C₆₀ (99.9%, powder) was purchased from Henan Fullerene Nano New Materials Technology Co. Ltd. (China). BSA (free fatty acid fraction V) and phosphate buffer saline (PBS) premixed powder were purchased from Solarbio (United States). Toluene (analytically pure) was purchased from Tianjin Ding Sheng Xin Chemical Co. Ltd. (China). All the dispersions and solutions were prepared with ultra-pure water. All experiments were performed at room temperature.

0.05 g of C₆₀ powder was dissolved in approximately 5 mL of toluene and then 300 mL ultra-pure water was added to the purple solution. The mixture was subjected to ultrasonic treatment continuously for 24 h, resulting in a brown-yellow nC₆₀ aqueous dispersion. Then removed toluene layer and placed it in a fume hood as long as the residual toluene was fully evaporated. The solution was preserved at room temperature, away from light. The concentration of nC₆₀ was determined as 2.45 × 10⁻⁵ mol/L, according to the method described (Deguchi et al., 2001).

Imaging of nC₆₀ was performed by HT-7700 transmission electron microscope (TEM) (Hitachi, Japan) and JEM-1011 TEM (JEOL, Japan).

The absorption spectra of nC₆₀ dispersion and BSA-nC₆₀ systems were measured by U2900 UV-Visible spectrophotometer (Hitachi, Japan) with a 10 mm pat length cuvette.

The Fluorescence measurements were performed on F4700 fluorescence spectrophotometer (Hitachi, Japan) with a 10 mm path length quartz cuvette. The excitation wavelength ( λ ex ) of the protein and the mixture solution was set at 280 nm, and the emission spectra of BSA (1.0 × 10⁻⁵ mol/L) were recorded in the absence or presence of nC₆₀ with different concentrations in the wavelength range of 300∼550 nm. All measurements were repeated in triplicate.

Fluorescence lifetime was measured using FLS-920 steady-state/time-resolved fluorescence spectrometers (Edinburgh, England). The samples were excited at 280 nm using nanosecond diode excitation source.

For the obtained BSA-nC₆₀ mixed system, the following four common mathematical models were chosen to correct the fluorescence data: F c o r r = F o b s × 10 A e x + A e m / 2 (1)

Equation 1 represents the Lakowicz’s model (Lakowicz, 2006). F c o r r is the corrected fluorescence intensity using the IFE equation, F o b s denotes the observed fluorescence intensity, and A e x and A e m are the absorbance of BSA-nC₆₀ mixed system at the excitation and emission wavelengths, respectively. F c o r r F o b s = 2.3 03 A e x y − x 10 − x A e x − 10 − y A e x × 2.3 03 A e m v − u 10 − u A e m − 10 − v A e m (2)

Equation 2 represents the Tucker’s model (Tucker et al., 1992). The parameters x, y, u, and v are distances specific to cell geometry depicted in Figure 1A. In this experiment, x = 0.1, y = 0.8, u = 0.1, and v = 0.8. All geometrical parameters are in centimeters. F c o r r F o b s = 2.3 d A e x 1 − 10 − d A e x × 10 g ⋅ A e m × 2.3 s A e m 1 − 10 − s A e m (3)

Equation 3 represents the Gauthier’s model (Gauthier et al., 1986). d is the pathlength of the quartz cuvette (generally 1 cm), and s and g are cell geometry parameters related to the exciting and emitting beams, illustrated in Figure 1B. In this experiment, d = 1, s = 0.7, g = 0.1. F c o r r 1 = 1 + 10 − A 2 / n 1 − 10 − A 1 / n 1 − 10 − A 1 + A 2 2 1 − 10 − A 1 1 − 10 − A 1 + A 2 / n × F o b s 1 (4) F c o r r 2 = 10 A λ e m / 2 × F o b s 2 (5)

Equations 4, 5 represent the Chen’s model (Chen et al., 2015), Figure 2 illustrated the theoretical concept diagram of Chen’s model, since this method is universally applicable to all fluorescent substances, the x-axis is labeled as ‘Wavelength (nm)’ without any specific values. Referring to Figure 2 and Equations above, F o b s 1 is the fluorescence intensity of the pure fluorophore from curve a, F c o r r 1 is the corrected result of pIFE from curve a’, A 1 and A 2 are the absorption data of fluorophore and quencher at excitation wavelengths, respectively. n is the theoretical layer number (usually equals to 100 or 1,000, in this experiment, n = 1,000), F o b s 2 is the fluorescence intensity with quencher from curve b, F c o r r 2 is the corrected result of sIFE from curve b’, A λ e m is the absorption data of quencher at emission wavelength.

Transmission Electron Microscopy (TEM) provides an intuitive means to observe the shape, size, and distribution of nanoparticles. Figure 3A showed the TEM image of nC₆₀ aqueous dispersion after drying, as observed, nC₆₀ nanoparticles exhibited irregular circular shapes and aggregated together, with a particle size ranging approximately between about 50 and 100 nm. And Figure 3B showed that, after adding BSA, the surface of nC60 was covered with a slightly transparent protein corona, and the overall morphology became more regular. This is consistent with the reported adsorption of proteins onto C60 nanoparticles in the previous studies (Deguchi et al., 2007; Wu et al., 2011; Vance et al., 2016).

Previous studies have already found that nC₆₀ has a quenching effect on proteins (Li et al., 2013; Noskov et al., 2021), but the influence of IFE has rarely been considered. In order to confirm there is an inner filter effect in BSA-nC₆₀ fluorescence system, the absorption spectra of nC₆₀ aqueous dispersion were measured in the range of 250–550 nm which was shown in Figure 4A. Figure 4A revealed that nC₆₀ aqueous dispersion had two notable absorption peaks at 270 nm and 354 nm, the latter being characteristic of C₆₀ nanoparticles. The fluorescence spectra of the BSA-nC₆₀ solution are shown in Figure 4. Combining Figure 4A, B, it can be observed that the absorption of nC₆₀ overlaps with the excitation (280 nm) and emission (350 nm) wavelengths in the fluorescence spectra of the subsequent solution. This overlap suggested that the mixed solution of nC₆₀ and BSA could had experienced some degree of interference from the fluorescence IFE during measurements.

IEF is hard to avoid in right-angle fluorometry. In order to ensure that the quenching effect of nC₆₀ on BSA is not solely caused by IFE, it is necessary to correct it. Researchers have proposed various mathematical models for different situations (Lakowicz, 2006; Tucker et al., 1992), and the effectiveness of the correction varies accordingly. Therefore, selecting an appropriate mathematical formula is crucial. For the BSA-nC₆₀ system, the four aforementioned mathematical models were applied for calibration. All the experimental dates required for calibration are listed in Table 1, and the calibration results are shown in Table 2. Then the fluorescence quenching dates were analyzed by the Stern-Volmer equation (Zhang et al., 2023). F 0 / F = k q τ 0 Q + 1 = K S V Q + 1 (6)

In Equation 6, F₀ and F represent the fluorescence intensity of BSA in the absence and presence of different concentrations of nC₆₀ respectively. τ₀ is the average fluorescence lifetime of biomacromolecules without quencher. k_q is the dynamic quenching rate constant (L mol⁻¹ s⁻¹) and K_SV is the dynamic quenching constant (L/mol). [Q] refers to the concentration of the quencher.

Figure 5 displayed the fluorescence quenching plots of BSA by nC₆₀. It showed that the quenching curve obtained without correcting the IFE was not linear but curved to the Y-axis as the quencher concentration increased. After correction, the degree of quenching significantly decreased, about 67.5% lower than before, indicating that all four correction methods can effectively reduce the influence of the IFE. So further analysis is required to assess which model was more suitable in this study. The conditions for using each model are described in detail as follows.

Firstly, the Lakowicz model is the simplest method and is therefore widely used. However, this is an approximate method, as its theoretical basis assumes that the emission radiation is observed at the center of a 1 cm path length cuvette, and it may not be true since the geometry of the sample compartment is different. An additional drawback is that this model is valid only up to A = 0.7, according to Panigrahi and Mishra (2019). For larger values of A, this model overestimates the loss of observed fluorescence due to IFE, resulting in an upward curvature of the corrected fluorescence. However, the absorbance of this experimental system is relatively high (up to 1.045), so applying the Lakowicz model may lead to over-correction.

Tucker’s model and Gauthier’s model are both based on different sample geometries (dependent on the fluorescence light collection position) and the absorption characteristics of the solution in a vertical monochromator slit system for correction. Yet the Hitachi fluorescence spectrophotometer used in this experiment employs a relatively uncommon horizontal monochromator slit system. In Gauthier’s model, the excitation beam with thickness s = 0.10 cm, and the distance between the beam to the cuvette g = 0.40 cm (Gauthier et al., 1986). However, in this experimental apparatus, the actual measured value of s = 0.7 cm, and g = 0.1 cm the different measurement of geometric factors may impact the final correction.

More importantly, in the calibration of pIFE, the three models mentioned above are predicated on the assumption that the emitted fluorescence is proportional to the entire system’s absorption of the excitation light. However, in a mixed system where a quencher is present, only the protein emits fluorescence, while both nC₆₀ and the protein absorb light. This results in a decrease in the effective absorbance of the protein, potentially leading to over-correction in the calculations of these models.

To address this limitation, Chen proposed a novel theoretical model based on an in-depth study of the physical mechanisms of IFE, which does not depend on geometric parameters. Theoretically, the observed fluorescence intensity is proportional to the effective absorption of excitation light (EAEF) by the fluorophore, which can be calculated using the Beer-Lambert law. In mixed solutions, the competition for absorption from quenching agents can modify the EAEF compared to pure solutions, complicating direct calculations.

Chen’s approach employs a layered method that divides the solution in the sample cell into n equal thin layers, calculating the absorbance of each layer step by step. This layered approach effectively addresses the interactions among components in mixed solutions, allowing for a more accurate calculation of transmitted light intensity. The number of layers in this method influences the calculation’s accuracy; specifically, when/n < 0.01, the error in Chen’s model is reduced to less than 1.2% (Chen et al., 2015).

In Figure 5, the first corrected dots of the Lakowicz’s and Tucker’s model showed F₀/F < 1. This indicated that, after correction, the fluorescence intensity of BSA with the addition of nC₆₀ exceeded that of pure BSA. It suggested that both the Lakowicz and Tucker models over-corrected the fluorescence intensity of the BSA-nC₆₀ mixed system. In contrast, the Gauthier’s and Chen’s models were more suitable for this system. Considering that Chen’s model does not involve the effects of geometric factors and accurately accounts for the effective absorbance of excitation light, Chen’s model was ultimately selected for further study. Nevertheless, the appropriateness of this model needs to be further confirmed based on the calibration results to ensure its suitability compared to other potential models.

The mechanism of fluorescence quenching is categorized into static quenching, dynamic quenching, and combined dynamic and static quenching (Noskov et al., 2021), which requires the selection of appropriate formulas for different quenching mechanisms when calculating the interactions of small molecules and proteins with binding sites and binding constants. The Stern-Volmer plot of dynamic quenching alone or static quenching with a binding site of 1 should be a straight line with an intercept close to 1, whereas the quenching curve curves toward the Y-axis in the case of combined dynamic-static interaction or static quenching with multiple binding sites.

Considering that the corrected quenching curves in Figure 5 still curved to the longitudinal axis, it can be preliminarily concluded that the mechanism for the quenching of BSA by nC₆₀ was likely to be multisite static quenching or dynamic and static combined quenching. Firstly, assumed that the quenching mechanism involved static quenching at multiple binding sites, which can be represented by Equation 7 (Song et al., 2011): F 0 / F = K Q n + 1 (7) where K is the formation constant of the fluorophore-quenching agent complex (L/mol), n is the number of binding sites. [Q] is the concentration of nC₆₀. The binding parameters obtained from Equation 6 were presented in Table 3.

Secondly, assuming that the fluorescence quenching of BSA by nC₆₀ was dynamic and static combined quenching. The Equation for dynamic and static quenching is depicted in Equation 8 (Liu et al., 2021), and the binding parameters obtained using Equation 8 were shown in Table 4. F 0 / F = K S V Q ] + K [ Q n + K S V K Q n + 1 + 1 (8)

In Equation 8, K S V is Stern-Volmer quenching constant. K is the formation constant of the fluorophore-quenching agent complex (L/mol). n is the number of binding sites.

According to Table 4, if the quenching was a combination of dynamic and static quenching, in the correction results of Lakowicz’s model, the fitted K S V was negative, while the dynamic quenching rate constant should be positive, which further demonstrates that Lakowicz’s model was not applicable to this system.

Comparing Tables 3, 4, it can be seen that regardless of whether the quenching mechanism was static quenching at multiple sites or a combination of dynamic and static quenching, the calculated results of Gauthier and Chen’s models were close to each other, and the number of binding sites were around 2, suggesting that there may be two potential binding sites for nC₆₀ with BSA. However, even under the assumption of a dynamic combined static quenching mechanism, the value of k_q, calculated using Equation 6 based on τ₀ (generally 10⁻⁸ s) and the K_SV data presented in Table 4, yielded a value of 1.23 × 10¹² L mol⁻¹ s⁻¹, which significantly exceeds the maximum scatter collision quenching constant of various quenchers (2 × 10¹⁰ L mol⁻¹ s⁻¹). This result suggested that the quenching mechanism is predominantly static in nature.

Merely comparing the results from the four correction formulas in Tables 3, 4 does not allow us to determine which assumption is more reasonable. To obtain precise binding information, it is essential to ascertain the proportion of static quenching involved.

Time-resolved fluorescence technology enables the determination of the fluorescence lifetime of biological macromolecules. To further confirm the quenching mechanism of BSA-nC₆₀ system, the fluorescence lifetimes of BSA were measured before and after the addition of nC₆₀. Theoretically, dynamic quenching typically increases the quenching effect with increasing concentration, leading to a significant shortening of the fluorescence lifetime. In contrast, static quenching tends to have minimal changes in fluorescence lifetime (Mohanty and Subuddhi, 2022).

The time-resolved fluorescence spectra of the system were shown in Figure 6, where the vertical axis represents the number of detected photons and the horizontal axis represents time. By fitting the fluorescence decay curve obtained from the time-resolved spectrum, the fluorescence lifetime (τ) of BSA was measured to be 6.13 nanoseconds in the absence of nC₆₀. Following the addition of varying concentrations of nC₆₀, the fluorescence lifetimes were observed to shift to 6.06 nanoseconds and 6.14 nanoseconds, respectively. The results indicated that although there were variations in these τ values, these minor differences can be attributed to photon scattering, as the fluorescence lifetime changes are minimal and do not deviate significantly from single-exponential decay. In other words, the quenching of BSA by nC60 did not significantly alter the fluorescence lifetime of BSA, further supporting that the quenching mechanism of BSA-nC₆₀ is primarily static quenching. Therefore, it is more reasonable to use the data from Table 3 for subsequent data analysis.

Given that the Chen’s model is immune to geometric factors and absorbance, and considers the effective absorbance of both the protein and the quencher, it was ultimately selected for the binding analysis. This model is suitable for interpreting the fluorescence data of BSA in the presence of low concentrations of nC₆₀. The corrected fitted curve demonstrated a significant decrease in the upward trend when compared to the uncorrected data, which indicates a substantial reduction of the fluorescence inner filter effect. Through the integration of fluorescence lifetime measurements, it was established that the BSA-nC₆₀ system undergoes static quenching, characterized by a binding constant of 2.95 × 10⁹ L/mol and approximately two binding sites. This methodology provides a more precise evaluation of the influence of nC60 on the fluorescence attributes of BSA, allowing researchers to gain deeper insights into the underlying molecular mechanisms. While this method has demonstrated its effectiveness in BSA and nC60 system, it is essential to acknowledge that its applicability to other materials and proteins remains unverified. To fully establish the general utility of this approach, future research should focus on expanding its application to a broader range of systems, including various proteins and nanomaterials. Moreover, due to the unique physicochemical properties of nanomaterials, the model needs further adjustments to achieve higher accuracy. The outcomes of this study will not only offer comprehensive insights into the interaction between nanomaterials and biomolecules but also provide foundational support for future investigations into nanomaterials biosafety.