DTT-induced aggregation of insulin was studied by DLS at 25 °C in 50 mM sodium phosphate buffer, pH 7.0, containing 0.15 M NaCl at various concentrations of the protein. Figure 1A demonstrates the increase in the light scattering intensity (I) in time accompanying DTT-induced aggregation of insulin. The increase in the concentration of insulin in the interval from 0.2 to 0.4 mg/mL resulted in the increase to the aggregation rate (curves 1–6).

A typical feature of the aggregation curves is the appearance of a lag period. To estimate the duration of the lag period, the initial parts of the dependences of I on time were analyzed using Equation (1) (see Experimental Section) containing parameters t₂ (the duration of lag period; in other words, the point in time at which the light scattering intensity begins to increase) and parameter K_agg characterizing the initial rate of aggregation. As an example, Figure 2 shows the fitting of the initial parts of the dependences of I on time obtained at concentrations of insulin of 0.20, 0.28 and 0.40 mg/mL.

The values of parameters t₂ and K_agg calculated at various concentrations of insulin are given in Table 1. The duration of lag period decreases from 18.4 ± 0.5 to 15.6 ± 0.2 min, when the concentration of insulin increases in the interval from 0.2 to 0.4 mg/mL. More significant changes are observed in the K_agg value. Parameter K_agg, which is a measure of the aggregation rate, increases by a factor of 200 at twofold increase in the concentration of insulin (from 0.2 to 0.4 mg/mL). Figure 1B shows the dependence of parameter K_agg on the concentration of insulin. The dependence follows the power law in accordance with Equation (4). Parameter n was found to be 6.3 ± 0.2.

Consider the time-course of the appearance of the protein aggregates in the solution of insulin after the addition of DTT. Figure 3 shows the insulin distribution of the particles by size (0.32 mg/mL) incubated at 25 °C in the presence of 20 mM DTT. The particle size distributions were recorded at 15 second intervals. Over the first 17 minutes, the single peak with R_h = 1.3 ± 0.1 nm is registered in the system (Figure 3A; t = 1 min). It is evident that this peak corresponds to the non-aggregated form of insulin. At t = 17.2 min the start aggregates, with R_h value higher than 90 nm, appear, and two peaks are registered on the distribution of the particles by size (Figure 3B). The point in time at which the start aggregates appear, was designated as t₁. It should be noted that intermediates between the peaks corresponding to the non-aggregated form of insulin and start aggregates are lacking. Thus, the formation of the start aggregates proceeds on an all-or-none principle.

In the interval from 17.2 to 19.3 min, the position of the peak corresponding to the start aggregates remains unchanged (see, for example, Figure 3C). Since the moment in time at which the start aggregates appear (t = 17.2 min), is very close to the precise moment at which the light scattering intensity begins to increase (t₂ = 16.7 min), one can conclude that the increase in the light scattering intensity in the interval from 16.7 to 19.3 min is due to accumulation of the start aggregates in the system; the size of the start aggregates remaining unchanged. At t > 19.3 min the size of the start aggregates begins to increase. Figure 3D shows the particle size distribution at t = 50 min. The hydrodynamic radius of the protein aggregates reaches a value of about 800 nm.

The analogous character of the changes in the particle size distribution in the solution of insulin after the addition of DTT was observed for other insulin concentrations (0.20, 0.24, 0.28, 0.36 and 0.40 mg/mL). The values of parameters t₁ and t₂ determined at various insulin concentrations are given in Table 1.

The time-course of the positions of the peaks on the distribution of the particles by size for DTT-induced aggregation of insulin at various concentrations of the protein substrate (in the interval from 0.20 to 0.40 mg/mL) is demonstrated in Figure 4. The solid and open circles correspond to the non-aggregated and aggregated forms of insulin, respectively. The insets show the dependences of R_h on time with the expanded ordinate axis.

A distinctive feature of the dependences of the hydrodynamic radius of the protein aggregates on time is the constancy of the R_h values over the definite time interval. This region of the R_h values corresponds to the start aggregates. The hydrodynamic radius of the start aggregates (R_h,0) remains practically unchanged at variation of the protein concentration (Table 1). The average value of R_h,0 was found to be 94 ± 7 nm.

As can be seen in Figure 4, at a definite moment in time the hydrodynamic radius of the start aggregates begins to increase. This moment in time was designated as t₃. The reason for such an increase in the R_h value is the sticking of the start aggregates provoked by their accumulation. The initial increase in the R_h value in time is linear. This allows the value of t₃ to be determined more precisely using Equation (2). The values of parameter t₃ are given in Table 1. The analysis of the values of t₂ and t₃ shows that the time interval (t₃ − t₂), over which the accumulation of the start aggregates occurs without sticking, is shortened by increasing the protein concentration.

Apart from parameter t₃, Equation (2) gives parameter K₁, which characterizes the increase in the R_h value in time (K₁ = dR_h/dt). The values of parameter K₁ are given in Table 1. When the insulin concentration increases from 0.2 to 0.4 mg/mL, a fivefold increase in the K₁ value is observed. The data presented in Figure 3 show that above a definite point in time (t > t*), the dependence of R_h on time follows the power law (see Equation (3). The values of t* and the fractal dimension of the aggregates (d_f) are given in Table 1. The fact that the values of d_f are close to 1.8 is indicative of the fulfillment of the regime of the diffusion-limited cluster-cluster aggregation.

To characterize the effect of α-crystallin on the kinetics of DTT-induced aggregation of insulin, we analyzed the time-course of the light scattering intensity (I) and the hydrodynamic radius values of the particles formed in the solution of insulin (0.32 and 0.4 mg/mL), after the addition of DTT in the presence of various concentrations of α-crystallin, in the interval from 0.08 to 1.2 mg/mL. Figure 5 shows the kinetic curves of aggregation in the coordinates {I; time}. When the concentration of insulin was 0.4 mg/mL, the effect of α-crystallin is clearly visible. The relatively low concentrations of α-crystallin (0.08, 0.32 and 0.64 mg/mL; curves 2, 3 and 4 in Figure 5B, respectively) induce acceleration of insulin aggregation. At higher concentrations of α-crystallin (0.8 and 1.2 mg/mL; curves 5 and 6, respectively) the suppression of insulin aggregation is observed.

At the insulin concentration of 0.4 mg/mL, the decrease in the rate of aggregation with increasing α-crystallin concentration is accompanied by the gradual increase in the duration of lag period. When the insulin concentration was 0.32 mg/mL, the accelerating effect of low concentrations of α-crystallin (0.08, 0.32 and 0.64 mg/mL; curves 2, 3 and 4, respectively) and inhibiting action of high concentrations of α-crystallin (1.2 mg/mL; curve 6 in Figure 5A), are also markedly expressed. However, in general, the character of the effect of α-crystallin on the insulin aggregation is more complicated because the decrease in the aggregation rate with increasing α-crystallin concentration is not accompanied by such a pronounced increase in the duration of lag period as in the case of insulin concentration of 0.4 mg/mL.

It is evident that to characterize the effects caused by different concentrations of α-crystallin, we should understand how α-crystallin influences the duration of lag period, and also understand the initial rate of aggregation. Figure 6 shows that the initial parts of the dependences of the light scattering intensity on time may be satisfactorily described by Equation (1). Thus, the use of this equation enables estimating parameters t₂ (the duration of lag period) and K_agg (the measure of the initial rate of aggregation). The values of parameters t₂ and K_agg calculated at the insulin concentrations of 0.32 and 0.4 mg/mL and various concentrations of α-crystallin are given in Table 2. As for the duration of lag period, parameter t₂ becomes lower than the corresponding values measured in the absence of α-crystallin (t₂ = 16.7 or 15.6 min at the insulin concentration of 0.32 or 0.4 mg/mL, respectively). However, at relatively high concentrations of α-crystallin, the values of t₂ exceed the control values. At the molar stoichiometric ratio (insulin:α-crystallin) less than 1:0.5, a pronounced accelerating effect of α-crystallin was observed, whereas at the ratio exceeding the value of 1:0.6 α-crystallin caused suppression of insulin aggregation. These effects could be observed at the concentrations of α-crystallin exceeding 0.64 and 0.8 mg/mL in the experiments with insulin at the concentration of 0.32 and 0.4 mg/mL, respectively (Table 2).

Figure 7 shows the dependences of the hydrodynamic radius of the protein aggregates formed in the solution of insulin (0.32 mg/mL) on time after the addition of DTT in the presence of α-crystallin at concentrations of 0.08, 0.32, 0.64 and 0.8 mg/mL (curves 1, 2, 3 and 4, respectively). As can be seen from Figure 7, the higher the concentration of α-crystallin, the lower the size of the aggregates.

The shape of the initial parts of the dependences of R_h on time is of special interest. As an example, Figure 8 shows the initial parts of such dependences in the presence of α-crystallin at the concentration of 0.08 mg/mL (Figure 8A) and 0.8 mg/mL (Figure 8B).

Immediately after the addition of DTT, the particles with R_h = 24.6 ± 1.2 nm (Figure 8A) and 18.4 ± 0.8 nm (Figure 8B) are registered in the system. The value of R_h remains constant over 6.5 and 11.8 min, respectively. When interpreting these results, we take into account that judging from the DLS measurements, the hydrodynamic radius of the α-crystallin preparation used in the present work was 13.2 ± 0.1 nm. One can assume that the particles with R_h = 24.6 and 18.4 nm are the complexes of α-crystallin with the insulin B chain. Let us designate the hydrodynamic radius of these complexes as R_h,complex. At a definite point in time, the hydrodynamic radius of the primary particles begins to increase. The linear parts of the increase in the R_h value in time were treated using an Equation (5).

Parameters K₁ and t₃ are given in Table 2. The comparison of the values of t₂ and t₃ shows that the moment in time at which the light scattering intensity begins to increase (t₂), coincides with the time at which the size of the α-crystallin–insulin B chain complexes begins to increase (t₃). The rate of the increase in the R_h value in time (parameter K₁) gradually decreases on increasing the α-crystallin concentration.

Figure 9A and B demonstrates the dual effect of α-crystallin on the initial rate of insulin aggregation. The horizontal dotted lines in this figure correspond to the K_agg value measured in the absence of α-crystallin ( K agg control). If the values of K_agg are located above the control level, acceleration of insulin aggregation takes place, whereas the K_agg values below the control level correspond to suppression of aggregation. To determine α-crystallin concentration, at which the initial rate of aggregation coincides with the value of K_agg measured in the absence of α-crystallin, we used the Equation (6).

It should be noted that K_agg,0 is the expected value of K_agg, if the mechanism of insulin aggregation realized in the presence of α-crystallin remains intact at C → 0. Since the mechanisms of insulin aggregation which are operative in the presence or in the absence of α-crystallin are different, the K_agg,0 value is not identical to K agg control. The following values of parameters K_agg,0, C_0.5 and h were found using this equation: K_agg,0 = 2180 ± 40 (counts/s)·min⁻², C_0.5 = 0.40 ± 0.01 mg/mL and h = 4.3 ± 0.2 at the insulin concentration of 0.32 mg/mL, and K_agg,0 = 5310 ± 160 (counts/s)·min⁻², C_0.5 = 0.62 ± 0.02 mg/mL and h = 5.4 ± 0.5 at the insulin concentration of 0.4 mg/mL.

With the knowledge of these parameters, we calculated the concentration of α-crystallin (C*), at which the K_agg value is numerically equal to K agg control : C * = C 0.5 ( K agg , 0 / K agg control − 1 ) 1 / h. The values of K agg control are equal to 460 and 1690 (counts/s)·min⁻² at the insulin concentration of 0.32 and 0.4 mg/mL, respectively. The corresponding values of C* were found to be 0.55 and 0.71 mg/mL, respectively. Insets in Figure 9C and D show the relationships between the parameters K_agg and t₂ in the coordinates {logK_agg; t₂}. When the concentration of insulin was 0.4 mg/mL, the point with coordinates corresponding to the values of K_agg and t₂, measured in the absence of α-crystallin (this point is designated by a cross), fall on the curve connecting the points corresponding to K_agg and t₂ values measured in the presence of α-crystallin. This explains the fact that the effect of α-crystallin on aggregation of insulin is clearly visible when the concentration of α-crystallin was 0.4 mg/mL (Figure 5B). As for the dependence of log K_agg on t₂ at the insulin concentration of 0.32 mg/mL, the point corresponding to the control values of K_agg and t₂ lies outside the curve connecting the points corresponding to the K_agg and t₂ values measured in the presence of α-crystallin. This results in the complicated influence of α-crystallin on insulin aggregation (Figure 5A).

It was of interest to study the effect of α-crystallin on the shape of the dependences of the initial rate of aggregation characterized by parameter K_agg on the insulin concentration. Figure 10 shows these dependences obtained in the absence (curve 1) and in the presence of α-crystallin at the concentrations of 0.08 and 1.2 mg/mL (curves 2 and 3, respectively). First of all, the dependences of parameter K_agg on the insulin concentration presented in this figure demonstrate the accelerating effect of the relatively low concentrations of α-crystallin (curve 2) and the inhibiting action of rather high concentrations of α-crystallin (curve 3). Furthermore, the dependences under discussion obtained in the presence of α-crystallin, similar to the corresponding dependence obtained in the absence of α-crystallin, follow the power law presented by Equation (4). The value of parameter n at the α-crystallin concentration of 0.08 mg/mL (n = 7.8 ± 0.2) exceeds the corresponding value obtained in the absence of α-crystallin (n = 6.3 ± 0.2). When the concentration of α-crystallin was 1.2 mg/mL, the value of this parameter (n = 5.9 ± 0.2) was close to that for the dependence of parameter K_agg on the insulin concentration obtained in the absence of α-crystallin.

The formation of the complex between two proteins was also confirmed by the tryptophan fluorescence measurements. Since α-crystallin, but not insulin, contains tryptophan residues, we used fluorescence spectroscopy to examine the tryptophan emission spectra of the individual α-crystallin and the chaperone within the complex α-crystallin–insulin. α-crystallin taken alone gives fluorescence spectra with emission maximum at 335 nm (data not shown). The results of the experiments show that insulin, in its original form, does not bind to α-crystallin. In the absence of DTT, the fluorescence intensity values are almost equal to those of the sum of the individual fluorescence emission spectra of insulin and α-crystallin (data not shown), implying that there was little, if any, interaction between the two proteins. Only the aggregation-prone reduced insulin was found to interact with α-crystallin. On reduction of disulfide bonds of insulin by DTT, an almost immediate increment on the dependences of the relative fluorescence intensity on time registered at 335 nm was observed. However, no shift in the emission maximum of intrinsic fluorescence was detected.

At the α-crystallin concentration of 0.3 mg/mL, the increment was shown to increase in a concentration-dependent manner in the presence of insulin at concentrations from 0.2 to 0.6 mg/mL (Figure 11A, curves 5–8, respectively) corresponding to the molar stoichiometric ratio (insulin:α-crystallin) less than 1:0.5. The increase in the intensity of tryptophan fluorescence of α-crystallin, under the conditions of the appearance of aggregation-prone reduced insulin, suggests that the α-crystallin–insulin complex is formed and that the tertiary structure of the complex is more compact than that of the individual chaperone [22].

At molar stoichiometric ratio (insulin:α-crystallin) exceeding the value of 1:0.6, at which α-crystallin caused suppression of insulin aggregation, almost no increment on the dependences of the relative fluorescence intensity on time was shown (Figure 11A, curves 2 and 3). Bovine α-crystallin possesses no disulphide bonds and therefore no change in its tryptophan emission spectrum could be observed upon addition of DTT; however, a quenching of tryptophan emission intensity by DTT was detected, the most pronounced effect being revealed in the absence of insulin (Figure 11A, curve 1).

The dependence of the relative increment of the fluorescence intensity (F_max/F₀) on the concentration of insulin is also shown (Figure 11B), where F₀ is the minimum value of the fluorescence intensity reached immediately after the addition of insulin, and F_max is the maximum value of the fluorescence intensity. At the fixed concentration of α-crystallin (0.3 mg/mL), the increment amplitude gradually increased at a concentration of insulin in the range from 0.05 to 0.4 mg/mL; whereas at higher insulin concentrations, no further increase of the relative fluorescence intensity (F_max/F₀) was observed.

In our experiments, an increase in tryptophan fluorescence of α-crystallin in the presence of insulin after the addition of DTT is followed by a gradual decrease in the fluorescence intensity at further incubation (Figure 11A, curves 4–8). The moment in time at which the fluorescence intensity begins to decrease, correlates well with the kinetics of DTT-induced aggregation of insulin (data not shown). Thus, the diminishing of the fluorescence intensity at rather high values of time is due to the increase in turbidity of the solution.

Human recombinant insulin and DTT were purchased from Sigma. All other chemicals were of reagent grade. All solutions for the experiments were prepared using deionized water obtained with Easy-Pure II RF system (Barnstead, U.S.).

Purification of α-crystallin from freshly excised lenses of two-year-old steers was performed according to the procedure described earlier [38]. The α-crystallin concentration was determined from the absorbance at 280 nm using the extinction coefficient A 208 1 % of 8.5 [39].

The kinetics of insulin aggregation was registered in 50 mM Na-phosphate buffer, pH 7.0, containing 0.15 M NaCl. Insulin was dissolved in 20 mM NaOH and then in sodium phosphate buffer to a concentration of 1 mg/mL. An aliquot of this solution was added to the buffer in the cell. Reduction of insulin (0.2–0.4 mg/mL) was initiated by adding DTT to 0.5 mL of the sample to a final concentration of 20 mM. To study the effect of α-crystallin on insulin aggregation, aliquots of α-crystallin solutions were added into the cell simultaneously with insulin. The experiments were performed at room temperature (25 °C).

DLS measurements were performed by a commercial instrument Photocor Complex (Photocor Instruments Inc., U.S.; www.photocor.com) as described in our previous works where DLS was used for the study of the kinetics of thermal and DTT-induced aggregation of proteins [3,40]. A He-Ne laser (Coherent, U.S., Model 31–2082, 632.8 nm, 10 mW) was used as a light source. The temperature of sample cell was controlled by the proportional integral derivative (PID) temperature controller to within ±0.1 °C. The quasi-cross correlation photon counting system with two photomultiplier tubes was used to increase the accuracy of particle sizing in the range from 1.0 nm to 5.0 μm. DLS data have been accumulated and analyzed with multifunctional real-time correlator Photocor-FC. DynaLS software (Alango, Israel) was used for polydispersity analysis of the DLS data. The diffusion coefficient D of the particles is directly related to the decay rate τ_c of the time-dependent correlation function for the light-scattering intensity fluctuations: D = 1/2τ_ck². In this equation, k is the wavenumber of the scattered light, k = (4τn/λ)sin(θ/2), where n is the refractive index of the solvent, λ is the wavelength of the incident light in vacuum and θ is the scattering angle. The mean hydrodynamic radius of the particles (R_h) can then be calculated according to the Stokes-Einstein Equation: D = k_BT/6τηR_h, where k_B is Boltzmann’s constant, T is the absolute temperature and η is the shear viscosity of the solvent.

To analyze the time-course of the increase in the light scattering intensity (I) accompanying aggregation of insulin, we used the approaches elaborated by us previously [23]. The following designations were used. The time of the appearance of the start aggregates was designated as t₁, and the designation t₂ was used for the duration of the lag period on the dependences of the light scattering intensity on time. To calculate parameter t₂, in the present work we used the empiric equation: (1) I = K agg ( t − t 2 ) 2where K_agg is a constant with the dimension of (counts/s)·min⁻². Parameter K_agg characterizes the initial rate of aggregation.

It should be noted that in some of our previous works (see, for example [3,41,42]) we used Equation (2) in the form: I = K_LS(t − t₂)². The constant K_LS in this equation has the following dimension: (counts/s)^1/2·min⁻¹. DLS allows monitoring the course of the protein aggregation by the increase in the hydrodynamic radius (R_h) of the growing particles. In this case, the rate of aggregation may be characterized by the value of 1/t_2R, where t_2R is the time interval, over which the R_h value is doubled. Since the dimension of the 1/t_2R value is min min⁻¹, we can directly compare parameter K_LS, which is calculated from the dependences of the light scattering intensity on time, with parameter 1/t_2R, which is calculated from the dependences of R_h on time. It is evident that parameters K_agg and K_LS are connected by the following relationship: K_agg = (K_LS)².

To analyze the dependences of the hydrodynamic radius (R_h) of the protein aggregates on time for DTT-induced aggregation of insulin, we used the approaches applied in the cases of thermal aggregation of proteins [40,43]. The following equation may be used for the description of the initial linear parts of the dependences of R_h on time: (2) R h = R h , 0 + K 1 ( t − t 3 )where R_h,0 is the hydrodynamic radius of the start aggregates, t₃ is the point in time at which the hydrodynamic radius of the start aggregates begins to increase and K₁ is a constant.

When studying the kinetics of thermal aggregation of proteins, we observed that the typical dependences of the hydrodynamic radius (R_h) of the protein aggregates on time were as follows. The initial parts of the dependences of R_h on time were linear. Above the definite point in time designated as t* the dependences of R_h on time followed the power law. The following equation may be used for the description of these parts of the dependences of R_h on time: (3) R h = R h * [ 1 + K 2 ( t − t * ) ] 1 / d fwhere R h * is the R_h value at t = t*, K₂ is a constant and d_f is the fractal dimension of the aggregates. The d_f value was found to be close to 1.8. This value of d_f is typical of the regime of diffusion-limited cluster-cluster aggregation, wherein each collision of the interacting particles results in their sticking [44–46].

To analyze the dependence of parameter K_agg on the concentration of insulin, we used the equation: (4) K agg = B [ P ] 0 nwhere [P]₀ is the initial concentration of the protein, n is the order of aggregation with respect to protein and B is a constant.

The linear parts of the increase in the R_h value of the complexes of α-crystallin with the insulin B chain (designated as R_h,complex) in time (Figure 8) were treated using an equivalent equation to Equation (2): (5) R h = R h , complex + K 1 ( t − t 3 )Parameters K₁ and t₃ are given in Table 2.

To determine α-crystallin concentration, at which the initial rate of aggregation coincides with the value of K_agg measured in the absence of α-crystallin, we used the following empiric equation: (6) K agg = K agg , 0 1 + ( C / C 0.5 ) hwhere C is the α-crystallin concentration, K_agg,0 is the limiting value of the function K_agg(C) at C → 0, C_0.5 is the α-crystallin concentration, at which K_agg/K_agg,0 = 0.5, and h is a constant (the Hill coefficient).

The tryptophan fluorescence measurements were performed using a Cary Eclipse fluorescence spectrophotometer (Varian, Inc.) with a temperature-controlled cuvette holder. Samples were excited at 297 nm and fluorescence emission spectra were recorded from 300 to 400 nm. The excitation and emission slit widths were set at 2.5 nm. Before measurement, protein samples (α-crystallin or insulin) were preincubated for 10 min at 25 °C in 50 mM sodium phosphate buffer, pH 7.0, containing 0.15 M NaCl. The interaction between two proteins was initiated by addition of DTT to a final concentration of 20 mM. The incubation mixtures were then subjected to the fluorescence measurements in a quartz cuvette with a 1 cm path length. In these experiments the time of sample exposition to illumination was minimized in order to avoid the UV-induced spectral effects as a result of reduction of S–S bonds and subsequent structural rearrangements in the protein molecule.

The dependences of the relative fluorescence intensity on time of the solutions containing α-crystallin (0.3 mg/mL), in the absence or presence of various concentrations of insulin, in the range from 0.1 to 0.6 mg/mL, were recorded immediately after addition of DTT, upon excitation and emission at 297 and 335 nm, respectively. Each spectrum was the average of 5 scans.