Brownian Dynamics

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MD-PNP simulations of Alpha-Hemolysin open
channel ion currents
Ioana Cozmuta, J. T. OKeeffe, D. Bose and
V. Stolc NASA Ames Research Center, Eloret
Corp.
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The alpha hemolysin ion channel
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Natural function

• Alpha hemolysin is a toxin produced by
  Staphylococcus aureus bacteria
• It spontaneously self-assembles into a water
  soluble ionic channel with a molecular weight of
  33.2 k-Dalton and a length of 10nm
• The channel contains 2051 AA residues organized
  in 7 sequence-identical chains (symmetry group
  C121)
• The channel is strongly surface active and it
  inserts into pre-formed lipid membranes, damaging
  the membrane properties
• Extra cellular Ca2 or other divalent cations
  prevent cell damage by closing the channel

Menestrina, G, The Journal of Membrane Biology,
90, 177-190, 1986
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Conductance

• measured in voltage-clamp experiments
• Asymmetric I-V characteristic over linear
  increase in the first quadrant and sub linear in
  the third.
• Linear relationship between the channel
  conductance and the conductivity (molarity) of
  the electrolyte solution at a constant clamp
  voltage.
• The channel is slightly anion- selective at pH 7.0

Biophysical Journal, 79, 4, 1967-1975, 2001
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A bio-engineering application

• Alpha hemolysin channel in 1.0 M KCl solution
  with an external applied voltage of 125 mV leads
  to an ionic current of 120 pA (channel
  conductance 1nS)
• ss-DNA or RNA molecules driven by an electric
  field through the ion channel generate a
  transient decrease of ionic current

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An atomistic view of the channel
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Atomistic model

• pdb file from the protein data bank
  http//www.rcsb.org/pdb/
• Structure resolved via X-ray diffraction 1.6 Å
  at 287K and a pH of 6
• Ramachandran plot backbone phi, F psi, Y
  angles (-180 to 180 deg)
• Topology file generated in Amber using the parm94
  force field

Song, L., Hobaugh, M. R., Shustak, C., Cheley,
S., Bayley, H., Gouaux, J. E., Structure of
staphylococcal alpha-hemolysin, a heptameric
transmembrane pore, Science 274 pp. 1859
(1996) Force field Cornell et al, 1995 AMBER,
http//www.scripps.edu/
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Geometry
C1 GLU(111) z-11Å, R7.4 Å acid turn
LYS(147) z-11Å, R6.1 Å basic
MET(113) z-19Å, R6.4 Å hydrophobic turn
THR(145) z-19Å, R8.2 Å hydrophilic C2 LEU(135)
z-47Å, R6.3 Å hydrophobic
C2
C1
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Amino Acids sequence
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Charged residues on the inner pore
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The MD-PNP model
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Multi-scale modeling
Goddard group, http//wag.caltech.edu/
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MD-PNP hybrid model
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MD simulations
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Benchmarking for NAMD
http//www.ks.uiuc.edu/Research/namd/
Solvated protein 175,364 atoms, cutoff 20Å,
UC130Å, Dt2fs 3.52days/ns 128 CPU
Benchmark system 92,000 atoms, cutoff 12Å,
UC109Å, Dt 1fs 1.61days/ns 128 CPU
Actual system 120,000 atoms, cutoff 20Å, Dt2fs
(MTS) 1.29 days/ns for 200 CPU
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SPC/E water model

• SPC/E model q(O)-0.8476e, q(H)0.4238e

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Ionic solution, 1MKCl

• crystal structure arrangement of atoms (NaCl)
• selected number to correspond to 1M solution
  (1KCl pair for 55 water molecules)
• box with 400 KCl pairs

• K Van der Waals parameters (Aquist)
• R 2.658Å e 0.000328
• DG -80.9kcal/mol

• Cl- Van der Waals parameters (SmithDang)
• R 2.47Å e0.01
• D(mutual) 2.910-9m2/s
• D(? dilution) 1.810-9m2/s

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MD procedure

• minimization for 5000 steps
• heating to 300K in steps of 50K
• NPT equilibration of solution for 400ps (time
  step 2fs)
• dynamics for 1ns using MTS-NVE
• Pure diffusion
• External applied electric field

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Checking the energy and density
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Diffusion coefficients
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KCl solution inside the pore
V125 mV Lz 100 Å 1 e-1.610-19 C 1Å
10-10 m E 0.0288 kcal/mol/Å /e-
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1K at z 60Å (center)
DIFFUSION
EEL 40 kcal/mol VdW -0.03 kcal/mol
EEL 15 kcal/mol VdW -0.02 kcal/mol
EEL -2 kcal/mol VdW -0.01 kcal/mol
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K diffusion coefficients
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Cl- diffusion coefficients
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Pore volume
CONNOLY CALCULATIONS PORE Rp1Å V1 97199.9
1186.3 Å3 Rp 1.4Å V1.4 98508.6 738.7 Å3 Rp
25Å V25 212437.4 2466.8 Å3 Vpore 114583
2835 Å3 n69 ions 1M N moles solute/1L
solution NA molecules/1027 Å3 6.023E-4 molec/
Å3
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Binding energies
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Binding energies in the pore
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PNP simulations
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2-D Poisson Nerst Plank (PNP)
Schematic representation of a-hemolysin channel.
In the PNP model a 2D grid (represented as
concentric rings) corresponding to a cylindrical
polar coordinate system (radial and axial) is
applied over the pore stem.
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Electrostatic potential maps
Pore constrictions and transmembrane voltage (no
fixed charges)
Pore constrictions, transmembrane voltage and
fixed charges
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Study at 120mV
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Channel selectivity
Anion selective
Experimental values 1M KCl, 120mV? G1nS 0.5M
t(K)/t(Cl-) 1.5
Menestrina, G, The Journal of Membrane Biology,
90, 177-190, 1986
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Open Channel Ion Current
MD-PNP calculations
Menestrina, G, The Journal of Membrane Biology,
90, 177-190, 1986
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CONCLUSIONS

• The MD calculations show that both K and Cl-
  ions are transported through the a-hemolysin
  channel
• The ions diffusion coefficient inside the pore is
  reduced by a factor of 5 for K and 6 for Cl-
  compared to pure solution.
• Overall (in solution and in the pore) D(K) gt
  D(Cl-) while in the pore-cap D(K) lt D(Cl-)
• Binding sites for K occur at the two ends of the
  pore (cis and trans) while for Cl- the best
  binding sites are located at the stem-cap
  connecting region
• There is a greater binding potential and also
  more binding sites for K than Cl-
• 2D-PNP model prediction show that
• I-V behavior is consistent with observed
  experimental profiles over-linear for positive
  voltages and sub-linear for negative voltages
• A smooth cylinder would have a larger conductance
  that is reduced by the presence of the two
  constrictions
• The polar walls of the pore increase the current
• Channel is slightly anion (Cl-) selective

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ACKNOWLEDGEMENTS

• MD simulations with NAMD (http//www.ks.uiuc.edu/R
  esearch/namd)
• Movies and analysis generated with VMD
  (http//www.ks.uiuc.edu/Research/vmd)
• Amber, VMD, NAMD lists, GRID (Molecular Inc)
• NAS support group (http//www.nas.nasa.gov)
• System administrators of the Nanotechnology
  Division Aldo Foot, Marcy Shull

VMD/NAMD - developed by the Theoretical and
Computational Biophysics Group in the Beckman
Institute for Advanced Science and Technology at
the University of Illinois at Urbana-Champaign.
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The temperature factor(B- or Debye-Waller factor)

• the molecular motions in the simulation (thermal
  vibrations) can be related to crystallographic Bi
  factors (calculated from X-ray scattering)
• Bi is the temperature factor of atom i
• Ui is the mean square displacement of atom i
• The pore stem and the pore inside are the
  dynamically active parts

B(eq) 8pi21/3U(1,1) U(2,2) U(3,3)
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Hydrophobicity map

• Alternating layers with high (blue) and
  respectively low (red) hydrophobicity
• Hydrophobicity influences the ongoing dynamics
  hydrophylic residues will form more HB with water
  thus the local friction coefficient will be
  larger

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Ingredients for the MD modeling
The a-hemolysin pore
1M KCl
Force field Cornell et al, 1995 AMBER,
http//www.scripps.edu/ Multi-CPU scalable MD
software NAMD, http//www.ks.uiuc.edu/
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1K at z35Å (trans)
DIFFUSION
Interaction energy K-protein Electrostatic 15
kcal/mol VdWaals -0.02 kcal/mol
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1K at z90Å (cis)
DIFFUSION
Interaction energy K-protein Electrostatic -2
kcal/mol VdWaals -0.01 kcal/mol
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1K along channel axis
Diffusion