# Paradoxical Acceleration of Dithiothreitol-Induced Aggregation of Insulin in the Presence of a Chaperone

^{1}

^{2}

^{*}

## Abstract

**:**

_{h}) of about 90 nm. When studying the effect of α-crystallin on the rate of DTT-induced aggregation of insulin, it was demonstrated that low concentrations of α-crystallin dramatically accelerated the aggregation process, whereas high concentrations of α-crystallin suppressed insulin aggregation. In the present study, at the molar stoichiometric ratio (insulin:α-crystallin) less than 1:0.5, a pronounced accelerating effect of α-crystallin was observed; whereas a ratio exceeding the value of 1:0.6 caused suppression of insulin aggregation. The mechanisms underlying the dual effect of α-crystallin have been proposed. It is assumed that heterogeneous nucleation occurring on the surface of the α-crystallin particle plays the key role in the paradoxical acceleration of insulin aggregation by α-crystallin that may provide an alternative biologically significant pathway of the aggregation process.

## 1. Introduction

^{2+}-containing hexamer. Its large size, however, prevents its efficient absorption into the blood stream. Hexamers are therefore broken down to dimers and then monomers that are transported efficiently into the blood stream [6]. The circulating biologically active form of insulin is a Zn

^{2+}-free monomer consisting of two chains linked by two disulfide bridges. Insulin can be induced to aggregation by the reduction of S–S bridges between its A and B chains resulting in their dissociation and formation of amorphous aggregates, but under non-physiological conditions, such as high temperatures (60–70 °C), low pH (1.5–2.0) and relatively high protein concentrations, insulin generates amyloid-like fibrils [9–11].

## 2. Results

#### 2.1. Kinetics of Dithiothreitol-Induced Aggregation of Insulin

_{2}(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.

_{2}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.

_{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 t

_{1}. 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.

_{2}= 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.

_{1}and t

_{2}determined at various insulin concentrations are given in Table 1.

_{h}on time with the expanded ordinate axis.

_{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.

_{3}. 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 t

_{3}to be determined more precisely using Equation (2). The values of parameter t

_{3}are given in Table 1. The analysis of the values of t

_{2}and t

_{3}shows that the time interval (t

_{3}− t

_{2}), over which the accumulation of the start aggregates occurs without sticking, is shortened by increasing the protein concentration.

_{3}, Equation (2) gives parameter K

_{1}, which characterizes the increase in the R

_{h}value in time (K

_{1}= dR

_{h}/dt). The values of parameter K

_{1}are given in Table 1. When the insulin concentration increases from 0.2 to 0.4 mg/mL, a fivefold increase in the K

_{1}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.

#### 2.2. The Effect of α-Crystallin on the Kinetics of Dithiothreitol-Induced Aggregation of Insulin

_{2}(the duration of lag period) and K

_{agg}(the measure of the initial rate of aggregation). The values of parameters t

_{2}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 t

_{2}becomes lower than the corresponding values measured in the absence of α-crystallin (t

_{2}= 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 t

_{2}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).

_{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).

_{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).

_{1}and t

_{3}are given in Table 2. The comparison of the values of t

_{2}and t

_{3}shows that the moment in time at which the light scattering intensity begins to increase (t

_{2}), coincides with the time at which the size of the α-crystallin–insulin B chain complexes begins to increase (t

_{3}). The rate of the increase in the R

_{h}value in time (parameter K

_{1}) gradually decreases on increasing the α-crystallin concentration.

_{agg}value measured in the absence of α-crystallin ( ${K}_{\text{agg}}^{\text{control}}$). 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).

_{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 ${K}_{\text{agg}}^{\text{control}}$. 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.

_{agg}value is numerically equal to ${K}_{\text{agg}}^{\text{control}}:C*={C}_{0.5}{({K}_{\text{agg},0}/{K}_{\text{agg}}^{\text{control}}-1)}^{1/h}$. The values of ${K}_{\text{agg}}^{\text{control}}$ 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 t

_{2}in the coordinates {logK

_{agg}; t

_{2}}. When the concentration of insulin was 0.4 mg/mL, the point with coordinates corresponding to the values of K

_{agg}and t

_{2}, 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 t

_{2}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 t

_{2}at the insulin concentration of 0.32 mg/mL, the point corresponding to the control values of K

_{agg}and t

_{2}lies outside the curve connecting the points corresponding to the K

_{agg}and t

_{2}values measured in the presence of α-crystallin. This results in the complicated influence of α-crystallin on insulin aggregation (Figure 5A).

_{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.

#### 2.3. Fluorescence Studies of α-Crystallin Interaction with Insulin

_{max}/F

_{0}) on the concentration of insulin is also shown (Figure 11B), where F

_{0}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}/F

_{0}) was observed.

## 3. Discussion

_{agg}, which is calculated from the light scattering intensity versus time plots, on the concentration of the protein substrate. In [23], where the quadratic equation was proposed for the description of the dependence of the light scattering intensity on time, the dependence of parameter K

_{agg}on the concentration of the protein substrate was analyzed for heat aggregation of glycogen phosphorylase b from rabbit skeletal muscle. The experimental data obtained by Kornilaev et al. [24] were used for the construction of the parameter K

_{agg}versus glycogen phosphorylase b concentration plot. It was found that parameter K

_{agg}was a linear function of the glycogen phosphorylase b concentration. This means that parameter n in Equation (4) is equal to unity and, consequently, the rate-limiting stage of the overall process of aggregation is the monomolecular stage of unfolding of the protein molecule. This conclusion agrees with the mechanism of thermal denaturation of glycogen phosphorylase b, established by Kurganov et al. [25]. The kinetic scheme of thermal denaturation of glycogen phosphorylase b, involves the stage of the conformational change of the dimeric molecule of the enzyme, followed by dissociation of dimer into monomers, and denaturation of labile monomeric forms.

_{agg}on the concentration of α-lactalbumin presented in the work [3] shows that parameter n calculated from Equation (4) is equal to 3.5 ± 0.2. The fact that the value of parameter n exceeds unity, is indicative of the involvement of several molecules of unfolded α-lactalbumin in the nucleation process. The results of the study of DTT-induced aggregation of insulin carried out in the present work, show that parameter n essentially exceeds unity (n ≥ 6). By this is meant that the rate-limiting stage of the process of DTT-induced aggregation of insulin, as in the case of DTT-induced aggregation of α-lactalbumin, is the stage of nucleation.

_{h}value did not approach the limiting value even after prolonged incubation. The increase in the R

_{h}value over time follows the power law (R

_{h}∼ t

^{1/1.8}= t

^{0.56}). The d

_{f}value calculated from Equation (3) was found to be close to 1.8. This fact suggests that the growth of the start aggregate proceeds as a result of sticking of the start aggregates, rather than due to the attachment of the unfolded insulin molecule to a nucleus, as is postulated in the nucleation-dependent models of aggregation.

_{3}value; see Table 2). The nuclei formed on the surface of the α-crystallin particle, serve as the sticky sites providing aggregation of the unfolded protein–α-crystallin complexes (state IV in Scheme 2).

## 4. Experimental Section

#### 4.1. Materials

#### 4.2. Isolation and Purification of α-Crystallin

#### 4.3. DTT-Induced Aggregation of Insulin

#### 4.4. Dynamic Light Scattering Studies

_{c}of the time-dependent correlation function for the light-scattering intensity fluctuations: D = 1/2τ

_{c}k

^{2}. 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

_{B}T/6τηR

_{h}, where k

_{B}is Boltzmann’s constant, T is the absolute temperature and η is the shear viscosity of the solvent.

_{1}, and the designation t

_{2}was used for the duration of the lag period on the dependences of the light scattering intensity on time. To calculate parameter t

_{2}, in the present work we used the empiric equation:

_{agg}is a constant with the dimension of (counts/s)·min

^{−2}. Parameter K

_{agg}characterizes the initial rate of aggregation.

_{LS}(t − t

_{2})

^{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}.

_{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:

_{h,0}is the hydrodynamic radius of the start aggregates, t

_{3}is the point in time at which the hydrodynamic radius of the start aggregates begins to increase and K

_{1}is a constant.

_{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:

_{h}value at t = t*, K

_{2}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].

_{agg}on the concentration of insulin, we used the equation:

_{0}is the initial concentration of the protein, n is the order of aggregation with respect to protein and B is a constant.

_{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):

_{1}and t

_{3}are given in Table 2.

_{agg}measured in the absence of α-crystallin, we used the following empiric equation:

_{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).

#### 4.5. Fluorescence Spectroscopy

## 5. Conclusions

## Acknowledgments

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**Figure 1.**Kinetics of DTT-induced aggregation of insulin. The dependences of the light scattering intensity (I) on time obtained at 25 °C in 50 mM sodium phosphate buffer, pH 7.0, containing 0.15 M NaCl and 20 mM DTT (

**A**). The concentrations of insulin were as follows: 0.20 (1), 0.24 (2), 0.28 (3), 0.32 (4), 0.36 (5) and 0.40 (6) mg/mL. The dependence of parameter K

_{agg}on the concentration of insulin (

**B**). The points are the experimental data. The solid curve was calculated from Equation (4) (see Experimental Section).

**Figure 2.**Analysis of the initial parts of the dependences of the light scattering intensity (I) on time for DTT-induced aggregation of insulin. The concentrations of insulin were as follows: 0.20 (1), 0.28 (2) and 0.40 (3) mg/mL. The final concentration of DTT is 20 mM. Points are the experimental data. Solid curves were calculated from Equation (1).

**Figure 3.**The distribution of the particles by size for insulin. Insulin (0.32 mg/mL) was incubated at 25 °C in the presence of 20 mM DTT for 1 (

**A**), 17.2 (

**B**), 19.3 (

**C**) and 50 (

**D**) min.

**Figure 4.**Analysis of the size of the particles in the solution of insulin after the addition of DTT. The dependences of the hydrodynamic radius (R

_{h}) of the non-aggregated form of insulin (solid circles) and protein aggregates (open circles) on time. The concentrations of insulin were as follows: 0.20 (

**A**), 0.28 (

**B**), 0.32 (

**C**) and 0.40 (

**D**) mg/mL. The solid curves were calculated from Equation (3). Insets show the dependences of R

_{h}on time with the expanded ordinate axis. The horizontal dotted lines correspond to the hydrodynamic radius of start aggregates (R

_{h,0}). The solid lines are calculated from Equation (2).

**Figure 5.**The effect of α-crystallin on the kinetics of DTT-induced aggregation of insulin at the concentrations of 0.32 (

**A**) or 0.4 (

**B**) mg/mL. The final concentration of DTT was 20 mM. The dependences of the light scattering intensity (I) on time at the following concentrations of α-crystallin: 0 (1), 0.08 (2), 0.32 (3), 0.64 (4), 0.8 (5) and 1.20 (6) mg/mL.

**Figure 6.**The analysis of the initial parts of the dependences of the light scattering intensity (I) on time for DTT-induced aggregation of insulin (0.32 mg/mL). The final concentration of DTT was 20 mM. The concentrations of α-crystallin were as follows: 0.08 (1), 0.16 (2), 0.64 (3) and 0.80 (4) mg/mL. The solid curves are calculated from Equation (1).

**Figure 7.**The dependences of the hydrodynamic radius (R

_{h}) of the particles formed upon addition of DTT to the solution of insulin (0.32 mg/mL) on time in the presence of α-crystallin. The concentrations of α-crystallin were as follows: 0.08 (1), 0.32 (2), 0.64 (3), and 0.80 (4) mg/mL.

**Figure 8.**The analysis of the initial parts of the dependences of the hydrodynamic radius (R

_{h}) on time for aggregation of insulin (0.32 mg/mL) in the presence of α-crystallin. The concentrations of α-crystallin were 0.08 (

**A**) and 0.80 (

**B**) mg/mL. Solid lines were calculated from Equation (2).

**Figure 9.**Analysis of parameters K

_{agg}and t

_{2}used for description of the dependences of the light scattering intensity on time for DTT-induced aggregation of insulin in the presence of various concentrations of α-crystallin. The dependences of parameter K

_{agg}on the concentration of α-crystallin at the concentrations of insulin of: 0.32 (

**A**) and 0.4 (

**B**) mg/mL. The horizontal dotted lines correspond to the K

_{agg}values obtained for insulin aggregation in the absence of α-crystallin ( ${K}_{\text{agg}}^{\text{control}}$). The solid curves were drawn from Equation (5). The relationships between Log K

_{agg}and parameter t

_{2}at the concentrations of insulin of: 0.32 (

**C**) and 0.4 (

**D**) mg/mL. Crosses correspond to insulin aggregation in the absence of α-crystallin.

**Figure 10.**The effect of α-crystallin on the dependence of parameter K

_{agg}on the concentration of insulin. The concentrations of α-crystallin were as following: 0 (1), 0.08 (2) and 1.20 (3) mg/mL. The points are the experimental data; the solid curves were calculated from Equation (4).

**Figure 11.**The interaction between insulin and α-crystallin monitored by tryptophan fluorescence. (

**A**) The dependences of the relative fluorescence intensity on time of the solution containing α-crystallin at the concentration of 0.3 mg/mL (1) or the mixtures of α-crystallin (0.3 mg/mL) and insulin at the concentrations of 0.1 (2), 0.12 (3), 0.16 (4), 0.2 (5), 0.3 (6), 0.4 (7) and 0.6 (8) mg/mL. The arrow shows the moment of addition of DTT. The final concentration of DTT was 20 mM. The fluorescence was recorded at 25 °C in 50 mM sodium phosphate buffer, pH 7.0, containing 0.15 M NaCl upon excitation and emission at 297 and 335 nm, respectively; (

**B**) Dependence of the increment of the fluorescence intensity (F

_{max}/F

_{0}) on the concentration of insulin. F

_{0}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.

**Scheme 1.**Schematic representation of DTT-induced aggregation of insulin in the presence of relatively low concentrations of α-crystallin causing acceleration of the aggregation process (1 is the α-crystallin particle and 2 is the unfolded B chain of insulin).

**Scheme 2.**Schematic representation of DTT-induced aggregation of insulin in the presence of relatively high concentrations of α-crystallin, causing suppression of the aggregation process (1 is the α-crystallin particle and 2 is the unfolded B chain of insulin).

**Table 1.**Parameters of DTT-induced aggregation of insulin at 25 °C in 50 mM sodium phosphate buffer, pH 7.0, containing 0.15 M NaCl.

[Insulin] (mg/mL) | t_{1} (min) | t_{2} (min) | K_{agg}, (counts/s min^{−2}) | R_{h,0} (nm) | t_{3} (min) | K_{1} (nm/min) | t* (min) | d_{f} |
---|---|---|---|---|---|---|---|---|

0.20 | 18.5 | 18.4 ± 0.5 | 8.4 ± 0.6 | 84 ± 3 | 31.3 ± 0.4 | 11.9 ± 0.5 | 47 | 1.80 ± 0.01 |

0.24 | 18.3 | 18.3 ± 0.5 | 25 ± 2 | 81 ± 2 | 29.0 ± 0.3 | 13.6 ± 0.6 | 42 | 1.80 ± 0.01 |

0.28 | 17.7 | 17.5 ± 0.2 | 144 ± 3 | 101 ± 3 | 26.2 ± 0.3 | 20.3 ± 0.6 | 38 | 1.80 ± 0.01 |

0.32 | 17.2 | 16.7 ± 0.2 | 460 ± 10 | 100 ± 2 | 19.3 ± 0.2 | 26.6 ± 0.9 | 28 | 1.80 ± 0.01 |

0.36 | 16.8 | 16.2 ± 0.2 | 1270 ± 20 | 100 ± 2 | 18.1 ± 0.1 | 31.0 ± 0.8 | 24 | 1.79 ± 0.01 |

0.40 | 16.2 | 15.6 ± 0.2 | 1690 ± 30 | 99 ± 3 | 17.7 ± 0.2 | 60 ± 2 | 22 | 1.79 ± 0.01 |

_{1}is the time of appearance of the start aggregates; t

_{2}(the duration of the lag period of the dependences of the light scattering intensity on time) and K

_{agg}(parameter characterizing the initial rate of aggregation) were calculated from Equation (1) (see Experimental Section); R

_{h,0}is the average value of the hydrodynamic radius of the start aggregates; t

_{3}is the point in time, at which the hydrodynamic radius of the start aggregates begins to increase; K

_{1}is a constant calculated from Equation (2); t* is the point in time above which the dependence of R

_{h}on time follows the power law represented by Equation (3); d

_{f}is the fractal dimension of the aggregates.

**Table 2.**Parameters of DTT-induced aggregation of insulin in the presence of various concentrations of α-crystallin.

[α-Crystallin] (mg/mL) | t_{2} (min) | K_{agg} (counts/s min^{−2}) | R_{h,complex} (nm) | t_{3} (min) | K_{1} (nm/min) | ||
---|---|---|---|---|---|---|---|

Concentration of insulin 0.32 mg/mL | |||||||

0.00 | 16.7 ± 0.1 | 460 ± 10 | |||||

0.08 | 6.4 ± 0.1 | 3460 ± 50 | 24.6 ± 1.2 | 6.5 ± 0.2 | 76.0 ± 5.0 | ||

0.16 | 8.6 ± 0.1 | 2130 ± 50 | 24.6 ± 1.1 | 9.1 ± 0.3 | 56.0 ± 4.0 | ||

0.32 | 9.3 ± 0.1 | 1620 ± 50 | 20.6 ± 0.8 | 10.0 ± 0.1 | 35.0 ± 2.0 | ||

0.48 | 9.8 ± 0.2 | 600 ± 20 | 22.3 ± 1.2 | 10.4 ± 0.1 | 23.5 ± 1.9 | ||

0.64 | 10.4 ± 0.1 | 300 ± 6 | 21.0 ± 0.8 | 11.1 ± 0.1 | 18.4 ± 0.8 | ||

0.80 | 11.4 ± 0.1 | 132 ± 3 | 18.4 ± 0.8 | 11.8 ± 0.2 | 13.0 ± 0.5 | ||

1.00 | 17.2 ± 0.3 | 119 ± 4 | 19.5 ± 0.8 | 17.7 ± 1.1 | 9.0 ± 0.5 | ||

1.20 | 18.9 ± 0.5 | 28 ± 3 | 18.9 ± 0.5 | 19.4 ± 1.4 | 5.6 ± 0.5 | ||

Concentration of insulin 0.4 mg/mL | |||||||

0.00 | 15.6 ± 0.1 | 1690 ± 30 | |||||

0.08 | 4.5 ± 0.1 | 17600 ± 350 | 22.6 ± 1.2 | 5.4 ± 0.1 | 82 ± 6 | ||

0.32 | 8.5 ± 0.1 | 5100 ± 100 | 21.8 ± 0.8 | 9.1 ± 0.2 | 71 ± 5 | ||

0.64 | 13.2 ± 0.1 | 2500 ± 100 | 23.1 ± 1.1 | 13.8 ± 0.5 | 63 ± 2 | ||

0.80 | 17.2 ± 0.1 | 840 ± 10 | 21.6 ± 0.8 | 17.9 ± 1.1 | 48.4 ± 1.8 | ||

1.00 | 21.9 ± 0.1 | 540 ± 10 | 21.2 ± 1.0 | 22.3 ± 1.2 | 23.0 ± 1.0 | ||

1.20 | 27.6 ± 0.1 | 321 ± 8 | 21.4 ± 0.9 | 27.9 ± 1.1 | 11.0 ± 0.8 |

_{2}(the duration of the lag period of the dependences of the light scattering intensity on time) and K

_{agg}(parameter characterizing the initial rate of aggregation) were calculated from Equation (1); R

_{h,complex}is the hydrodynamic radius of the complex of α-crystallin with the insulin B chain; t

_{3}is the point in time at which the R

_{h}value begins to increase; K

_{1}is a constant calculated from Equation (2).

© 2010 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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**MDPI and ACS Style**

Bumagina, Z.; Gurvits, B.; Artemova, N.; Muranov, K.; Kurganov, B.
Paradoxical Acceleration of Dithiothreitol-Induced Aggregation of Insulin in the Presence of a Chaperone. *Int. J. Mol. Sci.* **2010**, *11*, 4556-4579.
https://doi.org/10.3390/ijms11114556

**AMA Style**

Bumagina Z, Gurvits B, Artemova N, Muranov K, Kurganov B.
Paradoxical Acceleration of Dithiothreitol-Induced Aggregation of Insulin in the Presence of a Chaperone. *International Journal of Molecular Sciences*. 2010; 11(11):4556-4579.
https://doi.org/10.3390/ijms11114556

**Chicago/Turabian Style**

Bumagina, Zoya, Bella Gurvits, Natalya Artemova, Konstantin Muranov, and Boris Kurganov.
2010. "Paradoxical Acceleration of Dithiothreitol-Induced Aggregation of Insulin in the Presence of a Chaperone" *International Journal of Molecular Sciences* 11, no. 11: 4556-4579.
https://doi.org/10.3390/ijms11114556