Protein biosensing with fluorescent microcapillaries

S. Lane; P. West; A. François; A. Meldrum

doi:10.1364/OE.23.002577

Introduction

To meet most practical needs, a label-free optical biosensor should feature low detection limits, small sample volumes, easy and “low cost” analysis, and specificity to the desired analyte [1]. Achieving these requirements poses a difficult challenge, but at least two technologies appear especially promising: (i) those based on surface plasmon resonances (SPRs); and (ii) those due to the resonances of optical microcavities. Optical biosensors based on SPRs have exploded onto the scene in the last decade; progress which was partly enabled by the wealth of chemical functionalization methods for gold surfaces [2]. An enormous array of specific SPR biosensor experiments have now been done, for compounds spanning the range from Dengue fever [3] to cancer biomarkers [4]. In contrast, optical microcavities are often based on silica interfaces, which have a variety of well-established functionalization chemistries (e.g., silanization). Both of these approaches can be specific, require low sample volumes, and have detection limits as low as 10⁻⁷ refractive index units (RIU) [5,6]. Currently, optical microcavities can detect the binding of single molecules as light as a few thousand Daltons [7]. However, expensive equipment such as a narrow-bandwidth tunable laser is necessary to make these measurements. Commercial SPR devices are historically fairly expensive as well, but there is a push toward smaller devices (e.g., using cell-phone applications) [8] that could considerably lower the cost.

Of the various types of optical microcavities, whispering-gallery-mode optical resonators are currently setting records for single-molecule detection limits [7]. The most common types of WGM-based resonator include microscale spheres [9–11] toroids [12], disks [13], fibers [14], and thin-walled capillaries [15]. The basic idea behind each of these is the same: In the first four examples, light is confined by total internal reflection as it propagates around the circumference of the structure. Part of the mode field energy extends “evanescently” outside the device and samples the adjacent medium. In a thin-walled microcapillary, the situation is a bit different; here the outer capillary wall confines radiation and forms the resonances, while the tail of the mode field samples the interior channel region (hence the need for a thin wall).

Fluorescent microcavities (FMs) can be classified as a third type of optical biosensor. These structures combine some of the properties of SPR and evanescent cavity-based sensing. Like the case for SPR devices, fluorescent microcavities feature a broadband optical detection and do not require an expensive scanning laser or a finicky evanescent coupling system. In FMs, the fluorescence generally comes from dyes or quantum dots embedded into the structure; some of the emitted light couples into the cavity modes whose electric field samples the analyte. Instead of interacting with a single WGM, the typically broadband fluorescence couples into many modes, although at the cost of having a low light intensity in each one.

Much of the work on fluorescent microcavity sensors has focused on dye- or QD-doped microspheres [16–24]. There are many methods for embedding a fluorophore under the surface of a microsphere (e.g., diffusion of dye molecules into polystyrene spheres [25], or coating polystyrene or glass with a fluorescent surface layer) [22]. An advantage of this geometry is that the fluorophores are located close to the electric field maxima of the WGMs and can couple into the modes relatively strongly, to the point that lasing from fluorophores interacting with spherical WGMs can be achieved [26]. However, microspheres inevitably require an external chamber to hold the analyte. Potential solutions include inserting the microsphere into a capillary [24], channel waveguide [27], or specialized fluid cell [28], but this adds to the complexity of the sensor system.

An intriguing option is to use the cylindrical resonances of a capillary instead. Capillaries are inherently fluidic devices; thus external chambers are not necessary. The difficulty here is that one needs a fluorescent coating inside the capillary channel, and the coating must have a higher index of refraction than the glass wall in order to confine radiation. Several methods have recently been developed to fabricate this structure; these include rolling fluorescent multilayers into a tube-like formation [29], or injecting fluorescent polymers that dry inside the channel [30]. In the first case, coupling into the device is quite difficult; in the second case the polymer layer may not be sufficiently stable over the course of an experiment [30].

In contrast, a thin layer of fluorescent silicon QDs embedded inside a glassy silicon-oxide matrix can provide a stable, high-index fluorescent coating [31]. The effective refractive index of this layer is in the range of 1.67 at the peak wavelength of the QD fluorescence (around 800 nm). The high refractive index helps to confine the emitted fluorescence into the WGMs and leads to reasonably good Q factors. However, relatively little is known about the chemical methods to functionalize these structures for biosensing. In one previous example the silanization reactions yielded mainly non-specific streptavidin binding and suggested a fairly unstable functionalization [32]. In this work, we aimed to develop a suitable method to enable these devices for biosensing applications. This method is based around the deposition of polyelectrolye (PE) multilayers on the surface of the QD film in the channel. This functionalization scheme was characterized optically, and then used to test the specific detection of neutravidin on a biotinylated polyelectrolyte interface.

Experimental

Glass capillaries with inner and outer diameters of 50 μm and of 360 μm, respectively, were purchased from Polymicro Technologies. They were cut into ~5-cm lengths and the polyimide jacket was then removed by ashing at 600 °C in flowing O₂. The silicon quantum-dot layer was formed using the “HSQ method” [33]. Essentially the capillary is filled with a solution consisting of hydrogen silsesquioxane (HSQ) dissolved in methyl isobutyl ketone (MIBK) and is then annealed at a temperature of 1100 °C for one hour in flowing 95%N₂ + 5%H₂ forming gas. This causes the solvent to evaporate and the remaining HSQ to for a solid layer on the channel surface. This layer consists of silicon QDs with a mean diameter between 3 and 4 nm, embedded in a glassy silicon sub-oxide oxide film [34], forming a capillary-type fluorescent microcavity.

The capillaries were then mounted onto a microscope stage and interfaced to a syringe pump via a PTFE tubing system. The fluorescence was excited with the 442 nm line of a He Cd laser at a power of ~40 mW. The fluorescence was collected by the microscope objective and sent to an imaging spectrometer for analysis, as diagrammed in Fig. 1. The TM-polarized WGMs (radial electric field) were selected by aligning the analyzer accordingly, since these modes have a slightly higher sensitivity [35]. The WGM shifts were extracted from the spectra using an adaptation of the Fourier shift method [36] rather than by peak analysis [37].

Fig. 1 of the capillary and the experimental setup. In the cross-sectional diagram of the capillary, the refractive indices m₁, m₂, and m₃ refer to the analyte, fluorescent layer, and capillary wall, respectively. Radius “b” is measured to the QD layer while “a” is the capillary’s original inner radius (i.e., prior to QD layer deposition). The white wave represents a WGM electric field profile.

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The channel QD film was initially cleaned by pumping 10 M NaOH solution through the capillary while the fluorescence WGMs were being monitored. This procedure leaves the QD film surface clean and with a slight negative charge [38,39]. The FMs were then functionalized using a polyelectrolyte layering method [40], with the aim of producing well-defined PE multilayers that would coat the channel interface (i.e., the quantum dot layer). The first step was to pump a solution consisting of 2 mg/mL polyallyllamine hydrochloride (PAH) dissolved in a 2.5 M NaCl solvent. This solution was pumped at a rate of 5 μL/min for 15 minutes. PAH has a positively-charged functional group that should bind electrostatically to the silica surface, with the salt concentration effectively controlling the layer thickness [41]. The FM was then rinsed by pumping water through the channel for 25 minutes. Next, a solution of 2 mg/mL polystyrene sulfonate (PSS), also in 2.5 M NaCl solvent, was pumped through the capillary under the same conditions as for the PAH solution. PSS has a negative surface charge and should bind electrostatically to the PAH, forming a PAH-PSS bi-layer on the channel surface. This procedure was repeated up to five times to test the response of the WGMs to the layer-by-layer PE deposition on the channel walls; however, for biosensing experiments we used a PAH-PSS-PAH trilayer (Fig. 2). This is because the first PAH layer tends to be incomplete [42,43] implying that a multilayering approach should give a more uniformly functionalized interface. PAH has amine groups on each monomer which could be used to covalently immobilize the carboxylic termination of biotin, using carbodiimide coupling reagents. Therefore it has to be the final layer for the biosensing experiments.

Fig. 2 Diagram of the polyelectrolyte surface functionalization for the biosensing experiments corresponding to steps 1-10 below. The NaOH-treated glass surface has a polyelectrolyte trilayer, with the final PAH layer capturing biotin.

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After the multilayer deposition, a baseline phosphate buffer saline (PBS) solution of pH = 7.4 was pumped into the FM. Next, a solution consisting of 0.25 M N-hydroxysuccinimide (NHS), 0.25 M ethyl-(dimethylaminopropyl) carbodiimide (EDC), and 1 mg/mL biotin in PBS was injected into the device. The NHS/EDC mixture catalyzes the covalent binding of the carboxylic moiety of the biotin with the amine groups on the exposed PAH layer [44–46]. PBS was then pumped for 20 minutes. Next, a solution of 0.1 mg/mL neutravidin in PBS was injected into the FM. Neutravidin was chosen specifically because the alternatives, avidin and streptavidin, will be significantly charged in the buffer solution, potentially leading to nonspecific electrostatic binding (or repulsion) with the biotin molecules or the slightly positive PAH interface [47,48]. In contrast, neutravidin has an isoelectric point of 6.3 and will be nearly neutral in the buffer solution. To summarize:

Step 1: 10 M NaOH etch and clean
Step 2: water rinse
Step 3: 2 mg/mL PAH in saline solution
Step 4: water rinse
Step 5: 2 mg/mL PSS in saline solution
Step 6: water rinse
Step 7: 2 mg/mL PAH in saline solution
Step 8: water rinse
Step 9: PBS buffer
Step 10: biotin/NHS/EDC solution
Step 11: PBS buffer
Step 12: neutravidin in buffer
Step 13: PBS buffer
Step 14: rejuvenate with 1-10 M NaOH solution for next experiment

Two “control samples” were also measured. Control 1 differed from the primary run in that the neutravidin (in step 12) was mixed in a 1:4 ratio with biotin in order to block the biotin-binding sites. In control 2, the biotin conjugation step (step 10) was omitted. The second control should test whether the neutravidin can bind nonspecifically to the PAH interface [49]. Finally, the capillary was rejuvenated between experiments (i.e., controls, etc.). Although the biotin and neutravidin cannot be specifically disassociated, the functionalization can be stripped using 1-10 M NaOH. This removes both the bio-conjugation and polyelectrolyte layers.

Results and discussion

The fluorescence emitted from the FMs showed a clear mode structure, with a Q-factor, free spectral range, and finesse of ~700, ~2.6 nm, and ~2.5, respectively (Fig. 3). The QD films tended to show some variability along the length of the capillary; for this work, a reasonably uniform region was found and the entrance slit was aligned perpendicular to the FM axis, as illustrated in Fig. 3. This helps to minimize underlying WGM drifts associated with mechanical motion over the several hours needed to perform each experiment.

Fig. 3 (a) Fluorescence image of the capillary channel. The red glow is due to the QD emission. The representative slit direction (perpendicular to the channel) is diagrammed. (b) A typical WGM emission spectrum over the range from 760 to 780 nm.

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NaOH has been shown to etch silica [50] and other ceramic materials including silicon [51]; thus it might permit one to obtain experimental control over the QD film thickness. The QD film did in fact show signs of gradually etching as the strong NaOH solution was pumped through the channel. The WGM wavelength blueshifted with time (Fig. 4a), at a rate of approximately 35 pm/h. This blueshift occurs because the effective path length decreases as the high-index material is gradually removed. The spectral shift data could be related directly to an etching rate by using standard methods to calculate the resonance wavelength for a layered cylinder [52], as adapted from earlier theoretical work on TM-polarized layered spheres [53]. For the sake of brevity we don’t repeat the equations here but merely state the results: for conditions matching the experimental ones the resonance is calculated to blueshift by approximately 25 pm per nm etched, yielding an etching rate for the QD film of ~1.4 nm/h in continuously pumped 10 M NaOH solution. At the same time, the sensitivity increased, as shown in the inset to Fig. 4, again consistent with a thinner QD film. After 20 hours of etching, the sensitivity increased from 3.5 to 7.0 nm/RIU, representing a rate of increase of ~0.05 pm/RIU/s.

Fig. 4 WGM wavelength shift as a function of NaOH etching time. As the QD film becomes thinner, the WGMs gradually blueshift. The upper-right inset shows sensorgrams for the water-to-ethanol transition at different etching times. The sensitivity of a single fluorescent microcavity observed at many different etching times is shown in the lower-left inset.

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This is the first time that the QD layer has been controllably etched in an FM structure; it can be done without the use of hydrofluoric acid, which has been used for thinning liquid-core optical ring resonators [54]. Here, the capillary was judged suitable for biosensing experiments when it had reached a sensitivity of ~10 nm/RIU. One slightly tricky aspect is that the NaOH “rejuvenation” step is necessary to remove previously-deposited PE layers for each subsequent experiment. While a single capillary could therefore be used for dozens of runs (essentially until the capillary-tubing adhesive broke down), the sensitivity does slightly increase each time as the QD layer progressively dissolves.

One question concerns the optimal thickness of the QD layer needed to support WGMs for sensing. We recently reported the effect of the layer thickness [35], but some of the salient points can be mentioned here. First, a higher sensitivity is obtained with thinner QD films, as illustrated in Fig. 4. This is because, when the film is thin, more of the mode energy extends into the channel where it samples the analyte medium. However, the film cannot be made indefinitely thin or the Q-factor eventually begins to drop off noticeably. Thus, there should be an optimum thickness associated with the trade-off between the lower Q and the higher sensitivity. On the other hand, for thicker QD films, the sensitivity decreases because less of the mode energy extends into the capillary channel. The Q-factor never exceeds ~1500 for any thickness, however, because of absorption and scattering in the QD film [35].

In order to determine the approximate experimental thickness of the films in the present work, the electric field profiles were calculated following the methods developed in Ref [55]. For space reasons we do not repeat the derivation here but merely cite the relevant equations. Accordingly, the radial function (TM polarization) is given by:

T_{l} (r) = {\begin{matrix} a_{l} J_{l} (m_{1} k_{0} r), & r \leq b \\ b_{l} H_{l}^{(2)} (m_{2} k_{0} r) + H_{l}^{(1)} (m_{2} k_{0} r), & r < b \leq a \\ d_{l} H_{l}^{(1)} (m_{3} k_{0} r), & r > a \end{matrix}}

where J_l(x) is the cylindrical Bessel function describing the field in the inner layer, the Hankel functions of the first (H_l⁽¹⁾(x)) and second (H_l⁽²⁾(x)) kind describe the field in the two outer two layers, and a_l, b_l, and d_l are proportionality constants. The resonant wave vector is found by solving for k₀ under the appropriate boundary conditions, given by

\frac{m_{2} H_{l}^{(1)}' (m_{3} k_{0} a)}{m_{3} H_{l}^{(1)} (m_{3} k_{0} a)} = \frac{b_{l} H_{l}^{(2)}' (m_{2} k_{0} a) + H_{l}^{(1)}' (m_{2} k_{0} a)}{b_{l} H_{l}^{(2)} (m_{2} k_{0} a) + H_{l}^{(1)} (m_{2} k_{0} a)},

with

b_{l} = \frac{m_{1} J_{l} (m_{1} k_{0} b) H_{l}^{(1)}' (m_{2} k_{0} b) - m_{2} J_{l}' (m_{1} k_{0} b) H_{l}^{(1)} (m_{2} k_{0} b)}{- m_{1} J_{l} (m_{1} k_{0} b) H_{l}^{(2)}' (m_{2} k_{0} b) + m_{2} J_{l}' (m_{1} k_{0} b) H_{l}^{(2)} (m_{2} k_{0} b)} .

Finally, the refractometric sensitivity is

S_{T M} = λ_{0} \frac{(2 k_{1}^{2})}{m_{1}^{3} (k_{0}^{2} + {(k_{0}^{*})}^{2})} \cdot \frac{b {| a_{l} |}^{2} ({\frac{d J_{l}^{*} (m_{1} k_{0} r)}{d r} ‖}_{b} J_{l}^{} (m_{1} k_{0} b) + J_{l}^{*} (m_{1} k_{0} b) {\frac{d J_{l}^{} (m_{1} k_{0} r)}{d r} ‖}_{b}) + \frac{k_{0}^{2} + {(k_{0}^{*})}^{2}}{k_{0, 1}^{2}} I_{1}}{[\frac{I_{1}}{m_{1}^{2}} + \frac{I_{2}}{m_{2}^{2}} + \frac{I_{3}}{m_{3}^{2}}]},

in which the energy terms are given by

\begin{array}{l} I_{1} = \int_{0}^{m_{1} k_{0, 1} b} x {| a_{l} J_{l} (\tilde{x}) |}^{2} d x \\ I_{2} = \int_{m_{2} k_{0, 1} b}^{m_{2} k_{0, 1} a} x {| b_{l} H_{l}^{(2)} (\tilde{x}) + H_{l}^{(1)} (\tilde{x}) |}^{2} d x . \\ I_{3} = \int_{m_{3} k_{0} a}^{\infty} x {| d_{l} H_{l}^{(1)} (\tilde{x}) |}^{2} d x \end{array}

where i = 1,2,3 for each of the three regions (channel, film, and glass wall, respectively), k₀ = k_0,1 + ik_0,2, and

\tilde{x} \equiv x (1 + i k_{0, 2} / k_{0, 1})

. These equations can be solved numerically using standard math packages such as Mathematica. Once the field profile has been solved, 2D plots can be obtained by simply multiplying the solution by e ^{± ilϕ} and adding the two solutions to obtain the standing wave in Fig. 5(a).

Fig. 5 (a) Calculated 2D electric field amplitude for an n = 1, l = 310 TM mode for a 50-μm diameter capillary with 500-nm-thick QD film (marked by the black lines). Only part of the circumference is shown. (b) 1D intensity profile for the same conditions as in (a). The discontinuities in the field profile are due to the TM boundary conditions. The sensitivity of this structure is calculated from Eq. (4) to be 23.7 nm/RIU.

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Figure 5 shows the calculated energy profile for a 50-μm diameter capillary with a 500-nm-thick QD layer. Dispersion is taken into account by interpolating tables of optical constants for water [56], Si-QDs (ellipsometry measurements on flat Si-QD films taken in our lab), and silica glass [57]. The refractometric sensitivity for this particular simulation was 23.7 nm/RIU. In order to obtain the observed experimental sensitivities ranging from 3 – 10 nm/RIU depending on the amount of etching, one requires a QD film thickness ranging from 1.0 to 0.8 μm in thickness. These relatively large values imply room for improvement via further etching the films.

We next investigated whether the layers of PAH and PSS could be applied systematically and repeatedly to the FM channel walls. A representative sensorgram showing the deposition of a double bilayer is shown in Fig. 6. The larger jumps in the WGM wavelength (red and yellow points) is due to the higher index of refraction for the PAH and PSS saline solutions, as compared to the water baseline. Evidence in favor of a layer-by-layer PE buildup is clearly observed in the “water regions” of the sensorgram labeled a-e. The net redshift after four layers was ~170 pm, which corresponds to a mean single PE layer thickness of ~1 nm, again estimated by using the field calculations shown in Refs. 52 and 55. The PE layers appear stable and are not removed in water. After the double bilayer, the capillary was cleaned with a 10 M NaOH solution. The slight negative shift during the NaOH run is consistent with the removal of the PE layers. The final water rinse yielded a slightly negative WGM wavelength shift, possibly due to a slight etching of the QD film during the cleaning stage.

Fig. 6 Sensorgram showing the deposition of alternating layers of PAH (red points) and PSS (yellow), followed by cleaning with 10 M NaOH solution (pink). Water is in blue, labeled a to e. The inset shows representative spectra corresponding to steps a and e.

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One final observation was that the overall QD fluorescence intensity slightly decreased over the course of the PE layer deposition (Fig. 6, inset). We believe that this behavior is due to a gradual drift of the microscope focus over the course of several hours over which the experiment was conducted, possibly due to a gradual continuous mechanical motion of the capillary or the stage. However, this had no observable effect on the mode shifts or the sensorgrams, which were clearly independent of any changes in the collected PL intensity.

Some of the key points of the Fourier shift method can be mentioned in order to explain how one is able to obtain minimum wavelength shift resolution of a few pm using a spectrometer with a CCD pitch of about 0.1 nm per pixel and a Rayleigh resolution closer to 0.3 nm. Here, the signal-to-noise ratio (SNR) is approximately 100 (in linear units), the Q-factor is ~700 and the finesse is about 2.5, as discussed earlier. Inserting these values into Eq. (4) of Ref. 36, one obtains an optimal 3σ shift resolution of 14 pm using the Fourier shift technique. This calculated value is quite close to experimental the 3σ deviation of 18 pm in the present experiments, which was obtained by taking repeated measurements with flowing water in the capillary. The reason that the shift resolution is much better than the Rayleigh resolution is due to the need to measure the shift of the whole periodic waveform vs. the separation between two peaks.

An additional point is that the shift resolution is only weakly dependent on the Q-factor [36]. This should not be too surprising; for example, advanced curve-fitting methods for surface plasmon resonances (which have a very low Q) can measure refractive index changes of on the order of 4 x 10⁻⁷ RIU [37]. This corresponds to shifts of a few picometers or less despite the much lower resolution of the spectral system. Similarly, for the types of measurements in the present work, the spectral shift information is encoded over the entire spectral data set and one is not limited to the analysis of a single (potentially poorly-sampled) peak. Indeed, the requirement for a high-Q factor is really only applicable to “intensity-shift” methods (i.e., measuring the change in transmission at a fixed wavelength on the side of a high-Q mode) and not to wavelength shift methods like those used here.

The next step was to determine whether the PE functionalization scheme can be applied to biosensing in these fluorescent-type cylindrical microcavities, using the biotin-neutravidin test system. For this experiment, a PAH-PSS-PAH trilayer was first formed on the channel walls. Injection of the biotin/EDC/NHS solution was then followed by a PBS rinsing step and the subsequent injection of a 1.67 μM neutravidin solution in PBS buffer. As the neutravidin solution was pumped into the device (grey circles in Fig. 7), there was a pronounced redshift of 109 ± 5 pm that occurred over a timeframe of a few minutes. This redshift was retained upon returning to pure PBS, suggesting that the neutravidin had been bound to the biotinylated layer.

Fig. 7 Sensorgram showing the 13-step functionalization and biosensing experiment. The numbers label the steps according to the list given in Section 2. The key step is (12), corresponding to the specific binding of neutravidin.

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In order to determine whether the neutravidin had attached specifically to the biotinylated PAH layer, two separate control samples were run. In the first one, the neutravidin was biotinylated before being pumped through the capillary, as described in Section 2. This was accomplished by allowing it to react with free biotin in buffer for one hour, at a biotin concentration of four times the neutravidin one. This solution was then pumped into the capillary in step 12, in place of the unreacted neutravidin. Here, essentially no shift was observed (Fig. 8a). This is consistent with the idea the redshift reported in Fig. 7, step 12 was indeed due to specific neutravidin binding to the functionalized surface.

Fig. 8 (a) Sensorgram for control sample 1. The sequence is identical to that in Fig. 7, except that the neutravidin (step 12) had been pre-biotinylated before being pumped into the microcavity. (b) Sensorgram for control sample 2. Here, there is a slight redshift (grey points, step 12), likely due to a small amount of electrostatic binding of neutravidin to the PAH layer.

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The second control was performed in order to determine whether the neutravidin could react nonspecifically, for example by binding electrostatically to the PAH layer. For this control sample, step 10 (biotinylation) was skipped (Fig. 8b). As before, the PE layers were built up and followed by water and PBS washes, but the biotin conjugation solution was not performed. This time, we observed a relatively small redshift of 32 ± 6 pm upon injection of the neutravidin solution. This suggests that a small amount of nonspecific binding of neutravidin does occur, but the signal was only about 1/4 that observed in Fig. 7. This observation is consistent with the fact that the isoelectric point of neutravidin (pH(I)) is slightly below the pH of the buffer solution (6.3 vs. 7.4). Thus, while some nonspecific binding to the PE layer does happen, the protein detection is dominated by the specific biotin-neutravidin interaction.

The surface coverage, detection limit, and binding rate constants are important figures of merit for a microfluidic sensor device. This would be the first measurement of these values for fluorescent-WGM-type capillary sensors which are, essentially, a new class of sensor structure that shares some of the properties of fluorescent microspheres and thin-walled LCORRs. The neutravidin binding experiments were therefore repeated using several different concentrations. For these experiments, steps 1-11 were followed as before, but for step 12 the neutravidin concentration was changed from 1.67 μM to 0.8 nM. As the concentration decreased, the saturation wavelength shift decreased (Fig. 9). From these data, one can extract several of the key sensor parameters.

Fig. 9 Sensorgrams for neutravidin binding, for four different concentrations. These data show only step 12 of the reaction process; for each data set the capillary was cleaned with 10 M NaOH and steps 1-11 were performed prior to the running the neutravidin solution. The black lines are fits using first-order reaction kinetics (Eq. (8). The inset shows k_obs plotted against the neutravidin concentration, along with a linear fit.

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If the equilibrium binding constant, K_a, is large, as can be expected for the biotin-neutravidin reaction, then the fractional surface coverage should be close to unity. The functional avidin tetramer has dimensions of ~5.6 x 5 x 4 nm [58], so one can reasonably approximate the neutravidin molecule as a sphere of diameter 5 nm. This yields a maximum theoretical surface coverage of 2.8 x 10¹² cm⁻² (assuming that the projection of a sphere fills ~55% of a surface for random packing [59]), which corresponds to a surface mass density of ~280 ng/cm² for neutravidin. This result is quite close to an experimentally-estimated value of 295 ng/cm² using an SPR sensor [60].

The molecular surface density, σ_p, for a capillary-type microcavity can be estimated from the experimental data according to [61,62]:

σ_{p} = \frac{δ λ}{λ_{0}} \cdot \frac{ε_{0} a (m_{2}^{2} - m_{1}^{2})}{α_{e x}}

in which ε₀ is the vacuum permittivity, a is the radius (Fig. 1), α_ex is the excess polarizability of the neutravidin molecule, and the refractive indices are the same as shown in Fig. 1. The polarizability of neutravidin can be estimated from the Clausius-Mossotti equation:

α_{n} = \frac{ε_{n} - 1}{ε_{n} + 2} \cdot \frac{3 M ε_{0}}{N_{A} ρ_{n}}

where N_A is Avogadro’s number, M is the molar mass of neutravidin (~60 kg/mol), ε_n is the dielectric function of neutravidin and ρ_n is its density. For the latter two values, we take 2.25 and 1.37 g/cm³ as typical of proteins [63]. Accordingly, α_n is estimated to be 5.1 x 10⁻²¹ cm³, which is almost three orders of magnitude larger than that of water [64] and justifies the replacement of α_ex by α_n in Eq. (6). The surface mass density is then given by d = Mσ_p/N_A, yielding a saturation mass density of ~370 ng/cm² for the higher neutravidin concentrations. This is slightly larger than the theoretical value but is probably within the limits of the various approximations. The result appears consistent with the binding of a near-complete monolayer of neutravidin.

The equilibrium binding constant can also be estimated, under the assumption that it is a first-order reaction. Accordingly, the observed reaction rate at any concentration can be obtained from the relation

R_{t} = R_{0} [1 - \exp (- k_{o b s} t)]

in which R_t and R₀ are the signal at time t and initially, and k_obs is the observed reaction rate. The lines through the data in Fig. 3 are fits using Eq. (3), from which k_obs could be extracted for three concentrations. The data for the 8 nM neutravidin concentration could not be well fit, as the shift was too small. The intrinsic rate constants for association (k_a) and dissociation (k_d) are then related to the observed reaction rate according to

k_{o b s} = k_{a} [B] + k_{d}

where B is the concentration of neutravidin in the solution. Since the solution is continuously pumped, the reaction rate is not diffusion limited. Finally, the equilibrium association constant is given by K_a = k_a/k_d. By plotting the observed reaction rate as a function of concentration (inset to Fig. 9), one obtains a slope of k_a = 8.3 x 10⁴ M⁻¹min⁻¹ and an intercept of k_d = 0.076 min⁻¹. The estimated equilibrium association constant is then 1.1 x 10⁶ M⁻¹. This value is about an order of magnitude smaller than that reported for streptavidin on biotinylated gold nanorods [65] and is much lower than in the dissolved form (~10¹⁵ M⁻¹), implying that the biotin-neutravidin reaction rates are affected by the underlying PE layers and/or steric hindrance on the surface monolayer.

In Fig. 9, the lowest detected concentration was 33 nM. This corresponded to a mean 83 pm wavelength shift (or a surface density of 273 ng/cm²). The 3σ standard deviation was ~15 pm, yielding a detection limit of ~6 nM; i.e., quite close to the 8 nM run in which a shift could not clearly be observed. With certain improvements these values may approach the detection limits of devices such as the LCORR which, when probed by a tunable laser, has reached the picomolar range [66] although at the cost of a more complicated, expensive, and fragile device structure and measurement method. One limitation currently appears to be a combination of mechanical and thermal instabilities that could be improved if in future the microcapillary could be physically packaged so that it is immoveable with respect to the objective lens. Also, our relatively low-resolution spectrograph (which has a pitch of slightly over 0.1 nm/pixel) and the moderate sensitivity for the QD film thicknesses used here both offer room for improvement. The latter two methods could, in principle, improve the detection limits from the range of nM to tens of pm [52].

Conclusions

In this work, we report the first example of biosensing with a capillary-type WGM cavity structure. This clearly demonstrates the feasibility of fluorescent capillaries as an alternative type of whispering gallery mode biosensor. While the detection limits do not match those for microcavities probed with a tunable laser, they do offer several attractive features. These include a simple capillary-based fluidic setup, ease of fabrication, and high durability. The devices can withstand multiple usage, they can be readily removed from a setup for cleaning, they can be easily manipulated by hand, and they strictly need only a fairly simple apparatus (a microscope objective, a miniature spectrometer, and a blue light source). As with refractometric investigations, the trade-off, at least at the moment, is in the lower detection limits. Nevertheless, the methods developed in this work – polyelectrolyte layer functionalization for capillary-type FMs – could enable much wider application of these structures. Once the multilayer is deposited, for example, almost any type of biotin-related recognition scheme becomes possible. The method is quite robust and provides uniform results, as long as mechanical drift and temperature fluctuations can be minimized. Several methods were, finally, suggested to improve the detection limits. For example, a higher-resolution spectrograph and increased sensitivity via etching to achieve an optimal QD film thickness should push the detection limit significantly lower.

Acknowledgments

We thank the Veinot group for materials and discussions and the West group for assistance with chemical storage. Funding was from NSERC and AITF IciNano.

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Protein biosensing with fluorescent microcapillaries

Abstract

Introduction

Experimental

Results and discussion

Conclusions

Acknowledgments

References and links

Cited By

Figures (9)

Equations (9)

Optics Express