Potential of mean force calculations of ion permeation in ion c

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Structure and function of transportersfrom
molecular dynamics simulationsSerdar
Kuyucak University of Sydney
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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!

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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)
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Schematic picture of B12 import
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First structure of sodium-potassium pump (Poul
Nissen et al. Dec. 2007)
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Glutamate transporters and neuronal communication
Neurons communicate via neurotransmitters such as
glutamate, aspartate, acetylcholine, ...
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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.
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A second structure of GltPh from Pyrococcus
horikoshii
Boudker, Ryan et al. 2007 Binding sites for Asp
and two Na ions are observed.
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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.

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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
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Opening of the extracellular gate HP2
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Binding sites for the two Na ions Asp
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Initial MD simulations of GltPh with 2 Na ions
and Asp

• In the crystal structure, Na1 is coordinated by
  D405 side chain (2 Os) 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.

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Movement of the D312 sidechain in MD simulations
Initially, D312 (O) is gt 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.
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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 isnt the Na3 site seen in the
  crystal structure?)

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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)
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Comparison of N310 side chain configs with MD
simulations
Na3 (closed structure) Na3 (open
structure) Crystal structure (dark shade), MD
simulations (light shade)
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Coordination of the Na2 site
Na2 (crystal structure) Na2 (MD
simulations) T308, S349, I350 , T352 T308
(bbsc), I350 , T352, H2O
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Residues involved in the coordination of
Na1 (Pair distribution functions for the NaO
distances)
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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
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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.

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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?

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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 3.0 0.2 3.0 0.2
HP1 S278 (N) a-O1 2.8 2.8 0.1 2.8 0.1 2.8 0.1
HP1 S278 (OH) a-O2 3.8 2.7 0.1 2.8 0.2 2.8 0.1
TM7 T314 (OH) b-O2 2.7 2.7 0.1 2.8 0.1 2.8 0.1
HP2 V355 (O) a-N 2.9 2.9 0.2 11.9 0.4 11.9 0.3
HP2 G359 (N) b-O2 2.8 3.1 0.2 6.1 0.4 6.3 0.3
TM8 D394(O1) a-N 2.6 2.7 0.1 2.7 0.1 2.7 0.1
TM8 R397(N1) b-O2 4.6 4.2 0.2 2.7 0.1 2.7 0.1
TM8 R397(N2) b-O1 2.5 2.9 0.2 2.9 0.2 2.9 0.2
TM8 T398(OH) a-N 3.2 3.2 0.2 3.0 0.2 3.0 0.2
TM8 N401(ND) a-O2 2.8 2.8 0.1 3.0 0.2 2.9 0.2
In the open state HP2 gate moves away from Asp
but it remains bound
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H-bond network that couples Na1 Asp
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(No Transcript)
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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.

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Absolute binding free energies from free energy
perturbation (FEP) or thermodynamic integration
(TI) The total binding free energy can be
expressed as The
various sigmas are the translational and
rotational rmsds of ligand The last term is the
interaction energy calculated from FEP or TI
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Free energy perturbation (FEP) Zwanzigs
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.
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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 lt 2 kT, otherwise the
method may lose its validity.
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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).
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Na binding energy in glutamate transporter with
FEP
Window DG(Na b.s.? bulk) 40 eq. 22.9 60
eq. 26.3 65 exp. 27.1
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Free energy change DG at each step of FEP
calculation
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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
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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.
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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 DGint DGtr DGb
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 DGint DGtr DGb
Na2 -7.1 4.4 -2.7
Na2 -1.7 4.4 2.7
(exp -3.3)
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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
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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.
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Asp binding energies (open structure)
Contribution DG (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

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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.

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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
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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)
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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.

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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
  dont 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.