An effective microscopic model for plasmonic sensing of malaria

TL;DR

The paper tackles the challenge of highly sensitive malaria diagnostics by developing a predictive microscopic model for plasmonic metasurface sensors that detect pLDH. It combines SP field decay, Maxwell-Garnett effective-medium theory, and Langmuir binding to link bulk pLDH concentration to the effective refractive index of the bound protein layer and the sensor response. For a gold nanohole metasurface, the model yields a bulk sensitivity of about 237 nm/RIU and a local sensitivity around 24.6 nm/RIU, predicting an LOD of roughly 0.02 nM (0.70 ng/mL) that outperforms many rapid tests, with results in good agreement between COMSOL simulations and analytical predictions. The framework is general and can guide the design of other plasmonic biosensors and biomarkers, offering a practical route to optimize LODs prior to experimental fabrication, while acknowledging the need for field validation and refinement of kinetic and transport effects.

Abstract

Malaria remains a major health threat in low-resource regions and rapid diagnostic tests often lack the sensitivity required for early detection. To address this and help establish more sensitive testing devices, we develop a predictive microscopic model for plasmonic biosensing using metasurfaces. Specifically, we consider the detection of plasmodium lactate dehydrogenase (pLDH), a well-known malaria biomarker. An example metasurface is studied to showcase the effective microscopic model - it consists of a gold nanohole array (150nm film; 150nm diameter; 400nm period) and the biochemistry above it is modelled as stacks of closely packed adlayers. Using Maxwell Garnett effective medium theory we link the refractive index of the pLDH biomarker adsorbed layer on top of the metasurface to the bulk concentration of pLDH in the buffer. This effective microscopic model accounts for the combined optical properties of the biochemistry matrix, bound pLDH and the buffer medium. By simulating the sensor using the finite element method and an approximate analytical method, we show that the effective model allows one to determine the sensor response, predict binding interactions, and quantify concentration changes on the sensor surface. We then calculate the sensor sensitivity for our example metasurface and its theoretical limit of detection (LOD). The lowest LOD calculated based on the model is 0.02nM of pLDH, equivalent to 0.7ng/mL, which is a 30 times improvement over current rapid diagnostic tests. While this improvement in performance is highly promising, further work on transferring the ideal theory developed here to field-tested empirical performance will be required. The effective microscopic model we introduce is quite general and the framework developed offers a broadly applicable tool for the design and optimization of other types of highly sensitive plasmonic biosensors.

Figures (10)

• Figure 1: Formalism and working principle of a metasurface-based plasmonic biosensor. (a) A schematic drawing of the biosensor. Light is incident on the nanohole array (NHA) from the substrate side. (b) The spectra of the sensor before and after analyte binding. Plasmonic biosensing is achieved by monitoring the change in intensity or wavelength. Spectral sensing monitors the change of the transmission peak, $\delta \lambda_{R}$, when the refractive index $n$ is altered to $n+\delta n$, where $\delta n$ is the change or increase in the refractive index of the sensing medium. Intensity-based sensing monitors the change in transmittance, $\delta T$, at a fixed wavelength $\lambda_0$ off-resonance when $n$ changes to $n+\delta n$. (c) A three-layer SPR system that represents a typical configuration for exciting SPs. The parameters $\varepsilon_d,\;\varepsilon_m$, and $\varepsilon_s$, are the dielectric permittivity of the superstrate, metal, and substrate medium, respectively. (d) A cross-section view of the metasurface in panel (a). $D$ is the hole diameter, $a_0$ is the period, $d$ is the hole depth, $k_0$ is the free-space wavenumber of the incident wave and $\theta$ is the incidence angle.
• Figure 2: Contribution of SPs to the transmission spectrum of the metasurface with hole diameter $D = 150$ nm, period $a_0 = 400$ nm and gold thickness $t = 150$ nm in phosphate-buffered saline (PBS). (a) The simulated geometries used. (i) The bare metasurface in PBS with no chrome added. (ii) A chrome layer ($20$ nm thick) is added between the gold-PBS interface. (iii) A chrome layer ($20$ nm thick) is added between the gold-glass interface. The parameters $t_1$ and $r_1$ (resp. $t_2$ and $r_2$) are the transmission and reflection coefficients of the fundamental Bloch mode of the array at the $\varepsilon_s$ (resp. $\varepsilon_d$) interface. (b) Simulated transmission spectra for the metasurface using COMSOL multiphysics software. Transmission spectra of the three cases. (i) A bare metasurface in PBS solution, where no SPs are suppressed. (ii) The SPs at the top dielectric interface are suppressed and, (iii) The SPs at the bottom glass interface are suppressed. The inset shows the electric field distribution within the hole (a cross-section view of a quarter cell). The maximum electric field enhancement $|E|/|E_0|$, at resonant wavelengths $\lambda_R = 650$ nm for peak I and $\lambda_R = 715$ nm for peak II, is 6 and 21, respectively. The minimum $|E|/|E_0|$ is zero. $|E|$ is the electric field norm. The dielectric constant of the substrate $\varepsilon_s$ and superstrate $\varepsilon_d$ are given in terms of the refractive indices $n_s = 1.52$ and $n_d = 1.335$, respectively. The permittivity of gold $\varepsilon_m(\lambda)$ included in the simulation was based on a Lorentz-Drude model rakic1998optical, taken from the built-in COMSOL optical materials database. A TM plane wave polarized in the $x$ direction propagating along $z$ was incident on the metasurface from the substrate side.
• Figure 3: Microscopic model formalism using Maxwell Garnett effective medium theory. (a) The non-functionalized metasurface with analyte solution. Proteins are uniformly distributed throughout the buffer medium. (b) Antibody-functionalized metasurface. Proteins bind to the immobilized antibodies forming a layer with thickness $da$ and effective refractive index $na_{\text{eff}}$. The refractive index $na_{\text{eff}}$ depends on the number of bound proteins. (c) A zoomed-in sketch of a bound protein shows the corresponding unit cell used to derive the effective refractive index $na_{\text{eff}}$ using Maxwell Garnett theory. A dispersed phase ($\textit{e.g.}$ protein, $na_{\text{L}}$) is embedded in a continuous phase ($\textit{e.g.}$ PBS buffer solution, $nb_{\text{soln}}$).
• Figure 4: A schematic of the simulated model involving a quarter of a unit cell. (a) The cross-section view of our sensor, where $\delta_d$ is the SP decay length. (b) A zoomed-in region of the sensor shows the surface chemistry and a binding event near the sensor surface. The biochemistry layer (DSP + Protein A) has a thickness $t_{cm} = 6$ nm, the antibody layer has a thickness $t_{Ab} = 8.4$ nm, and the analyte layer has a thickness $da = 7.9$ nm--the size of pLDH. Dashed arrows represent the kinetic interaction of the analyte to the immobilized antibody. Alternating dots represent the buffer solution with index $nb_{\text{soln}}$. (c) Adlayers are packed in series from the gold surface: DSP coating + protein A + IgG and a pLDH bound layer. Buffer solution covers the whole sensor surface. Gold is poorly bound to glass, and so an adhesion layer of ITO ($5$ nm thick) is used. Glass with refractive index $n_s = 1.52$ is used as a substrate. Light (red arrow) enters the sensor from below.
• Figure 5: Sensor spectral response and sensitivity. (a) Transmission spectra of the non-functionalized metasurface in different liquids, $nb_{\text{soln}} = 1.335$ (PBS buffer solution) to $1.390$. (b) Transmission spectra of the functionalized sensor where $na_{\text{eff}}$ is the refractive index of the pLDH layer bound to the antibody layer with $n_c = 1.45$. The inset shows the adsorbate layer architecture above the gold (Au) surface. (c) The bulk spectral-sensitivity of a functionalized sensor, $S_{\lambda_R,\;\text{f}}$, and non-functionalized sensor, $S_{\lambda_R,\;\text{nf}}$, are compared. (d) The calculated local sensitivity $S^L_{\lambda_R}$ using the simulated data in panel (b) and the microscopic model from Eq. \ref{['resonance_shift_estimate']}. (e) The bulk intensity-sensitivity of a functionalized sensor, $S_{T,\;\text{f}}$, and non-functionalized sensor, $S_{T,\;\text{nf}}$, are compared. (f) The calculated local sensitivity $S^L_{T}$ using the simulated data in panel (b) and the microscopic model from Eq. \ref{['resonance_shift_estimate']}. The $n_{\text{eff}}$ values in panels (c) and (e) are calculated from Eq. \ref{['frist_model11']}, where $na_{\text{eff}}$ was varied from $1.335-1.375$. The inset in panel (e) shows how the change in the effective refractive index, $na_{\text{eff}}$, of the pLDH layer, affects the change in the effective refractive index, $n_{\text{eff}}$, above the Au surface, as given by Eq. \ref{['frist_model11']}. The deviation in the $S_{\lambda_R}$ magnitude, in panel (c), of $237.09$ nm/RIU to $236.98$ nm/RIU for the non-functionalized and functionalized cases, respectively, is attributed to the small modification of probe depth, $\delta_d$, due to the presence of adsorbate layers in the functionalized sensor. To achieve optimal fitting of the microscopic model in panels (d) and (f), the probe depth, $\delta_d$, was varied from $100-160$ nm, giving 108.9 nm and 151.7nm, repectively. Further details on sensor sensitivities are given in Appendix A, in Section 1.