)                (30 Å/ns)
SMD Simulation of Glycerol PassageTrajectory of glycerol pulled by constant force
Constructing the Potential of Mean Force    4 trajectories    v = 0.03, 0.015 Å/ps    k = 150 pN/Åf (t ) = − k[ z (t ) − z...
Features of the Potential of Mean Force  •  Captures major features of the channel  •  The largest barrier ≈ 7.3 kcal/mol;...
Features of the Potential                       of Mean Force                                                    Cytoplasm...
Artificial induction of glycerol             conduction through AqpZY. Wang, K. Schulten, and E. Tajkhorshid Structure 13,...
Three fold higher barriers             periplasm                     cytoplasm                 SF                         ...
Could it be simply the size?Y. Wang, K. Schulten, and E. Tajkhorshid Structure 13, 1107 (2005)
It is probably just the size that                        matters!Y. Wang, K. Schulten, and E. Tajkhorshid Structure 13, 11...
Water permeation                         5 nanosecond                          Simulation  18 water conducted        7-8 w...
Correlated Motion of Water in the Channel                                   Water pair correlationThe single file ofwater ...
Diffusion of Water in the channelOne dimensional diffusion: 2 Dt   = ( zt − z0 )   2Experimental value for AQP1: 0.4-0.8 e-5
Diffusion of Water in the channel    2 Dt = ( zt − z0 ) 20            1                 2           3            4        ...
Water Bipolar Configuration in Aquaporins
Water Bipolar Configuration in Aquaporins
R E M E M B E R:One of the most useful advantages ofsimulations over experiments is that youcan modify the system as you w...
Electrostatic Stabilization of Water Bipolar Arrangement
Proton transfer through water                                  H+                               H+ H+ H    O   H   O      ...
Cl- channelK+ channel    Aquaporins
A Complex Electrostatic Interaction                                                                      SF               ...
A Repulsive Electrostatic Force at    the Center of the ChannelQM/MM MD of the behaviorof an excessive proton
Simulating Membrane Channels, E. Tajkhorshid, Part 2
Simulating Membrane Channels, E. Tajkhorshid, Part 2
Simulating Membrane Channels, E. Tajkhorshid, Part 2
Simulating Membrane Channels, E. Tajkhorshid, Part 2
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Simulating Membrane Channels, E. Tajkhorshid, Part 2

  1. 1. A Recipe for Membrane Protein Simulations•  Continue to constrain the protein (heavy atoms), but release everything else; minimize/simulate using a short “constant- pressure” MD (NPT) to “pack” lipids and water against the protein and fill the gaps introduced after removal of protein-overlapping lipids.•  Watch water molecules; They normally stay out of the hydrophobic cleft. If necessary apply constraints to prevent them from penetrating into the open cleft between the lipids and the protein.•  Monitor the volume of your simulation box until the steep phase of the volume change is complete (.xst and .xsc files). Do not run the system for too long during this phase (over-shrinking; sometimes difficult to judge).•  Now release the protein, minimize the whole system, and start another short NPT simulation of the whole system.•  Switch to an NPnAT or an NVT simulation, when the system reaches a stable volume. Using the new CHARMM force field, you can stay with NPT.
  2. 2. Lipid-Protein Packing During the Initial NpT Simulation
  3. 3. Adjustment of Membrane Thickness to the Protein Hydrophobic Surface
  4. 4. Glycerol-Saturated GlpF
  5. 5. Description of full conduction pathway
  6. 6. Complete description of the conduction pathwayConstriction region Selectivity filter
  7. 7. Channel Hydrogen Bonding Sites…{set frame 0}{frame < 100}{incr frame}{ animate goto $frame set donor [atomselect top “name O N and within 2 of (resname GCL and name HO)”] lappend [$donor get index] list1 set acceptor [atomselect top “resname GCL and name O and within 2 of (protein and name HN HO)”] lappend [$acceptor get index] list2}…
  8. 8. Channel Hydrogen Bonding SitesGLN 41 OE1 NE2 LEU 197 OTRP 48 O NE1 THR 198 OGLY 64 O GLY 199 OALA 65 O PHE 200 OHIS 66 O ND1 ALA 201 OLEU 67 O ASN 203 ND2ASN 68 ND2ASP 130 OD1 LYS 33 HZ1 HZ3GLY 133 O GLN 41 HE21SER 136 O TRP 48 HE1TYR 138 O HIS 66 HD1PRO 139 ON ASN 68 HD22ASN 140 OD1 ND2 TYR 138 HNHIS 142 ND1 ASN 140 HN HD21 HD22THR 167 OG1 HIS 142 HD1GLY 195 O GLY 199 HNPRO 196 O ASN 203 HN HD21HD22 ARG 206 HE HH21HH22
  9. 9. Channel Hydrogen Bonding SitesGLN 41 OE1 NE2 LEU 197 OTRP 48 O NE1 THR 198 OGLY 64 O GLY 199 OALA 65 O PHE 200 OHIS 66 O ND1 ALA 201 OLEU 67 O ASN 203 ND2ASN 68 ND2ASP 130 OD1 LYS 33 HZ1 HZ3GLY 133 O GLN 41 HE21SER 136 O TRP 48 HE1TYR 138 O HIS 66 HD1PRO 139 ON ASN 68 HD22ASN 140 OD1 ND2 TYR 138 HNHIS 142 ND1 ASN 140 HN HD21 HD22THR 167 OG1 HIS 142 HD1GLY 195 O GLY 199 HNPRO 196 O ASN 203 HN HD21HD22 ARG 206 HE HH21HH22
  10. 10. The Substrate Pathwayis formed by C=O groups
  11. 11. The Substrate Pathway is formed by C=O groupsNon-helical motifsare stabilized bytwo glutamateresidues.N E NPA E NPAR C
  12. 12. Conservation of Glutamate Residue in Human Aquaporins
  13. 13. Glycerol – water competition for hydrogen bonding sites
  14. 14. Revealing the Functional Role of Reentrant Loops Potassium channel
  15. 15. AqpZ vs. GlpF•  Both from E. coli•  AqpZ is a pure water channel•  GlpF is a glycerol channel•  We have high resolution structures for both channels
  16. 16. Steered Molecular Dynamics is anon-equilibrium method by nature •  A wide variety of events that are inaccessible to conventional molecular dynamics simulations can be probed. •  The system will be driven, however, away from equilibrium, resulting in problems in describing the energy landscape associated with the event of interest.Second law of thermodynamics W ≥ ΔG
  17. 17. Jarzynski’s Equality ΔG WTransition between two equilibrium states e-βWp(W) W ≥ ΔG T T λ = λ(t) λ = λi λ = λf work W heat Q p(W) ΔG = G f − Gi C. Jarzynski, Phys. Rev. Lett., 78, 2690 (1997) C. Jarzynski, Phys. Rev. E, 56, 5018 (1997) e − βW =e − βΔG β= 1 k BT In principle, it is possible to obtain free energy surfaces from repeated non- equilibrium experiments.
  18. 18. Steered Molecular Dynamicsconstant force constant velocity (250 pN) (30 Å/ns)
  19. 19. SMD Simulation of Glycerol PassageTrajectory of glycerol pulled by constant force
  20. 20. Constructing the Potential of Mean Force 4 trajectories v = 0.03, 0.015 Å/ps k = 150 pN/Åf (t ) = − k[ z (t ) − z0 − vt ] tW (t ) = ∫ dt ʹ′ vf (t ʹ′) 0
  21. 21. Features of the Potential of Mean Force •  Captures major features of the channel •  The largest barrier ≈ 7.3 kcal/mol; exp.: 9.6±1.5 kcal/molJensen et al., PNAS, 99:6731-6736, 2002.
  22. 22. Features of the Potential of Mean Force Cytoplasm Periplasm Asymmetric Profile in the VestibulesJensen et al., PNAS, 99:6731-6736, 2002.
  23. 23. Artificial induction of glycerol conduction through AqpZY. Wang, K. Schulten, and E. Tajkhorshid Structure 13, 1107 (2005)
  24. 24. Three fold higher barriers periplasm cytoplasm SF NPA AqpZ 22.8 kcal/mol GlpF 7.3 kcal/molY. Wang, K. Schulten, and E. Tajkhorshid Structure 13, 1107 (2005)
  25. 25. Could it be simply the size?Y. Wang, K. Schulten, and E. Tajkhorshid Structure 13, 1107 (2005)
  26. 26. It is probably just the size that matters!Y. Wang, K. Schulten, and E. Tajkhorshid Structure 13, 1107 (2005)
  27. 27. Water permeation 5 nanosecond Simulation 18 water conducted 7-8 water In 4 monomers in 4 ns molecules in each1.125 water/monomer/ns channel Exp. = ~ 1-2 /ns
  28. 28. Correlated Motion of Water in the Channel Water pair correlationThe single file ofwater molecules ismaintained.
  29. 29. Diffusion of Water in the channelOne dimensional diffusion: 2 Dt = ( zt − z0 ) 2Experimental value for AQP1: 0.4-0.8 e-5
  30. 30. Diffusion of Water in the channel 2 Dt = ( zt − z0 ) 20 1 2 3 4 Time (ns) Improvement of statistics
  31. 31. Water Bipolar Configuration in Aquaporins
  32. 32. Water Bipolar Configuration in Aquaporins
  33. 33. R E M E M B E R:One of the most useful advantages ofsimulations over experiments is that youcan modify the system as you wish: Youcan do modifications that are not evenpossible at all in reality!This is a powerful technique to testhypotheses developed during yoursimulations. Use it!
  34. 34. Electrostatic Stabilization of Water Bipolar Arrangement
  35. 35. Proton transfer through water H+ H+ H+ H O H O H O H+ H+ H H H H+ H+ O H O H O H H+ H+ H+ H H H H+ H O H O H O H+ H+ H+ H H H
  36. 36. Cl- channelK+ channel Aquaporins
  37. 37. A Complex Electrostatic Interaction SF NPA “Surprising and clearly not a hydrophobic channel”M. Jensen, E. Tajkhorshid, K. Schulten, Biophys. J. 85, 2884 (2003)
  38. 38. A Repulsive Electrostatic Force at the Center of the ChannelQM/MM MD of the behaviorof an excessive proton

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