### Properties of combi-matrix

The concept of a combi-matrix was (1) to enhance the absorption of UV radiation energy and (2) to transfer it for the thermal desorption of analytes by mixing solid materials, as shown in Fig. 1a. The organic matrix of CHCA is mixed with carbon-based nanostructures of graphene, CNTs, Pt, and P25 with high thermal conductivity to prepare the combi-matrix, as summarized in Table 1. First, the solid matrices of graphene, CNT, Pt NPs, and P25 were utilized to ionize T_{4} molecules without any organic matrix. For the comparison of mass peaks, the concentration of solid matrices was set at 0.5 mg mL^{−1}, and the same amount of solid matrix was used by dropping the same volume (1 µL, the absolute amount of 500 ng) for analyzing T_{4}. As shown in Fig. 1b, the intensity of the mass peak (S/N ratio) of the T_{4} molecule (at a concentration of 200 ng mL^{−1}) was 237.5 (2.7), no signal (− 0.5), 5.2 (− 0.4), and 19.9 (− 0.2) for graphene, CNTs, Pt NPs, and P25, respectively. Under similar conditions, the mass peak from the analysis using CHCA was 1248.5 (16.5). The results suggested that the intensity of the mass peak was significantly lower than that of CHCA when only solid matrices were used for ionizing T_{4} molecules. After mixing CHCA with the solid matrices, the intensity of the mass peaks (S/N ratio) of T_{4} molecules was 3341.8 (45.0), 2093.8 (28.0), 1650.6 (23.6), and 1513.8 (24.5) for graphene, CNTs, Pt NPs, and P25, respectively. The results indicated that the mass intensity and the S/N ratio were significantly increased after mixing CHCA with solid matrices of graphene, CNTs, Pt NPs, and P25. Furthermore, the mass peaks of the combi-matrices consisting of CHCA and solid matrices of graphene, CNTs, P25, and Pt NPs were higher than those of the conventional organic matrix of CHCA. Additionally, the mass peak intensity of different combi-matrices coincided with the order of thermal conductivity and the effective surface area of used solid matrices, as summarized in Table 1 (Grinou et al. 2012; Choo et al. 2012; Kim and Park 2007; Sikdar et al. 2011). Combi-matrix of graphene and graphene showed the highest mass intensity, as graphene showed the highest thermal conductivity (4500–5000 W/(m K)), electron mobility (200,000 cm^{2}/(V s)), and effective surface area (700 m^{2}/g) among the solid matrices. Thus, the concept of a combi-matrix: (1) to enhance the absorption of UV radiation energy and (2) to transfer it for the thermal desorption of analytes by mixing solid materials was feasible.

The optical properties before and after mixing the solid matrices with CHCA were analyzed by UV/Vis spectrometry to estimate the enhancement of the absorption of UV radiation energy. As shown in Fig. 2a, CHCA and graphene have maximum absorptions at wavelengths (*λ*_{max}) of 350 and 270 nm, respectively, which was also reported in previous studies (Robinson et al. 2017; Low et al. 2004; Uran et al. 2017). When graphene was mixed with CHCA, the maximum absorption was observed at a wavelength (*λ*_{max}) of approximately 285 nm; the absorption increased at a wavelength of 337 nm of the laser radiation for the ionization of the sample. As the turbidity of graphene and the mixture of CHCA and graphene were controlled to be the same at a wavelength of 500 nm, the amount of graphene was similar before and after mixing with CHCA. However, the absorption at wavelengths less than 350 nm was significantly higher than that of graphene before mixing with CHCA. These results indicated that the absorption of the combi-matrix achieved a significantly increased absorption of laser radiation for the effective ionization of T_{4} molecules. The combi-matrix of DHB and graphene demonstrated an identical trend of increased absorbance of laser radiation at a wavelength of 337 nm, as shown in Fig. 2b. The UV/Vis spectra of 9-AA showed two broad peaks in the wavelength range of 200 to 500 nm. The absorbance at 337 nm increased when graphene was mixed with 9-AA matrix, as shown in Fig. 2c. Compared with the UV/VIS spectra, the enhancement of absorption of laser radiation at the wavelength of 337 nm was estimated to increase by 9.7%, 7.1%, 6.1%, and 3.1% for graphene, CNTs, Pt NPs, and P25, respectively (Additional file 1: Fig. S1). The results suggested that the combi-matrix enhanced the absorption of UV radiation energy during MALDI-TOF MS, and graphene was the optimal solid matrix for the combi-matrix formation.

Next, the enhancement of the thermal properties of the combi-matrix for the transfer of laser radiation energy was estimated using DSC. The *T*_{onset}, *T*_{peak}, and Δ*H*_{fus} are estimated from the DSC spectrum through the measurement of heat flow in the controlled temperature range to analyze the heat absorption property, as shown in Fig. 3a. The heat flow was observed for CHCA and the combi-matrix of CHCA and graphene in the temperature range of 200–300 °C at an increasing rate of 15 °C/min, and Asn was used as a model heat sink to absorb the heat flow from the combi-matrix to melt. From the slope of the DSC heat flow curve, the relative thermal conductivity was estimated, representing the amount of heat flow required at the phase change of the heat sink.

The DSC spectra were measured for Asn only, Asn with graphene, Asn with CHCA, and Asn with combi-matrix composed of CHCA and graphene. As shown in Fig. 3b, the (ΔH_{fus}) of Asn significantly decreases compared to Asn only, Asn with graphene, and Asn with CHCA. The results implied that Asn melted with a lower heat flow by mixing the organic matrix (CHCA) with a solid graphene matrix. Additionally, from comparing the slope of the DSC spectra, the combi-matrix had a lower relative thermal conductivity than other conditions, indicating a more effective transfer of thermal energy to the heat sink material. The same DSC measurements are taken using DHB and 9-AA as organic matrices of the combi-matrix, as shown in Fig. 3c and Fig. 3d. For the two organic matrices, the Δ*H*_{fus} of Asn and the relative thermal conductivity from the slope of the DSC spectrum were significantly reduced by mixing graphene compared to those of Asn only, Asn with graphene, and Asn with organic matrix. Thus, the combi-matrix composed of the conventional organic matrix and graphene transferred the energy from UV radiation, which effectively transferred to the analyte for MALDI-TOF MS.

When three different kinds of organic matrices are mixed with graphene, the Δ*H*_{fus} of Asn and the relative thermal conductivity are minimum for the organic matrix of CHCA, as shown in Fig. 3e and f. These results indicated that the optimal combi-matrix was composed by mixing the conventional organic matrix of CHCA and graphene for the energy transfer from UV radiation for MALDI-TOF MS.

The combination of the solid matrix of graphene and the organic matrices of CHCA, DHB, and 9-AA was also applied for the MALDI-TOF MS of Asn. For the MALDI-TOF MS, the Asn sample at a concentration of 100 μg mL^{−1} was dropped to the combi-matrices of organic matrix and graphene. The mass peak of Asn was observed at the m/z ratio of [Asn + H]^{+} = 133.1 [reflective positive (RP) mode] and [Asn-H]^{−} = 131.1 [reflective negative (RN) mode]. When graphene is mixed with the organic matrix of CHCA, the mass peak of Asn has a significantly high S/N ratio of 4.9, comparison to Asn only (S/N ratio of 0.5), Asn with graphene (0.7), and Asn with CHCA (2.7), as shown in Fig. 4a. Furthermore, when DHB and 9-AA were used as the organic matrix of the combi-matrix with graphene, the S/N ratio was significantly higher than Asn only, Asn with graphene, and Asn with organic matrix. The S/N ratio of the mass peak of Asn was 4.9 for CHCA (Fig. 4a), 3.3 for DHB (Fig. 4b), and 3.3 for 9-AA (in RN mode, Fig. 4c) when the mass peak of Asn from the combi-matrices of different organic matrices. From the previous results, the optimal combi-matrix was composed by mixing the conventional organic matrix of CHCA and graphene to absorb the laser energy from the UV/Vis spectrum and the transfer of energy from DSC analysis. These results confirmed that the combi-matrix with graphene and CHCA enhanced the absorption of UV radiation energy and the transfer of laser energy during MALDI-TOF MS analysis.

### Analysis of L-thyroxine (T_{4}) using the combi-matrix

The combination of the solid matrix of graphene and the organic matrices of CHCA, DHB, and 9-AA was also applied for MALDI-TOF MS of T_{4}. For the MALDI-TOF MS, the T_{4} sample at a concentration of 200 ng mL^{−1} was dropped on the combi-matrices of the organic matrix and graphene. The mass peak of T_{4} was observed at the m/z ratio of [T_{4} + H]^{+} = 777.8 (RP mode) and [T_{4}—H]^{−} = 775.8 (RN mode). When graphene was mixed with the organic matrix of CHCA, the mass peak of T_{4} had a significantly higher S/N ratio of 20.6 than T_{4} only (S/N ratio of − 0.1), T_{4} with graphene (0.8), and T_{4} with CHCA (7.8). For the mass peak of T_{4} from the combi-matrices of different organic matrices, the S/N ratio of the Asn mass peak was 20.6 CHCA [Fig. 5a], 18.9 for DHB [Fig. 5b], and 1.6 for 9-AA [in RP mode, Fig. 5c]. These results confirmed that the combi-matrix with graphene and CHCA was optimal for MALDI-TOF MS.

Quantitative analysis of T_{4} molecules was performed using a combi-matrix organic matrix (CHCA) and a solid matrix (graphene). The inhomogeneous co-crystallization of the matrix analyte made quantitative analysis difficult, and the feasibility of the quantitative analysis of T_{4} was demonstrated by investigating the reproducibility of the inter- and intra-spot measurements. Five different sample spots are independently detected, as shown in Additional file 1: Fig. S2a and Fig. 6a to measure the inter-spot reproducibility. Based on the analysis of the mass spectra, the inter-spot reproducibility was 6.7% for T_{4} (200 ng mL^{−1}). MALDI-TOF mass spectra were obtained at five different positions in one sample spot to estimate the intra-spot reproducibility, as shown in Additional file 1: Fig. S2b and Fig. 6b. Based on the mass spectra, the intra-spot reproducibility was 4.6% for T_{4} (200 ng mL^{−1}). Therefore, the analysis of T_{4} molecules was conducted with high inter- and intra-spot reproducibility using MALDI-TOF MS based on the combi-matrix of organic matrix and solid matrix.

A combi-matrix consisting of CHCA and graphene was used for quantitative analysis of the T_{4} molecules. T_{4} samples at the concentration range of 12.5–200 ng mL^{−1} were prepared by considering the cutoff concentration of 50 ng mL^{−1} for the diagnosis of congenital hypothyroidism (Desai et al. 1994), as shown in Fig. 6c. The standard curve for analyzing T_{4} molecules was prepared from the repeated measurement and the mass peak, demonstrating high linearity (*r*^{2} = 0.971) at the corresponding concentration range. Therefore, the quantitative analysis of T_{4} was feasible with high linearity in the concentration range, including the cutoff concentration of 50 ng mL^{−1}, for diagnosing congenital hypothyroidism.

The combi-matrix consisting of CHCA and solid matrices of graphene, CNTs, Pt NPs, and P25 was compared for the quantitative analysis of T_{4} molecules at the concentration range of 12.5–200 ng mL^{−1} (Additional file 1: Fig. S3). Figure 6d shows the test results with four different combi-matrices from the quantitative analysis of T_{4} molecules. The combi-matrix of CHCA and graphene had the widest intensity range than the conventional organic matrix of CHCA and other combi-matrices. From the statistical analysis (Mann–Whitney unpaired test), the test results between the organic matrix of CHCA and the combi-matrices of CHCA and graphene, CNTs, Pt NPs, and P25 were independent, with P-values less than 0.0001. Whiskers show the minimum and maximum values, the boxes represent 25–75% data ranges, horizontal lines within boxes are medians, and diamond symbols are the means of the mass spectrometric results. These results showed that the combi-matrix of CHCA and graphene was effectively used for the quantitative analysis of T_{4} molecules in a wider concentration range compared to CHCA and other kinds of combi-matrices. T4 molecules were detectable in the low concentration range (below 75% range) when using CHCA and graphene as a combi-matrix from the box plot.

As shown in Fig. 7a, T_{4} samples at a concentration range of 12.5–200 ng mL^{−1} are prepared in human serum after methanol extraction to precipitate proteins, and the extracts of T_{4} samples were analyzed using the combi-matrices. When T_{4} analysis was performed using only CHCA as a matrix, the mass peak of T_{4} was observed at a concentration of more than 100 ng mL^{−1}. When the combi-matrix consisting of CHCA and graphene was used for analyzing T_{4}, the mass peak of T_{4} was observed over the entire concentration range, including the cutoff concentration of 50 ng mL^{−1} for diagnosing congenital hypothyroidism. As shown in Fig. 7(b), the standard curve for analyzing T_{4} molecules is obtained from the repeated measurements and the mass peaks, exhibiting high linearity (*r*^{2} < 0.99) at the corresponding concentration range. These results indicated that the combi-matrix consisting of CHCA and graphene was used for the quantitative analysis of T_{4} samples spiked in serum.

The box plot shows the test results with four different combi-matrices from the quantitative analysis of T_{4} molecules, indicating that the combi-matrix of CHCA and graphene had the widest intensity range than the conventional organic matrix of CHCA and other kinds of combi-matrices [Fig. 7c]. From the statistical analysis (Mann–Whitney unpaired test), the test results between the organic matrix of CHCA and the combi-matrix of CHCA and graphene were independent, with *P*-values of less than 0.0001. These results showed that the combi-matrix of CHCA and graphene could be effectively used for the quantitative analysis of T_{4} molecules spiked in serum in a wider concentration range compared to the conventional organic matrix of CHCA.

The clinical laboratories commonly quantify T_{4} by RIA, an immunoassay that is complicated to handle and dispose of radioactive materials. In this study, the free T_{4} ELISA kit was used as a reference method, and its quantitative analysis results for T_{4} were compared to those from MALDI-TOF MS based on the combi-matrix of CHCA and graphene. The Bland–Altman plot and Passing–Bablok regression were conducted using MedCalc software (version 18.6) to estimate the statistical coincidence of the two methods for T_{4} analysis. The Bland–Altman test revealed that a signal difference is distributed within a confidence level of 95% (± 1.96 σ), as shown in Fig. 8a. This result demonstrated that the two methods were highly correlated and provided similar analysis results for detecting T_{4}. In the case of the Passing–Bablok regression, the signals from one method were plotted against the other method when the signals of the two methods had a linear correlation. The analysis data from both methods are distributed at a confidence level of 95%, with a Spearman correlation coefficient (*ρ*) of 0.973 (*p* < 0.0001), as shown in Fig. 8b. These results indicated that the two different methods were statistically and highly coincident. Moreover, the two methods were highly correlated and provided similar analysis results for detecting T_{4}.