  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/.
