**3. Results**

*3.1. Detections of Individual Cancer Markers*

3.1.1. PSA

Figure 2 shows a series of experimental results regarding PSA detection. In Figure 2a, FL images at high PSA concentrations from 40 μg/mL to 0 g/mL are presented from left to right, respectively. The all-dielectric metasurfaces are located near the center of the images; bright horizontal areas are explicitly seen at 40, 4.0, and 0.4 μg/mL; the metasurfaces at the other concentrations are placed similarly though it is not seen brightly. FL intensities were most intense at the center of the excitation LED spots, which take a broad Gaussian shape and can be seen explicitly at 40 and 4.0 μg/mL. The FL intensities were quantified with setting and analyzing a circular region around the center in common with the six MF channels.

The FL intensities in Figure 2a were quantified in the circular regions around the center of excitation spots and plotted in Figure 2b using orange closed circles with error bars on a log-log scale. The error bars were evaluated using Gaussian fitting, being standard deviation *σ* of the FL-intensity distributions. The detection profile was fitted using Hill equation [29], which is mathematically equivalent to the so-called four-parameter logistic equation:

$$y = y\_0 + (S - y\_0)\frac{\mathbf{x}^{\text{n}}}{\mathbf{x}^{\text{n}} + K\_D^{\text{n}}} \tag{1}$$

where *y* denotes the FL intensity, *y*<sup>0</sup> is the zero level without any target, *S* is the saturation FL intensity that is regarded as a proportional constant in fitting, *x* is the concentration of target, *n* is the degree of cooperative reaction, and *KD* is the dissociation constant [30,31]. In the MF paths, stable liquid flow rates are maintained; therefore, the immobilization process on the metasurface is an equilibrium chemical reaction, which is described using the Hill equation (Equation (1)). From the fitted results, it was determined that *S* = 36148.3, *n* = 1.18, *KD* = 195.2 ng/mL, and *y*<sup>0</sup> = 110.0 in Figure 2b. When the fitted value of *n* is more than 1, it is suggested that the reaction is cooperative [32]. Therefore, the fitted value *n* indicates that immobilization of detection Abs with the FL label occurred in a cooperative manner. The value *y*<sup>0</sup> indicates a zero level in the FL measurement, being approximately six times smaller than the FL intensity at 4.0 ng/mL, which is currently the clinical criterion

value for PSA [2]. Figure 2b shows that even 100-fold higher PSA concentrations can be detected by the metasurface biosensors in a scaled manner. The parameter *KD* denotes the dissociation constant and indicates the target concentration at the half height of the Hill curve.

**Figure 2.** PSA detection. (**a**) FL images at high PSA concentrations from 40 μg/mL to 0 g/mL (from left to right, respectively). The target PSA was diluted using the sample diluent buffer. (**b**) and (**c**) Detection curves of high-concentration PSA diluted with the sample diluent buffer and human serums, respectively. These are presented on a log-log scale. Dashed curves represent fitted curves by the Hill equation (Equation (1)). (**d**,**e**) Detection curves of PSA diluted with the sample diluent buffer and human serums, respectively, presented on a semi-log scale. Dashed curves are fitted curves using the Hill equation. The target concentrations were in a range from 4.0 ng/mL to 0 g/mL. Insets magnify a range near 0 g/mL, presented on a linear scale.

The PSA in a human serum was successfully detected, as shown in Figure 2c. The detection profile is quite similar to that in Figure 2b. This result indicates that PSA detection using the metasurface biosensor is robust, even in human serums. The fitting parameters in Figure 2c were *S* = 29620.3, *n* = 1.41, *KD* = 206.9 ng/mL, and *y*<sup>0</sup> = 72.2. As a result, the binding reaction is evaluated by *n*, suggesting that the cooperative reaction is similar to that without human serums. In addition, the interplay of PSA and the Abs is not affected by human serums.

Figure 2d,e shows the FL detection results in a PSA concentration range lower than that in Figure 2b,c, respectively, and is presented on a semi-log scale; insets magnify a range near 0 ng/mL in a linear scale. Orange closed circles with error bars denote measured data, and dashed curves are fitted curves using the Hill equation (Equation (1)). The measured data are well-reproduced using the Hill equation and are scaled. We here define dynamic range, such as a range where we can discriminate measured signals more than 1*σ* and read out concentrations using a reasonable scale (e.g., linear or the Hill curve). The dynamic range of the PSA detection in the step-flow protocol is found to be 0.16–1000 ng/mL, which is almost four orders of concentrations. In the semi-log plots, it is difficult to see the changes in FL intensity at low concentrations below 1 ng/mL; however, the linear plots in the insets exhibit the scaled responses of the metasurface biosensors, even at the range that is 25-fold smaller than the clinical criterion. We refer to that of the dynamic range, which is mainly limited by the performance of the uncooled CCD camera; indeed, a confocal FL microscopy enabled us to access much lower concentrations when we detected the spike proteins of SARS-CoV-2 [21].
