OverviewThis example will examine the differing polar solvation free energies of an alpha helix as it translates through a lowdielectric slab, a model membranelike environment. The low dielectric slab is intended to crudely represent the nonpolar membrane environment. Note that the peptide used in this example is largely nonpolar (glycine, alanine, and leucine) with a centrallylocated arginine.
The starting configuration of this example has the peptide nearly completely buried in the membrane environment:
The helix (arginine in blue, nonpolar residues in white, glycine in green) in the membrane environment (gray planes)
The final configuration of this example has the peptide significantly exposed to solvent:
The helix (arginine in blue, nonpolar residues in white, glycine in green) in the membrane environment (gray planes)
This example will use APBS to solve the Poisson equation for these different configurations to determine the polar solvation energy. The resulting polar solvation energy profile (as a function of helix position) is called a "potential of mean force" for the solvation of this helix through this low dielectric slab membrane mimic.
Software requirementsIn addition to APBS, you will also need the draw_membrane2 program written by Michael Grabe. The source code for this program is attached below and can be compiled very easily by
gcc draw_membrane2.c lm o draw_membrane2 to create an executable named
draw_membrane2 . Note that gcc is used only for illustration purposes; most C compilers should work.The basic stepsWe will illustrate the basic steps of the polar solvation calculation with the peptide in its membraneimmersed started configuration. The PQR file for this starting configuration is attached below as
Membranehelix0.pqr .Generating the peptide dielectric mapThe system will have three dielectric regions:
and two regions of ionaccessibility:
We will model these regions in APBS using OpenDXformat coefficient maps read into APBS through a READ statement.
The first step in such modeling is to construct the ionaccessibility and dielectric maps for the isolated peptide in the absence of the membrane environment. This can be accomplished through APBS mgdummy calculations. These calculations simply construct the coefficient input maps and write them out in the desired format without performing any numerical solutions of the PoissonBoltzmann equation.
In the latter steps of this example, we'll be calculating solvation energies using sequential focusing to solve the PoissonBoltzmann equation. We'll need three sets of maps for the focusing procedure:
All of these maps will have 97 × 97 × 97 grid points. This coarse grid resolution is necessary for a relatively quick example; however, it is not recommended for calculations where quantitative accuracy is desired. The APBS mgdummy input file for these calculations is available for download below (
Apbs_dummy.in ). Run APBS with this input file to generate the following dielectric maps:
Adding the membrane environmentThe next step is to incorporate the membrane environment through the draw_membrane2 program described above. This program is invoked separately for the small, medium and large systems as follows:
./draw_membrane2 dielx_S.dx zmem Lmem pdie 0.0 I R_top R_bottom ./draw_membrane2 dielx_M.dx zmem Lmem pdie 0.0 I R_top R_bottom ./draw_membrane2 dielx_L.dx zmem Lmem pdie 0.0 I R_top R_bottom and assumes a common naming scheme for all dielectric, kappa, and charge maps. It also assumes that the membrane is oriented such that its plane is in the xyplane and the bilayer normal is aligned along the zaxis. Finally, it sets the solvent dielectric to 80.0 and the membrane dielectric to 2.0. The parameters for this program are
For the current example, we will invoke the
draw_membrane2 program as ./draw_membrane2 dielx_S.dx 20 40 10.0 0.0 0.1 0.0 0.0 ./draw_membrane2 dielx_M.dx 20 40 10.0 0.0 0.1 0.0 0.0 ./draw_membrane2 dielx_L.dx 20 40 10.0 0.0 0.1 0.0 0.0 This will produce a number of
*m.dx files (e.g., dielx_Lm.dx ) that are the modified coefficient maps incorporating the membrane environment.Performing the electrostatic calculationFinally, we will use these input coefficient maps in an APBS calculation to solve the linearized PoissonBoltzmann equation using sequential focusing. The APBS input file available for download below (
Apbssolv.in ) performs six calculations:
The difference between the finest "solvated" calculation and the finest "reference" calculation is an estimate of the polar solvation energy associated with transferring the peptide from solution into the membrane.
Visualizing the resultThe result of these electrostatic potential calculations can be visualized with VMD as described elsewhere in this documentation. Perhaps one of the most interesting VMD features to use with this example is the FieldLines representation of the electrostatic potential which demonstrates how the dielectric interface between the membrane and bulk solution significantly perturbs the electrostatic field:
An argininecontaining alpha helix in a low dielectric (membrane) slab. The gray surfaces represent the surface of the membrane. The blue and red surfaces are +1 and 1 kT/e electrostatic isocontours, respectively. The lines show the direction of the electric field in the system.
This image was generated using VMD 1.8.6. The membrane was represented as an isocontour of the
dielx_Sm.dx map with a value of 72. The field lines were colored by potential values from pot_S.dx and displayed with a GradientMag value of 1.61, a minimum length of 7.24, and a maximum length of 50.00. Finally, the isocontours were displayed from the pot_S.dx file with values of +1 kT/e (blue) and 1 kT/e (red).The steps above should be repeated for every structure in the potential of mean force (attached below):
and doing so demonstrates an interesting trend in solvation energies:
What causes the shape of this curve?
Automating the PMF calculationRepeating the above calculations by hand can be very tedious; the bash script available below (
Run_membranehelix.sh ) was designed to simplify the process. Note that, in addition to the software described above, this script requires:
You will also need to modify the bash script to specify the correct locations of your APBS and
draw_membrane2 executables.Caveats and commentsAs mentioned above, this calculation was performed using a grid with 97 × 97 × 97 points for the sake of efficiency. However, this is almost certainly too coarse for quantitative work. For real applications, one should increase the number of grid points until the desired observable (e.g., solvation energy) stops changing with increasing grid points.
Additionally, this calculation in no way represents a real membrane. Instead, it is a model of the low dielectric environment commonly assumed for membrane systems. Of course, real membranes deform, include some water permeation, form defects of large and small scale, and have very inhomogeneous dielectric properties. Additionally, real peptides can also deform and rearrange sidechains to maximize solvent exposure of polar or charged groups.
