Detecting Antibody-Antigen Interactions with Chiral Plasmons: Factors Influencing Chiral Plasmonic Sensing

Chiral near fields possessing enhanced asymmetry (superchirality), created by the interaction of light with (chiral) nanostructures, potentially provide a route to novel sensing and metrology technologies for biophysical applications. However, the mechanisms by which these near fields lead to the detection of chiral media is still poorly understood. Using a combination of numerical modelling and experimental measurements on an antibody-antigen exemplar system we illustrate important factors that influence the efficacy of chiral sensing. We demonstrate that localised and lattice chiral resonances display enantiomeric sensitivity. However, only the localised resonances exhibit strong dependency on the structure of the chiral media detected. This can be attributed to the ability of birefringent chiral layers to strongly modify the properties of near fields by acting as a sink / source of optical chirality, and hence alter inductive coupling between nanostructure elements. In addition, we highlight how surface morphology / defects may amplify sensing capabilities of localised chiral plasmonic modes by mediating inductive coupling.


Introduction
Spectroscopic techniques based on the differential interaction of circularly polarised light, such as circular dichroism, can provide a rapid method for the detection and low-resolution structural characterisation of biologically relevant molecular materials 1 . The inherent weakness of the optically active response intrinsically limits the sensitivity of chiroptical spectroscopic methods, with maximum detection sensitivities typically at the  g level. It has been proposed that the sensitivities of chiroptical spectroscopies can be amplified using electromagnetic (EM) fields which in highly localised regions of space can have greater chiral asymmetries than circularly polarised light (CPL), a property sometimes referred to as superchirality 2,3 . The chiral asymmetry of EM fields is parameterised using optical chirality density (C) 4 typically normalised against the value for the equivalent CPL. Near fields created by light scattering from nanostructures can have | | > 1 5 , this has been demonstrated using chiral plasmonic [5][6][7][8] and achiral dielectric nanostructures [9][10][11] . Introducing chiral media into the near field regions of chiral nanostructure can lead to asymmetric changes in the chiroptical response measured in the far field. This phenomenon offers an appealing route to novel ultrasensitive biosensing technologies with  pg detection limits 8,[12][13][14][15][16][17][18][19] . For this phenomenon to be exploited effectively requires an understanding of chiral light -matter interactions. The crucial issues to be addressed are: how the introduction of chiral media into the near field region of nanostructures leads to a significant asymmetry in a far-field chiroptical response; and is the detection phenomena generic or are there constraints placed on the nature of the types of chiral media that can be detected? The ability of chiral layers to induce asymmetric changes in the chiroptical responses of enantiomorphic structures is associated with an ability to induce differential changes in the properties of near fields. In the absence of chiral media, symmetry equivalent combinations of light circular polarisation and nanostructure handedness, near fields have opposite signs of optical chirality but are otherwise identical. Introduction of chiral layers breaks this relationship, with the largest divergence occurring when the chiral layers possess birefringence. This effect is attributed to the ability of chiral birefringent layers to act as a sink (source) of optical chirality. Consequently, compared to isotropic chiral media, birefringent layers induce greater asymmetries in near field properties, resulting in a greater change in far field optical response.

Background
Optical chirality (C), is a conserved property of light 4, 20, 21 , like energy, and is equivalent to optical spin-density. When chiral EM fields interact with chiral matter, optical chirality can be either exchanged or dissipated through absorption. Thus, the optical chirality flux of a light beam can be changed in a chiral lightmatter interaction [22][23][24][25] . These processes depend on the handedness of both the circular polarisation of light and the media. The differential absorption of CPL (dissipation of optical chirality) by chiral media is the basis of the chiroptical technique circular dichroism. Optical chirality can be exchanged between CPL and a medium without absorption. For instance, optical chirality can be transferred to a non-absorbing birefringent material resulting in the depolarisation of the CPL beam. Alternatively, linearly polarised light can also become elliptically polarised (i.e. gains optical chirality) by passing through birefringent materials. The transfer of optical spin angular momentum from CPL sufficient to create an opto-mechanical torque to rotate macroscopic objects was first demonstrate by Beth in 1936 26 .
The central premise of this study is that chiral birefringent layers act as efficient sinks of near field optical chirality. This causes significant divergence in the reciprocity of the C and intensities of fields possessed by left (LH) and right-handed (RH) nanostructures. Consequently, this causes asymmetric changes in the chiroptical properties of LH and RH structures, measured in the far field, which enhances chiral sensing capabilities.

Results
A gammadion has four-fold rotational symmetry and in free space belongs to the C4h point group.
When placed on to a surface, mirror symmetry is broken, and it becomes chiral with a point group Mode III is located a wavelength, 780 nm. close to the periodicity of the structure; and is associated with a field distribution which has intense regions between gammadia. Both factors point to mode III being a Bloch (surface lattice) mode 36 .
A group theory analysis based on the (C4) point group symmetry of the gammadion provides information on the non-Bloch modes localised on the structure. The symmetry analysis is based on considering the gammadion structure to consist of 8 rods each being assigned a vector (representing a dipole moment). Using this as a basis it can be determined that there are 6 modes, 2A+2B+2E, with only the doubly degenerate E modes contributing to CD spectra. The two E modes can then be assigned to the two out-/ in-phase combinations, modes I and II respectively. Thus, the symmetry analysis is consistent with the predictions of the coupled oscillator model and the numerical simulations.
The mode assignments made above are also supported by experimental observation. We have collected spectra from the two enantiomorphic structures which have been given a gradually increasing incline, shown in Parameterising spectral asymmetry.
The ability to detect chiral (bio)materials with chiral metamaterials is based on the premise that they asymmetrically change the optical properties of enantiomorphic structures. These asymmetries can manifest as differential shifts in the positions of resonances which can be parameterised by: where L/R are shifts in the position of resonances (I, II, II) in the presence of the chiral media, relative to an achiral reference, which in this case is buffer solution. In addition the presence of chiral media can cause asymmetric changes in the amplitudes of resonances of the CD spectra, without causing differential shifts in the position 17 .
Reference measurements using achiral solutions were performed prior to experiments with chiral materials (supplementary). As expected there was no significant asymmetries between spectra from LH and RH structures, with I,II,II being  0. It should be noted that the surface lattice (Bloch) mode III was more sensitive to the refractive index of the surrounding liquid the L/R being  2 times greater than those for modes I and II.

The chiral layers.
An intrinsically chiral protein streptavidin has been used in this study, it is a tetramer with a predominately -sheet structure 37 . Streptavidin was chosen because it can be utilised to produce both structurally isotropic and anisotropic chiral layers, the two cases referred to as specific and nonspecific binding. If adsorbed directly from solution on to the nanostructures the protein adopts a broad range of orientations on the surface, characteristic of non-specific interactions, resulting in a layer with an isotropic structure. The small molecule biotin (sometimes referred to as vitamin B7) binds very strongly to streptavidin, with a binding constant (kd)  10 -14 M 38 . This very strong interaction can be used to specifically bind streptavidin in a well-defined orientation. In particular, Au nanostructures were functionalised with self-assembled monolayers (SAMs) of a thiol with a biotin head group. Streptavidin specifically binds to these SAMs adopting a well-defined orientation 39 . It should be noted that biotin is also chiral, thus the SAMs will also be chiral. In addition to studying specifically and non-specifically bound streptavidin we have also made measurements from complexes formed by them and an antibody. Explicitly, a polyclonal mouse IgG which has been produced against streptavidin, subsequently referred to as anti-strept.

CD data isotropic layers
Spectra collected from the non-specific bound streptavidin layers are shown in figure 5. A red shift in the positions of the CD resonances occurs when unfunctionalized LH and RH structures are exposed to buffered solutions of streptavidin. This is consistent with an increase in the local refractive index around the nanostructures due to the adsorption of streptavidin. The spectra are not significantly changed after replacing the protein solution with buffer, indicating that the streptavidin is irreversibly adsorbed. The presence of the streptavidin induces no measurable asymmetry in the chiroptical properties, with I, II, III  0. Binding anti-strept to streptavidin causes a further red shift in the CD resonances due to the increase in the thickness of the adsorbed layer. However, the (anti-strept)streptavidin layer still does not cause a measurable asymmetry between CD spectra from LH and RH structures.

CD data anisotropic layers
The functionalisation of the gammadia with biotin SAMs causes a red shift in the spectra shown in figure 6, and there is a small but measurable asymmetry between CD spectra from LH and RH Altering the level of coupling within the structure 31, 41 will result in a commensurate change in the far field chiroptical response. Consequently, the proposal is that the largest asymmetry in chiroptical response between LH and RH structures must be corelated to large differentials in the properties of near field regions between arms.

Numerical simulations
EM numerical simulations have been used to provide validation for the hypothesis proposed above.
To accurately mimic protein layers we have defined dielectric slabs 20 nm thick, which cover each of the exterior surfaces of the gammadion, figure 8. The chiral properties of the dielectric slab are defined by  a second rank complex tensor the sign of which is dependent on handedness, and is zero for achiral media. In the case where the electric dipole -magnetic dipole (E1M1) interaction is the dominant contributor to optical activity, then only the three diagonal elements xx. yy. zz are non-zero.
The interaction of EM fields with chiral media are given by the following constitutive equations: Here, ( ) is the (relative) permittivity of free space, and ( ) 0 is the (relative) permeability of free space. is the complex electric field, and is the magnetic field. Constitutive equations (3) and (4) were used in these simulations, and it was assumed that the chiral dielectric layers were continuous unstructured slabs.
To mimic the isotropic layers produced by the non-specific adsorption of proteins, the slabs were considered to have a homogeneous refractive index of 1.4, with a | | = 5 × 10 −4 . When proteins are adsorbed on to a surface with a well-defined orientation, such as streptavidin via the biotin SAM, the properties of the layer are no longer isotropic. The refractive index in the direction of the surface normal will be different to those in the directions of the two orthogonal axes parallel to the surface, which are equal to each other due to azimuthal averaging. Thus, an oriented protein layers should be considered birefringent. It should be pointed out, that the anisotropy of chir(optical) properties in oriented proteins is due to the spatial distribution of the compound building blocks, rather than an intrinsic optical anisotropy of the building blocks themselves. We have simulated the birefringent layers with refractive index (n) components of nx = ny = 1.3 and nz = 1.6, these values comparable to that previously measured for a protein system 42 . Simulated spectra for non-birefringent (isotropic) and birefringent (anisotropic) layers are displayed in figures 9 and 10.
The simulations for the isotropic layer display significant asymmetries in the amplitudes of modes I, II and III, but only the lattice mode III has a ≠ 0. In contrast simulated spectra for the birefringent  Table 1 contains averaged field and C intensities for mode II, taken from regions between the arms of the gammadion. The level of breaking of the mirror relationships, is significantly greater for the birefringent slabs, with largest changes in both field intensity and C occurring in the region between the arms. We attribute the stronger influence of birefringent layers on near field properties to the ability to act as an additional sink / source of optical chirality. The birefringent layers have the largest differential effects on the near fields between the arms, with less pronounced differences in the fields between adjacent structures.
It is worth noting that the numerical simulations do underestimate the magnitude of the  for resonances I and II compared to experiment. This however is not surprising given that the near fields of the gap region would be very sensitive to the morphology / roughness /defect of the nanostructure which are not accounted for in the idealised model. For instance, hotspots associated with defects / roughness of the arms could strongly perturb the coupling.

Conclusions
The ability of birefringent layers to strongly perturb the chiral near fields is analogous to how they affect CPL. A beam of CPL propagating through a birefringent layer will suffer a level of depolarisation, becoming elliptically polarised, and reducing the C of the beam. Alternatively, a linear polarised light beam, with polarisation that is not parallel to an optical axis will develop elliptical polarisation, hence gaining C. Consequently, (weakly absorbing) birefringent materials can act as a sink (or source) of optical chirality. The exchange of optical spin angular momentum from light to birefringent materials create opto-mechanical torques. In the current case, these torques would induce rotational motion of the immobilised protein molecules. Effectively, changes in C of the near fields are due to the conversion of optical spin into molecular motion of the proteins.
This work provides insight in to the mechanism of enantiomeric sensing with gammadia, which could be generally applied to other structures. Numerical simulations suggest that chiral lattice modes are more sensitive to isotropic chiral media than localised modes. The greater sensitivity may be So, to some extent the aggregation state of the adsorbed protein will be a function of both how the sample was fabricated and its previous history, leading to variability and uncertainty in measurements.
This variability can be drastically reduced, and the robustness of the methodology enhanced, by employing surface immobilisation techniques, such as the one used here, which were originally developed for biosensing applications. Additionally, the ability of point defects / surface roughness to influence the inductive coupling between structural elements will clearly affect the sensing capabilities of a chiral structure. Hence, the sensing efficiency would be expected to be dependent on anything that influences nanostructure morphology, such as metal deposition strategy used and whether the sample had been plasma cleaned.
In summary, by considering the ability of birefringent chiral layers to act as sinks / sources of optical chirality (optical spin angular momentum), the dependency of enantiomeric sensing on structural anisotropy can be understood. Our work highlights the potential strengths sensing with chiral near fields. In particular, the novel sensitivity to higher order biological structure of some chiral localised resonances which are derived from coupling between modes.

Gammadion Sample Fabrication
The gammadia structures were fabricated using an electron beam lithography process. Quartz glass slides were cleaned under ultrasonic agitation in acetone, methanol and isopropyl alcohol (AMI) for 5 minutes each, dried under N2 flow and exposed to O2 plasma for 5minutes at 100W. gold layer. The process was completed with a lift-off procedure in acetone at 50C overnight and then agitated to remove all remaining resist and excess metal.

Sample Preparation
Biotin-PEG-thiol (C34H65O13S) was purchased from Polypure and dissolved in (Gibco) PBS buffer (10x, pH7.4) to a concentration of 60μM. Streptavidin protein was acquired from Thermo Fisher and diluted in PBS to a concentration of 2μM. Anti-streptavidin antibody produced in rabbit was obtained from Sigma-Aldrich and diluted in PBS to make up a 4μM solution.
Gammadion substrates were placed in a custom printed sample holder, with a FastWell Silicone seal and clear borosilicate glass slide above it. Solutions were injected through the seal. Samples were secured in a JASCO J-810 Spectropolarimeter to perform CD measurements. Biotin depositions were performed overnight to allow sufficient time for the SAM layer to form. The samples were then rinsed in PBS to remove unbound Biotin. Streptavidin solution in PBS was then introduced to the sample and left overnight, prior to rinsing in 0.1% NaOH/Tween which removed non-specifically bound streptavidin. Finally, antibody solution was injected and left to deposit for 2 hours, at which point a 0.05% NaOH/Tween solution was used to remove non-specifically bound antibody.
Measurements were performed with biomolecule solutions and with PBS replacement. Samples were cleaned between experiments using AMI and a low power plasma clean.

Numerical Simulations
Simulations were performed using commercial finite element analysis software, COMSOL Multiphysics v5.4 (Wave optics module). Periodic boundary conditions were applied to emulate the array of structures. Perfectly matched layers were used above and below input and output ports. LCP-and RCP-light was applied at normal incidence through the quartz on to the gammadion. Additional 20nm 'protein' domains were extruded from the outer surface of each gammadion and split into discrete domains. The domains were identified by the axis of their surface normal (x, y or z). Protein domains were made chiral, with a | | = 5 × 10 −4 . Protein domains were also assigned a refractive index of 1.4 in the isotropic case. For birefringent simulations, domains were given a birefringence of 1.3/1.6, with the largest values being assigned to the axial component of the respective surface normal.