Image analysis optimization for nanowire-based optical detection of molecules

3.1 Signal quantification metrics

Once the locations of fluorescent nanowires are obtained, the signal can be evaluated. Kinked or missing nanowires, which fail to enhance the signal due to disrupted geometry, appear as undetected dark spots in image analysis, thus are normally below the detection threshold and remain unaccounted for in the signal quantification. To quantify the signal of individual bright nanowires, we calculate the average pixel intensity I ̄ i for each successfully localized nanowire:

where I _i,k represents the individual pixel intensity of each kth pixel in the local neighborhood K of ith nanowire, and N is the total number of bright nanowires. In our analysis, we used a window of size 3 × 3 pixels around the nanowire location, thus K = 9. In Regime II and III, I ̄ i increases alongside N and is expected to be proportional to the number of bound molecules to each individual nanowire:

Here, < σ enh > is the combined enhancement factor due to all optical enhancement effects and represents σ _enh averaged over the axial positions of fluorophores [11]. I j f l is the intensity of an individual fluorescent molecule, and M is the expected number of molecules bound to each nanowire.

As N and I ̄ i capture two different quantities sensitive to analyte concentrations in two different regimes, we also introduce the overall fluorescence signal I _tot, which incorporates nanowire digital count and intensity integration along the nanowire axis:

We also use I avg = I tot N to quantify the average intensity per individual bright nanowire across the whole specimen.

In order to obtain the relative signal from the specimen compared to the blank, we acquire and analyze images before adding the fluorescent analyte and determine the number (N ₀) and the total intensity I _0,tot for each blank sample. The normalized values for each specimen are then:

In time-resolved processes, we omit image pre- and postprocessing steps (steps 1 and 3 in Figure 2) for simplicity and direct comparison with TIRFM, as image fusion and outlier exclusion algorithms are not applicable for glass surfaces. See Supplementary Methods, Section 1.6 for additional information on data analysis.

3.2 Nanowire growth and characterization

Gallium phosphide (GaP) nanowire were grown using metalorganic vapor-phase epitaxy (MOVPE) from gold (Au) seed nanoparticles of density 1.19 Au seeds/µm² on 3″ (111) GaP substrates in an Aixtron 200/4 reactor (Aixtron, Herzogenrath, Germany) [33]. GaP nanowires and the substrate from which they are grown were coated with a SiO₂ layer of thickness d _coat = 10 nm using atomic layer deposition (ALD, Fiji, Cambridge Nanotech, Cambridge, MA, USA) to provide an adsorptive surface for molecular binding. Values for the nanowire diameters at the top (d _top) and bottom (d _bot) and other dimensions are provided in Table 1.

The tapering factor of nanowires, calculated as (d _bot − d _top)/(d _bot + d _top), yields 0.03, which means that it does not have a negative effect on the signal enhancement properties of nanowires [8].

3.3 Surface functionalization and image acquisition

GaP nanowire platforms of size 2.5 × 2.5 × 0.3 mm³ were first functionalized with 6 µM biotinylated bovine serum albumin (bBSA) dissolved in phosphate-buffered saline (PBS) for 1 h at room temperature. After incubation with bBSA, the samples were washed with PBS, followed by incubation with the analyte, AlexaFluor647 labeled streptavidin (StvA647, ThermoFisher Scientific, USA), and prepared from 1 mg/mL stock solution. See Supplementary Methods, Section 1.1 for additional details.

3.3.1 Single-frame titration measurements

The samples were imaged with an inverted epifluorescence microscope (Eclipse Ti2, Nikon), water immersion objective (magnification of 60×, numerical aperture (NA) = 1.2), and a Sona sCMOS camera (Andor, Oxford instruments). A 640 nm laser was used as an excitation source at approximately 10 mW excitation power with 100 ms exposure time. Reference blank images were taken following bBSA incubation and washing step for each individual specimen. Prior to imaging, bBSA-coated samples were prebleached at a maximum laser intensity for 10 s to suppress the nonspecific signal. Seven consecutive concentrations (0.01 pM, 0.1 pM, 1 pM, 10 pM, 1 nM, 10 nM, and 100 nM) of StvA647 were prepared and imaged both in bright-field and fluorescence regimes. For each concentration as well as blank measurements, 6 different regions of size 92.85 µm × 92.85 µm were imaged. The reference images were analyzed and used to normalize the number of detections (N) and total intensities (I _tot) in Figure 3(b) and (c) according to Eq. (3).

Figure 3:

Titration experiments of Stv-Alexa647 binding to a nanowire array. (a) Micrographs representing fluorescence emission upon additions of StvA647 at 10 fM, 10 pM, and 10 nM. The illustrations depict the three regimes identified (see main text). (b) The normalized number of localized bright nanowires (N′) versus StvA647 concentration. (c) I _avg, the average intensity per bright nanowire versus StvA647 (orange curve). The dashed black line represents the average intensity of the blank measurements. (d) The normalized total intensity detected from nanowires I tot ′ , serving as a readout signal (orange curve). Nonsingle emitter methods, such as averaging the pixel values ( I px ′ , purple) and thresholding averaging the pixel values ( I thr ′ , cyan), are plotted for a comparison. Detections from blank images were used to normalize the number of molecules (b) and total intensities (d). See Eq. (3) and Supplementary Methods, Section 1.6.1 for additional details on the calculation of intensity metrics and normalization.

3.4 Simulated dataset

In order to evaluate the performance of NanoLoci and other image analysis approaches, we simulated the image formation of fluorophores bound to vertically aligned SiO₂-coated GaP (n _GaP = 3.34 at the modeled wavelength of λ = 640 nm) nanowires immersed in aqueous solution ( n H 2 O = 1.33 ) (see [11] for technical details and summary of the modeling). This has the advantage that simulated images can be used as ground truth, and to unambiguously determine the precision of imaging and image analysis.

The modeling was performed by solving Maxwell’s equations for Alexa647 fluorophore, described as an isotopic dipole in the vicinity of nanowire scatterer using finite-element method (FEM) in COMSOL Multiphysics [11], [14]. The simulations were performed for widefield microscopy, modeling the incident light as a combination of incoherent plane waves within the NA of the objective. We modeled GaP nanowires of diameter d _top = d _bot = 100 nm, as the tapering of the nanowires is negligible in terms of the waveguiding of nanowires [8]. The length of the nanowires was set at L = 3 µm, and the thickness of the coating layer was d _coat = 10 nm. Given the lateral separation of the nanowires (p = 0.99 µm), no interference effects were considered between the individual nanowires.

The excitation enhancement was obtained from modeling the electric field | E ⃗ | 2 at the fluorophore position, separately for each incident angle allowed by the numerical aperture of the objective and two polarization states similar to Refs. [14], [34]. The emission modeling was done for fluorophores bound to different axial positions on the nanowire, with 50-nm stepsize. A near-to-far-field transform is performed using the RETOP package [35]. The Purcell factor (C_Purcell), representing the modification of emission compared to a reference medium (H₂O in this case), was calculated and used to obtain the emission enhancement based on the modification of the quantum yield of the fluorophore.

The optical image is created from far-field solutions of Maxwell’s equations [36], [37] in the Fourier space. This leads to an image of nanowire-modified fluorescence for each given axial position proportional to the intensity of the electric field at that location for a given objective (water immersion, NA = 1.2).

Photons were sampled from the modeled image (numerical PSF) onto discrete imaging pixels corresponding to the imaging camera’s pixel size using the generation of random numbers from discrete 2D functions [38]. The excitation and quantum yield enhancement factors, calculated for each z position, were used to modify the effective photon count. Different fluorophore concentrations ranging from single molecule binding to multiple binding on a single nanowire were simulated. Each simulated molecule was randomly assigned to either bind to the substrate or to a nanowire. Additionally, the selection of binding sites on individual nanowires, as well as their respective z-coordinates, was determined randomly (see Supplementary Methods, Sections 1.4 and 3.2 for additional details.)

In the event of multiple binding, the photons were sampled from each position and added to form the final image. In case of fluorophore binding to GaP substrate instead of nanowires, we used a conventional z-dependent Gaussian PSF [39], [40], as the fluorophores bound to substrate do not couple to nanowire light-guiding modes and no significant enhancement is assumed. Based on the nanowire distribution observed in SEM measurements, 15 % of the nanowires in the simulations were modeled as missing or kinked at random heights. To approximate this, the same z-dependent Gaussian PSF used for substrate-bound molecules [39], [40] was applied to the corresponding z positions.

The final image (I _fin) is then created by adding the emission from nanowires (I _NW), GaP substrate (I _sub), and imaging noise, including dark current and photon shot noise (see Figure S3 for more details).

3.5 Ground truth evaluation metric

We choose Jaccard index (JI), Precision, and Recall as a way to evaluate the performance of the algorithms by comparing the ground truth (GT) to the obtained detections [41]:

where TP stands for true positives, which is the number of detections which were matched between the ground truth (locations of waveguiding nanowires) and detected locations. Respectively, false positives (FP) correspond to detections in simulated images, which do not match with ground truth. False negatives (FN) represent the number of nanowire-bound fluorophores present in ground truth but undetected with evaluated algorithms. To obtain the number of TPs, FPs, and FNs in each frame, we calculate pairwise distances between each entry in the ground truth and each detection: D ( i , j ) = ( x i − x ̃ j ) 2 + ( y i − y ̃ j ) 2 ; ∀ i ∈ M , ∀ j ∈ N . Here, (x _i , y _i ) are the locations in ground truth and ( x ̃ j , y ̃ j ) are the detected locations. The closest pairs of detections were found based on nearest-neighbors algorithm, if the Euclidean distance D(i, j) was smaller than the threshold (d _M ). Note, that in this comparison, we only compare the detected locations to true locations without any consideration of intensity values.

4.1 Digital counting and signal integration enables large dynamic range

We performed titration experiments using streptavidin-biotin assay and applied the image analysis pipeline illustrated in Figure 2. N and I _tot were normalized using the corresponding blank measurements according to Eq. (3). For the lowest concentrations (0.01 fM − 1 pM), where less than 10 % of the nanowires are bright, N′ increases with increasing concentration (Figure 3(b)), while I _avg remains essentially unchanged and close to the background level (Figure 3(c)). These concentrations correspond to Regime I, attributed to binding of single molecules to each individual nanowire (Figure 3(a)). Between 1 nM and 10 nM analyte concentration, N′ saturates as all nanowires become bright (Figure 3(a) and (b)), while the increase in I _avg is due to the increase of the number of molecules bound to individual nanowires (Figure 3(a) and (c), Regime III). At intermediate concentrations (10 pM, Regime II), both N and I _avg increase (Figure 3(b) and (c)) as a transition is happening from low to high concentration coverage, resulting both in increasing nanowire counts and average intensity (Figure 3(b) and (c)).

Using NanoLoci, I tot ′ (see Eqs. (2) and (3)) exhibits a linear response well above background across the full range of measured concentrations, as depicted by the orange curve in Figure 3(d). This linear response spans five orders of magnitude in intensity and analyte concentration, from 10 fM to 10 nM. The comparison between the performance of NanoLoci and methods that do not utilize single wire localization steps, such as pixel averaging or simple thresholding, is illustrated in Figure 3(d). When using average pixel intensity as a signal readout (purple curve in Figure 3(d)), detections are observed from 10 pM, with a dynamic range of two magnitudes extending up to 10 nM. Similarly, intensity thresholding (cyan curve in Figure 3(d)) detects concentrations ranging from 1 to 10 pM to 10 nM, also with a dynamic range of two orders of magnitude, which is 10–100 times less than when single nanowire analysis is performed. Notably, methods not utilizing single emitter localization demonstrate detection above background only starting from Regime II, where most nanowires become bright (Figure 3(c)), and where I _avg begins to increase (Figure 3(d)).

Thus, we can conclude that the use of single-nanowire localization steps, that is, making use of the digital nature of our images, increases the dynamic range and LoD by two to three orders of magnitude in sample concentration.

4.2 Imaging simulations confirm the accuracy of nanowire localization

To verify the performance of NanoLoci (Figure 2, steps 1–3), we simulated a dataset, where the positions of bright nanowires are known. We utilized Jaccard index (JI), Precision, and Recall (see Eq. (4)) as our comparison metrics. Two different exposure times and six analyte concentrations spanning the described three nanowire coverage regimes were simulated. In Regime I, the number of bright nanowires is less than 15 %, and one molecule bound to an individual bright nanowire. In Regime II, where around half of the nanowires are bright, the signal per individual bright nanowire can still vary due to variation of the number of bound molecules. In Regime III, all vertically aligned nanowires are bright due to multiple bound molecules. Nanowires appearing dark in Regime III are clear growth defects unable to enhance the fluorescence of bound fluorophores, thus only contribute to image background (see Figure 4(a)).

Figure 4:

Image analysis verification using simulated dataset. (a) Micrographs representing simulated fluorescence images at surface concentrations of 0.05, 1.22, and 30.4 molecules/µm², with exposure times of t ₁ = 50 ms and t ₂ = 100 ms. The illustrations represent the three regimes simulated (see main text). (b) The number of bright nanowires, which serves as ground truth (blue, left axis) and JI (orange, right axis) measuring the accuracy of matching detections between the obtained localizations and the ground truth as defined in Eq. (4). (c) Precision and recall curves as defined in Eq. (4) quantify the relation between occurrence of FPs and FNs, respectively.

We exclusively present the final results of the comprehensive image analysis pipeline, NanoLoci (Figure 2, steps 1–3) photon number. Further insights into the enhanced detection capabilities facilitated by image pre- and postprocessing are available in Supplementary Methods, Figures S8 and 9.

For t ₂ = 100 ms, JI is in the range of 0.8–1 across all concentrations (Figure 4(b), solid line). High Precision rates are observed across all concentrations, indicating accurate positive predictions and a low number of FPs (Figure 4(d)). Less than 2 % of all detections are FPs across all concentrations and intensity conditions (see Figure S9(b)). However, Recall decreases at intermediate concentrations (Regime II, Figure 4(c)), indicating that part of the signal remains undetected (see Figure S9(c)). In this concentration regime (Regime II, c = 1.22 molecules/µm²), around half of the nanowires have one or more molecule (see Table S1).

When the simulated exposure time, and thus the number of emitted photons, is halved, the performance efficiency decreases as well (see Figure 4(b) and (c), dashed lines). The Recall and JI remain high for the highest concentrations (Regime III), where more than 7–15 fluorophores are bound to an individual nanowire. However, both drop by a factor of two in Regimes I and II, which can be attributed to lower number of emitted photons.

The application of the full NanoLoci pipeline (Figure 2, steps 1–3) consistently increases JI by 0.05 − 0.30 (5 − 30 %) in Regimes I and II (Figures S8 and 9(a) and (d)). It is achieved by decreasing the number of FPs and FNs while increasing the number of TPs. However, a number of undetected and falsely detected nanowires still remain (see Supplementary Methods, Figure 9(b)–(f)).

The comparison of photon count and signal-to-noise ratio (SNR) in the intermediate concentrations (Regime II) in simulations (c = 1.22 molecules/µm²) and in experiments (c = 10 pM) suggests that simulations where t ₂ = 100 ms have similar photon count and SNR as streptavidin-biotin experiments (see Figure S12).

4.3 Time-resolved measurements to benchmark against TIRF microscopy

One of the primary advantages of TIRFM is its capability to perform time-resolved single molecule detections of surface binding events, even in the presence of suspended fluorescently labeled molecules. Therefore, we conducted an experimental benchmark of time-dependent NEW-FM against TIRFM directly, in the very same microfluidic channel, enabling a direct comparison of StvA647 binding under identical experimental and imaging conditions (see Figure 1). The comparison centered on two distinct analyte concentrations, 1 nM and 10 nM, representing Regimes I and III, respectively, in Figure 5(a). It’s noteworthy to mention that while both concentrations fall within Regime III for titration experiments (see Figure 3(a)), variations in experimental conditions and channel designs can lead to differences in binding outcomes.

Figure 5:

Comparison of NEW-FM and TIRFM. (a) Micrographs at different time points using NEW-FM on nanowires (top) and TIRFM on glass (bottom) demonstrating the three regimes of molecular binding (see main text). (b) The number of detections is depicted, with the count of bright nanowires represented in blue (N _NW on the left axis) and the detected molecules in TIRFM shown in red (N _TIRF on the right axis). (c) The average intensity I _avg in each frame. (d) The total intensity (I _tot) in NEW-FM originating from nanowires (blue) and total intensity originating from molecules bound to planar glass in TIRFM (red). (e) The intensity distributions of detections. Note that for NEW-FM, this corresponds to c ₁ = 1 nM (Region I), and for TIRFM, it is c ₂ = 10 nM (Region III). (f) The cumulative binding (see Supplementary Methods, Eq. S(2) on how N _mol is obtained) as a quantification of bound fluorophores on nanowires (blue) and on glass (red).

For the lower analyte concentration (Regime I, t < 40 min, c ₁ = 1 nM), we find that the number of detections on nanowires exceeds that on planar glass and monotonically increases until saturation is reached at around t = 20 min (Figure 5(b)–(d)). In contrast, the average intensity per detection does not change neither on nanowires nor on glass in this region (Figure 5(d)), indicating that only one molecule is bound at any identified location. Notably, the average intensity for TIRFM is more noisy and unstable than that of NEW-FM, reflecting that fewer binding events occur on glass in this regime.

At t = 40 min, a higher concentration of the analyte (c ₂ = 10 nM) is introduced, leading to a transition from a single-molecule binding regime (Regime I) to subsequent Regimes II and III on the nanowire substrate (see Figure 5(a)–(c)). The binding on glass is still resolved at the single-molecule level (Figure 5(b)–(d)). At around t = 60 min, no overall increase of intensity is observed on both substrates (Regime III in Figure 5(b)–(d)), suggesting that the surfaces have reached saturation. Across these two concentrations, TIRFM and NEW-FM display changes in the overall intensity spanning two and three orders of magnitude, respectively (Figure 5(d)). We estimate the cumulative binding rate on nanowires and glass (see Supplementary Methods, Section 1.6.2), which demonstrates that nanowire substrate is more sensitive to analyte capture at low coverage (Figure 5(b)–(d)), Region I, c ₁ = 1 nM), at which the overall number of bound molecules on glass is two order of magnitude lower. A significant response is observed on planar glass only in the higher concentration regimes, in which case multiple fluorophores are already bound to individual nanowires (Region II and III, Figure 5(a) and (c)).

Furthermore, a comparison of the intensity distribution of detections in the single molecule regimes (Regime I for NEW-FM and Regime III for TIRFM) reveals different patterns. NEW-FM displays a near normal distribution, whereas TIRFM appears to exhibit a truncated distribution, as depicted in Figure 5(e). There is also a twofold higher emission intensity at the peak of the distributions for NEW-FM compared to TIRFM. One can also conclude that the cumulative binding on glass and on nanowires in these single molecule regimes (see Supplementary Methods, Figure 12) resembles each other (Figure 5(f)).