# Computational nanoplasmonics in the quasistatic limit for biosensing applications

## TL;DR

This paper extends the open-source PyGBe software to compute the localized surface plasmon resonance (LSPR) response of biosensors with metallic nanoparticles, demonstrating accurate, scalable simulations of sensor-analyte interactions in the quasistatic limit.

## Contribution

It introduces a method for modeling biosensing using nanoplasmonics with an open-source tool, including validation and sensitivity analysis of nanoparticle-protein systems.

## Key findings

- PyGBe accurately computes extinction cross-section with grid convergence.
- A 0.5 nm red-shift in resonance frequency due to BSA proteins was observed.
- The software handles large boundary element problems efficiently.

## Abstract

This work uses the long-wavelength limit to compute LSPR response of biosensors, expanding the open-source PyGBe code to compute the extinction cross-section of metallic nanoparticles in the presence of any target for sensing. The target molecule is represented by a surface mesh, based on its crystal structure. PyGBe is research software for continuum electrostatics, written in Python with computationally expensive parts accelerated on GPU hardware, via PyCUDA. It is also accelerated algorithmically via a treecode that offers O(N log N) computational complexity. These features allow PyGBe to handle problems with half a million boundary elements or more. Using a model problem consisting of an isolated silver nanosphere in an electric field, our results show grid convergence as 1/N, and accurate computation of the extinction cross-section as a function of wavelength (compared with an analytical solution). For a model of a sensor-analyte system, consisting of a spherical silver nanoparticle and a set of bovine serum albumin (BSA) proteins, our results again obtain grid convergence as 1/N (with respect to the Richardson extrapolated value). Computing the LSPR response as a function of wavelength in the presence of BSA proteins captures a red-shift of 0.5 nm in the resonance frequency due to the presence of the analytes at 1-nm distance. The final result is a sensitivity study of the biosensor model, obtaining the shift in resonance frequency for various distances between the proteins and the nanoparticle. All results in this paper are fully reproducible, and we have deposited in archival data repositories all the materials needed to run the computations again and re-create the figures. PyGBe is open source under a permissive license and openly developed. Documentation is available at http://barbagroup.github.io/pygbe/docs/.