PAME: plasmonic assay modeling environment


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;

Kraziński, 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

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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.

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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.

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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

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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

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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

n1 cosθi − n2 cosθtn1 cosθi + n2 cosθt
2 +

n1 cosθt − n2 cosθin1 cosθt + n2 cosθi
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, ñ = n + iκ, or dielectric function, ẽ = e + iϵ, which are

related through a complex root (ẽ =
√

ñ), which gives the relations

e = n2 − κ 2 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

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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 − B21
+

A2λ2

λ2 − B22
+

A3λ2

λ2 − B23
+ ···. (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

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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
ẽ 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,

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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 ≈
128π 5

3λ4
R6Im


m2 − 1

m2 + 2

2
  

≈σscatt

−
8π 2

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

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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 Trügler (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.

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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,

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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

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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 = φ1ñAu + φ2ñAg. 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

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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

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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

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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.

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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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	PAME: plasmonic assay modeling environment
	Introduction
	Theory and Design
	Substrate types
	Multilayer stack
	PAME material classes
	Simulation and data analysis

	Examples of Use
	Case 1: refractometer
	Case 2: multiplexed Ag--Au sensor

	Implementation and Performance
	Future Improvements
	Conclusion
	About
	Acknowledgements
	References