peerj-cs-17

Submitted 16 May 2015
Accepted 24 July 2015
Published 26 August 2015
Corresponding author
Adam Hughes,
hugadams@gwmail.gwu.edu
Academic editor
Feng Gu
Additional Information and
Declarations can be found on
page 16
DOI 10.7717/peerj-cs.17
Copyright
2015 Hughes et al.
Distributed under
Creative Commons CC-BY 4.0
OPEN ACCESS
PAME: plasmonic assay modeling
environment
Adam Hughes, Zhaowen Liu and Mark E. Reeves
The George Washington University, Washington, D.C., USA
ABSTRACT
Plasmonic assays are an important class of optical sensors that measure biomolecular
interactions in real-time without the need for labeling agents, making them especially
well-suited for clinical applications. Through the incorporation of nanoparticles and
fiberoptics, these sensing systems have been successfully miniaturized and show great
promise for in-situ probing and implantable devices, yet it remains challenging to
derive meaningful, quantitative information from plasmonic responses. This is in
part due to a lack of dedicated modeling tools, and therefore we introduce PAME,
an open-source Python application for modeling plasmonic systems of bulk and
nanoparticle-embedded metallic films. PAME combines aspects of thin-film solvers,
nanomaterials and fiber-optics into an intuitive graphical interface. Some of PAME’s
features include a simulation mode, a database of hundreds of materials, and an
object-oriented framework for designing complex nanomaterials, such as a gold
nanoparticles encased in a protein shell. An overview of PAME’s theory and design is
presented, followed by example simulations of a fiberoptic refractometer, as well as
protein binding to a multiplexed sensor composed of a mixed layer of gold and silver
colloids. These results provide new insights into observed responses in reflectance
biosensors.
Subjects Computational Biology, Scientific Computing and Simulation, Software Engineering
Keywords Assays, Bioengineering, Python, Modeling, Biosensing, Simulation, Software,
Plasmonics, Nanoparticles, Fiberoptics, Thin films
INTRODUCTION
Plasmonic sensors refer to a class of label-free detection platforms that utilize the optical
properties of metals as a transduction mechanism to measure physical, chemical and
biomolecular processes. These sensors have been utilized in immunology research (Pei
et al., 2010; Tang, Dong & Ren, 2010), drug discovery (Chen, Obinata & Izumi, 2010;
Krazi´nski, Radecki & Radecka, 2011), DNA mutations (Litos et al., 2009), and in many
other novel applications. The conventional configuration of a plasmonic sensor is a thin
layer of metal, most commonly gold or silver, deposited on a glass chip and illuminated
from below at oblique incidence. This induces plasmon excitations along the surface of
the film. This design has been successfully commercialized by BiacoreTM, and has been
extended to include multilayer and mixed-alloy films (Sharma & Gupta, 2006; Sharma
& Gupta, 2007), and films deposited on optical fibers. Over the same time period, gold
and silver nanoparticles (AuNPs, AgNPs) gained attention for their potential in drug
delivery (Jong, 2008; Wilczewska et al., 2012), and their intrinsic sensing properties, as
How to cite this article Hughes et al. (2015), PAME: plasmonic assay modeling environment. PeerJ Comput. Sci. 1:e17;
DOI 10.7717/peerj-cs.17

each individual nanoparticle acts as a nanoscale transducer. Surface plasmons localized
to roughly a 50 nm region around the colloid (Malinsky et al., 2001) are excited by light
of any angle of incidence, and exhibit strong electromagnetic hotspots (Barrow et al.,
2012; Cheng et al., 2011) with greater sensitivity to their local environment than bulk
films. This is especially true for non-spherical nanoparticles like nanorods and nanostars
(Yin et al., 2006; Nikoobakht & El-sayed, 2003; Kessentini & Barchiesi, 2012), and leads
to great field-enhancements for Raman spectroscopy (Freeman et al., 1995; Sau et al.,
2010). While free solutions of colloids alone can serve as sensors (Jans et al., 2009; Tang,
Dong & Ren, 2010), they are easily destabilized by surface agents, and alterations in
salinity and pH of their surrounding environment, resulting in particle aggregation (Pease
et al., 2010; Zakaria et al., 2013). Nanoparticle monolayers engineered through vapor
deposition (Singh & Whitten, 2008), lithography (Haes et al., 2005), or self-assembly onto
organosilane linkers (Nath & Chilkoti, 2002; Brown & Doorn, 2008; Fujiwara, Kasaya &
Ogawa, 2009) now commonly replace their bulk film counterparts, since they retain the
enhanced sensitivity and flexible surface chemistry of the colloids, while being less prone1
1 Chemically-deposited nanoparticles
are slightly mobile in the film, and still
tend to form dimers, trimers and higher
order clusters under certain conditions
(Scarpettini & Bragas, 2010; Hughes et
al., 2015).
to aggregation.
Label-free measurements are indirect and prone to false-positives, as it can be difficult to
distinguish specific binding events from non-specific binding, adsorption onto the sensor
surface, and changes in the environment due to heating, convection and other processes.
To mitigate these effects, plasmonic sensors undergo an extensive standardization process.
First, they are calibrated to yield a linear response to bulk refractive index changes. Next,
the sensor surface is modified2 to be neutral, hydrophillic and sparsely covered with
2 For planar gold chips, Dextran provides
an optimal coating; however, for
nanoparticles, short-chain alkanethiols
and polyethylene glycols are preferred
due to their smaller size (Malinsky et al.,
2001; Mayer et al., 2008).
covalently deposited ligands. To measure ligand-analyte association and dissociation
constants, ka,kd, solutions of varying concentration of analyte are washed over the surface,
and the response is measured and interpreted within a protein interaction model (Pollard,
2010; Chang et al., 2013). Each of these steps impose challenges for plasmonic sensors
utilizing nanoparticle-embedded films. Primarily, the sensor response becomes highly
sensitive to the film topology (Quinten, 2011; Lans, 2013), which is difficult to interpret
and optimize without modeling tools. Furthermore, measurements of ka and kd require
varying analyte concentrations under identical surface conditions. Commercial systems
often employ multichannel-sampling on a single surface (Attana, 2014), or multiplex
multiple surfaces in a single run (ForteBio, 2013), while researchers mostly rely on the
presumption of identical sensor surface topology, chemistry and experimental conditions.
Without a quantitative model for sensor response to protein binding, it is impossible to
estimate how many molecules are adsorbed on the sensor. This information is critical to
validating binding models; for example, whether a measured response is too large to be
described by a 1:1 monomeric reaction. Is the amount of deposited ligand likely to lead to
avidity effects? In non-equilibrium applications such as monitoring the hormone levels of
cells, the analyte concentration is unknown and only a single excretion event may occur; in
such cases, the ability to translate optical responses directly into quantitative estimations of
ligand and receptor through modeling is paramount.
Hughes et al. (2015), PeerJ Comput. Sci., DOI 10.7717/peerj-cs.17 2/23

Researchers modeling plasmonic systems may opt to use monolithic design tools
like COMSOLTM Multiphysics and LumericalTM Solutions. While such tools offer
comprehensive photonic design environments, they are quite general in design and carry
more overhead than is needed to model the basic fiber and chip geometries described in
this paper. On the other hand, related open-source tools are too disjoint to be effectively
integrated into a single workflow. For example, thin-film solvers are widely available
(for a comprehensive list, see Optenso, 2014), and the MNPBEM Toolbox (Hohenester
& Trugler, 2012) offers a MatlabTM interface for nanomaterial design. Yet, to design
materials in MNPBEM and integrate them into film solvers requires a customized pipeline.
Furthermore, simple geometric fill models for nanoparticle-protein binding are not
available in these tools, even though these fill models have been successful (Klebstov,
2004; Lopatynskyi et al., 2011; Tsai et al., 2011) in describing AuNP-protein binding
in free solution. With an abundance of parameters, ranging from the nanoscale to the
macroscopic, characterizing a biosensor can quickly become intractable and a specialized
solution is needed.
Herein, the Plasmonic Assay Modeling Environment (PAME) is introduced as an
open-source Python application for modeling plasmonic biosensors. PAME is a fully
graphical application that integrates aspects of material science (material modeling,
effective medium theories, nanomaterials), thin-film design, fiberoptics, ellipsometry and
spectroscopy, with the goal of providing a simple framework for designing, simulating and
characterizing plasmonic biosensors. PAME helps to illuminate non-obvious relationships
between sensor parameters and response. After an overview of its theory and design,
several examples are presented. First, PAME is used to model the refractometric response
of an AuNP-coated optical fiber to increasing concentrations of glycerin. It is shown that
the response peaks at λmax ≈ 485 nm , a result supported by experiment, even though the
nanoparticles absorb most strongly at λmax ≈ 528 nm. Next, PAME simulates protein
binding events onto a mixed layer of gold and silver nanoparticles in a multiplexed
fiber setup. Finally, a brief overview of PAME’s requirements, performance and future
development is presented. Additional examples in the form of IPython notebooks (Perez &
Granger, 2007), as well as video tutorials, are available in the Supplemental Information.
THEORY AND DESIGN
Many plasmonic sensors can be modeled as a multilayer stack of homogeneous materials,
also referred to as films or dielectric slabs, arranged on a substrate so as to transduce
interactions between light and the stack. The substrate represents a light guide such as a
chip or an optical fiber. The transduced signal is some optical property of the multilayer,
commonly transmittance or spectral reflectance, or in the case of ellipsometry, changes
in the reflected light’s polarization state (Moirangthem, Chang & Wei, 2011). Much of the
diversity in plasmonic sensors is therefore due to design parameters rather than dissimilar
physics, and has been described thoroughly by BD Gupta (Sharma & Gupta, 2006; Sharma
& Gupta, 2007; Gupta & Verma, 2009; Singh, Verma & Gupta, 2010; Mishra, Mishra &
Gupta, 2015). PAME was designed specifically to model these types of systems.

Figure 1 PAME’s user interface. (A) Panel to view material quantities such as index of refraction, n(λ), and nanoparticle extinction cross section,
σext(λ). Currently shown is e(λ) for a layer of gold nanoparticles in water at a fill fraction of about 30% using Garcia’s mixing model. (B) Panel of
plotted optical properties such as transmittance, T(λ), and reflectance, Γ(λ). Here the reflectance coefficient for P-polarized light rP(λ) is shown.
The spread in the linewidth corresponds to variations in light modes over the range 0 > θ ≥ 16◦. (C) Five primary panels and tabular interface
(D) for constructing the dielectric stack: silica (substrate) | organosilanes (2 nm) | AuNPs in H2O (24 nm) |H2O (solvent) for 300 ≤ λ ≤ 800 nm.
PAME is designed with four integrated subprograms: a materials adapter to model
bulk, composite, and nanomaterials; a multilayer thinfilm calculator; a substrate design
interface; and a simulation and data analysis framework. Figure 1 shows a screenshot of
the PAME’s main window, with its five primary panels: Main, Substrate, Stack, Material
and Simulations. Main refers to global settings, for example the operating wavelength
range. The remaining tabs correspond directly to the four aforementioned subprograms.
Together, they provide a complete framework for modeling a plasmonic sensor, and
lend a useful narrative that will be followed in the ordering of the remaining sections of
this paper. Incidentally, the progression from Substrate, Stack and Material represents a
top-down view of the model, starting from macroscopic parameters and working down to
the microscopic.
Substrate types
PAME supports two substrates: optical fibers and chips. Substrates mediate the interaction
between light and the multilayer stack through a weighting function,
N
i f (θi), where θi
corresponds to the angle of the ith incident light ray onto the substrate. The chip is meant
to describe simple configurations, for example a gold film deposited on a glass slide and
illuminated from below at a single angle, θo. In this case,
N
i f (θi) = δ(θo). For optical
fibers, the propagation modes are determined by properties of the fiber itself, such as its
numerical aperture, core and cladding materials, and its ability to maintain polarization
states. Furthermore, the placement of the multilayer on different regions of the fiber has a

Figure 2 Light propagation in fiber optic biosensor. (A) A light ray propagating in an optical fiber core.
Transverse refers to a multilayer deposited along the propagation direction, while axial is perpendicular
and deposited on the fiber endface. The fiber cladding and jacket are hidden for clarity. (B) The θ = 0
plane wave incident on the stack. (C) Illustration of the homogenized multilayers, and some of the
electromagnetic quantities associated with each interface, reproduced with permission from (Orfanidis,
2008).
significant effect on f (θi), and hence on the optical response of the sensor. The two most
common orientations, either transversally3 along the propagation direction on the fiber,
3 See Mishra, Mishra & Gupta (2015)
Eq. (5) for an example of f (θ) for a
transversal fiber with collimated light
source.
or axially on the cleaved fiber endface, are shown in Fig. 2. Both of these orientations have
been realized as biosensors (Lipoprotein et al., 2012; Shrivastav, Mishra & Gupta, 2015),
with the axial configuration, often referred to as a “dip sensor” because the endface is
dipped into the sample, appearing more often in recent years (Mitsui, Handa & Kajikawa,
2004; Wan et al., 2010; Jeong et al., 2012; Sciacca & Monro, 2014). PAME does not presently
support multilayers along bent regions of the fiber, or along sharpened optical tips (Issa
& Guckenberger, 2006; Library et al., 2013) and assumes all rays to be plane waves. For
advanced waveguide design and modal analysis, we recommend LumericalTM MODE
solutions.
PAME’s Substrate interface queries users to configure chip and optical fiber parameters,
rather than working directly with f (θi). Users can choose between multilayer orientation,
polarization state (P, S or unpolarized), and range of angles, all from which PAME builds
f (θ). The interface is user-friendly, and attempts to obviate incompatible or unphysical
settings. For instance, the ellipsometric amplitude (Ψ) and phase (δ) depend on ratios
of P-polarized to S-polarized light reflectance, but users may opt to only compute
S-waves, resulting in errant calculations downstream. Anticipating this, PAME provides
an ellipsometry mode, which when enabled, prevents the polarization state from being
changed. By combining substrate types with context modes, PAME provides a simple
interface for modeling a number of common optical setups.
Multilayer stack
Figure 2 depicts the multilayer stack, in which each dielectric slab is assumed to be
homogenous, and of uniform thickness; heterogeneous materials must be homogenized
through an effective medium theory (EMT). Furthermore, the multilayer model presumes
that layers are connected by smooth and abrupt boundaries to satisfy Fresnel’s equations.
The first and last layers, conventionally referred to as “substrate” and “solvent,” are
assumed to be semi-infinite, with incident light originating in the substrate. The treatment

of anisotropic layers without effective medium approximations is discussed in the Future
Improvement section.
A light ray incident on the stack at angle θ, as set by f (θ), will reflect, refract and absorb,
in accordance with Fresnel’s equations. For example, in a simple 2-layer system, the light
reflectance, Γ(λ), at the boundary between n1,n2 is
R =
1
2
(rs + rp) (1)
R =
1
2




n1cosθi − n2cosθt
n1cosθi + n2cosθt




2
+




n1cosθt − n2cosθi
n1cosθt + n2cosθi




2

, (2)
where θi,θt are the angles of incidence upon, and transmission into n2 from n1, and rs
and rp are the complex reflection coefficients of the S and P-polarized light. For N-layers,
Fresnel’s equations are solved recursively using the transfer matrix method(TMM), also
referred to as the recursive Rouard method (Rouard, 1937; Lecaruyer et al., 2006). In
addition to the reflectance, transmittance and absorbance, a variety of optical quantities
are computed in the multilayer, including the Poynting vector, the complex wave vector
angle, ellipsometric parameters, and film color. For a thorough treatment of light
propagation in multilayer structures, see Orfanidis (2008) and Steed (2013). PAME offers
a simple tabular interface for adding, removing, and editing materials in arbitrarily many
layers, as shown in Fig. 2C. PAME delegates the actual TMM calculation to an adapted
version of the Python package, tmm (Byrnes, 2012).
PAME material classes
PAME includes three material categories: bulk materials, composite materials and
nanomaterials. A bulk material such as a gold film is sufficiently characterized by its index
of refraction. The optical properties of a gold nanoparticle, however, depend on the index
of gold, particle size, the surrounding medium, a particle-medium mixing model, and
other parameters. A nanoparticle with a shell is even more intricate. PAME encapsulates a
rich hierarchy of materials in an object-oriented framework to ensure compatibility with
the multilayer stack and interactive plotting interface.
Bulk material
In PAME, a “bulk” material refers to a single, homogeneous substance, fully characterized
by its complex index of refraction, ˜n = n + iκ, or dielectric function, ˜e = e + iϵ, which are
related through a complex root (˜e =
√
˜n), which gives the relations
e = n2
− κ2
n =
√
e2 + ϵ2 + e
2
ϵ = 2nκ κ =
√
e2 + ϵ2 − e
2
.
Here n and e, and optical quantities derived from them, are understood to be dispersive
functions of wavelengths, n(λ),e(λ). The refractive index n is assumed to be independent

of temperature and non-magnetic at optical frequencies4. The index of refraction of
4 Ferromagnetic nanoparticles do exist,
and are have already been utilized in
sensing applications (Pellegrini & Mattei,
2014).
bulk materials is obtained through experimental measurements, modeling, or through
a combination of the two; for example, measuring n at several wavelengths, and fitting to a
dispersion model such as the Sellmeier equation,
n(λ) =

1 +
A1λ2
λ2 − B2
1
+
A2λ2
λ2 − B2
2
+
A3λ2
λ2 − B2
3
+ ···. (3)
PAME is bundled with several dispersion models, including the Cauchy, Drude and
Sellmeier relations, as well as two freely-available5 refractive index catalogs: Sopra (2008)
5 Materials are supplied as is with no
guarantee of accuracy: use at your own
discretion.
and RefractiveIndex.INFO (Polyanskiy, 2015), comprising over 1,600 refractive index files.
PAME includes a materials adapter to browse and upload materials as shown in Fig. 3.
Selected materials are automatically converted, interpolated, and expressed in the working
spectral unit (nm, eV, cm, ...) and range. PAME’s plots respond to changes in material
parameters in real time.
Composite materials
A composite consists of two materials bound by a mixing function. For example, a
gold-silver alloy could be modeled as bulk gold and silver, mixed through an effective
mixing theory (EMT). The complexity of the EMT is related to the electromagnetic
interactions between the materials. For example, for binary liquid mixtures with
refractive indicies, n1,n2, and fill fraction, φ, the composite can be approximated as
nmixed = n1φ + n2(1 − φ), with more complex liquid mixing models like Weiner’s relation
and Heller’s relation yielding negligible differences (Bhatia, Tripathi & Dubey, 2002). For
solid inclusions, the extension of the Maxwell–Garnett (MG) mixing rule (Garnett, 1904)
by Garcıa, Llopis & Paje (1999) has been shown effective, even when the particles are
non-spherical and anisotropically clustered (Li et al., 2006). At present, PAME includes
MG, with and without Garcia’s extension, the Bruggeman equation (Bruggeman, 1935),
the quasi-crystalline approximation with coherent potential (Liu et al., 2011; Tsang, Kong
& Shin, 1985), and various binary liquid mixing rules. These are hardly exhaustive, and
new methods are continually appearing (Amendola & Meneghetti, 2009; Battie et al., 2014;
Malasi, Kalyanaraman & Garcia, 2014). Adding EMTs to PAME is straightforward, and
more will be added in upcoming releases.
Composite materials are not limited to bulk materials, but include combinations of
composites and/or nanomaterials, for example gold and silver nanoparticles embedded in
a glass matrix. However one must be aware of the limitations of implicit mixing models.
For example, consider a layer of gold nanoparticles. As coverage increases, particle–particle
interactions are taken into account in Garcia’s EMT through the parameter K. EMTs
describing inclusions of two or more material types have been described (Zhdanov, 2008;
Bossa et al., 2014), and will be available in future versions. PAME’s geometric fill models are
also implemented as composite material classes. For example, small spheres of material
X binding to the surface of a larger sphere of material Y serves as a useful model for
proteins binding to gold nanoparticles (Lopatynskyi et al., 2011). An ensemble of spherical

Figure 3 Screenshot of PAME’s material adapter. (A) Tree view of available bulk material models, files and bundled catalogues. (B) Preview of the
selected material includes available material metadata, notes and an interpolated fit to the current spectral range and unit system. Currently showing
˜e for gold from Johnson & Christy (1972). (C) Search utility to find and batch upload materials.
inclusions on a disk is the correct geometry for modeling gold nanoparticles adhered to
the cleaved end of a fiber surface. PAME’s fill models track the number of inclusions, fill
fraction, and other quantitative parameters at any given time. This enables macroscopic
quantities like sensor sensitivity to be measured against microscopic parameters like the
number of proteins bound to the nanoparticles.
Nanomaterials
In PAME, nanomaterials are treated as a special instance of a composite material6 whose
6 A layer of nanoparticles is always
embedded in some other media, for
example in a slab of water or a sol–gel
matrix of glass. Therefore, in an object-
oriented framework, a nanomaterial is
a subclass of a composite material, with
additional attributes like particle size
and implicit optical properties.
properties depend on a core material, a medium material, possibly an intermediate
shell material, and particle size. A key distinction between nanomaterials and their bulk
counterparts is that the optical properties of nanoparticles are highly sensitive to both
the particle size and the permitivity of the surrounding medium. The implicit optical
properties of spheroidal nanoparticles, such a extinction cross section, σext, are solved
analytically through Mie Theory (Bohren, 1983; Jain et al., 2006). This is a fundamentally
important quantity, as the position and shift in the extinction cross section maximum,

Figure 4 Theoretical optical absorption and scattering properties of gold and silver nanoparticles. Ex-
tinction, absorption and scattering cross sections of (A) 60 nm silver and (B) 80 nm gold nanoparticles
computed in PAME using reported permittivities from Hagemann, Gudat & Kunz (1975) and Gao,
Lemarchand & Lequime (2011), respectively, which produced more accurate cross sections than the
typically-used Drude model.
known as the localized plasmon resonance (Willets & Van Duyne, 2007; Anker et al., 2008),
is often the best indicator of the state of the nanoparticles comprising the system. While the
full solution to the extinction cross section is described by the sum of an infinite series of
Ricatti–Bessel functions, described in full in Lopatynskyi et al. (2011), for brevity consider
the approximate expression (Jeong et al., 2012; Van de Hulst, 1981):
σext ≈
128π5
3λ4
R6
Im

m2 − 1
m2 + 2
2
  
≈σscatt
−
8π2
λ
R3

m2 − 1
m2 + 2

  
≈σabs
, (4)
where m is the ratio of the refractive index of the core particle material to that of the
suspension medium (e.g., gold to water). The polynomial dependence of R, λ and
m demonstrate the high variability in the optical properties of nanoparticles, and by
extension, the biosensors that utilize them. Typical cross sections from silver and gold
nanospheres are depicted in Fig. 4.
While optical constants derived from Mie Theory are computed analytically, it is
important to recognize that in a dielectric slab, nanomaterials are represented by an
effective dielectric function; thus, optical constants like transmittance or reflectance will
be computed using an effective dielectric function representing the nanoparticle layer.
PAME currently supports nanospheres and nanospheres with shells; planned support for
exotic particle morphologies is described in the Future Improvements section. Similar
treatments of nanoparticle layers with effective media approximations have been successful
(Li et al., 2006; Liu et al., 2011), even for non-spherical particles, and for ensembles of
different sized particles (Battie et al., 2014). This is a salient difference between PAME,
and numerical approaches like the boundary element method(BEM), discrete dipole
approximation(DDA) and finite-difference time-domain(FDTD): PAME relies on mixing
theories, and hence is constrained by any underlying assumptions of the mixing model. For

Figure 5 PAME’s simulation interface, showing the Selection, Notes/IO and Storage tabs.
a more in-depth discussion on nanoparticle modeling, see Myroshnychenko et al. (2008)
and Tr¨ugler (2011).
Simulation and data analysis
PAME’s interactivity makes it ideal for exploring the relationships between system
variables, while the simulation environment provides the means to systematically
increment a parameter and record the correspond response; for example, incrementing
the fill fraction of inclusions in a nanoparticle shell to simulate protein binding, or
incrementing the refractive index of the solvent to simulate a refractometer. Because
most updates in PAME are automatically triggered, simulations amount to incrementing
parameters in a loop and storing and plotting the results.
PAME’s simulation interface simplifies the process of setting simulation variables and
storing results. It is comprised of three tabs: a Selection tab (Fig. 5) for setting simulation
parameters and value ranges. Variable names like layer1.d refers to the thickness of the first
layer in the multilayer stack, and material2.shell thickness is the size of the nanoparticle
shell in nanometers of material2. PAME provides suggestions, documentation and a tree
viewer to choose simulation variables, and alerts users to errant inputs, or invalid ranges;
for example, if users try to simulate a volume fraction beyond its valid range of 0.0 to 1.0.
The Notes/IO tab provides a place to record notes on the simulation, and configure the
output directory. PAME can store all of its state variables in every cycle of the simulation,
including the entire multilayer structure, and all computed optical quantities, but this
can lead to storing large quantities of redundant data. The Storage tab lets users pick and
choose their storage preference, and even specify the quantities that should be regarded as
“primary” for easy access when parsing.
PAME provides a SimParser object to interact with saved simulations, which while
not required, is intended to be used inside an IPython Notebook (Perez & Granger, 2007)
environment. The SimParser stores primary results in Pandas (McKinney & Millman, 2010)
and scikit-spectra (Hughes & Liu, 2014) objects for easy interaction and visualization, and
the remaining results are stored in JSON. This allows for immediate analysis of the most
important simulation results, with the remaining data easily accessed later through a tree
viewer and other SimParser utilities.

EXAMPLES OF USE
Case 1: refractometer
Plasmonic sensors respond to changes in their surrounding dielectric environments,
and are commonly utilized as refractometers (Mitsui, Handa & Kajikawa, 2004; Punjabi
& Mukherji, 2014), even going so far as to measure the refractive index of a single
fibroblast cell (Lee et al., 2008). Refractive index measurements can also be used to measure
sensitivity and linear operating ranges. A common approach is to immerse the sensor in
a medium such as water, and incrementally change the index of refraction of the medium
by mixing in glycerine or sucrose. Because the index of refraction as a function of glycerine
concentration is well-known (Glycerine Producers’ Association , 1963), sensor response
can be expressed in refractive index units (RIU). This is usually taken a step further in
biosensor designs, where the RIUs are calibrated to underlying biophysical processes (e.g.,
protein absorption), either through modeling as PAME does, or through orthogonal
experimental techniques such as Fourier Transform Infrared Spectroscopy (Tsai et al.,
2011). This calibration process has been described previously (Jeong & Lee, 2011; Richard
& Anna, 2008), and is usually carried through in commercial plasmonic sensors. This
quantifies the analyte binding capacity of the sensor, an important parameter for assessing
binding models7, non-equilibrium sensing, and performing one-step measurements, for
7 Schasfoort et al. (2012) has enumerated
seven interfering effects that lead to
errant calculations of equilibrium
affinity constants. Estimations of
nanoparticle and ligand density at the
sensor surface provide insights as to
whether or not some of these effects are
likely occurring.
example estimating the glucose levels in a blood sample. As a first use case, PAME is used
to calibrate sensor response to increasing concentrations of glycerine for an axial fiber
comprised of a 24 nm layer of gold nanoparticles.
A dip sensor was constructed using a protocol and optical setup similar to that of
Mitsui, Handa & Kajikawa (2004). In brief, optical fiber probes were cleaved, submerged
in boiling piranha (3:1 H2SO4 : H2O2), functionalized with 0.001% (3-Aminopropyl)
trimethoxysilane for 60 min in anhydrous ethanol under sonication, dryed in an oven at
120 ◦C, and coated with 24 nm AuNPs to a coverage of about 40 ± 5%, as verified by SEM
imaging (Hughes et al., 2015). The fiber was submerged in 2 mL of distilled water under
constant stirring, and glycerine droplets were added incrementally until the final glycerine
concentration was 32%, with each drop resulting in a stepwise increase in the reflectance
as shown in Figs. 6A and 6C). This system was simulated using the stack described in Fig.
1, where the organosilanes were modeled as a 2 nm-thick layer of a Sellmeier material
(Eq. (4)), with coefficients: A1 = 6.9,A2 = 3.2,A3 = 0.89,B1 = 1.6,B2 = 0.0,B3 = 50.0.
These coefficients led to excellent agreement between experiment and simulation during
the self-assembly process of the AuNP film.
Figures 6C and 6D shows the strong agreement between measured and simulated
response to increasing glycerine, and PAME is able to show the reflectance spectrum
free of the influence of the LED light source in the dataset(b,a). It is clear that while
the nanoparticle’s reflectance is prominent around λmax ≈ 560 nm, the combination of
both an increase in reflectance, and a blue-shift of spectral weight yield a 485 nm peak in
the normalized reflectance spectrum. Neither is indicative of the free-solution plasmon
resonance peak at λmax ≈ 528 nm , and maintaining a correspondence between the
reflectance centroid and plasmon resonance can lead to misinterpretation. Furthermore,

Figure 6 Simulated and measured spectral reflectance from a fiberoptic biosensor. Increase in spectral
reflectance (Γ) from a fiber dip sensor at 40% AuNP coverage immersed in water glycerine mixture
as glycerine fraction is increased from 0 to 32% for the experiment (A) and simulation (B). The same
response, normalized to the reflectance of the probe in water (Γo) prior to the addition of glycerine (C,
D). The AuNPs layer reflects most strongly at λmax ≈ 560 nm, yet the normalized reflectance peaks at
λmax ≈ 485 nm.
the shape of this glycerine response profile is very sensitive to parameters like organosilane
layer thickness and nanoparticle size and coverage, and by fitting to the simulated
response, one may then estimate these parameters which are otherwise difficult to measure.
This simple example provides valuable insights into the relationship between glycerine
concentration and reflectance on a dip sensor.
Case 2: multiplexed Ag–Au sensor
Sciacca & Monro (2014) recently published a multiplexed biosensor in which both gold
and silver nanoparticles were deposited on the endface of a dip sensor and their reflectance
was monitored simultaneously. In their experiment, the gold colloids were functionalized
with anti-apoE, the antibody to an overexpressed gastric cancer biomarker, apoE. The
silver colloids were functionalized with a non-specific antibody. The authors showed
that the plasmon resonance peak of the gold particles shifted appreciably in response
to apoE, while the silver did not. Furthermore, the gold peak did not respond to CLU,
an underexpressed gastric cancer biomarker while the uncoated silver particles did,
presumably due to non-specific binding. In effect, the multiplexed sensor provides a
built-in negative control and can identify specific events more robustly. The ability to
multiplex two or more colloids to a single sensor has great potential. To gain insights into

Figure 7 Simulation of multiplexed biosensor response. Simulation of a multiplexed biosensor with a
combined 80 nm gold and 60 nm silver nanoparticle layer. Simulated NeutrAvidin binding to AgNPs (A,
C) while AuNPs are kept bare, and vice versa (B, D). The coverage is varied until 95% of the available sites
are occupied (617 proteins per AuNP, 363 per AgNP). The reflectance normalized to zero coverage (Γo)
is shown in (C, D).
this system, the sensor’s response to a mid-sized protein like NeutrAvidin (60 kDa) was
simulated8. To our knowledge, this is the first attempt at modeling a multiplexed dip sensor
8 The NeutrAvidin simulation is an
idealization of Sciacca & Monro (2014)’s
configuration, as it only considers a
single protein layer rather than an
antigen-antibody bilayer.
containing two nanoparticle species.
A dip sensor was configured in PAME, composed of a 2.5 nm thick layer of organosi-
lanes9 and a 92 nm layer of mixed protein-coated nanoparticles in water. A 3-layer
9 Sciacca & Monro (2014) actually
used a thick layer of PAH to bind the
nanoparticles. It was unclear how best to
model this material, so the organosilane
layer from the previous example was
used. The thickness of the PAH layer
might explain why Sciacca & Monro
(2014)’s silver reflectance is peaked at
λmax ≈ 425 nm; whereas, our simulation
and other reported silver nanoparticle
films (Hutter & Fendler, 2002) exhibit
maxima at λmax ≈ 405 nm.
composite material model was used to represent the mixed nanoparticles. Materials 1
and 2 were set to 80 nm AuNPs and 60 nm AgNPs, respectively, using the dielectric
functions described in Fig. 4; material 3 was set to water. Au–Au effects and Ag–Ag
effects are taken into account, but PAME’s 2-phase EMTs cannot account for Au–Ag
effects (3-phase and N-phase EMTs (Luo, 1997; Zhdanov, 2008) will be implemented in
upcoming releases). Therefore, the combined layer, ñAuAg, is weighted in proportion to the
fill fraction as, ñAuAg = φ1 ñAu + φ2 ñAg. Nanoparticle coverage was chosen so as to produce
a large reflectance, with approximately equal contributions from gold and silver; the actual
coverage used in Sciacca & Monro (2014) is not stated. Ultimately, 45.56% of the surface
sites were covered in gold, and 18.64% in silver. NeutrAvidin was modeled as a 6 nm sphere
(Tsortos et al., 2008) of dispersive refractive index, n ≈ 1.5 (Sarid & Challener, 2010), filling
a 6 nm-wide shell on the nanoparticles from 0 to 95% coverage (617 proteins per AuNP
and 363 per AgNP), as shown in Fig. 7.
Despite using several approximations, the simulation provides many insights into
multiplexed sensors. First, the 60 nm AgNPs reflect much more efficiently, despite AgNPs

and AuNPs having nearly identical extinction cross sections (Fig. 4). This is because silver
particles are more efficient scatterers (Lee & El-Sayed, 2006), and reflectance depends
exponentially on scattering cross section (Quinten, 2011). Therefore, reflectance sensors
composed of highly-scattering particles can utilize sparse nanoparticle films, which are
less susceptible to aggregation (Scarpettini & Bragas, 2010) and electrostatic and avidity
effects. Secondly, the normalized response to protein binding is about 0.08 units for silver,
and 0.06 for gold; however, there are 2.33 more proteins on gold than silver. Therefore,
considering the response per molecule, 60 nm silver spheres are 3.12 time more sensitive to
protein binding than 80 nm gold spheres. Experiments have confirmed similar three-fold
enhancement to protein-induced plasmon resonance shifts in aqueous solutions of
AuNPs and AgNPs (Sun & Xia, 2002; Mayer, Hafner & Antigen, 2011). This suggests a
correspondence between shifts measured in free solution and the reflectance in optical
fibers, despite little similarity in the qualitative profile of the response. Nusz et al. (2009) has
suggested a figure of merit to objectively compare shifts vs. intensity responses.
Finally, if response is partitioned into two spectral regions, such that 385 nm <
λ ≤ 500 nm corresponds to silver, and λ ≥ 500 nm to gold, then Fig. 7 illuminates an
important result: despite a clear separation in the peaks of the reflectance spectra, the
response to NeutrAvidin spans both partitions. For example, in Fig. 7C the gold region
(λ ≥ 550 nm) clearly responds to proteins binding to silver nanoparticles. This could lead
to misinterpretations; for example, the response at λ ≈ 570 nm could be misattributed to
non-specific binding onto gold, when in fact there is only binding to silver. In Sciacca &
Monro (2014), both the gold and silver spectral regions responded to apoE, when only gold
is coated with anti-apoE. While the signal in the silver region could be due to non-specific
interactions between the anti-apoE and AgNPs, these simulations show that it could simply
be due to spectral overlap in the gold and silver response, the extent of which depends on
the dielectric function of the protein, the Au–Ag coupling and other factors.
IMPLEMENTATION AND PERFORMANCE
PAME’s graphical interface and event-handling framework is built on the Enthought Tool
Suite, especially Traits and TraitsUI. Traits is particularly useful for rapid application
development (Varoquaux, 2010). TraitsUI leverages either PyQT, Pyside or WxPython on
the backend to generate the graphical interface. Some discrepancies in the user interface
may be encountered between different backends, and possibly between operating systems.
PAME has been tested on Ubuntu, OSX and Windows 7. A future refactor to supplant
TraitsUI with Enaml (NucleicDevelopmentTeam, 2013) should resolve view inconsistencies.
To enhance speed, PAME utilizes Numpy (Oliphant, 2007) and Pandas to vectorize
most of its computations. Complex structures such as multilayers of 20 or more materials,
with over a thousand datapoints per sample, are reasonably handled on a low-end laptop
(IntelTM Core 2 Duo, 4GB DDR2 RAM). The intended operating conditions for PAME are
stacks of less than 10 layers, and dispersive media of 100 or fewer datapoints. At present,
the main performance bottleneck is redundant event triggering. Because PAME is highly
interactive, changing a global parameter such as the working spectral range will trigger

updates in every material in the multilayer stack. For nanoparticles, this means the core,
medium and possibly shell materials are all recomputed, each of which triggers a separate
recalculation and redraw of the Mie-scattering cross sections. Streamlining global event
handlers should yield appreciable performance gains, followed by additional vectorization
of the TMM calculation, and finally implementing calculations that cannot be vectorized
in Cython (Behnel et al., 2010).
FUTURE IMPROVEMENTS
Currently, PAME’s nanoparticle support is limited to nanospheres and core–shell particles
because analytical solutions to these systems exist, and because many effective medium
approximations are implemented with spheres in mind. The electromagnetic properties
of nanoparticles of arbitrary morphology can be solved with numerical methods such as
DDA, FDTD, or BEM, and libraries like MNPBEM implement common particle mor-
phologies out-of-the-box. The recently released PyGBe (Cooper, Bardhan & Barba, 2014)
library brings this potential to Python. PyGBe has been used to simulate protein interac-
tions near the surface of materials (Lin, Liu & Wang, 2015), meaning it has the potential
to supplant the current geometrical fill models used to describe protein-nanoparticle
interactions. By analyzing interactions in the near-field with PyGBe and in the far-field
with PAME, comprehensive insights into nanoparticle systems may be obtained.
Even if exotic nanoparticle are incorporated into PAME, they would still need to be
homogenized through an effective mixing theory to fit the TMM multilayer model. While
classical EMTs can account for non-spherical inclusions through a dipole polarizability
parameter (Garcıa, Llopis & Paje, 1999; Quinten, 2011), modern two-material EMTs
derived from spectral density theory (Bergman, 1978; Sancho-Parramon, 2011; Lans, 2013),
N-material generalized tensor formulations (Habashy & Abubakar, 2007; Zhdanov, 2008),
and multipole treatments (Malasi, Kalyanaraman & Garcia, 2014) give better descriptions
of real films topologies, and will be incorporated into PAME in the near future.
Some systems cannot be adequately described with EMTs, for example films composed
of large, highly-scattering particles (Quinten, 2011). In such cases, is still possible to
compute the reflectance of a film of a few hundred spheres through generalized Mie theory,
which is a coherent superposition of the multipole moments of each particle, or for larger
films using incoherent superposition methods (Elias & Elias, 2002; Quinten, 2011), but
such approaches don’t readily interface to the multilayer model. Rigorous coupled-wave
analysis (RCWA) may be a viable alternative, as it as it incorporates periodic dielectric
structures (Moharam et al., 1995) directly into TMM calculations, and is already imple-
mented in Python (Rathgen, 2008; Francis, 2014). RCWA could be integrated into PAME
without major refactoring, and has already been demonstrated as a viable alternative to
EMTs in describing nanoparticle-embedded films in biosensors (Wu & Wang, 2009).
CONCLUSION
Plasmonic biosensing offers a promising alternative to conventional label-free protein
detection techniques like enzyme-linked immunosorbent assays (ELISA) and Western
blots, but dedicated software tools for the common sensor geometries are not readily

accessible. PAME fills the gap by providing an open-source tool which combines aspects
of thin-film design, effective medium theories, and nanoscience to provide a modeling
environment for biosensing. In this work, it has been shown that PAME can simulate
a refractometer made from a dip sensor of AuNPs, and experimental data shows good
agreement without invoking extensive fit parameters. Furthermore, PAME is flexible
enough to reproduce results on new multiplexed sensor designs like those proposed by Lin
et al. (2012) and Sciacca & Monro (2014). As plasmonic biosensors continue to develop,
PAME should prove a useful tool for characterizing sensor response, a necessary step
towards in-situ studies.
ABOUT
PAME documentation, source code, examples and video tutorials are hosted at: https://
github.com/hugadams/PAME. We are looking for developers to help extend the project.
Please contact if interested.
Programming Language: Python 2.7
License: 3-Clause BSD
Version: 0.3.2
Dependencies: Enthought Tool Suite, Pandas, scipy (IPython ≥ 2.0 or greater and
scikit-spectra recommended)
OS: Windows, Mac and Linux
Persistent Identifier: DOI 10.5281/zenodo.17578
Binary Installers: Under development
ACKNOWLEDGEMENTS
We’d like to thank Robert Kern and Jonathan March for many helpful discussions on Traits
and TraitsUI, and Rayhaan Rasheed for helping to create the illustrations.
ADDITIONAL INFORMATION AND DECLARATIONS
Funding
This work was supported in part by the George Gamow Research Fellowship, Luther Rice
Collaborative Research fellowship programs, the George Washington University (GWU)
Knox fellowship and the GWU Presidential Merit Fellowship. The funders had no role
in study design, data collection and analysis, decision to publish, or preparation of the
manuscript.
Grant Disclosures
The following grant information was disclosed by the authors:
George Gamow Research Fellowship.
Luther Rice Collaborative Research Fellowship.
George Washington University Knox Fellowship.
GWU Presidential Merit Fellowship.

Competing Interests
The authors declare there are no competing interests.
Author Contributions
• Adam Hughes analyzed the data, contributed reagents/materials/analysis tools, wrote
the paper, prepared figures and/or tables, performed the computation work.
• Zhaowen Liu analyzed the data, contributed reagents/materials/analysis tools, prepared
figures and/or tables, performed the computation work.
• Mark E. Reeves wrote the paper, reviewed drafts of the paper.
Data Availability
The following information was supplied regarding the deposition of related data:
Source code is hosted on github:
https://github.com/hugadams/PAME
PAME v. 0.3.2 is archived on Zenodo
DOI 10.5281/zenodo.17578
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