The Hydration Shell of Monomeric and Dimeric Insulin Studied by Terahertz Time-Domain Spectroscopy

Abstract

Protein aggregation is believed to be a significant biological mechanism related to neurodegenerative disease, which makes the early-stage detection of aggregates a major concern. We demonstrated the use of terahertz (THz) time-domain spectroscopy to study protein-water interaction of monomeric and dimeric bovine insulin in aqueous samples. Regulated by changing pH and verified by size-exclusion chromatography and dynamic light scattering, we then measured their concentration-dependent changes in THz absorption between 0.5 and 3.0 THz and quantitatively deduced the extended hydration shell thickness by cubic distribution model and random distribution model. Under a random distribution assumption, the extended hydration thickness is 15.4 ± 0.4 Å for monomeric insulin and 17.5 ± 0.5 Å for dimeric insulin, with the hydration number of 6700 and 11,000, respectively. The hydration number of dimeric insulin is not twice but 1.64 times that of monomeric insulin, further supported by the ratio of solvent-accessible surface area. This “1.64-times” relation probably originates from the structural and conformational changes accompanied with dimerization. Combined with the investigations on insulin samples with different single amino acid mutations, residue B24 is believed to play an important role in the dimerization process. It is demonstrated that THz time-domain spectroscopy is a useful tool and has the sensitivity to provide the hydration information of different protein aggregates at an early stage.

Significance

The concentration-dependent terahertz (THz) absorptions of monomeric and dimeric insulin solutions are plotted, consistent with molecular dynamics simulations. Combined with two distribution models, the hydration thickness and hydration number are quantitatively estimated, providing a new, to our knowledge, perspective to comprehensively understand the protein aggregation behavior. Compared to previous researches on the discrepancy between different protein types or homologous proteins with native and denatured structure, investigations on single-residue mutant insulin illustrate the sensitivity of THz time-domain spectroscopy to structural changes lies at the level of different oligomers. The importance of residue B24 in dimerization process is evaluated. The validity of random distribution model and solvent-accessible surface area is addressed. Therefore, THz time-domain spectroscopy is a feasible way to characterize different protein aggregates at early stage.

Introduction

In living organisms, proteins perform various functions, including catalyzing metabolic reactions, DNA replication, responding to stimuli, and transporting molecules from one location to another (1, 2). Protein aggregation has been regarded as a common but important molecular mechanism in regulating cell growth and survival (3). It is also considered to be the cause of several pathologies such as neurodegenerative disease (4) (Alzheimer’s disease, Parkinson’s disease, Huntington’s disease, etc.). In the physiological environment, water molecules are active players in the structure and function of proteins, which can be generally divided into three types (5) according to the water-protein interactions: 1) bulk water, which surrounds the protein molecule at a distance out of van der Waals contact; 2) individually bound water, which forms hydrogen bonds with polar atoms in cavities inside protein molecules, acting as the stabilizer of protein structure (6, 7); and 3) hydrated water at the interfacial region of proteins with direct interactions (8). It is worth noting that water motion in the hydration layer is central to protein fluctuation and essential to its structural stability, dynamics, and function (9), such as protein folding (10), solubility (11), ligand docking (12), and oligomer formation (13). The information of tightly bounded water molecules is available by NMR (14) and x-ray scattering (15), but the protein-water interactions can generally influence the surrounding water beyond the monolayer, resulting in the perturbation of the hydrogen bonding network.

Insulin is regarded as an excellent model for protein aggregation studies because of the physiological and therapeutic importance of diabetes (16) and the property that insulin easily aggregates in vitro. It consists of two peptide chains referred to as the A chain (21 amino acids) and B chain (30 amino acids). It is in hexamer form when synthesized and stored in the pancreas. A hexamer contains three dimers, and tends to form smaller oligomers as pH decreases (17). The monomer interacts with the cell-surface receptor directly (18), and the dimer is the direct form to be decomposed into the monomer (19). Although the process of insulin aggregation has been widely studied by various methods such as spectroscopy (20, 21), microscopy (22, 23), and chromatography (24), the hydration information is not fully investigated. A useful tool is terahertz (THZ) time-domain spectroscopy (TDS). The electromagnetic field in THz range is strongly absorbed by polar liquids such as water, which limited the measurements of solution at the beginning. With the development of THz sources and detectors, THz spectroscopy is becoming a supplementary method to probe the change in hydrogen bonding network (25), making it possible to characterize hydrated biomolecules in aqueous samples.

In previous work, the influence of protein on surrounding water molecules was reported to reach to over 20 Å from the protein surface (26, 27, 28), forming the “extended hydration shell.” But the spectral comparisons were made between different types of protein or the homologous proteins with big difference such as the native one and the denatured one. The potential of THz spectroscopy in distinguishing protein with slight difference has not been properly evaluated. Besides, previous work about insulin samples studied by THz-TDS is generally focused on the spectral difference between native insulin and insulin fibrils in solid state (29), which is far from the physiological environment. Therefore, we use the THz-TDS to study the monomeric and dimeric bovine insulin in aqueous state at room temperature. By investigating the concentration-dependent trend of the THz absorption coefficient and calculating the hydration shell by two distribution models, the numbers of hydration water in monomeric and dimeric bovine insulin are quantitatively determined. Further researches on insulin samples with single amino acid mutation are conducted to qualitatively illustrate the sensitivity of THz-TDS to structural change, the role of specific amino acid in dimerization process, and the robustness of the distribution model. The feasibility of THz-TDS in characterizing different protein aggregates at an early stage is demonstrated.

Materials and Methods

Fundamental insights into the properties of hydration shell can be obtained from concentration-dependent THz absorption measurements (30, 31). High-precision solution measurements were carried out at 20°C to detect the changes in THz absorption coefficient Δα (0.5–3.0 THz).

Sample preparation

Lyophilized bovine insulin was purchased from Sigma-Aldrich (Shanghai, China) without further purification. The mutant insulin samples were synthesized with the purity of over 95%. Two different residues, A8 and B24, were selected because A8 is one of the different residues between bovine insulin and human insulin and B24 is considered as an important residue in the dimerization process. For the amino acid at A8, the alanine in bovine insulin was replaced by threonine. For the amino acid at B24, the phenylalanine in bovine insulin was replaced by glycine. Acetic acid and hydrochloric acid were purchased from the Aladdin Reagent Corporation (Shanghai, China). All sample containers were cleaned by absolute ethyl alcohol and dried in a vacuum drying oven at the temperature of 60°C. To prepare monomeric insulin solution, lyophilized insulin was firstly dissolved in the solvent of 20% acetic acid at the highest concentration of 5.0 mM (29.0 mg/mL). The impurities in the solution were removed with 0.20 μm filter membrane. This filtration step was also performed on the solvent for the same purpose. Monomeric insulin solutions with a concentration range from 0 to 5.0 mM were prepared by mixing 5 mM insulin solution and solvent in different proportions with a concentration gradient of 0.5 mM (2.9 mg/mL). To form dimeric insulin solutions, the processes were generally identical to the preparation of monomeric insulin solutions, except for a different solvent, namely hydrochloric solution (pH 2.0).

SEC measurements

To verify the rationality of the pH-regulated method on insulin aggregation, experiments of size-exclusion chromatography (SEC) were conducted by General Electric ÄKTA Purifier (Boston, MA), with a high-performance column of Superdex 75 (General Electric). The measuring range of this column is from 3 to 70 kDa in molecular weight, which is suitable for the detection of insulin oligomers because insulin monomer is a predominantly helical structure with the molecular weight of ∼5.8 kDa. The velocity of the mobile phase was set as 0.5 mL/min. For monomeric and dimeric insulin, the corresponding solvent was selected as the mobile phase to keep the aggregation state unchanged.

DLS measurements

Dynamic light scattering (DLS) measurements were performed on a DynaPro NanoStar system (Wyatt Technology Corporation, Santa Barbara, CA). Light scattering was monitored at a 90° angle, and the temperature of the sample holder was controlled at 20°C. The same batches of insulin solutions were measured twice to simulate the condition of THz-TDS measurements. One measurement was conducted within 5 min and the other was conducted after 1 day to evaluate the time-induced difference.

THz absorption measurements

A commercial THz-TDS system, TAS7400TS (Advantest Corporation, Tokyo, Japan), was used in the experiments as illustrated in Fig. 1. It is used under normal incidence with a dynamic frequency range of 0.5–4.5 THz, a frequency resolution of 1.9 GHz, and a signal/noise ratio of 60 dB. Based on the principle of asynchronous optical sampling, the electrical-controlled dual lasers magnify the time evolution of the ultrafast transient signal arbitrarily in the timescale. This system sharply shortens the measurement time to hundreds of milliseconds for one scan. For each sample, three consecutive measurements were conducted, and each measurement was an average of 1024 scans. The experiments were repeated for three times on different days to minimize the measurement error.

Figure 1.

Schematic diagram of the TAS7400 THz-TDS system. To see this figure in color, go online.

Changes in air humidity and temperature influence the THz transmission greatly and will lead to systematic error in valuing the absolute absorption coefficient. Therefore, the system was kept in a box purged with dried air to keep the humidity as low as 1.0%. The room temperature was kept constant at 293 K (20°C) to minimize the systematic error.

The monomeric and dimeric insulin solutions with different concentrations were put into the optical path to obtain the THz absorption coefficient. By using a standard quartz liquid sample cuvette (Hellma Analytics, Müllheim, Germany), the sample thickness was fixed with two pieces of quartz slice. One piece is smooth and the other one is with a 100-μm-thick groove. Nearly 30 μL of the aqueous sample was injected into the groove, adsorbed with the smooth slice by surface tension. The cuvette holder provided extra pressure to make sure the sample thickness equaled the groove’s depth. Considering the same process of sample preparation and the identical cuvette used in experiments, the deviation of the groove’s depth is eliminated. The variation rate of THz absorption coefficient Δα stands for the difference between THz absorption of insulin solution and the solvent, which is regarded as a function of insulin concentration.

Quantitative estimation of hydration shell thickness

According to Beer-Lambert’s law, the total absorption is attributed to the absorption of the insulin α_insulin, the absorption of hydration shell α_shell and the absorption of solvent α_solvent. The volume of insulin V_insulin, the volume of hydration shell around the insulin V_shell and the total volume V_total are distinguished, respectively.

$$\alpha ={\alpha }_{insulin}\frac{V_{insulin}}{V_{total}}+{\alpha }_{shell}\frac{V_{shell}}{V_{total}}+{\alpha }_{solvent}\frac{V_{total}-V_{insulin}-V_{shell}}{V_{total}}$$ (1)

Usually, as shown in Fig. 2 a, we apply the spherical approximation of protein to explain the characteristics of the hydration layer, reducing the difficulty of mathematical expression and making it available to other experimental systems. The volume of the spherical hydration shell is as follows:

$$V_{shell}^0=\frac{4}{3}\pi \left(R^3-r^3\right),$$ (2)

where R is the radius of insulin-hydration structure and r is the radius of insulin.

Figure 2.

(a) A diagram of the three components in protein solution: 1) the protein molecule, 2) the hydration shell, and 3) the bulk water. (b) A diagram of the cubic distribution model is shown. (c) A diagram of the random distribution model is shown. To see this figure in color, go online.

Generally, there are two ways widely used in the calculation of hydration shell thickness. One method is the cubic distribution model, as shown in Fig. 2 b. For simplicity, the proteins are assumed to be arranged in a cubic lattice with a center-to-center distance a = c^−1/3, where c is the concentration. At lower concentration, the insulin-hydration structure is isolated with each other, until a certain concentration c₁ when the sphere of insulin-hydration structure is inscribed to the cubic surfaces. When the insulin concentration increases continuously, the hydration shell begins to overlap, influencing the volume proportion between the hydration shell and insulin molecules. Therefore, the concentration c₁ is regarded as the corresponding inflection concentration in THz spectra. Based on this concentration, the number of insulin molecules n in unit volume is determined. The insulin molecules are assumed to be arranged at the vertices of the cube. Each edge is evenly divided by$\sqrt[3]{n}$insulin molecules. $\frac{1}{\sqrt[3]{n}}$equals to the sum of insulin diameter and twice of the hydration shell size. By subtracting the insulin diameter, the hydration shell size is quantitatively estimated.

The other method is the random distribution model based on Monte Carlo simulation (32), shown in Fig. 2 c. The insulin molecules are distributed randomly in the box with unit size under the “hard sphere” assumption (33). Considering the concentration with a maximum of Δα, the number of molecule particles n in the box is determined. From the generated coordinates of these n points, the average distance of any two points is calculated. Similar to the cubic distribution model, the averaged hydration shell size is obtained by subtracting the insulin diameter.

It is worth noting that a dimer particle contains two molecules, so the concentration of dimer particles is half of the concentration of insulin molecules.

Results and Discussion

SEC and DLS results

As shown in Fig. 3 a, the retention volume is 20.14 mL for the monomer and 19.01 mL for the dimer, respectively. The sharp absorption peak in each curve represents a single molecular weight, indicating a single aggregation state.

Figure 3.

(a) The retention volume of monomeric and dimeric bovine insulin studied by size-exclusion chromatography (SEC). (b) The hydrodynamic radius of monomeric and dimeric bovine insulin detected by dynamic light scattering (DLS) is shown. To see this figure in color, go online.

A quantitative estimation of the molecular weight was conducted by measuring four samples with known molecular weight (see “The Determination of Insulin Aggregation States” in Supporting Materials and Methods for details). By plotting the logarithm of molecular weight against the retention volume, a linear fitting curve is generated as follows:

$$y=-0.2738x+9.26802,$$ (3)

where y is the log of molecular weight $\log MW$and x is the retention volume. By substituting the retention volume of monomeric insulin (20.14 mL) and dimeric insulin (19.01 mL) into this linear fitting curve, the estimated molecular weights are 5671 and 11,707 g/mol, which are consistent with their theoretical values, 5733 and 11,466 g/mol, respectively. The slight difference between estimated values and theoretical values could be originated from the error in linear fitting or the precision of experimental data.

Besides, the radius of insulin monomer and dimer were obtained. As shown in Fig. 1 b, it is ∼1.4 nm for the insulin monomer and ∼1.8 nm for the insulin dimer. These values are consistent with previous reports (34, 35). Theoretically, several models have been proposed to calculate the protein size. The minimal radius of a sphere can be deduced directly from the molecular weight (36), which is 11.8 Å for monomeric insulin and 14.9 Å for dimeric insulin. Because proteins have an irregular surface, even those approximately spherical ones will have an average radius larger than the minimum. Based on the diffusion coefficient and molecular weight, the gyration radius of protein can be estimated (37), which is 16.1 Å for monomeric insulin and 23.4 Å for dimeric insulin. From the insulin crystal structure, the diameters of monomeric insulin and dimeric insulin can be directly measured, which are 27.9 and 34.5 Å, respectively. Considering that the molecular dynamics (MD) simulation is further conducted based on the crystal structure, we select the measured radius as the size of monomeric and dimeric insulin in the following hydration estimation section, which is consistent with the DLS results as well.

Both SEC and DLS results illustrate the feasibility of regulating the monomeric and dimeric insulin by changing pH. Therefore, the same method was adopted for subsequent THz experiments.

THz-TDS results

The absorption spectra of monomeric and dimeric insulin were collected from 0.5 to 3.0 THz for a range of protein concentrations between 0 and 29.0 mg/mL (Fig. 4). The curves of different concentrations are generally intertwined with each other. It is because water makes up the vast majority of the aqueous samples, largely covering the THz absorption difference. Therefore, the absorption coefficients were averaged to reduce the effect of noise. The averaged THz absorption differences Δα in four frequency bands are displayed in Fig. 5. Each point represents the average value. The error bar is drawn according to the standard error of nine measurements. The zoom-in graphs of absorption coefficient in different frequency bands are shown in Figs. S2 and S3.

Figure 4.

The absorption coefficient of (a) monomeric bovine insulin solution and (b) dimeric bovine insulin solution between 0.5 and 3.0 THz, for protein concentrations between 0 and 29.0 mg/mL, with a concentration gradient of 2.9 mg/mL. To see this figure in color, go online.

Figure 5.

The average THz absorption difference, Δα, of monomeric bovine insulin (black panel) and dimeric bovine insulin (red panel) solutions in four frequency bands: (a) 0.8–1.2 THz, (b) 1.3–1.7 THz, (c) 1.8–2.2 THz, and (d) 2.3–2.7 THz. The error bar is drawn according to the standard error. To see this figure in color, go online.

Generally, for both of the monomeric and dimeric bovine insulin solutions, the absorption coefficient shares the same trend that it increases at lower concentration to its maximum, followed by a decrease at higher concentration. The maximum of Δα is up to ∼4%, which is in accordance with previous work (38). In addition, this trend is similar to that of natively folded protein rather than denatured protein (30), indicating that the pH-regulated aggregation of insulin keeps its native structure. It makes the hydration shell study more significant compared to previous study on the insulin monomer and aggregates in solid state (39).

Although the biomolecule solids generally absorb less than bulk water in THz range, there are still many situations in which the biomolecule-water solution absorbs more than either the biomolecule or bulk water, namely “THz excess.” This can be attributed only to the hydration shell. The presence of biomolecules perturbs neighboring water molecules through intermolecular interactions, forming hydration shell. Correspondingly, the water in dynamical hydration shell has a distinct character from bulk water, showing a higher THz absorption coefficient. The minimal fitting model required to describe the solute-solvent system must incorporate a third component, representing the dynamical hydration shell around the biomolecule solute, shown as Eq. 1. For simplicity, the model assumes a step transition to bulk water at a certain distance from the insulin surface.

More sophisticated models have been introduced to fit experiment data more precisely, such as nonspherical model, but this model optimization results in the same consequences within the experimental uncertainty (40). Based on this three-component model, the concentration corresponding to the maximum of THz excess is regarded as the situation that hydration shells of two neighboring insulin molecules begin to overlap, as illustrated in Quantitative Estimation Of Hydration Shell Thickness. Combined with this spherical approximation, the radius of hydration shell is determined.

By averaging the concentration in four frequency bands, shown as the vertical dash lines in Fig. 5, the concentration shift is clearly observed from 11.19 ± 0.29 mg/mL for the monomer to 14.47 ± 0.24 mg/mL for the dimer. For monomeric bovine insulin solution, the particle concentration of maximal point is ∼1.93 ± 0.05 mM and the diameter of monomeric insulin is 27.9 Å. The hydration shell is deduced to be 33.6 ± 0.4 Å by the cubic distribution model and 15.4 ± 0.4 Å by the random distribution model. For dimeric bovine insulin solution, the particle concentration of the maximal point is 1.25 ± 0.02 mM and the diameter of insulin dimer is 34.5 Å. The hydration shell is 37.7 ± 0.3 Å in the cubic distribution model and 17.5 ± 0.5 Å in the random distribution model, respectively. In either assumption, the hydration thickness of the monomer is thinner than that of the dimer. Although both results meet the same order of magnitude as previous reports (26, 27, 28, 41), the difference lies between the results from different distribution models. Because the protein-water interactions can extend beyond two to three water solvation layers (42), the result from the random distribution model is more reasonable and further selected in quantitative calculation. Under the assumption that the diameter of the water molecule is 3 Å, the hydration number is approximately 6700 for monomeric bovine insulin and approximately 11,000 for dimeric bovine insulin. The proportion is not twice, but 1.64-times. If the hydration number is evenly assigned to insulin molecules, there is a decreasing trend with insulin aggregation, from 6700 for the monomer to 5500 for the dimer. Therefore, the dimerization process is probably accompanied with structural changes, which reduces the average area accessible to solvent and further leads to this 1.64-times relation.

MD simulation

To further support the THz-TDS results, we performed classical MD simulations of monomeric and dimeric insulin by using Groningen Machine for Chemical Simulations 5.1.2 software package. The Groningen Molecular Simulation 96 force field was used to describe the potential energy contributions of insulin, and flexible simple point charge force field was used for water molecules. The protein structure of insulin hexamer was downloaded from Protein Data Bank database (Protein Data Bank: 2A3G), with three dimers contained. The topology structures of the insulin monomer and dimer were obtained by deleting the duplicate parts and repairing the missing atoms. Before the MD simulations, the insulin molecule was solvated by water molecules in a cubic simulation box with periodic boundary conditions applied in all directions. The concentration was quantitatively determined by changing the edge length of the box, shown in Table 1.

Table 1.

The Relationship between the Edge Lengths of the Simulation Box and the Concentrations of Monomeric and Dimeric Bovine Insulin Solution

Aggregation State	Concentration (mg/mL)	Edge Length (Å)
Monomeric insulin	29.00	69.3
	21.75	76.2
	14.50	87.3
	7.25	109.9
Dimeric insulin	29.00	87.3
	21.75	96.0
	14.50	109.9
	7.25	138.5

Counterions were put into the box to achieve electrical balance. A 5-ns MD simulation was performed after three processes: 100-ps energy minimization with the steepest descent method, 100-ps constant number, volume, and temperature relaxation balance, and 100-ps constant number, pressure, and temperature relaxation balance. The average autocorrelation function C_M of dipole moment M is as follows:

$$C_M\left(t\right)=\langle M\left(0\right)M\left(t\right)\rangle$$ (4)

C_M was then used to calculate the absorption line shape function I(ω) and the absorption cross-section α(ω) as follows:

$$I\left(\omega \right)=\underset{-\infty }{\overset{+\infty }{\int }}{C}_M\left(t\right)\exp \left(i\omega t\right)dt,$$ (5)

$$\alpha \left(\omega \right)=\frac{4{\pi }^2\omega \left(1-\exp \left(\hslash \omega /kT\right)\right)}{3\hslash cn\left(\omega \right)}I\left(\omega \right)$$ (6)

The relative difference in THz absorption for several insulin concentrations is shown in Fig. 6. The horizontal coordinate of the maximal point is approximately 10.5 mg/mL for the monomer and approximately 14.5 mg/mL for the dimer, consistent with the experimental data.

Figure 6.

Simulated relative difference in THz absorption of monomeric and dimeric bovine insulin with different concentrations: 0, 7.25, 14.5, 21.75, and 29.0 mg/mL. To see this figure in color, go online.

During the dimerization process, this concentration is a balance of two factors. One is the increased radius of insulin particles, leading to a possible reduction of the inflection concentration. The other is the decreased concentration of dimeric particles, which will show the influence to the opposite direction. In this case, a bigger inflection concentration of dimeric solution is found when Δα reaches the maximum.

In previous discussions, insulin molecule was treated as a homogenous sphere to simplify the hydration shell calculation. In fact, it contains two polypeptide chains linked by two disulfide bridges, showing hydrophobicity and hydrophilicity at different sites. The study on the equilibrium dissociation constant of the insulin monomer-dimer system shows that dimer association involves a concerted monomer conformational and dimer-interface folding to stably bind (43). Specifically, the intermonomer hydrogen bonding and hydrophobic interactions between residues Phe B24 and Tyr B26 are believed to play an important role in dimer stability (44), supported by the mutant research at these residues (45).

Considering the inhomogeneity of protein surface, the solvent-accessible surface area (SASA) was further investigated, which is 39.65 nm² for monomeric bovine insulin and 65.62 nm² for dimeric bovine insulin, respectively. Although dimeric insulin contains two insulin molecules, the dimeric insulin’s SASA is only nearly 1.65 times of monomeric insulin’s SASA, implying the structural changes during the dimerization process. The number of water molecules in the first hydration layer was calculated as$v_{\text{H}}=A_S/a_W$, where A_S is the SASA of the protein and a_W is the amount of SASA occupied by one water molecule on average (46). Because a_W is a constant, the number of hydration water is proportional to the SASA. In this work, the estimated hydration shell thickness for both monomeric and dimeric insulin supports the previous finding that the protein-water interactions can extend beyond two to three hydration layers. It is worth noting that the SASA ratio between dimeric and monomeric insulin is consistent with the ratio of hydration water numbers. The slight difference of the proportion can be attributed to the error in evaluating the concentration of hydration overlap. Therefore, the SASA has the potential to be applied to quantitatively characterize the ratio of hydration water numbers in extended hydration layers.

To estimate the sensitivity of THz-TDS on single amino acid mutation, the role of specific residue (B24) involved in dimerization process, as well as the validity of random distribution model and SASA in characterizing mutant insulin, THz experiments on insulin samples with A8 mutation and B24 mutation were further conducted. By following the same experimental protocol, the results are shown in Fig. 7.

Figure 7.

The average THz absorption difference, Δα, of the monomeric A8 mutant insulin (green square), dimeric A8 mutant insulin (orange square), monomeric B24 mutant insulin (blue square), and dimeric B24 mutant insulin (purple square) solutions in four frequency bands: (a) 0.8–1.2 THz, (b) 1.3–1.7 THz, (c) 1.8–2.2 THz, and (d) 2.3–2.7 THz. The error bar is drawn according to the standard error. To see this figure in color, go online.

As shown in the green and blue panels of Fig. 7, the concentration-dependent THz absorptions of mutant monomers are plotted. The inflection concentration is 11.34 ± 0.12 mg/mL for A8 mutant monomer and 11.28 ± 0.09 mg/mL for B24 mutant monomer, respectively. The values are both very close to that of bovine insulin within statistic error. Combined with the random distribution model, the calculated hydration thickness and hydration number of both mutants stay the same as bovine insulin, implying that the effect caused by single amino acid mutation is lower than the detection limit of THz-TDS. Therefore, a qualitative conclusion can be drawn that the THz spectral sensitivity to structural change lies at a level of different protein aggregates.

When all the panels in Fig. 7 are considered, an obvious difference can be seen between the inflection concentrations of the mutant dimer. It is 14.34 ± 0.06 mg/mL for the A8 mutant dimer, whereas it is11.27 ± 0.11 mg/mL for the B24 mutant dimer. For the A8 mutant dimer, the inflection concentration, the calculated hydration thickness, and hydration number are regarded as the same as bovine insulin within statistic error, illustrating that the mutations at A8 have little influence on the dimerization process. For the B24 mutation dimer, the calculated hydration thickness is 19.6 ± 0.5 Å and the hydration number is approximately 13,300, respectively, from the random distribution model. It is worth noting that the hydration number is twice that of monomeric insulin. However, the dimerization will result in a “nontwice” relation because of the accompanying structural changes. This contradiction implies that the B24 mutant insulin does not dimerize in the HCl solution, which is supported by the previous work (47) and the DLS result shown as Fig. S4. Therefore, the residue B24 is highly involved and plays an important role in the dimerization process. Unlike SASA, which needs the aggregation state in advance to calculate the ratio, the hydration information deduced by the random distribution model could provide us some clues to further speculate the aggregation state, although it is not known. From this point of view, the random distribution model is more suitable and robust than SASA when studying insulin mutants.

Conclusions

In conclusion, the hydration shell thickness of monomeric and dimeric bovine insulin is studied by THz-TDS and further quantitatively analyzed by two different distribution models. According to the random distribution model, the hydration thickness is 15.4 ± 0.4 Å for the monomer and 17.5 ± 0.5 Å for the dimer. The hydration number of the dimer and monomer meets the 1.64-times relation, which can be attributed to the structural change during the dimerization process, supported by the ratio in SASA. Further investigations on mutant insulin illustrate the importance of residue B24 in the dimerization process. The random distribution model is believed to be more suitable and robust than SASA in studying mutant samples. Therefore, THz-TDS is a sensitive tool to probe the hydration information of different protein oligomers, providing a new, to our knowledge, insight into comprehensively understanding the protein aggregation behavior at an early stage.

Author Contributions

P.W. performed the DLS and THz experiments, analyzed data, and wrote the manuscript. X.W. performed the SEC experiments and molecular simulations. L.L. and H.Z. contributed theoretical discussions. W.Q. and M.H. designed the research.

Editor: Heping Cheng.