The application of numerical methods to enable the trivially parallel solution of …

• Abstract
• Introduction
• Multigrid Solution Through Parallel Focusing
• Electrostatic Properties of Microtubules
• Electrostatic Properties of the Ribosome
• Conclusions
• Abbreviations
• References
• Figures

Biology Articles » Biophysics » Molecular Biophysics » Electrostatics of nanosystems: Application to microtubules and the ribosome » Conclusions

Conclusions

- Electrostatics of nanosystems: Application to microtubules and the ribosome

We have described the combination of standard finite difference focusing techniques and the Bank-Holst algorithm into a parallel focusing method to facilitate the solution of the PBE for nanoscale systems. Unlike previous multiprocessor algorithms for solving the PBE, this method has excellent parallel complexity that permits the solution of these problems on massively parallel computational platforms. Furthermore, the finite difference discretization on a regular mesh allows for fast solution by highly efficient multigrid solvers. This algorithm has been implemented in the APBS software by using the PMG multigrid solver and tested on the NPACI IBM Blue Horizon supercomputer.

Using these methods for the parallel multigrid solution of elliptic differential equations, the electrostatic properties of very large biomolecular assemblages are now amenable to computation. This technique relies on the efficient solution of the PBE combined with parallel focusing techniques to solve these large problems in a variety of distributed computational environments. Solution of the LPBE for the 1.2 million-atom microtubule system provided electrostatic potential data, which revealed interesting features near drug binding sites and provided possible insight into stability differences at the + and  ends of the microtubule. Such detailed electrostatic information will be central to future studies that examine the possible collective effects involved in the formation of structural defects and the stabilizing effects of taxol binding to the interior of microtubules. Likewise, application of this methodology to ribosome systems elucidated intriguing electrostatic properties of the ribosomal active site, which will provide the starting point for investigation of the stabilization of the tRNA- and mRNA-ribosome complexes during translation and the rational design of novel antibiotics. Finally, the ability to determine the contribution of electrostatics to the forces and energies of nanoscale systems should extend the scale of implicit solvent dynamics methods to much larger macromolecular complexes.