# Presentation: 473876

## MD-PNP simulations of Alpha-Hemolysin open channel ion currents

- Ioana Cozmuta**, J. T. O’Keeffe*, D. Bose** and V. Stolc*
- *NASA Ames Research Center, **Eloret Corp.

## The alpha hemolysin ion channel

## ‘Natural’ function*

- ‘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

## Conductance*

- Conductance*

- * Biophysical Journal, 79, 4, 1967-1975, 2001

- 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

## 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

| polymer | speed | inhibition |
| --- | --- | --- |
| poly [rU] | ~1 s/nucl | 85-100% |
| poly [rA] | ~20 s/nucl | 85% |
| poly [rC] | ~3 s/nucl | 95% |

-  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

## An atomistic view of the channel

## Atomistic model

- **Force field: Cornell et al, 1995 –AMBER, http://www.scripps.edu/

| Coordinate | MIN | MAX | Length |
| --- | --- | --- | --- |
| X | -5.13 | 103.9 | 109 |
| Y | -17.27 | 84.93 | 102.2 |
| Z | -13.66 | 96.18 | 109.8 |

- 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, – psi,  angles (-180 to 180 deg)
- Topology file generated in Amber using the parm94 force field**

## Geometry

- C2

**C1****:** GLU(111) z=-11Å, R=7.4 Å      **acid**
-    turn  LYS(147) z=-11Å, R=6.1 Å     **basic**
-        MET(113) z=-19Å, R=6.4 Å   **hydrophobic**
-    turn  THR(145) z=-19Å, R=8.2 Å **hydrophilic**
**C2****:** LEU(135) z=-47Å, R=6.3 Å   ** ****hydrophobic**

- C1

## Amino Acids sequence

## Charged residues on the inner pore

## Slide 11

## The MD-PNP model

## Multi-scale modeling*

- * Goddard group, http://wag.caltech.edu/

## MD-PNP hybrid model

## MD simulations

## Benchmarking for NAMD

- Solvated protein: 175,364 atoms, cutoff 20Å, UC~130Å, t=2fs: 3.52days/ns **128 CPU**

- Benchmark system: 92,000 atoms, cutoff 12Å, UC~109Å, t= 1fs: 1.61days/ns **128 CPU**

- Actual system: 120,000 atoms, cutoff 20Å, t=2fs (MTS): 1.29 days/ns for **200 CPU**

- http://www.ks.uiuc.edu/Research/namd/

## SPC/E water model

** ****SPC/E model: q(O)=-0.8476e, q(H)=0.4238e**

| Water | RDF
g(OO) | RDF
Peak(Å) | Ep
kcal/mol | D
10-9 m2/s | 
g/cc |
| --- | --- | --- | --- | --- | --- |
| SPM model | 3 | 3 | -9.89 | 2.8 | 0.998 |
| experiments | 2.5 | 3 | -9.9 | 2.4 | 0.995 |

## 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**

| KCl | DSPM
10-9 m2/s | DK+
10-9 m2/s | DCl-
10-9 m2/s |
| --- | --- | --- | --- |
| 400 pairs | 2.7 | 1.8 | 1.5 |
| experiments | 2.5 | 1.83±0.05 | 1.8-2.9 |

**K****+**** Van der Waals parameters (Aquist):**
**R* = 2.658****Å; ********= 0.000328**
******G = -80.9kcal/mol; **

**Cl****-**** Van der Waals parameters (Smith&Dang):**
**R* = 2.47****Å; ********=0.01;**
**D(mutual) = 2.9*10****-9****m****2****/s**
**D(******** dilution) = 1.8*10****-9****m****2****/s**

## 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**

## Checking the energy and density

## Diffusion coefficients

## KCl solution inside the pore

- V=125 mV; Lz = 100 Å; 1 e-=1.6·10-19 C; 1Å = 10-10 m;
- E = 0.0288 kcal/mol/Å /e-;

## Slide 23

## 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**

## K+ diffusion coefficients

| K+ selection | D (10-9 m2/s) |
| --- | --- |
| Cap | 0.43 |
| Stem | 0.22 |
| Pore | 0.38 |
| All K+ | 1.95 |
| All K+ no pore | 2.01 |

- K+ diffusion coefficients

## Cl- diffusion coefficients

| Cl- selection | D (10-9 m2/s) |
| --- | --- |
| Cap | 0.45 |
| Stem | 0.18 |
| Pore | 0.31 |
| All Cl- | 1.75 |
| All Cl- no pore | 1.81 |

- Cl- diffusion coefficients

## Pore volume

- CONNOLY CALCULATIONS
**PORE:**
- Rp=1Å 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
- n~69 ions
- 1M = N moles solute/1L solution
- =NA molecules/1027 Å3 =6.023E-4 molec/ Å3

## Binding energies

## Binding energies in the pore

| Pore | E_best (kcal/mol) |
| --- | --- |
| +water | -15.7 |
| +Cl- | -9.0 |
| + K+ | -39.4 |

## PNP simulations

## 2-D Poisson Nerst Plank (PNP)

- Schematic representation of -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.

**Notes:**
We apply constant voltage boundary conditions at the grid edge, corresponding to the external electrodes. 
The ion concentration is held at the bulk 1Mol value in the ion baths. Outside the pore the concentrations fall to the bulk value over the debye length scale. It is necessary to extend the grid several debye lengths from the pore ends to meet the bulk value 1Mol boundary conditions.

## Electrostatic potential maps

- (**no fixed charges**)

- Pore constrictions, transmembrane voltage and fixed charges

## Study at 120mV

| Case | D
(10-9 m2/s) |  | I
(pA) |  |  | Flux
(108 ions/s) |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| V=120mV, R_cylinder = 8.75Å | K+ | Cl- | total | K+ | Cl- | K+ | Cl- |
| Pore geometry | 0.38 | 0.31 | 132.9 | 73.2 | 59.7 | 4.57 | 3.73 |
| Pore geometry + 
2 constrictions 
R_min = 5.75 Å | 0.38 | 0.31 | 95.2 | 52.4 | 42.8 | 3.27 | 2.67 |
| Pore geometry + 2 constrictions + fixed charges | 0.38
 | 0.31
 | 115.5
 | 55.8 | 59.8 | 3.48 | 3.73 |

| V=-120mV (reverse) |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| Pore geometry + 2 constrictions + fixed charges | 0.38 | 0.31 | -72 | -38.6 | -44.4 | 2.41 | 2.77 |

## Channel selectivity

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

- Experimental values:
- 1M KCl, 120mV G~1nS;
- 0.5M t(K+)/t(Cl-) ~ 1.5

- Anion selective

## Open Channel Ion Current

**MD-PNP calculations**

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

**Notes:**
The point here is that the fixed charges are very important for determining the open channel current

## CONCLUSIONS

- The MD calculations show that both K+ and Cl- ions are transported through the -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+) > D(Cl-) while in the pore-cap D(K+) < 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

## ACKNOWLEDGEMENTS

- MD simulations with **NAMD** **(http://www.ks.uiuc.edu/Research/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.

## 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) = 8pi**2{1/3[U(1,1) + U(2,2) + U(3,3)]}

## 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

## ‘Ingredients’ for the MD modeling

- Force field: Cornell et al, 1995 –AMBER, http://www.scripps.edu/
- Multi-CPU scalable MD software: **NAMD*, **http://www.ks.uiuc.edu/

- 1M KCl

- The -hemolysin pore

## 1K at z=35Å (trans)

**DIFFUSION**

**Interaction energy K+-protein**
**Electrostatic ~ 15 kcal/mol**
**VdWaals ~ -0.02 kcal/mol**

## 1K at z=90Å (cis)

**DIFFUSION**

**Interaction energy K+-protein**
**Electrostatic ~ -2 kcal/mol**
**VdWaals ~ -0.01 kcal/mol**

## 1K along channel axis

**Diffusion**