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Poisson–Boltzmann profile for an ion channel

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Practical: Poisson–Boltzmann profile for an ion channel

In this practical, we will take the transmembrane domain of an ion channel, the nicotinic acetylcholine receptor, and perform a Poisson–Boltzmann profile along its pore, to see what electrostatic environment a cation encounters when it passes through the pore.

The theory is explained in this presentation: Electrostatics and pKa calculations. For more tutorials about APBS, see the APBS wiki and the CCPB workshop tutorials there. For pKa calculations (not covered here), see Jens Nielsen’s pKa tutorial.

This practical is designed as a group activity with several computers in a GNU/Linux environment. However, it is possible to carry it out as an individual exercise, and the software required may also be available on other operating systems and computing platforms.

Understanding the structure

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Molecular model of a nicotinic acetylcholine receptor.

Download the entry 1OED (transmembrane domain of the nicotinic acetylcholine receptor) from the Protein Data Bank and save it as a file 1OED.pdb. Using a molecular visualization tool such as VMD, look at the structural model contained therein. Convince yourself of the following structural features:

  • There are five monomers, forming a pentamer with a central pore.
  • The pore goes along the z-axis, and has the coordinates of (65 Å, 65 Å, z), where z is something between 30 Å and 120 Å.

For this, try identifying some of the atoms around the pore-forming helices by going into the graphics window, press 0, and clicking on the atoms. In the VMD console window their coordinates should show. To rigorously identify a point in the pore, pick one corresponding atom in each helix and take the average of the coordinates.

Parallel processing: pick your sample point

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A précis of the theory.

Dividing up the work amongst the group, make sure each of the suggested points will be sampled. One can also try to increase the resolution of sampling by inserting more points inbetween, or extend out into the bulk solvent.

Suggested sample points (in ångström): 

65.000  65.000  30.000
65.000  65.000  40.000
65.000  65.000  50.000
65.000  65.000  60.000
65.000  65.000  70.000
65.000  65.000  80.000
65.000  65.000  90.000
65.000  65.000 100.000
65.000  65.000 110.000
65.000  65.000 120.000

Now each of us has some work to do. Each of us will calculate at a sample point, doing three calculations: protein-only, ion-only (at the point), and the protein–ion complex (with the ion at the point).

Add charge and radius information to the protein

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Using one of the PDB2PQR web servers, add charge and radius information to the PDB entry 1OED. It will take a while for the web server to generate the results: be patient and pay attention to the informative messages. (Alternatively, install PDB2PQR locally and use that.) This should give you the file 1OED.pqr. The suffix ‘pqr’ stands for ‘protein coordinates, charge, and radius’. If you look at the file, you will notice two extra columns after the coordinates, one with the (partial) charges of the atoms, and the next with the radii.

Preparing the ion

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Make a file called ion.pqr and put one line in it, something like: 

ATOM  20000  Na+ ION 10000      65.000  65.000  65.000 +1.00   1.6800

This is a very small ‘pqr’ file containing only one line, describing the sodium ion at the specified coordinates. The spacing of the line matters a little bit, so please copy-and-paste into the file rather than retyping it. On the other hand, the parser in APBS is resaonably tolerant, so don’t worry too much.... Change this coordinate to that of the sample point you were assigned to calculate at. Make sure the columns conform to that in the other ‘pqr’ file containing the protein.

Preparing the protein–ion complex

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Now we prepare the ‘pqr’ file for the protein–ion complex. To do this, run the following command in your Linux terminal: 

cat 1OED.pqr ion.pqr > complex.pqr

(cat for ‘concatenate’). This concatenates the files for the protein and the ion, giving that for the protein–ion complex. Check the resulting file complex.pqr. Remove any stray blank lines.

Input file for APBS

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Look at the following content of an input file for the APBS program. Create a file with such content and name it nAChR.in. 

    read
         mol pqr 1OED.pqr
         mol pqr ion.pqr
         mol pqr complex.pqr
    end
    elec name protein
         mg-auto
         mol 1
         dime 97 97 97
         cglen 100.000000 100.000000 105.000000
         fglen 10 10 10    
         cgcent mol 3
         fgcent mol 2
         # NaCl ionic strength in mol/l
         ion  1 0.15 0.95 # sodium ions
         ion -1 0.15 1.81 # chloride ions

         lpbe
         bcfl mdh
         pdie 2.0 # protein and faux-lipid
         sdie 78.5 # Eisenberg and Crothers Phys. Chem. book 1979
         srfm smol
         chgm spl2
         srad 1.4
         swin 0.3
         sdens 10.0
         temp 300
         # gamma 0.105 # Uncomment for old versions of APBS -- deprecated for APBS 1.0.0
         calcenergy total
         calcforce no
    end
    elec name ion
         mg-auto
         mol 2
         dime 97 97 97
         cglen 100.000000 100.000000 105.000000
         fglen 10 10 10    
         cgcent mol 3
         fgcent mol 2
         # NaCl ionic strength in mol/l
         ion  1 0.15 0.95 # sodium ions
         ion -1 0.15 1.81 # chloride ions

         lpbe
         bcfl mdh
         pdie 2.0 # protein and faux-lipid
         sdie 78.5 # Eisenberg and Crothers Phys. Chem. book 1979
         srfm smol
         chgm spl2
         srad 1.4
         swin 0.3
         sdens 10.0
         temp 300
         # gamma 0.105 # Uncomment for old versions of APBS -- deprecated for APBS 1.0.0
         calcenergy total
         calcforce no
    end
    elec name cpx
         mg-auto
         mol 3
         dime 97 97 97
         cglen 100.000000 100.000000 105.000000
         fglen 10 10 10    
         cgcent mol 3
         fgcent mol 2
         # NaCl ionic strength in mol/l
         ion  1 0.15 0.95 # sodium ions
         ion -1 0.15 1.81 # chloride ions

         lpbe
         bcfl mdh
         pdie 2.0 # protein and faux-lipid
         sdie 78.5 # Eisenberg and Crothers Phys. Chem. book 1979
         srfm smol
         chgm spl2
         srad 1.4
         swin 0.3
         sdens 10.0
         temp 300
         # gamma 0.105 # Uncomment for old versions of APBS -- deprecated for APBS 1.0.0
         calcenergy total
         calcforce no
    end

    print energy cpx - ion - protein end
    quit

Notice that there are several sections:

The first, flanked by read and end, reads in the three ‘pqr’ files we have just prepared.

Then there are three sections flanked by elec and end, looking much the same, but the mol statement reads in a different molecule each time. The detailed description of the parameters can be found in the APBS user guide. Can you find where the grid dimensions and lengths are specified? The mobile ion concentrations? The dielectric coefficients?

Finally, we calculate the energy changes in the print statement (ΔEPB = Ecomplex − Eion − Eprotein), and quit.

Calculation and analysis

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The resulting Poisson–Boltzmann energy profiles for a sodium ion (under various ionic strengths) and a chloride ion upon encountering the nAChR pore, sampling every 5 Å.

To run APBS, do 

apbs --output-file=nAChR.out nAChR.in

This writes out our results to a file called nAChR.out so we can refer to it later. This calculation took about 20 min on my Intel® Xeon™ 1.7 GHz computer.

Look into the output file nAChR.out. Towards the bottom, you will see something like: 

print energy 3 - 2 - 1
    localEnergy 2.158304339453E+01 kJ/mol
    globalEnergy 2.158304339453E+01 kJ/mol

Take a note of this energy value for your sample point.

Using a piece of grid paper, plot the Poisson–Boltzmann electrostatic energy profile along the pore (z-axis).

Programs required

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References

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If you use this method in your scientific publication, please consider citing at least these three papers:

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