Detection of insulin oligomeric forms by a novel surface plasmon resonance‐diffusion coefficient based approach

Abstract

Insulin is commonly used to treat diabetes and undergoes aggregation at the site of repeated injections in diabetic patients. Moreover, aggregation is also observed during its industrial production and transport and should be avoided to preserve its bioavailability to correctly adjust glucose levels in diabetic patients. However, monitoring the effect of various parameters (pH, protein concentration, metal ions, etc.) on the insulin aggregation and oligomerization state is very challenging. In this work, we have applied a novel Surface Plasmon Resonance (SPR)‐based experimental approach to insulin solutions at various experimental conditions, monitoring how its diffusion coefficient is affected by pH and the presence of metal ions (copper and zinc) with unprecedented sensitivity, precision, and reproducibility. The reported SPR method, hereby applied to a protein for the first time, besides giving insight into the insulin oligomerization and aggregation phenomena, proved to be very robust for determining the diffusion coefficient of any biomolecule. A theoretical background is given together with the software description, specially designed to fit the experimental data. This new way of applying SPR represents an innovation in the bio‐sensing field and expanding the potentiality of commonly used SPR instruments well over the canonical investigation of biomolecular interactions.

1. INTRODUCTION

The misfolding and aggregation of specific proteins are often associated with some pathological states named “conformational diseases” (Soto & Pritzkow, 2018). Understanding the biomolecular mechanisms triggering the misfolding and the subsequent aggregation of proteins is of paramount importance for tackling many diseases, including diabetes and Alzheimer's disease, among others (Laneri et al., 2022). Notably, insulin is a protein deeply involved in the development and management of diabetes and, for this reason, its structure (Weiss, 2009), folding (Hua, 2010; Liu et al., ²⁰¹⁸), protease susceptibility (Farris et al., 2003; Tundo et al., ²⁰¹⁷), oligomerization and fibrillation (Nettleton et al., 2000; Zingale et al., ^2023a), as well as interactions with different metal ions also involved in diabetes (Carpenter & Wilcox, 2014; Gavrilova et al., ²⁰¹⁴; Kant et al., ²⁰²¹; Lisi et al., ²⁰¹⁴), have been widely investigated with a variety of experimental approaches. Moreover, molecules capable of inhibiting and/or monitoring insulin aggregation have also been recently studied (Frankær et al., 2017; Lisi et al., ²⁰¹⁴), as well as how insulin aggregation is affected by metal ions (Ben‐Shushan & Miller, 2021; Frankær et al., ²⁰¹⁷; Patriati et al., ²⁰²¹; Pounot et al., ²⁰²¹). Indeed, copper and zinc ions have an important role in diabetic retinopathy and the interplay between these metal ions and insulin deserves attention (Dascalu et al., 2022; Miao et al., ²⁰¹³). Although it is well known that zinc ions stabilize the formation of insulin hexamers, the search for optimal stable insulin formulations that can provide the most biologically active form of the hormone upon injection is still ongoing (Bolli et al., 2022).

In this scenario, although there are many experimental techniques normally used to investigate the above‐mentioned protein features and aggregation phenomena (Gupta et al., 2022), many of them need special environmental conditions (high concentration, specific pH, lack of interference, fluorescent or isotopic tag, etc.) in order to be applied, which drastically limit the investigation of the natural occurring oligomerization/aggregation phenomena (Cristóvão et al., 2019; Gregory, ²⁰⁰⁹; Zhang et al., ²⁰¹⁸). A way to obtain information on the oligomerization/aggregation state of a biomolecule is to measure its diffusion coefficient (D) value, which is strictly correlated with the hydrodynamic radius of the molecular entity, through the well‐known Stokes–Einstein equation (Parker & Lollar, 2021). Recently, we have managed to obtain the D value of small molecules in water by applying a novel surface plasmon resonance (SPR) based method, which has been proven to be highly sensitive, reliable and reproducible for any molecule that does not interact with the gold surface of the SPR sensor chip (Zingale, Pandino, et al., 2023). The latter condition is of vital importance, as the interaction of the analyte with the surface would affect the SPR diffusion response, hindering the fitting of the experimental curves to obtain a reliable value of D. Indeed, any protein is electrostatically attracted by the negatively charged gold surface, and its D value cannot be determined by SPR, unless the surface is rendered inert to nonspecific interactions. Even for a canonical usage of the SPR instrumentation, that is to measure the kinetic parameters of specific biomolecular interactions between a molecule immobilized on a gold surface and another one (analyte) flowing into the microfluidic channel above the surface, nonspecific interactions with the surface must be taken into account. For this reason, a reference channel specifically designed to minimize and subtract nonspecific interactions of the analyte from the measured SPR response is commonly used to obtain the kinetic parameters of the interaction between two biomolecules. Therefore, searching for antifouling surfaces is a very active field of research in the SPR community (Liu et al., 2016). For biomolecules with an isoelectric point (IP) low enough to have a net negative charge on their surfaces at physiological pH, bovine serum albumin (BSA) is often used to minimize nonspecific interactions (Distefano et al., 2022).

In this work, we have covalently immobilized BSA on the SPR gold surface in order to minimize the interaction of the latter with insulin. Using such an inert surface, we have then managed to measure the D values by a novel SPR approach for various insulin solutions under different experimental conditions (presence of metal ions and different pH values), giving an insight into the protein oligomerization and early‐stage aggregation states.

2. THEORETICAL BACKGROUND

We have recently reported that SPR can measure D for a variety of small molecules (Zingale et al., ^2023b). Experiments are performed with solute particles, here insulin, that are introduced into a capillary tube filled with a carrier fluid, here the buffer solution. The solute particles will experience both radial and axial diffusion as they move through the tube. The concentration profile of the solute particles along the length of the capillary tube can be measured using various techniques, such as fluorescence, absorbance, or other appropriate methods (d'Orlyé et al., ²⁰⁰⁸; Jelińska et al., ²⁰¹⁷; Moser et al., ²⁰²²). Here we employed SPR response to track the concentration of the analyte as it traverses the gold surface within a capillary tube. To facilitate diffusion analysis, the capillary tube length is strategically chosen to ensure that axial diffusion, the movement along the tube length, is inconsequential compared with radial diffusion across its cross section. This prerequisite is fundamental for reliable diffusion analysis. In the field of Diffusion‐Surface Plasmon Resonance (D‐SPR) analysis, we used long and narrow capillary tubes (internal diameter of 254 μm, length of 70 cm), where the carrier fluid flow rate is appropriately controlled. In this condition, the movement of particles due to the axial diffusion is negligible, since, in this direction, they are mainly moved by the transporting flow. D plays a pivotal role in radial diffusion, influencing the shape of the SPR signal, because it influences the radial diffusion. For systems involving low D, like proteins such as insulin and its aggregates, careful consideration of tube dimensions and flow conditions is essential; thus, the experimental setup is crucial. Here, we used 70 cm and 10 μL/min because they represent the maximum possible length and lowest drift rate, at our experimental conditions, respectively, so as not to have problems with the instability of the instrumental signal. By neglecting axial diffusion, the movement of particles in the capillary tube can be described by the Fick's second law of diffusion, which relates the diffusion rate to the concentration gradient. Here, we released a plug of molecules large enough to obtain a cassette‐like SPR signal profile. Using air bubble trapping to prevent diffusion during sample loading into the instrument loop system, we can obtain a sharp interface between the plug containing the diffusing molecules and the carrier liquid. Before injection, air bubbles are excluded, and the sample is put into contact at the interface with the carrier fluid. Initially sharp, this interface undergoes distortion due to the field of laminar forces and radial dispersion, resulting in a concentration profile similar to an error function detected by the SPR detector. By calculating the numerical first derivative, a distorted Gaussian shape is obtained. The experimental SPR profile is then fitted with the Exponential‐Centered Skew‐Normal Distribution Equation (1):

$$\text{PDF}\_\text{EG}\left(x\right)=\frac{A}{\tau }{e}^{\frac{{\sigma }^2}{2\tau }-\frac{x-\mu }{\tau }}\mathrm{\Phi }\left(\frac{x-\mu }{\sigma }-\frac{\sigma }{\tau }\right),$$ (1)

where x represents time, $\tau$ is the parameter related to the exponential decay, and A, $\mu$, and $\sigma$, are amplitude, position, and width of the Gaussian, respectively (Martínez‐Flórez et al., 2020). The D value is calculated by Equation (2)

$$m=\mu +\tau ,$$

$$\mathrm{sq}={\sigma }^2+{\tau }^2,$$

$$\mathrm{sk}=\frac{2{\left(\frac{\tau }{\sigma }\right)}^3}{{\left(1+{\left(\frac{\tau }{\sigma }\right)}^2\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}},$$

$$D=\alpha \left[\left(\frac{r^{2}m}{24\times \mathit{sq}}\right)\left(1+\mathrm{sk}\right)\right].$$ (2)

where r is the tube radius and $\alpha$ is a calibration parameter that is obtained experimentally. Comparison with well‐known D values of several molecules is used to identify the calibration factor. Data fitting techniques or optimization algorithms iteratively adjust the value of α until the theoretical D closely matches the calibration dataset. Once the best fit between the experimental and theoretical profile is achieved, D is considered a valid estimation of the diffusion coefficient of the solute particles in the capillary tube. It is important to note that the accuracy of the estimated D depends on various factors, including the quality of the experimental data, the validity of the assumptions, and the appropriateness of the theoretical model used. Deviations from ideal conditions or the presence of complex interactions can introduce uncertainties in the estimation.

3. RESULTS AND DISCUSSION

Different experimental techniques can be used to measure insulin diffusion under various conditions, such as real‐time UV imaging (Jensen et al., 2014), DLS (Lorber et al., 2012) and NMR (Patil et al., 2017). In this work, the insulin D values obtained at various experimental conditions have been measured by a novel SPR‐based approach (D‐SPR) and the results have been correlated with the protein oligomeric forms and validated by DLS investigations. In our SPR setup, the limits, mainly given by the nonspecific interaction of the analyte with the gold surface and the tube not sufficiently long for the diffusion of the analyte to occur, have been overcome by functionalizing the surface of the gold sensor with a BSA layer, as well as by using noninteracting pH conditions and by doubling the size of the tube, respectively. As a result, the insulin D values obtained herein are comparable with those in the literature (Jensen et al., 2014; Patil et al., ²⁰¹⁷). For further developments, we have also investigated other proteins to consolidate our D‐SPR method and among them, here we report the diffusion analysis of lysozyme (see the Supplementary materials). In particular, we calculated that the D of lysozyme is 1.45 × 10⁻¹⁰ m²/s (Figure S1 and Table S1), and the value is consistent with the tabulated data (Kim & Myerson, 1996). Moreover, our method allows us to discriminate different oligomerization states or isoforms of insulin; indeed, we studied the insulin solutions under different experimental conditions, such as different pH levels (3.3, 6.6, and 7.3), in the presence and absence of zinc, and in different buffers (Tris–HCl and PBS) to assess the presence of different oligomeric states (Frankær et al., 2017; Groenning et al., ²⁰⁰⁹; Xu et al., ²⁰¹²). The insulin concentration was 100 μM, and the metal ion concentration reached a metal‐to‐peptide ratio 1:1.

The SPR curves of insulin solutions and their respective 1st derivatives are reported in Figure 1, showcasing differences reflecting insulin behavior in solution under the various experimental conditions. These findings reveal that changes in the equilibria between the different insulin oligomerization states are easily detected as changes in the SPR signal. Remarkably, the 1st derivative Gaussian curves exhibit a growing positive skewness following insulin shifts toward higher oligomerization forms and lower D values, as predicted by our mathematical model.

FIGURE 1.

Experimental SPR data from diffusion study of insulin (100 μM) under different experimental conditions. Solid lines (left panels) represent the SPR response due to analyte diffusion; dotted lines (right panels) represent the relative 1st derivative. Zinc or copper ions were added to insulin solutions at a 1:1 metal‐to‐peptide ratio by adding ZnCl₂ 4.4 mM or CuSO₄ 4.4 mM, respectively.

The average D value for each insulin solution was obtained by fitting the Gaussian curves with the equation derived from Taylor's theory (Equation (2)). In our case, the calibration factor α was set to 0.93, and the results obtained are reported in Table 1. Experimental conditions increasing protein oligomerization cause a decrease in the D value as a reflection of an increased hydrodynamic radius. Unfortunately, at this stage it is not possible to have a quantitative distribution of the various oligomeric forms present in solution at the different experimental conditions, as the calculated D values reported in Table 1 cases represent a weighted average of the existing equilibria in solution. However, the reported change in insulin D‐SPR values and the resulting hydrodynamic radii (Table 1) are consistent with the values found in the literature (Jensen et al., 2014; Patil et al., ²⁰¹⁷) and give a clear estimation of the size of the predominant species present in solution at the various experimental conditions. In addition, Chimera UCSF software was used to generate a depiction of insulin 3D structures (Pettersen et al., 2004). To compare our experimental findings with the in silico ones, the hydrodynamic radius of insulin in both monomeric and dimeric states was calculated from the volume of the structure assuming the molecule as a sphere in water, as shown in Figure 2. The influence of metal ions in the oligomerization pathways of aggregation‐prone proteins has been extensively investigated, but the evidence proposed is still controversial and needs to be further elucidated. In this work, we studied by D‐SPR analysis how zinc(II) and copper(II) ions change the insulin oligomerization status. We report, in the case of Zn, a D value that decreases when the metal is added and changes significantly if the insulin‐Zn ²⁺ solution is incubated 1 or 72 h. Specifically, in the presence of Zn²⁺ the D drops from 1.65 × 10⁻¹⁰ to 1.24 × 10⁻¹⁰ m²/s if the solution is incubated 1 h, while it further decreases if the mixture is incubated 72 h, showing a D value of 0.28 × 10⁻¹⁰ m²/s and corresponding to a growing quaternary organization. In the case of the insulin‐Cu ²⁺ solution, on the other hand, we derive a D value of 1.18 × 10⁻¹⁰ m²/s showcasing the presence of smaller species with a D near to the one obtained for insulin at pH 6.6 in PBS (1.30 × 10⁻¹⁰ m²/s), supposing the presence of a dimer‐tetramer equilibrium in solution as evidenced by DLS data.

TABLE 1.

Results obtained through D_SPR analysis at 25°C: D _SPR values refer to the D calculated with Equation 1; SD refers to the standard deviation values and represents the variability in the mean of four experimental replicates; D _tab values refer to the D tabulated in literature (Jensen et al., 2014; Patil et al., ²⁰¹⁷); r _H‐calc are the hydrodynamic radii calculated using the Stokes–Einstein equation in PBS and Tris–HCl at 25°C, respectively; the hydrodynamic radius values measured by DLS are reported in the r _H‐DLS column with its SD referring to the standard deviation of DLS results.

Sample	pH	Buffer	D SPR ± SD (10−10 m2/s)	D tab (10−10 m2/s)	r H‐calc (nm)	r H‐DLS ± SD (nm)
Insulin	3.3	PBS‐HCl	1.60 ± 0.10	1.60	1.52	2.1 ± 0.1
Insulin	6.6	PBS‐HCl	1.30 ± 0.20	1.17	1.87	2.8 ± 0.2
Insulin + Zn2+	3.3	PBS‐HCl	1.17 ± 0.06	‐	2.08	2.3 ± 0.2
Insulin + Cu2+	3.3	PBS‐HCl	1.18 ± 0.02	‐	2.06	2.0 ± 0.2
Insulin	7.3	Tris–HCl	1.65 ± 0.02	‐	1.47	2.5 ± 0.2
Insulin + Zn2+	7.3	Tris–HCl	1.24 ± 0.02	‐	1.95	3.0 ± 0.3
Insulin + Zn2+ (72 h)	7.3	Tris–HCl	0.28 ± 0.01	0.86	8.70	11.0 ± 1.0

FIGURE 2.

Depiction of 3D structure and hydrodynamic radius of insulin (PDB: 3W7Z and 4AIY) in monomeric (top), dimeric (bottom left) and hexameric states (bottom right). The ribbon structure is purple, with disulfide bonds in yellow. Molecular surfaces are represented with the Coulombic surface coloring feature to highlight the differently charged portion of the molecular surface.

Indeed, to validate our D‐SPR approach for determining the insulin D values and to obtain information about the oligomeric states assumed by the protein under various conditions, we also performed DLS measurements. DLS offers one of the most straightforward means of estimating protein size (Lorber et al., 2012; Stetefeld et al., ²⁰¹⁶) and has proven its capability and efficiency in assessing the size distribution of naturally occurring insulin assemblies (Banerjee & Das, 2012; Sklepari et al., ²⁰¹⁶). Furthermore, it has proven effective in monitoring the development of larger oligomeric particles that arise from the aggregation of insulin (Chen et al., 2021; Zingale et al., ^2023a). Depending on the conditions of the solution, insulin can be found in various forms, including hexamers, tetramers, dimers, and monomers. Indeed, the assembly and aggregation of insulin are influenced by pH, concentration, and other parameters. Monomer, dimer, tetramer, and hexamer sizes have been previously reported (Kadima et al., 1993; Sklepari et al., ²⁰¹⁶). Insulin solution (pH 3.3) at 25°C showed a hydrodynamic radius of ≈ 2.1 nm corresponding to an equilibrium between dimeric and tetrameric states (Table 1), according to the literature data (Sklepari et al., 2016). The hydrodynamic radius of insulin changed at pH 7.3, both in the presence and in the absence of zinc(II) (Table 1). In these conditions, the hexameric species appears to be predominant when comparing our dynamic light scattering (DLS) data with the hydrodynamic size reported in the literature for this species (2.8 nm) (Sklepari et al., 2016). Finally, the insulin solution incubated with zinc for 72 h, on the other hand, exhibited larger oligomeric species with an average size of 11 nm.

By comparing the values in Table 1 for the radius calculated from both D‐SPR and DLS measurements, we can conclude that they are very consistent for all the considered conditions. The slight overestimation of the DLS values respect to the D‐SPR ones is most likely due to the higher scattering intensity of the larger species, a phenomenon not affecting the SPR response. Overall, DLS data validate our D‐SPR approach. Indeed, it is important to highlight that the assumption that particles are spherical in the DLS technique may lead to uncertainties when determining the size of particles with a shape that differs significantly from that of a sphere. In addition, sensitivity and precision in determining particles size by DLS strongly decreases if the particles are near the detection limit of this analytical technique and/or if adsorption phenomena of insulin to the solid interface occurs (Dathe et al., 1990). On the other hand, D‐SPR technique is independent of the spherical assumption and it is gives very reliable results for particles as small as 100 Da (Zingale et al., 2023).

4. CONCLUSIONS

A new experimental SPR‐based methodology, hereby named D‐SPR, to monitor the protein oligomerization state has been proposed and applied in the case of lysozyme and insulin at various experimental conditions. Mainly, D‐SPR has been used for the first time to assess changes in insulin oligomerization state at various pH values and in the presence or the absence of copper and zinc ions. The reported results are compared with those reported in the literature by other commonly used experimental techniques and measured in this work by DLS. It is important to highlight that such experimental design also guarantees that the oligomerization state of the protein under analysis is not perturbed in any way by the presence of molecular probes or tags. In addition, the proposed method is highly sensitive, so it does not require high protein concentrations, giving very reproducible results. To the best of our knowledge, the D value of insulin in the presence of copper ions has never been reported before, possibly due to the experimental difficulties commonly encountered when other experimental techniques are applied. Here, we report the possibility of measuring the insulin D value at any experimental condition of interest, as this SPR‐based approach does not have any limitations in this sense, demonstrating the potential applicability of the novel experimental approach to any biomolecules of interest.

5. MATERIALS AND METHODS

5.1. Chemicals

Insulin (dry powder, MW = 5807.65 g/mol, CAS: 11061‐68‐0), zinc chloride (CAS: 7646‐85‐7), copper (II) sulfate (CAS: 7758‐98‐7), glycine (CAS: 56‐40‐6), trizma base (CAS: 77‐86‐1), phosphate buffer saline (PBS tablets pH 7.4 CAS:9048‐46‐8) were purchased by Sigma Aldrich. Bovine serum albumin (BSA, lyophilized powder, crystallized, MW: 66430.3 g/mol, purity ≥98%, CAS: 9048‐46‐8) was purchased by Thermo Scientific. The PBS 10 mM was obtained by dissolving one tablet in 100 mL of MilliQ water. The 50 mM Tris buffer was prepared by dissolving 3 g of Tris in 500 mL of MilliQ ultrapure water. Prior to experiments, buffers were filtered with polyamide membrane filters 0.2 μm (purchased by Whatman) and degassed in an ultrasonic bath for 20 min.

5.2. Sample preparation

A 200 μM stock solution of insulin was prepared by dissolving it in HCl 5 mM; the final insulin concentration (100 μM, expressed as monomer concentration) was obtained by 1:2 dilution with PBS 10 mM. HCl 6 M was added when required to adjust the pH to 3.3. To study the effect of metal ions (such as Zn²⁺ or Cu²⁺) in insulin solutions (pH 3.3), an appropriate amount of ZnCl₂ 4.4 mM or CuSO₄ 4.4 mM was added to obtain a 1:1 metal‐to‐peptide ratio. Moreover, the effect of zinc ions was also studied at pH 7.3: 100 μM insulin solution in Tris 50 mM buffer was prepared and the pH was lowered through the addition of HCl 6 M to favor the solubilization of the insulin; 4 M NaOH was used to reach the proper pH and, finally, an appropriate amount of 4.4 mM ZnCl₂ was added to obtain a 1:1 metal‐to‐peptide ratio. All the solutions were filtered with a non‐pyrogenic syringe filter (Minisart purchased from “Sartorius” cutoff = 0.2 μm), degassed for 5 min, and incubated for 1 h—the only exception regards the insulin‐Zn²⁺ aggregated solution that was incubated 72 h to reach higher oligomeric states. All the sample buffers used during the diffusion experiments presented the same composition as the running buffers, guaranteeing that the D measured is only given by the analyte dispersion into the microfluidic system.

5.3. DLS measurements

DLS analyses were performed using a Zetasizer instrument (Nano ZS; Malvern Instruments) to determine the hydrodynamic radius (r _H) of the protein. DLS is a method that gauges the time‐dependent fluctuations in the intensity of scattered light resulting from particle movement. By analyzing these fluctuations, it becomes possible to determine the translational D values of the particles, which are converted into a size distribution through Non‐Negative Least Square algorithms used by Zetasizer Nano instruments.

The measurements were carried out in disposable cuvettes, assuming a viscosity of 0.9110 mPa × s for PBS solutions and 0.9000 for Tris solutions. Backscattered light at a consistent angle of 173° was detected using a 633 nm wavelength He‐Ne laser. The temperature of the cell holder was maintained at 25°C throughout the measurement process. The scattering information was gathered by averaging at least three separate measurements. Subsequently, the data were processed using the software provided by Malvern Instruments for the Zetasizer. All measurements were performed three times for accuracy.

5.4. SPR measurements

The diffusion experiments were carried out using a multiparametric BioNavis Surface Plasmon Resonance (SPR) Navi 210A instrument. The instrument is equipped with two separate and parallel fluidic channels, one commonly used as a reference channel to subtract nonspecific interactions and the other used to monitor the specific interactions between two biomolecules. The system mounts two distinct lasers at two different wavelengths, 670 and 750 nm, respectively. We used both wavelengths for our purpose, whereas the two channels could be used independently for parallel experiments, as no subtraction with references is needed in the SPR diffusion experiments (Zingale et al., 2023). The latter were run on a surface which has been previously functionalized with a BSA layer to avoid any interaction of insulin with the gold surface (Distefano et al., 2022). The SPR102‐ AU gold sensor chip is made up of 50 nm of gold and 2 nm of chromium on a glass substrate. The gold sensor chip used is 20‐mm long, 12‐mm wide, and 0.55‐mm thick, whereas the area in contact with the flow is 12 mm². The whole SPR Navi 210A fluidic system comprises the flow cell with its tubing connectors and a dual‐channel syringe pump (buffer pump) operating two independent flow paths, one for each of the two measurement chambers. Liquid flows from the buffer container through the injection valve system to the measurement chambers in the flow cell and out to the waste bottle. A single syringe pump is used for automatic loading and cleaning of sample loops. The PEEK tubes connecting the loop to the flow cell have an internal diameter of 254 μm. For insulin D measurements, a tailored connecting tube was used, having a double length with respect to the canonical size (70 cm instead of 35 cm). This was necessary to allow a molecule as large as insulin to diffuse appreciably during its permanence inside the tubing system. The flow rate of the injected solution was set at 10 μL/min.

The instrument was set to record an SPR response point roughly every 2 s. An injection pulse was performed for each analyte before starting the diffusion experiments at different flow rates. This was done for two reasons: the first is that it is necessary to condition the microfluidic tubes, including the loops, used for the sample injection; the second is that it is necessary to verify that the analyte does not interact with the gold chip surface, that is after the passage of the analyte into the flow cell, the SPR signal must return to the baseline. Indeed, it is important to highlight that the SPR curve should have a rectangular shape for a noninteracting analyte due to the change in the refractive index of the solution containing the analyte with respect to the pure buffer solution. However, even for a noninteracting analyte, the shape of the curve is not rectangular, but gaussian or sigmoidal. This is confirmed for all noninteracting analytes and it is due to the analyte diffusion occurring inside the tubing system, which, in turn, allows the measurement of D. The injection profile is set to let the analyte flow at the chosen speed for 2 min to ensure that the SPR signal reaches saturation. Between each experiment, the system is rinsed with the buffer, for the time necessary for the SPR signal to return to the baseline. This indicates that the sample has left the flow cell and the system has returned to the starting conditions.

AUTHOR CONTRIBUTIONS

Gabriele Antonio Zingale: Conceptualization; methodology; supervision; writing – review and editing; visualization. Damiano Calcagno: Investigation; formal analysis; data curation; writing – review and editing; visualization. Maria Luisa Perina: Investigation; formal analysis; data curation; writing – review and editing; visualization. Irene Pandino: Conceptualization; methodology; supervision; writing – review and editing; visualization. Nunzio Tuccitto: Conceptualization; software; methodology; validation; writing – review and editing. Valentina Oliveri: Data curation; formal analysis; writing – review and editing; investigation; validation. Maria Cristina Parravano: Resources; supervision; funding acquisition. Giuseppe Grasso: Funding acquisition; conceptualization; project administration; resources; supervision; writing – original draft; writing – review and editing; methodology.

CONFLICT OF INTEREST STATEMENT

The authors declare no potential conflicts of interest.

Supporting information

Figure S1. A Python script, based on Equations 1 and 2 (see the main text), was used to analyze the SPR curve of the Lysozyme, with the upper panel showing the curve and the lower panel showing its 1st derivative.

Table S1. Results obtained through D_SPR analysis at 25°C: D_SPR value stands for the experimental D obtained using Equations 1 and 2 (see the main text); the standard deviation values (SD) represent the variability in the mean of four experimental replicates; D_ext value refers to the D extrapolated from the literature [a]. (a) Kim, Yeong‐C'bul, and Allan S. Myerson. “Diffusivity of Protein in Aqueous Solutions.” Korean Journal of Chemical Engineering 13, no. 3 (May 1, 1996): 288–93. https://doi.org/10.1007/BF02705952.

Calcagno D, Perina ML, Zingale GA, Pandino I, Tuccitto N, Oliveri V, et al. Detection of insulin oligomeric forms by a novel surface plasmon resonance‐diffusion coefficient based approach. Protein Science. 2024;33(4):e4962. 10.1002/pro.4962