Electrostatics of nanosystems: application to microtubules and the ribosome

Abstract

Evaluation of the electrostatic properties of biomolecules has become a standard practice in molecular biophysics. Foremost among the models used to elucidate the electrostatic potential is the Poisson-Boltzmann equation; however, existing methods for solving this equation have limited the scope of accurate electrostatic calculations to relatively small biomolecular systems. Here we present the application of numerical methods to enable the trivially parallel solution of the Poisson-Boltzmann equation for supramolecular structures that are orders of magnitude larger in size. As a demonstration of this methodology, electrostatic potentials have been calculated for large microtubule and ribosome structures. The results point to the likely role of electrostatics in a variety of activities of these structures.

Figure 1

Parallel focusing subdomains for four processors on simple two-dimensional mesh. Parallel computations occur on subset (hashed areas) of global mesh. Each processor performs calculations over a domain (colored hashed patterns) that combines a unique partition (inside heavy, black lines) with an overlap region (between heavy black lines and dashed lines).

Figure 2

Scaling of the parallel focusing algorithm to solve the LPBE for the microtubule (black line), 50S ribosome subunit (green line), and 30S ribosome subunit (red line) systems on the NPACI IBM Blue Horizon supercomputer. As discussed in the text, the inverse element volume (a measure of the mesh resolution) is a linear function of the number of processors, v(P)⁻¹ = (h_xhyhz)⁻¹ = cP, where c = 0.011, 0.043, and 0.032 Å⁻³/processor for the microtubule, 30S, and 50S systems, respectively.

Figure 3

Electrostatic properties of the microtubule exterior. Potential isocontours are shown at +1 kT/e (blue) and −1 kT/e (red) and obtained by solution of the LPBE at 150 mM ionic strength with a solute dielectric of 2 and a solvent dielectric of 78.5. (a) Exterior view of entire microtubule with − end (α tubulin monomer exposed) forward. (b) View of − end. (c) View of + end of microtubule (β tubulin monomer exposed).

Figure 4

Electrostatic properties of microtubule interior. Cross-section view with − end to the left and tubulin dimer outlined by green box. (a) View of microtubule molecular surface with regions implicated in vinblastine, colchicine, and taxol binding shown in red. (b) Same view of microtubule with electrostatic potential isocontours at +1 kT/e (blue) and −1 kT/e (red). Potential calculated as in Fig. 3.

Figure 5

Electrostatic properties of the 30S ribosomal subunit. Potential obtained by solution of the LPBE at 150 mM ionic strength with a solute dielectric of 2 and a solvent dielectric of 78.5 by using the 30S structure from the 1FJG Protein Data Bank entry (29, 34). (a) Front view (face that contacts the 50S subunit) of the 30S backbone with protein shown in gold; nucleic acids shown in silver. Selected components of the A-site (16S residues 525–535, 955–965, 1055–1060, 1490–1493; S12 residues 45–49) are shown in red, components of the P-site (16S residues 789–791, 925–927, 965–967, 1229–1230, 1338–1341, 1399–1403, 1497–1499; S9 residues 124–128; S13 residues 122–126) are shown in blue, and components of the E-site (16S residues 691–695, 792–797; S7 residues 80–90, 150–170; S11 residues 45–60) are shown in green. (b) Front view of the electrostatic potential mapped on the 30S molecular surface; a blue color indicates regions of positive potential (> +2.6 kT/e) whereas red depicts negative potential (< −2.6 kT/e) values. (c) Back view (opposite the 50S-binding face) of the 30S backbone. (d) Back view of the electrostatic potential mapped on the 30S molecular surface.

Figure 6

Electrostatic properties of the 50S ribosomal subunit. Potential obtained by solution of the LPBE at 150 mM ionic strength with a solute dielectric of 2 and a solvent dielectric of 78.5 by using the 50S structure from the 1FFK Protein Data Bank entry (27). (a) Front view (face that contacts the 30S subunit) of the 50S backbone with protein component (L10e) of the A-site shown as green tube, protein component (L5) of the P-site shown as gold tube, nucleic P-loop portion of P-site shown as gold spheres, protein component (L44e) of E-site shown as white tube, various protein components (L2, L14, L19) of 50S-30S interface shown in purple. Remaining protein components are shown in gold and nucleic acid components in silver. (b) Front view of the electrostatic potential mapped on the 50S molecular surface; a blue color indicates regions of positive potential (>0 kT/e) whereas red depicts negative potential values (< −9.6 kT/e). (c) Back view (opposite the 30S-binding face) of the 50S backbone. (d) Back view of the electrostatic potential mapped on the 50S molecular surface.