APBSmem: a graphical interface for electrostatic calculations at the membrane

Abstract

Electrostatic forces are one of the primary determinants of molecular interactions. They help guide the folding of proteins, increase the binding of one protein to another and facilitate protein-DNA and protein-ligand binding. A popular method for computing the electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation, and there are several easy-to-use software packages available that solve the PB equation for soluble proteins. Here we present a freely available program, called APBSmem, for carrying out these calculations in the presence of a membrane. The Adaptive Poisson-Boltzmann Solver (APBS) is used as a back-end for solving the PB equation, and a Java-based graphical user interface (GUI) coordinates a set of routines that introduce the influence of the membrane, determine its placement relative to the protein, and set the membrane potential. The software Jmol is embedded in the GUI to visualize the protein inserted in the membrane before the calculation and the electrostatic potential after completing the computation. We expect that the ease with which the GUI allows one to carry out these calculations will make this software a useful resource for experimenters and computational researchers alike. Three examples of membrane protein electrostatic calculations are carried out to illustrate how to use APBSmem and to highlight the different quantities of interest that can be calculated.

Figure 1. A screenshot of the user interface.

Parameters pertaining to the calculation are entered in the field on the left, and the molecule and membrane can be viewed in the embedded Jmol viewer on the right. Pictured here is the membrane-embedded single transmembrane helix used for the calculations in CASE I.

Figure 2. Convergence properties of test cases I–III.

We computed the absolute value of the percent error, , for each test case using a number of different discretization values. All energies are reported with respect to the solution value at the finest level of discretization, , which was 0.312 Å in test Case I and 0.375 Å in Cases II and III. Values along the x-axis are spaced using a log base 2 scale. In all graphs, the number of grid points used to achieve the grid spacing on the x-axis was 17, 33, 65, 97, 129, and 161 (). (A) Convergence of the protein solvation energy, Case I. A grid spacing of 0.512 Å gives a solution 1.5% of the highest resolution value. The energy values smoothly converge as the resolution increases. (B) Convergence of the ion solvation energy, Case II. The error monotonically decreases as the level of discretization increases. At  = 0.625 Å the energy value is within 2.5% of the final value. (C) Convergence of the gating charge energy in the closed state, Case III. Rather than report the gating charge, here we plot the energy of the closed state. This method converges much more quickly than the other Cases since it does not involve Born Self energy terms. The energy at the second finest level is 0.33% of the value at the finest level. Even at a grid spacing of  = 0.938 Å the computed energy is within 3% of the best value. In all cases, the convergence properties and the accuracy of the solutions depend critically on the refinement of the protein surface boundaries. Here we use the spl2 method for charge mapping in APBS, which gives very desirable convergence properties.

Figure 3. Top view of the KcsA channel (green) and the  = 2.01 isocontour highlighting the membrane interface (gray).

The K ion in the center of the channel is shown in blue. (A) When the membrane is not excluded from the channel pore, we observe that membrane is added to the pore region. (B) With the exclusion radii set too high at 28 Å, there are large gaps of water between the outer membrane and the protein. (C) The channel should be clear of membrane and the membrane should fit snugly around the outside of the protein as shown here. Membrane exclusion radii are 24 Å and 16 Å at the top and bottom of the channel, respectively.

Figure 4. A cartoon representation of the distinct dielectric environments in each calculation.

The orange regions represent protein, the gray membrane, and all white areas indicate water. The inner solution space at the bottom is assigned a voltage of , and correspondingly an effective charge density is assigned and a value of one for the variable . The water in the center of the channel is assigned values for and that correspond to the outer solution space. The lower value of the membrane (dashed line) separates the inner and outer solution spaces. In the gray region, and are set to 0 and , respectively, to mimic the membrane.

Figure 5. States used to compute protein solvation energies.

(A) The helix (orange) is pictured embedded in the membrane, which is delineated by the upper blue and lower gray lines. The membrane core between the two red lines is assigned a dielectric value  = 2. A headgroup region of 8 Å is indicated between the water and membrane core. Bulk water above and below the membrane is assigned a dielectric value of  = 80. (B) The helix in the bulk water ( = 80) in the absence of the membrane. The helix carries one charged residue (Arg14) shown in green in (A) and (B). The protein solvation energy is calculated by computing the total electrostatic energy of systems A and B and then calculating the quantity: . Images rendered with VMD .

Figure 6. States used to compute ion solvation energies.

(A) KcsA ion channel (orange) embedded in a slab of low-dielectric material (gray) with two ions in the selectivity filter (blue) and a single ion in the water filled cavity (red). For clarity only two subunits are shown. (B) Set up in panel A without the cavity ion. (C) The cavity ion in bulk water in the absence of KcsA and the membrane. The ion solvation energy is calculated by computing the total electrostatic energy of each system in A, B and C and then calculating the quantity: .

Figure 7. Hypothetical gating motion involving movement of N-terminal helix (green) out of the pore and into the outer bath.

(A) mVDAC1 x-ray structure (PDB ID 3EMN) embedded in a slab of low-dielectric material (gray). (B) Hypothetical closed state structure embedded in the membrane. In (A) and (B), the potential at the outer bath is held at 0 mV and the potential at inner bath is varied from −50 mV to +50 mV.