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Multiscale analytic continuation approach to nanosystem simulation: applications to virus electrostatics.

Abhishek Singharoy¹, Anastasia M Yesnik, Peter Ortoleva

¹Department of Chemistry, Center for Cell and Virus Theory, Indiana University, Bloomington, Indiana 47405, USA.

The Journal of Chemical Physics

|May 13, 2010

Summary

Researchers developed a new computational method to accurately and efficiently approximate electrostatic potential in nanosystems. This approach unifies mobile ion and fixed charge behaviors, offering insights into viral structures and beyond.

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Area of Science:

Nanoscience and nanotechnology
Computational physics
Biophysics

Background:

Electrostatic effects in nanosystems are complex, involving multiscale phenomena and distinct behaviors of mobile ions and fixed charges.
The Poisson-Boltzmann equation is a key model, but its nondimensionalization reveals challenges in relating mobile ion density to fixed charges.

Purpose of the Study:

To develop a computationally efficient and accurate method for approximating electrostatic potential in nanosystems.
To introduce a unified treatment of mobile ions and fixed charges based on system geometry.
To validate the method on viral systems and explore broader applications.

Main Methods:

Nondimensionalization of the Poisson-Boltzmann equation to introduce a charge density ratio (lambda).

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Introduction of a geometric ratio (sigma) relating atomic distances to nanostructure size.

Unified treatment (lambda proportional to sigma) and perturbation expansion around sigma=0.

Analytic continuation and Padé approximants for approximation.

Main Results:

A unified treatment (lambda proportional to sigma) provides a computationally efficient and accurate approximation of electrostatic potential.
The perturbation expansion around sigma=0, via analytic continuation, yields high-accuracy results.
The method was successfully demonstrated on viral system electrostatics.

Conclusions:

The developed method offers a significant advancement in calculating electrostatic potentials in nanosystems.
The approach is generalizable to extended Poisson-Boltzmann models and applicable to electrodiffusion and quantum systems.
This work provides a powerful tool for understanding electrostatic interactions at the nanoscale.