Accepted Manuscript Title: Relationship between the initial rate of protein aggregation and the lag period for amorphous aggregation Author: Vera A. Borzova Kira A. Markossian Boris I. Kurganov PII: DOI: Reference:
S0141-8130(14)00273-6 http://dx.doi.org/doi:10.1016/j.ijbiomac.2014.04.046 BIOMAC 4313
To appear in:
International Journal of Biological Macromolecules
Received date: Revised date: Accepted date:
7-3-2014 22-4-2014 22-4-2014
Please cite this article as: V.A. Borzova, K.A. Markossian, B.I. Kurganov, Relationship between the initial rate of protein aggregation and the lag period for amorphous aggregation, International Journal of Biological Macromolecules (2014), http://dx.doi.org/10.1016/j.ijbiomac.2014.04.046 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Relationship between the initial rate of protein aggregation and the lag period for amorphous aggregation
Vera A. Borzova, Kira A. Markossian, Boris I. Kurganov*
ip t
Bach Institute of Biochemistry, Russian Academy of Sciences, Leninsky 33, Moscow, 119071,
te
d
M
an
us
cr
Russia
Ac ce p
*Corresponding author. Bach Institute of Biochemistry, Russian Academy of Sciences, Leninsky pr. 33, Moscow, 119071, Russia. Tel.: +7 495 9525641; fax: +7 495 9542732. E-mail address: [email protected] (B.I. Kurganov).
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ABSTRACT Lag period is an inherent characteristic of the kinetic curves registered for protein aggregation. The appearance of a lag period is connected with the nucleation stage and the stages of the formation of folding or unfolding intermediates prone to aggregation (for example, the stage of
ip t
protein unfolding under stress conditions). Discovering the kinetic regularities essential for elucidation of the protein aggregation mechanism comprises deducing the relationship between
cr
the lag period and aggregation rate. Frändrich proposed the following equation connecting the
us
duration of the lag phase (tlag) and the aggregate growth rate (kg) in the amyloid fibrillation: kg = const/tlag. To establish the relationship between the initial rate of protein aggregation (v) and the
an
lag period (t0) in the case of amorphous aggregation, the kinetics of dithithreitol-induced aggregation of holo-α-lactalbumin from bovine milk was studied (0.1 M Na-phosphate buffer,
M
pH 6.8; 37 °C). The order of aggregation with respect to protein (n) was calculated from the dependence of the initial rate of protein aggregation on the α-lactalbumin concentration (n =
d
5.3). The following equation connecting v and t0 has been proposed: v1/n = const/(t0 - t0,lim),
Ac ce p
te
where t0,lim is the limiting value of t0 at high concentrations of the protein.
Keywords: α-Lactalbumin Amorphous aggregation Lag period Start aggregates 2
Page 2 of 35
1. Introduction
Numerous investigations are concerned with the mechanism and kinetics of the formation of amyloid-like aggregates and fibrils [1-12]. The kinetics of aggregation consists of two phases: an
ip t
initial lag phase that is slow and represents the formation of nuclei and a subsequent rapid
growth phase proceeding as a result of elongation of the preformed nuclei. A large body of data
cr
shows that there is a correlation between the aggregate growth rate (kg) and the lag period (tlag):
us
the shorter the lag period, the higher is the rate of growth, i.e., the samples that nucleate very readily and possess a short lag phase show a very rapid growth reaction. Fändrich [13] proposed
an
a simple equation connecting kg and tlag values:
kg = α/tlag ,
(1)
M
where α is a constant. The applicability of this equation for the kinetics of amyloid fibrils
formation was demonstrated by Fändrich [13] and other authors [2,14-20].
d
Screening of agents possessing anti-aggregation activity is one of the important lines of
te
modern biotechnological research. To carry on such a screening, a number of test systems have
Ac ce p
been proposed. A distinguishing characteristic of test systems, which are based on thermal aggregation of proteins or dithiothreitol (DTT)-induced aggregation of proteins containing disulphide bonds, is formation of amorphous aggregates. To elucidate the mechanism of protein aggregation in test systems under study and select the most effective agents with antiaggregation activity, an investigator should be able to apply strict quantitative methods for the estimation of the initial rate of aggregation (and lag period). For the test systems under investigation the nucleation and aggregation stages are preceded by the stage of unfolding of the protein molecule. This circumstance should be taken into account when analyzing the relationship between the initial rate of aggregation and the lag period. The goal of the present work was to establish a quantitative relationship between the initial rate of aggregation (v) and the lag period (t0) for one of the test systems used for screening of 3
Page 3 of 35
agents possessing anti-aggregation activity, namely for the test system based on DTT-induced aggregation of α-lactalbumin. The molecule of α-lactalbumin contains four disulphide bonds [21], their reduction resulting in unfolding of the protein molecule and subsequent irreversible aggregation [22-25]. In the present work the kinetics of α-lactalbumin aggregation was
ip t
registered using dynamic light scattering (DLS). It was shown that determination of the order of aggregation with respect to protein or with respect to a reducing agent (n) is essential for
cr
establishing a relationship between v and t0 values. When modifying the Fändrich equation, we
us
took into account the n value and the limiting value of t0 at high concentrations of the protein or
an
DTT.
M
2. Materials and Methods
d
2.1. Chemicals
te
α-Lactalbumin from bovine milk (catalogue no L5385; calcium-saturated) and DL-
Ac ce p
dithiothreitol (99% of purity) were purchased from Sigma-Aldrich and used without further purification. All solutions for the experiments were prepared using deionized water obtained with Easy-Pure II RF system (Barnstead, USA). α-Lactalbumin samples were prepared by dissolving solid protein in 0.1 M Na-phosphate buffer solutions at pH 6.8. α-Lactalbumin concentration was determined spectrophotometrically at 280 nm using the absorption coefficient 1% Acm of 20.1 [26].
2.2. DTT-induced aggregation of α-lactalbumin
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Page 4 of 35
Aggregation of α-lactalbumin was studied in 0.1 M Na-phosphate, pH 6.8. Reduction of αlactalbumin was initiated by adding DTT to 0.5 mL of the sample to a final concentration of 20 mM. The experiments were performed at 37 °C.
ip t
2.3. Dynamic light scattering studies
For light scattering measurement a commercial instrument Photocor Complex (Photocor
cr
Instruments, Inc., USA) was used. An He-Ne laser (Coherent, USA, Model 31-2082, 632.8 nm,
us
10 mW) was used as a light source. DynaLS software (Alango, Israel) was used for polydisperse analysis of DLS data. The diffusion coefficient D of the particles is directly related to the decay
an
rate τc of the time-dependent correlation function for the light scattering intensity fluctuations: D = 1/2τck2. In this equation k is the wave number of the scattered light, k = (4πn/λ)sin(θ/2), where
M
n is the refractive index of the solvent, λ is the wavelength of the incident light in a vacuum and θ is the scattering angle. The mean hydrodynamic radius of the particles, Rh, can then be
te
d
calculated according to the Stokes-Einstein equation: D = kBT/6πηRh, where kB is Boltzmann’s constant, T is the absolute temperature and η is dynamic viscosity of solvent.
Ac ce p
The kinetics of DTT-induced aggregation of α-lactalbumin was studied in 0.1 M Na-
phosphate buffer at pH 6.8. The buffer was placed in a cylindrical cell with the internal diameter of 6.3 mm and preincubated for 5 min at a given temperature (37 °C). Cells with stopper were used to avoid evaporation. The aggregation process was initiated by the addition of an aliquot of DTT to a α-lactalbumin sample to the final volume of 0.5 mL. When studying the kinetics of aggregation of α-lactalbumin, the scattering light was collected at a 90° scattering angle. To analyze the time-course of the increase in the light scattering intensity (I) accompanying aggregation of α-lactalbumin, we used the approaches developed by us previously [25,27-31]. To calculate the lag period (t0) on the dependences of I value on time and to characterize the initial rate of aggregation, we used the empiric equation: I = I0 + Kagg(t – t0)2, where I0 is the
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initial value of the light scattering intensity and Kagg is a parameter characterizing the initial rate of aggregation. In the following parameter Kagg was replaced by v: I = I 0 + v (t − t0 ) 2 .
(2)
It should be noted that in our previous papers [25,28,32] Eq. (2) was written in the form I = I0 +
ip t
[KLS(t − t0)]2. Thus, v and KLS are connected by the following relationship: KLS = v1/2. The expanded variant of Eq. (2)
cr
I = I 0 + v {exp[K1 (t - t0 ) 2 ] - 1} K1
(3)
us
(K1 is a constant) allows us to use a wider time interval in the fitting procedure and to obtain the
an
more reliable values of parameters v and t0. It is significant that at t → t0 Eq. (3) is transformed into Eq. (2).
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If the values of the initial rate of aggregation (v) are determined at various initial concentrations of the protein ([P]0), the order of aggregation with respect to protein (n) can be
d
calculated:
(4)
te
v = kn [P]0n ,
where kn is a constant. To determine the n value from the experimental data, the logarithmic
Ac ce p
coordinates {log(v); log([P]0)} can be used [30]: log(v) = log(kn ) + nlog([P]0 ) .
(5)
The following equation can be used for the description of the initial part of the dependence
of the hydrodynamic radius (Rh) of the protein aggregates on time [25,33,34]:
⎡ ln(2) ⎤ ⎪⎫ ⎪⎧ Rh = Rh,0 ⎨exp ⎢ (t − t0 ) ⎥ ⎬ , ⎣ t2R ⎦ ⎭⎪ ⎩⎪
(6)
where t0 is the moment of time at which the start aggregates with Rh = Rh,0 emerge, and t2R is the time interval over which the Rh value is doubled (i.e., Rh = 2Rh,0 at t = t0 + t2R). With the knowledge of parameter t0, we can then calculate parameters Rh,0 and t2R. The reciprocal value of t2R can be considered as a measure of the rate of the aggregation process.
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2.4. Calculations
Origin 8.0 (OriginLab Corporation, USA) software was used for the calculations. To
ip t
characterize the degree of agreement between the experimental data and calculated values, we
cr
used the coefficient of determination R2 [35].
us
3. Results
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Fig. 1A shows the kinetic curves of DTT-induced aggregation of α-lactalbumin at 37 °C registered by the increment in the light scattering intensity (I). The concentration of α-
M
lactalbumin was varied in the interval of 0.4-1.0 mg mL-1. The initial parts of the kinetic curves were analyzed using Eq. (3), which allows determining the initial rate of aggregation (v) and the
d
lag period (t0). The applicability of Eq. (3) is demonstrated on the inset in Fig.1A ([α-
te
lactalbumin = 0.4 mg mL-1]). The following values of parameters were derived from the
Ac ce p
experimental curve: v = (24 ± 2) (counts/s) min-2 and t0 = 27.0 ± 0.2 min (R2 = 0.999). The values of v and t0 obtained at various concentrations of α-lactalbumin are given in Table 1. As it can be seen from Table 1, the increase in α-lactalbumin concentration is accompanied by the increase in the v value with simultaneous decrease in the lag period (t0). [Table 1 to be inserted here]
The measurements of the hydrodynamic radius (Rh) of the protein aggregates by DLS shows
that the increment in the light scattering intensity is due to the enlargement of the particles under study (Fig. 1B). The initial parts of the dependences of Rh on time allow us to calculate parameters Rh,0 (the hydrodynamic radius of the start aggregates ) and t2R. The following values of parameters were found at [α-lactalbumin] = 0.4 mg mL-1 (see the inset in Fig. 1B): Rh,0 = 36 ± 3 nm and t2R = 5.7 ± 0.4 min (R2 = 0.897). The values of Rh,0 and t2R obtained at various 7
Page 7 of 35
concentrations of α-lactalbumin are given in Table 1. The increase in the protein concentration in the interval from 0.4 to 1.0 mg mL-1 is accompanied by a slight decrease in the Rh value from 36 to 24 nm and 6.2-fold increase in the 1/t2R value, which characterizes the initial rate of
[Fig. 1 to be inserted here]
ip t
aggregation.
In the case of thermal aggregation of creatine kinase from rabbit skeletal muscle the
cr
correlation between parameter KLS (KLS = v1/2) and 1/t2R value has been demonstrated [28]. It is
us
evident from Fig. 2 that such a correlation is also fulfilled for DTT-induced aggregation of αlactalbumin (R2 = 0.908).
an
[Fig. 2 to be inserted here]
To determine the order of aggregation (n) with respect to the protein, the dependence of the
M
initial rate (v) on the concentration of α-lactalbumin was constructed in the logarithmic coordinates (Fig. 3). The dependence of log([α-lactalbumin]) on log(v) is linear and the
d
following values of parameters of kn and n have been found: n = 5.3 ± 0.3 and kn = (3.3 ±
te
1.0)×104 (counts/s) min-2 (mg mL-1)-n (R2 = 0.965).
Ac ce p
[Fig. 3 to be inserted here]
Before proceeding to the relationship between the initial rate of α-lactalbumin aggregation
and lag period it is expedient to discuss the dependence of t0 value on α-lactalbumin concentration. As it can be seen from Fig. 4, the value of t0 is a linear function of the reciprocal value of the protein concentration. Thus, the following equation can be used for description of the dependence of t0 on [α-lactalbumin]: t0 = t0,lim + K [P]0 ,
(7)
where t0,lim is the limiting value of t0 at [α-lactalbumin] → ∞ and K is a constant. The following values of t0,lim and K were found: t0,lim = 6.0 ± 0.5 min and K = 8.0 ± 0.7 min mg mL-1 (R2 = 0.920).
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Page 8 of 35
[Fig. 4 to be inserted here] Taking into account Eqs. (4) and (7), we can obtain the following expression describing the relationship between the initial rate of aggregation and the lag period: v1/n = α (t0 − t0,lim ) ,
(8)
ip t
where α is a constant (α = K(kn)1/n). This equation can be linearized in the coordinates {1/v1/n;
cr
t0}:
(9)
us
t 1 1 = − 0,lim + t0 . 1/n v α α
The length cut off on the abscissa axis by the linear dependence of 1/v1/n on t0 corresponds to
an
t0,lim value.
In Fig. 5A the v1/n value is plotted as a function of t0. Solid curve was calculated from Eq. (8)
M
at n = 5.3, t0,lim = 6 min and α = 58 min [(counts/s) min-2]1/n. The dotted vertical line corresponds to t0 = t0,lim. Fig. 5B shows a linear anamorphosis corresponding to Eq. (9). Thus, the
te
value to zero.
d
construction of the 1/v1/n versus t0 plot allows us to check whether it is possible to set the t0,lim
Ac ce p
[Fig. 5 to be inserted here]
The kinetics of DTT-induced aggregation of α-lactalbumin is affected not only by α-
lactalbumin concentration but also by DTT (a reducing agent) concentration. Therefore it was of interest to check the validity of Eq. (8) in a situation where variation of DTT concentration causes the change in the aggregation rate. Fig. 6A shows the kinetic curves of aggregation obtained at fixed concentration of α-lactalbumin (0.7 mg/ml) and various concentrations of DTT. The initial rate of aggregation (v) versus DTT concentration plot constructed in logarithmic coordinates allows determining order of aggregation (n) with respect to DTT (Fig. 6B). The n value was found to be 0.45 ± 0.05. One can expect that order of aggregation with respect to DTT will vary from unity at relatively low DTT concentrations to zero at relatively high DTT concentrations. The obtained value of n (n = 0.45) can be considered as a constant value suitable 9
Page 9 of 35
for use in given operating range of DTT concentrations. Analysis of the dependences of the hydrodynamic radius of the protein aggregates on time shows that the Rh value for the start aggregates (Rh,0) is slightly changed with increasing DTT concentration: from 22 ± 2 nm at [DTT] = 7 mM to 29 ± 4 at [DTT] = 40 mM. As in the case with variation of α-lactalbumin
ip t
concentration, the dependence of the lag period on the reciprocal concentration of DTT is linear (Fig. 6C) and the length cut off on the ordinate axis by the linear dependence of t0 on 1/[DTT]
cr
corresponds to the limiting value of t0 (t0,lim) which is reached at [DTT] → ∞. The linear
us
character of the dependence of 1/v1/n on t0 (Fig. 6D) supports satisfiability of linear anamorphosis represented by Eq. (9). Paramerer α was found to be 2.3×109 min [(counts/s) min-2]1/n. Thus, Eq.
an
(8) describing the relationship between the initial rate of aggregation and lag period can be used, irrespective of whether concentration of α-lactalbumin or DTT is varied.
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[Fig. 6 to be inserted here]
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d
4. Discussion
Ac ce p
As in the case of apo-α-lactalbumin [25], the results of the study of holo-α-lactalbumin DTT-induced aggregation shows that, aggregation proceeds through the stage of formation of start aggregates. The moment of time t = t0 (t0 is the lag period) corresponds to the emergence of the start aggregates. When studying DTT-induced aggregation of apo-α-lactalbumin, the average value of the hydrodynamic radius of the start aggregates was found to be 93 nm (50 mM sodium phosphate buffer, pH 6.8, containing 0.15 M NaCl and 1 mM EGTA; 37 °C) [25]. Smaller values of Rh,0 were obtained for aggregation of more stable form of α-lactalbumin, namely holo-αlactalbumin (Rh,0 = 22-36 nm). It should be noted that the mechanism of protein aggregation involving formation of the start aggregates with the hydrodynamic radius of several tens of nanometers was demonstrated for
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Page 10 of 35
DTT-induced aggregation of insulin [36] and thermal aggregation of a broad range of proteins [28,33,34,37-44]. Analysis of the dependence of the initial rate of aggregation on protein concentration allows determining the order of aggregation with respect to protein (n). In the event that n = 1, the rate-
ip t
limiting stage of the aggregation process is the stage of protein unfolding. If n > 1, we may conclude that the rate-limiting stage of the aggregation process is the stage of nucleation or
cr
aggregation of unfolded protein molecules. For example, when studying thermal aggregation of
us
intact and UV-irradiated glyceraldehyde 3-phosphate dehydrogenase (GAPDH; EC 1.2.1.12), we showed that n = 1 for the intact protein and n = 2 for the UV-irradiated protein [45]. UV
an
irradiation induces denaturation of GAPDH, and, consequently, aggregation of UV-irradiated GAPDH does not contain the stage of protein unfolding. As it could have been expected, the
M
order of aggregation with respect to protein for UV-irradiated GAPDH exceeds unity. In some cases non integer values of the order of aggregation with respect to protein were
d
obtained. For example, in the case of DTT-induced aggregation of bovine serum albumin (BSA)
te
n is equal to 1.6 [29]. The reason for the appearance of non integer values of n can be the
Ac ce p
following. Strictly speaking, if the measurements of the order of aggregation with respect to protein were carried out in the wide interval of the protein concentration, the n value should decrease from n = 2 at relatively low [P]0 values to n = 1 at high [P]0 values. Jain and Udgaonkar [46] studied fibrillation of mouse prion protein at pH 2 in the presence of 0.15 M NaCl. The dependence of the observed rate of fibrillation on protein concentration suggested that aggregate growth was rate-limiting at low protein concentration and that conformational change, which was independent of protein concentration, became rate-limiting at higher protein concentrations. Since usually there are limitations in the selection of operating range of protein concentrations, the experimentally determined order of aggregation with respect to protein can accept non integer values. However, it is precisely these n values that should be used for analysis of
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Page 11 of 35
aggregation kinetics (analysis of the relationship between the initial rate of aggregation and lag period, estimation of the anti-aggregation activity of chaperones and so on). The order of aggregation with respect to protein for apo-α-lactalbumin was found to be 5.9 ± 0.4 (the data obtained by Bumagina et al. [25] were analyzed in [30]). A similar value of n was
ip t
obtained for holo-α-lactalbumin in the present work (n = 5.3 ± 0.3). The fact that the value of parameter n exceeds unity is indicative of the involvement of several unfolded protein molecules
cr
in the nucleation process.
us
As it can be seen from Eq. (8), determination of the order of aggregation with respect to protein is essential for establishing a relationship between the v and t0 values. Another distinctive
an
feature of Eq. (8) in comparison with Eq. (1) is the emergence of parameter t0,lim in the denominator. It is evident that the emergence of parameter t0,lim is connected with the stages of
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reduction of the disulphide bonds in the α-lactalbumin molecule and unfolding of the protein molecule, which proceed before the nucleation and aggregation stages.
d
When studying DTT-induced aggregation of BSA at 45 °C (0.1 M Na-phosphate, pH 7.0; 2
te
mM DTT) [29], we observed that the lag period (t0) approaches the limiting value at sufficiently
Ac ce p
high concentrations of BSA. As in the case of DTT-induced aggregation of α-lactalbumin, the t0,lim value for DTT-induced aggregation of BSA corresponds to the stages of reduction of the disulphide bonds in the BSA molecule and unfolding of the protein. The order of aggregation with respect to protein (n) was found to be 1.60 ± 0.05. The analogous kinetic regularities are observed for thermal aggregation of proteins. Consider
for example the experimental data on thermal aggregation of yeast alcohol dehydrogenase (50 mM Na-phosphate buffer, pH 7.5, 100 mM NaCl; 56 °C) [43]. The initial parts of the dependences of the light scattering intensity on time were analyzed using Eq. (2). The order of aggregation with respect to protein calculated from the log(v) versus log([P]0) plot was found to be 2.1 ± 0.1. One can assume that the rate-limiting stage of the aggregation process is the stage of protein aggregation. The t0 value decreases with increasing protein concentration, and the 12
Page 12 of 35
limiting value of t0 (t0,lim) obtained by extrapolation to infinitely high concentrations of the protein is equal to 12.4 ± 0.1 min. Thus, when analyzing the relationship between the initial rate of protein aggregation and the lag period for thermal or DTT-induced aggregation of proteins, one should take into account that there is a lower limit for the t0 values.
ip t
The kinetics of protein aggregation can be modulated by low-molecular-weight chemical chaperones [47-53]. It was demonstrated in [29] that the decrease in the initial rate of DTT-
cr
induced aggregation of BSA (v/v0) in the presence of chemical chaperones (arginine, arginine
us
ethylester, arginine amide and proline) was accompanied by an increase in the lag period (t0). Fig. 7A shows the relationship between the v/v0 and t0 values. The t0 value in the absence of the
an
additives, i.e., at v/v0 = 1, was found to be 4.5 min (this value of t0 was designated as an initial lag period, t0,in). In these experiments the fixed concentration of BSA (1 mg mL-1) was used. By
M
analogy with Fig. 5B we decided to construct the reciprocal value of the relative initial rate of aggregation (i.e., 1/(v/v0)) versus t0. We set the n value equal to unity, because the shape of the
d
dependence of the initial rate of aggregation on the concentration of a chemical chaperone is
te
independent of the protein concentration [29]. Then we subtracted unity from the 1/(v/v0) value,
Ac ce p
so that the ordinate of the initial point at t0 = t0,in was equal to zero. Thus, we constructed the [1/(v/v0)] − 1 = (v0 − v)/v versus t0 plot. Fig. 7B shows that this plot is linear. The coefficient of determination (R2) was found to be 0.828. Thus, the following linear anamorphosis can be used to describe the relationship between the initial rate of aggregation and the lag period in the case of chemical chaperones:
t v0 − v 1 = − 0,in + t0 , v β β
(10)
where β is a constant. The length cut off on the abscissa axis corresponds to the t0,in value. The β value was found to be 5.6 ± 0.3 min. [Fig. 7 to be inserted here] Eq. (10) can be transformed as follows:
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Page 13 of 35
v 1 . = v0 1 + (t0 − t0,in ) β
(11)
This equation can be used for description of the coordinated changes in the initial rate of aggregation and the lag period in the presence of chemical chaperones.
ip t
One of the classes of agents used as chemical chaperones is cyclodextrins and their derivatives, which effectively suppress protein aggregation [28,45,54-56]. However with some
cr
test systems cyclodextrins reveal anti-chaperone activity. The acceleration of the aggregation
us
process in the presence of 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) was observed in test systems based on thermal aggregation of GAPDH and glycogen phosphorylase b from rabbit
an
skeletal muscles [32,57,58]. Such an effect of HP-β-CD is due to the destabilization of the protein molecule upon binding this agent, as indicated by the data on differential scanning
M
calorimetry. An increase in the initial rate of aggregation in the presence of HP-β-CD is accompanied by the decrease in the lag period. As it was expected, the lag period (t0) approached
d
the limiting value (t0,lim) at high concentrations of HP-β-CD. To demonstrate this fact, Fig. 8A
te
shows the dependence of the t0 value on the HP-β-CD concentration in the coordinates {t0;
Ac ce p
1/[HP-β-CD]}. This plot was constructed on the basis of the experimental data obtained for thermal aggregation of GAPDH [32]. The length cut off on the ordinate axis by the linear dependence of t0 on 1/[HP-β-CD] corresponds to the t0,lim value (t0,lim = 1.56 ± 0.02 min). The relationship between the relative initial rate of aggregation (v/v0) and lag period (t0) is represented in Fig. 8B. The dependence of v/v0 on t0 asymptotically approaches vertical line at t0 = t0,lim, as the HP-β-CD concentration increases. To describe the dependence of v/v0 on t0, the following empiric equation can be used: 1/ 2
v ⎛ t0,in − t0,lim ⎞ =⎜ ⎟ , v0 ⎜⎝ t0 − t0,lim ⎟⎠
(12)
where t0,in is the t0 value in the absence of HP-β-CD. [Fig. 8 to be inserted here]
14
Page 14 of 35
Conclusions
Establishing quantitative relationships between the initial rate of aggregation and the lag
ip t
period extends the methodology of quantification of anti-aggregation activity of chaperones (chaperones of protein nature and the chemical chaperones). This methodology has been
cr
developed in our previous works [29-31,59]. In the case of protein chaperones the adsorption
us
capacity of chaperone with respect to target protein is used as a measure of the anti-aggregation activity of the chaperone. For chemical chaperones the concentration of semi-saturation is used
an
as a characteristic of the anti-aggregation activity of the chaperone. Methods of estimation of the effects of combined action of protein chaperones and chemical chaperones have been proposed.
M
This methodology also involves test systems based on registration of protein aggregation under the regime of temperature elevating with a constant rate [29,60]. Implementation of this
d
methodology allows comparing the anti-aggregation activity of different chaperones and can be
Ac ce p
te
used for selecting agents that provide effective suppression of protein aggregation.
Acknowledgements
This study was funded by the Russian Foundation for Basic Research (grant 14-04-01530-a)
and the Program “Molecular and Cell Biology” of the Presidium of the Russian Academy of Sciences.
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Page 15 of 35
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Figure captions
Fig. 1. Kinetics of DTT-induced aggregation of α-lactalbumin at 37 °C in 0.1 M Na-phosphate,
pH 6.8. The final concentration of DTT was 20 mM. (A) The dependences of light scattering
ip t
intensity on time. The concentrations of α-lactalbumin were as follows: (1) 0.4, (2) 0.5, (3) 0.7 and (4) 1.0 mg mL-1. The inset shows the initial part of the kinetic curve at [α-lactalbumin] = 0.4
cr
mg mL-1. Points are the experimental data. Solid curve was calculated from Eq. (3) at v = 24
us
(counts/s) min-2, t0 = 27 min and K1 = 3.6 min-2. The arrow corresponds to the moment of time t = t0. (B) The dependences of hydrodynamic radius (Rh) of the protein aggregates on time. The
an
concentrations of α-lactalbumin were as follows: (1) 0.4, (2) 0.65, (3) 0.7 and (4) 1.0 mg mL-1. The inset shows the initial part of the dependence of Rh on time at [α-lactalbumin] = 0.4 mg mL. Points are the experimental data. Solid curve was calculated from Eq. (6) at Rh,0 = 36 nm and
M
1
d
t2R = 5.7 min.
te
Fig. 2. Correlation between v1/2 value (v was calculated from the dependences of light scattering
Ac ce p
intensity on time) and 1/t2R value calculated from the dependences of Rh on time for DTTinduced aggregation of α-lactalbumin at 37 °C.
Fig. 3. Determination of the order of aggregation with respect to protein (n). The dependence of
the initial rate (v) of DTT-induced aggregation of α-lactalbumin on the protein concentration in logarithmic coordinates.
Fig. 4. Dependence of the lag period (t0) on the reciprocal value of α-lactalbumin concentration.
Fig. 5. Relationship between the initial rate (v) of DTT-induced aggregation of α-lactalbumin
and the lag period (t0). The experimental data are represented in coordinates {v1/n; t0} (A) and 23
Page 23 of 35
coordinates {1/v1/n; t0} (B). The solid curve in panel A was calculated from Eq. (8) at n = 5.3, t0,lim = 6.0 and α = 58 min [(counts/s) min-2]1/n.
Fig. 6. Kinetics of DTT-induced aggregation of α-lactalbumin (0.7 mg/ml) studied at various
ip t
concentrations of DTT. (A) The dependences of the light scattering intensity on time obtained at the following concentrations of DTT: (1) 7, (2) 10, (3) 12, (4) 15, (5) 20, (6) 25 and (7) 40 mM.
cr
(B) The dependence of the initial rate (v) of DTT-induced aggregation of α-lactalbumin on DTT
us
concentration in logarithmic coordinates. (C) Dependence of the lag period (t0) on the reciprocal value of DΤΤ concentration. (D) Relationship between the initial rate (v) of DTT-induced
an
aggregation of α-lactalbumin and the lag period (t0). The experimental data are represented in
M
coordinates {1/v1/n; t0}.
Fig. 7. Relationship between the relative initial rate (v/v0) of DTT-induced aggregation of BSA
d
and the lag period (t0). The changes in v/v0 and t0 values are due to suppression of DTT-induced
te
aggregation of BSA by chemical chaperones, namely, arginine (Arg), arginine ethylester
Ac ce p
(ArgEE), arginine amide (ArgAd) and proline (Pro). (A) The dependence of the relative initial rate (v/v0) of DTT-induced aggregation of BSA on t0 value (v0 is the initial rate of aggregation in the absence of chemical chaperones). The plot was constructed from the experimental data represented in [29]. The dotted vertical line corresponds to t0 = t0,in. The solid curve was calculated from Eq. (11) at t0,in = 4.5 min and β = 5.6 min. (B) The (v0 − v)/v versus t0 plot. Solid curve was calculated from Eq. (10) at t0,in = 4.5 min and β = 5.6 min.
Fig. 8. Relationship between the relative initial rate of aggregation (v/v0) and the lag period (t0)
for thermal aggregation of GAPDH (0.4 mg mL-1) at 45 °C (10 mM Na-phosphate buffer, pH 7.5, containing 0.1 M NaCl). The changes in v/v0 and t0 values are due to acceleration of GAPDH aggregation in the presence of HP-β-CD [32]. The dependence of the lag period (t0) on 24
Page 24 of 35
the reciprocal value of HP-β-CD concentration. (B) The v/v0 versus t0 plot (v0 is the initial rate of GAPDH aggregation in the absence of HP-β-CD). Solid curve was calculated from Eq. (12) at
Ac ce p
te
d
M
an
us
cr
ip t
t0,in = 3.03 min and t0,lim = 1.56 min. The dotted vertical line corresponds to t0 = t0,lim.
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us
cr
ip t
Table 1 Parameters of DTT-induced aggregation of α-lactalbumin at 37 °C in 0.1 N Na-phosphate buffer, pH 6.8. α-Lactalbumin, v × 104, t0, min Rh,0, nm t2R, min mg mL-1 (counts/s) min-2 0.4 36 ± 3 5.7 ± 0.4 0.0024 ± 0.0002 27.0 ± 0.2 0.45 0.0048 ± 0.0003 25.2 ± 0.1 38 ± 5 4.9 ± 0.4 0.5 0.014 ± 0.001 21.7 ± 0.1 32 ± 3 3.0 ± 0.1 0.55 0.24 ± 0.02 19.8 ± 0.1 26 ± 3 2.0 ± 0.1 0.6 0.15 ± 0.01 21.5 ± 0.1 30 ± 5 2.8 ± 0.2 0.65 0.26 ± 0.02 20.9 ± 0.1 39 ± 3 2.7 ± 0.2 0.7 0.63 ± 0.06 17.3 ± 0.1 28 ± 5 1.5 ± 0.1 0.8 1.5 ± 0.2 16.0 ± 0.1 32 ± 5 1.2 ± 0.1 0.9 14.8 ± 0.1 26 ± 2 0.97 ± 0.06 2.2 ± 0.3 1.0 15.0 ± 0.1 24 ± 4 0.92 ± 0.06 2.0 ± 0.3
Ac ce p
te
d
M
an
Parameter v characterizes the initial rate of aggregation; t0 is the duration of the lag period on the dependences of the light scattering intensity on time (v and t0 were calculated from Eq. (3)). Rh,0 is the hydrodynamic radius of the start aggregates; t2R is the time interval, over which the Rh value increases from Rh,0 to 2Rh,0 (Rh,0 and t2R were calculated from Eq. (6)).
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S0141-8130(14)00273-6 http://dx.doi.org/doi:10.1016/j.ijbiomac.2014.04.046 BIOMAC 4313
To appear in:
International Journal of Biological Macromolecules
Received date: Revised date: Accepted date:
7-3-2014 22-4-2014 22-4-2014
Please cite this article as: V.A. Borzova, K.A. Markossian, B.I. Kurganov, Relationship between the initial rate of protein aggregation and the lag period for amorphous aggregation, International Journal of Biological Macromolecules (2014), http://dx.doi.org/10.1016/j.ijbiomac.2014.04.046 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Relationship between the initial rate of protein aggregation and the lag period for amorphous aggregation
Vera A. Borzova, Kira A. Markossian, Boris I. Kurganov*
ip t
Bach Institute of Biochemistry, Russian Academy of Sciences, Leninsky 33, Moscow, 119071,
te
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M
an
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cr
Russia
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*Corresponding author. Bach Institute of Biochemistry, Russian Academy of Sciences, Leninsky pr. 33, Moscow, 119071, Russia. Tel.: +7 495 9525641; fax: +7 495 9542732. E-mail address: [email protected] (B.I. Kurganov).
1
Page 1 of 35
ABSTRACT Lag period is an inherent characteristic of the kinetic curves registered for protein aggregation. The appearance of a lag period is connected with the nucleation stage and the stages of the formation of folding or unfolding intermediates prone to aggregation (for example, the stage of
ip t
protein unfolding under stress conditions). Discovering the kinetic regularities essential for elucidation of the protein aggregation mechanism comprises deducing the relationship between
cr
the lag period and aggregation rate. Frändrich proposed the following equation connecting the
us
duration of the lag phase (tlag) and the aggregate growth rate (kg) in the amyloid fibrillation: kg = const/tlag. To establish the relationship between the initial rate of protein aggregation (v) and the
an
lag period (t0) in the case of amorphous aggregation, the kinetics of dithithreitol-induced aggregation of holo-α-lactalbumin from bovine milk was studied (0.1 M Na-phosphate buffer,
M
pH 6.8; 37 °C). The order of aggregation with respect to protein (n) was calculated from the dependence of the initial rate of protein aggregation on the α-lactalbumin concentration (n =
d
5.3). The following equation connecting v and t0 has been proposed: v1/n = const/(t0 - t0,lim),
Ac ce p
te
where t0,lim is the limiting value of t0 at high concentrations of the protein.
Keywords: α-Lactalbumin Amorphous aggregation Lag period Start aggregates 2
Page 2 of 35
1. Introduction
Numerous investigations are concerned with the mechanism and kinetics of the formation of amyloid-like aggregates and fibrils [1-12]. The kinetics of aggregation consists of two phases: an
ip t
initial lag phase that is slow and represents the formation of nuclei and a subsequent rapid
growth phase proceeding as a result of elongation of the preformed nuclei. A large body of data
cr
shows that there is a correlation between the aggregate growth rate (kg) and the lag period (tlag):
us
the shorter the lag period, the higher is the rate of growth, i.e., the samples that nucleate very readily and possess a short lag phase show a very rapid growth reaction. Fändrich [13] proposed
an
a simple equation connecting kg and tlag values:
kg = α/tlag ,
(1)
M
where α is a constant. The applicability of this equation for the kinetics of amyloid fibrils
formation was demonstrated by Fändrich [13] and other authors [2,14-20].
d
Screening of agents possessing anti-aggregation activity is one of the important lines of
te
modern biotechnological research. To carry on such a screening, a number of test systems have
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been proposed. A distinguishing characteristic of test systems, which are based on thermal aggregation of proteins or dithiothreitol (DTT)-induced aggregation of proteins containing disulphide bonds, is formation of amorphous aggregates. To elucidate the mechanism of protein aggregation in test systems under study and select the most effective agents with antiaggregation activity, an investigator should be able to apply strict quantitative methods for the estimation of the initial rate of aggregation (and lag period). For the test systems under investigation the nucleation and aggregation stages are preceded by the stage of unfolding of the protein molecule. This circumstance should be taken into account when analyzing the relationship between the initial rate of aggregation and the lag period. The goal of the present work was to establish a quantitative relationship between the initial rate of aggregation (v) and the lag period (t0) for one of the test systems used for screening of 3
Page 3 of 35
agents possessing anti-aggregation activity, namely for the test system based on DTT-induced aggregation of α-lactalbumin. The molecule of α-lactalbumin contains four disulphide bonds [21], their reduction resulting in unfolding of the protein molecule and subsequent irreversible aggregation [22-25]. In the present work the kinetics of α-lactalbumin aggregation was
ip t
registered using dynamic light scattering (DLS). It was shown that determination of the order of aggregation with respect to protein or with respect to a reducing agent (n) is essential for
cr
establishing a relationship between v and t0 values. When modifying the Fändrich equation, we
us
took into account the n value and the limiting value of t0 at high concentrations of the protein or
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DTT.
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2. Materials and Methods
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2.1. Chemicals
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α-Lactalbumin from bovine milk (catalogue no L5385; calcium-saturated) and DL-
Ac ce p
dithiothreitol (99% of purity) were purchased from Sigma-Aldrich and used without further purification. All solutions for the experiments were prepared using deionized water obtained with Easy-Pure II RF system (Barnstead, USA). α-Lactalbumin samples were prepared by dissolving solid protein in 0.1 M Na-phosphate buffer solutions at pH 6.8. α-Lactalbumin concentration was determined spectrophotometrically at 280 nm using the absorption coefficient 1% Acm of 20.1 [26].
2.2. DTT-induced aggregation of α-lactalbumin
4
Page 4 of 35
Aggregation of α-lactalbumin was studied in 0.1 M Na-phosphate, pH 6.8. Reduction of αlactalbumin was initiated by adding DTT to 0.5 mL of the sample to a final concentration of 20 mM. The experiments were performed at 37 °C.
ip t
2.3. Dynamic light scattering studies
For light scattering measurement a commercial instrument Photocor Complex (Photocor
cr
Instruments, Inc., USA) was used. An He-Ne laser (Coherent, USA, Model 31-2082, 632.8 nm,
us
10 mW) was used as a light source. DynaLS software (Alango, Israel) was used for polydisperse analysis of DLS data. The diffusion coefficient D of the particles is directly related to the decay
an
rate τc of the time-dependent correlation function for the light scattering intensity fluctuations: D = 1/2τck2. In this equation k is the wave number of the scattered light, k = (4πn/λ)sin(θ/2), where
M
n is the refractive index of the solvent, λ is the wavelength of the incident light in a vacuum and θ is the scattering angle. The mean hydrodynamic radius of the particles, Rh, can then be
te
d
calculated according to the Stokes-Einstein equation: D = kBT/6πηRh, where kB is Boltzmann’s constant, T is the absolute temperature and η is dynamic viscosity of solvent.
Ac ce p
The kinetics of DTT-induced aggregation of α-lactalbumin was studied in 0.1 M Na-
phosphate buffer at pH 6.8. The buffer was placed in a cylindrical cell with the internal diameter of 6.3 mm and preincubated for 5 min at a given temperature (37 °C). Cells with stopper were used to avoid evaporation. The aggregation process was initiated by the addition of an aliquot of DTT to a α-lactalbumin sample to the final volume of 0.5 mL. When studying the kinetics of aggregation of α-lactalbumin, the scattering light was collected at a 90° scattering angle. To analyze the time-course of the increase in the light scattering intensity (I) accompanying aggregation of α-lactalbumin, we used the approaches developed by us previously [25,27-31]. To calculate the lag period (t0) on the dependences of I value on time and to characterize the initial rate of aggregation, we used the empiric equation: I = I0 + Kagg(t – t0)2, where I0 is the
5
Page 5 of 35
initial value of the light scattering intensity and Kagg is a parameter characterizing the initial rate of aggregation. In the following parameter Kagg was replaced by v: I = I 0 + v (t − t0 ) 2 .
(2)
It should be noted that in our previous papers [25,28,32] Eq. (2) was written in the form I = I0 +
ip t
[KLS(t − t0)]2. Thus, v and KLS are connected by the following relationship: KLS = v1/2. The expanded variant of Eq. (2)
cr
I = I 0 + v {exp[K1 (t - t0 ) 2 ] - 1} K1
(3)
us
(K1 is a constant) allows us to use a wider time interval in the fitting procedure and to obtain the
an
more reliable values of parameters v and t0. It is significant that at t → t0 Eq. (3) is transformed into Eq. (2).
M
If the values of the initial rate of aggregation (v) are determined at various initial concentrations of the protein ([P]0), the order of aggregation with respect to protein (n) can be
d
calculated:
(4)
te
v = kn [P]0n ,
where kn is a constant. To determine the n value from the experimental data, the logarithmic
Ac ce p
coordinates {log(v); log([P]0)} can be used [30]: log(v) = log(kn ) + nlog([P]0 ) .
(5)
The following equation can be used for the description of the initial part of the dependence
of the hydrodynamic radius (Rh) of the protein aggregates on time [25,33,34]:
⎡ ln(2) ⎤ ⎪⎫ ⎪⎧ Rh = Rh,0 ⎨exp ⎢ (t − t0 ) ⎥ ⎬ , ⎣ t2R ⎦ ⎭⎪ ⎩⎪
(6)
where t0 is the moment of time at which the start aggregates with Rh = Rh,0 emerge, and t2R is the time interval over which the Rh value is doubled (i.e., Rh = 2Rh,0 at t = t0 + t2R). With the knowledge of parameter t0, we can then calculate parameters Rh,0 and t2R. The reciprocal value of t2R can be considered as a measure of the rate of the aggregation process.
6
Page 6 of 35
2.4. Calculations
Origin 8.0 (OriginLab Corporation, USA) software was used for the calculations. To
ip t
characterize the degree of agreement between the experimental data and calculated values, we
cr
used the coefficient of determination R2 [35].
us
3. Results
an
Fig. 1A shows the kinetic curves of DTT-induced aggregation of α-lactalbumin at 37 °C registered by the increment in the light scattering intensity (I). The concentration of α-
M
lactalbumin was varied in the interval of 0.4-1.0 mg mL-1. The initial parts of the kinetic curves were analyzed using Eq. (3), which allows determining the initial rate of aggregation (v) and the
d
lag period (t0). The applicability of Eq. (3) is demonstrated on the inset in Fig.1A ([α-
te
lactalbumin = 0.4 mg mL-1]). The following values of parameters were derived from the
Ac ce p
experimental curve: v = (24 ± 2) (counts/s) min-2 and t0 = 27.0 ± 0.2 min (R2 = 0.999). The values of v and t0 obtained at various concentrations of α-lactalbumin are given in Table 1. As it can be seen from Table 1, the increase in α-lactalbumin concentration is accompanied by the increase in the v value with simultaneous decrease in the lag period (t0). [Table 1 to be inserted here]
The measurements of the hydrodynamic radius (Rh) of the protein aggregates by DLS shows
that the increment in the light scattering intensity is due to the enlargement of the particles under study (Fig. 1B). The initial parts of the dependences of Rh on time allow us to calculate parameters Rh,0 (the hydrodynamic radius of the start aggregates ) and t2R. The following values of parameters were found at [α-lactalbumin] = 0.4 mg mL-1 (see the inset in Fig. 1B): Rh,0 = 36 ± 3 nm and t2R = 5.7 ± 0.4 min (R2 = 0.897). The values of Rh,0 and t2R obtained at various 7
Page 7 of 35
concentrations of α-lactalbumin are given in Table 1. The increase in the protein concentration in the interval from 0.4 to 1.0 mg mL-1 is accompanied by a slight decrease in the Rh value from 36 to 24 nm and 6.2-fold increase in the 1/t2R value, which characterizes the initial rate of
[Fig. 1 to be inserted here]
ip t
aggregation.
In the case of thermal aggregation of creatine kinase from rabbit skeletal muscle the
cr
correlation between parameter KLS (KLS = v1/2) and 1/t2R value has been demonstrated [28]. It is
us
evident from Fig. 2 that such a correlation is also fulfilled for DTT-induced aggregation of αlactalbumin (R2 = 0.908).
an
[Fig. 2 to be inserted here]
To determine the order of aggregation (n) with respect to the protein, the dependence of the
M
initial rate (v) on the concentration of α-lactalbumin was constructed in the logarithmic coordinates (Fig. 3). The dependence of log([α-lactalbumin]) on log(v) is linear and the
d
following values of parameters of kn and n have been found: n = 5.3 ± 0.3 and kn = (3.3 ±
te
1.0)×104 (counts/s) min-2 (mg mL-1)-n (R2 = 0.965).
Ac ce p
[Fig. 3 to be inserted here]
Before proceeding to the relationship between the initial rate of α-lactalbumin aggregation
and lag period it is expedient to discuss the dependence of t0 value on α-lactalbumin concentration. As it can be seen from Fig. 4, the value of t0 is a linear function of the reciprocal value of the protein concentration. Thus, the following equation can be used for description of the dependence of t0 on [α-lactalbumin]: t0 = t0,lim + K [P]0 ,
(7)
where t0,lim is the limiting value of t0 at [α-lactalbumin] → ∞ and K is a constant. The following values of t0,lim and K were found: t0,lim = 6.0 ± 0.5 min and K = 8.0 ± 0.7 min mg mL-1 (R2 = 0.920).
8
Page 8 of 35
[Fig. 4 to be inserted here] Taking into account Eqs. (4) and (7), we can obtain the following expression describing the relationship between the initial rate of aggregation and the lag period: v1/n = α (t0 − t0,lim ) ,
(8)
ip t
where α is a constant (α = K(kn)1/n). This equation can be linearized in the coordinates {1/v1/n;
cr
t0}:
(9)
us
t 1 1 = − 0,lim + t0 . 1/n v α α
The length cut off on the abscissa axis by the linear dependence of 1/v1/n on t0 corresponds to
an
t0,lim value.
In Fig. 5A the v1/n value is plotted as a function of t0. Solid curve was calculated from Eq. (8)
M
at n = 5.3, t0,lim = 6 min and α = 58 min [(counts/s) min-2]1/n. The dotted vertical line corresponds to t0 = t0,lim. Fig. 5B shows a linear anamorphosis corresponding to Eq. (9). Thus, the
te
value to zero.
d
construction of the 1/v1/n versus t0 plot allows us to check whether it is possible to set the t0,lim
Ac ce p
[Fig. 5 to be inserted here]
The kinetics of DTT-induced aggregation of α-lactalbumin is affected not only by α-
lactalbumin concentration but also by DTT (a reducing agent) concentration. Therefore it was of interest to check the validity of Eq. (8) in a situation where variation of DTT concentration causes the change in the aggregation rate. Fig. 6A shows the kinetic curves of aggregation obtained at fixed concentration of α-lactalbumin (0.7 mg/ml) and various concentrations of DTT. The initial rate of aggregation (v) versus DTT concentration plot constructed in logarithmic coordinates allows determining order of aggregation (n) with respect to DTT (Fig. 6B). The n value was found to be 0.45 ± 0.05. One can expect that order of aggregation with respect to DTT will vary from unity at relatively low DTT concentrations to zero at relatively high DTT concentrations. The obtained value of n (n = 0.45) can be considered as a constant value suitable 9
Page 9 of 35
for use in given operating range of DTT concentrations. Analysis of the dependences of the hydrodynamic radius of the protein aggregates on time shows that the Rh value for the start aggregates (Rh,0) is slightly changed with increasing DTT concentration: from 22 ± 2 nm at [DTT] = 7 mM to 29 ± 4 at [DTT] = 40 mM. As in the case with variation of α-lactalbumin
ip t
concentration, the dependence of the lag period on the reciprocal concentration of DTT is linear (Fig. 6C) and the length cut off on the ordinate axis by the linear dependence of t0 on 1/[DTT]
cr
corresponds to the limiting value of t0 (t0,lim) which is reached at [DTT] → ∞. The linear
us
character of the dependence of 1/v1/n on t0 (Fig. 6D) supports satisfiability of linear anamorphosis represented by Eq. (9). Paramerer α was found to be 2.3×109 min [(counts/s) min-2]1/n. Thus, Eq.
an
(8) describing the relationship between the initial rate of aggregation and lag period can be used, irrespective of whether concentration of α-lactalbumin or DTT is varied.
M
[Fig. 6 to be inserted here]
te
d
4. Discussion
Ac ce p
As in the case of apo-α-lactalbumin [25], the results of the study of holo-α-lactalbumin DTT-induced aggregation shows that, aggregation proceeds through the stage of formation of start aggregates. The moment of time t = t0 (t0 is the lag period) corresponds to the emergence of the start aggregates. When studying DTT-induced aggregation of apo-α-lactalbumin, the average value of the hydrodynamic radius of the start aggregates was found to be 93 nm (50 mM sodium phosphate buffer, pH 6.8, containing 0.15 M NaCl and 1 mM EGTA; 37 °C) [25]. Smaller values of Rh,0 were obtained for aggregation of more stable form of α-lactalbumin, namely holo-αlactalbumin (Rh,0 = 22-36 nm). It should be noted that the mechanism of protein aggregation involving formation of the start aggregates with the hydrodynamic radius of several tens of nanometers was demonstrated for
10
Page 10 of 35
DTT-induced aggregation of insulin [36] and thermal aggregation of a broad range of proteins [28,33,34,37-44]. Analysis of the dependence of the initial rate of aggregation on protein concentration allows determining the order of aggregation with respect to protein (n). In the event that n = 1, the rate-
ip t
limiting stage of the aggregation process is the stage of protein unfolding. If n > 1, we may conclude that the rate-limiting stage of the aggregation process is the stage of nucleation or
cr
aggregation of unfolded protein molecules. For example, when studying thermal aggregation of
us
intact and UV-irradiated glyceraldehyde 3-phosphate dehydrogenase (GAPDH; EC 1.2.1.12), we showed that n = 1 for the intact protein and n = 2 for the UV-irradiated protein [45]. UV
an
irradiation induces denaturation of GAPDH, and, consequently, aggregation of UV-irradiated GAPDH does not contain the stage of protein unfolding. As it could have been expected, the
M
order of aggregation with respect to protein for UV-irradiated GAPDH exceeds unity. In some cases non integer values of the order of aggregation with respect to protein were
d
obtained. For example, in the case of DTT-induced aggregation of bovine serum albumin (BSA)
te
n is equal to 1.6 [29]. The reason for the appearance of non integer values of n can be the
Ac ce p
following. Strictly speaking, if the measurements of the order of aggregation with respect to protein were carried out in the wide interval of the protein concentration, the n value should decrease from n = 2 at relatively low [P]0 values to n = 1 at high [P]0 values. Jain and Udgaonkar [46] studied fibrillation of mouse prion protein at pH 2 in the presence of 0.15 M NaCl. The dependence of the observed rate of fibrillation on protein concentration suggested that aggregate growth was rate-limiting at low protein concentration and that conformational change, which was independent of protein concentration, became rate-limiting at higher protein concentrations. Since usually there are limitations in the selection of operating range of protein concentrations, the experimentally determined order of aggregation with respect to protein can accept non integer values. However, it is precisely these n values that should be used for analysis of
11
Page 11 of 35
aggregation kinetics (analysis of the relationship between the initial rate of aggregation and lag period, estimation of the anti-aggregation activity of chaperones and so on). The order of aggregation with respect to protein for apo-α-lactalbumin was found to be 5.9 ± 0.4 (the data obtained by Bumagina et al. [25] were analyzed in [30]). A similar value of n was
ip t
obtained for holo-α-lactalbumin in the present work (n = 5.3 ± 0.3). The fact that the value of parameter n exceeds unity is indicative of the involvement of several unfolded protein molecules
cr
in the nucleation process.
us
As it can be seen from Eq. (8), determination of the order of aggregation with respect to protein is essential for establishing a relationship between the v and t0 values. Another distinctive
an
feature of Eq. (8) in comparison with Eq. (1) is the emergence of parameter t0,lim in the denominator. It is evident that the emergence of parameter t0,lim is connected with the stages of
M
reduction of the disulphide bonds in the α-lactalbumin molecule and unfolding of the protein molecule, which proceed before the nucleation and aggregation stages.
d
When studying DTT-induced aggregation of BSA at 45 °C (0.1 M Na-phosphate, pH 7.0; 2
te
mM DTT) [29], we observed that the lag period (t0) approaches the limiting value at sufficiently
Ac ce p
high concentrations of BSA. As in the case of DTT-induced aggregation of α-lactalbumin, the t0,lim value for DTT-induced aggregation of BSA corresponds to the stages of reduction of the disulphide bonds in the BSA molecule and unfolding of the protein. The order of aggregation with respect to protein (n) was found to be 1.60 ± 0.05. The analogous kinetic regularities are observed for thermal aggregation of proteins. Consider
for example the experimental data on thermal aggregation of yeast alcohol dehydrogenase (50 mM Na-phosphate buffer, pH 7.5, 100 mM NaCl; 56 °C) [43]. The initial parts of the dependences of the light scattering intensity on time were analyzed using Eq. (2). The order of aggregation with respect to protein calculated from the log(v) versus log([P]0) plot was found to be 2.1 ± 0.1. One can assume that the rate-limiting stage of the aggregation process is the stage of protein aggregation. The t0 value decreases with increasing protein concentration, and the 12
Page 12 of 35
limiting value of t0 (t0,lim) obtained by extrapolation to infinitely high concentrations of the protein is equal to 12.4 ± 0.1 min. Thus, when analyzing the relationship between the initial rate of protein aggregation and the lag period for thermal or DTT-induced aggregation of proteins, one should take into account that there is a lower limit for the t0 values.
ip t
The kinetics of protein aggregation can be modulated by low-molecular-weight chemical chaperones [47-53]. It was demonstrated in [29] that the decrease in the initial rate of DTT-
cr
induced aggregation of BSA (v/v0) in the presence of chemical chaperones (arginine, arginine
us
ethylester, arginine amide and proline) was accompanied by an increase in the lag period (t0). Fig. 7A shows the relationship between the v/v0 and t0 values. The t0 value in the absence of the
an
additives, i.e., at v/v0 = 1, was found to be 4.5 min (this value of t0 was designated as an initial lag period, t0,in). In these experiments the fixed concentration of BSA (1 mg mL-1) was used. By
M
analogy with Fig. 5B we decided to construct the reciprocal value of the relative initial rate of aggregation (i.e., 1/(v/v0)) versus t0. We set the n value equal to unity, because the shape of the
d
dependence of the initial rate of aggregation on the concentration of a chemical chaperone is
te
independent of the protein concentration [29]. Then we subtracted unity from the 1/(v/v0) value,
Ac ce p
so that the ordinate of the initial point at t0 = t0,in was equal to zero. Thus, we constructed the [1/(v/v0)] − 1 = (v0 − v)/v versus t0 plot. Fig. 7B shows that this plot is linear. The coefficient of determination (R2) was found to be 0.828. Thus, the following linear anamorphosis can be used to describe the relationship between the initial rate of aggregation and the lag period in the case of chemical chaperones:
t v0 − v 1 = − 0,in + t0 , v β β
(10)
where β is a constant. The length cut off on the abscissa axis corresponds to the t0,in value. The β value was found to be 5.6 ± 0.3 min. [Fig. 7 to be inserted here] Eq. (10) can be transformed as follows:
13
Page 13 of 35
v 1 . = v0 1 + (t0 − t0,in ) β
(11)
This equation can be used for description of the coordinated changes in the initial rate of aggregation and the lag period in the presence of chemical chaperones.
ip t
One of the classes of agents used as chemical chaperones is cyclodextrins and their derivatives, which effectively suppress protein aggregation [28,45,54-56]. However with some
cr
test systems cyclodextrins reveal anti-chaperone activity. The acceleration of the aggregation
us
process in the presence of 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) was observed in test systems based on thermal aggregation of GAPDH and glycogen phosphorylase b from rabbit
an
skeletal muscles [32,57,58]. Such an effect of HP-β-CD is due to the destabilization of the protein molecule upon binding this agent, as indicated by the data on differential scanning
M
calorimetry. An increase in the initial rate of aggregation in the presence of HP-β-CD is accompanied by the decrease in the lag period. As it was expected, the lag period (t0) approached
d
the limiting value (t0,lim) at high concentrations of HP-β-CD. To demonstrate this fact, Fig. 8A
te
shows the dependence of the t0 value on the HP-β-CD concentration in the coordinates {t0;
Ac ce p
1/[HP-β-CD]}. This plot was constructed on the basis of the experimental data obtained for thermal aggregation of GAPDH [32]. The length cut off on the ordinate axis by the linear dependence of t0 on 1/[HP-β-CD] corresponds to the t0,lim value (t0,lim = 1.56 ± 0.02 min). The relationship between the relative initial rate of aggregation (v/v0) and lag period (t0) is represented in Fig. 8B. The dependence of v/v0 on t0 asymptotically approaches vertical line at t0 = t0,lim, as the HP-β-CD concentration increases. To describe the dependence of v/v0 on t0, the following empiric equation can be used: 1/ 2
v ⎛ t0,in − t0,lim ⎞ =⎜ ⎟ , v0 ⎜⎝ t0 − t0,lim ⎟⎠
(12)
where t0,in is the t0 value in the absence of HP-β-CD. [Fig. 8 to be inserted here]
14
Page 14 of 35
Conclusions
Establishing quantitative relationships between the initial rate of aggregation and the lag
ip t
period extends the methodology of quantification of anti-aggregation activity of chaperones (chaperones of protein nature and the chemical chaperones). This methodology has been
cr
developed in our previous works [29-31,59]. In the case of protein chaperones the adsorption
us
capacity of chaperone with respect to target protein is used as a measure of the anti-aggregation activity of the chaperone. For chemical chaperones the concentration of semi-saturation is used
an
as a characteristic of the anti-aggregation activity of the chaperone. Methods of estimation of the effects of combined action of protein chaperones and chemical chaperones have been proposed.
M
This methodology also involves test systems based on registration of protein aggregation under the regime of temperature elevating with a constant rate [29,60]. Implementation of this
d
methodology allows comparing the anti-aggregation activity of different chaperones and can be
Ac ce p
te
used for selecting agents that provide effective suppression of protein aggregation.
Acknowledgements
This study was funded by the Russian Foundation for Basic Research (grant 14-04-01530-a)
and the Program “Molecular and Cell Biology” of the Presidium of the Russian Academy of Sciences.
15
Page 15 of 35
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Figure captions
Fig. 1. Kinetics of DTT-induced aggregation of α-lactalbumin at 37 °C in 0.1 M Na-phosphate,
pH 6.8. The final concentration of DTT was 20 mM. (A) The dependences of light scattering
ip t
intensity on time. The concentrations of α-lactalbumin were as follows: (1) 0.4, (2) 0.5, (3) 0.7 and (4) 1.0 mg mL-1. The inset shows the initial part of the kinetic curve at [α-lactalbumin] = 0.4
cr
mg mL-1. Points are the experimental data. Solid curve was calculated from Eq. (3) at v = 24
us
(counts/s) min-2, t0 = 27 min and K1 = 3.6 min-2. The arrow corresponds to the moment of time t = t0. (B) The dependences of hydrodynamic radius (Rh) of the protein aggregates on time. The
an
concentrations of α-lactalbumin were as follows: (1) 0.4, (2) 0.65, (3) 0.7 and (4) 1.0 mg mL-1. The inset shows the initial part of the dependence of Rh on time at [α-lactalbumin] = 0.4 mg mL. Points are the experimental data. Solid curve was calculated from Eq. (6) at Rh,0 = 36 nm and
M
1
d
t2R = 5.7 min.
te
Fig. 2. Correlation between v1/2 value (v was calculated from the dependences of light scattering
Ac ce p
intensity on time) and 1/t2R value calculated from the dependences of Rh on time for DTTinduced aggregation of α-lactalbumin at 37 °C.
Fig. 3. Determination of the order of aggregation with respect to protein (n). The dependence of
the initial rate (v) of DTT-induced aggregation of α-lactalbumin on the protein concentration in logarithmic coordinates.
Fig. 4. Dependence of the lag period (t0) on the reciprocal value of α-lactalbumin concentration.
Fig. 5. Relationship between the initial rate (v) of DTT-induced aggregation of α-lactalbumin
and the lag period (t0). The experimental data are represented in coordinates {v1/n; t0} (A) and 23
Page 23 of 35
coordinates {1/v1/n; t0} (B). The solid curve in panel A was calculated from Eq. (8) at n = 5.3, t0,lim = 6.0 and α = 58 min [(counts/s) min-2]1/n.
Fig. 6. Kinetics of DTT-induced aggregation of α-lactalbumin (0.7 mg/ml) studied at various
ip t
concentrations of DTT. (A) The dependences of the light scattering intensity on time obtained at the following concentrations of DTT: (1) 7, (2) 10, (3) 12, (4) 15, (5) 20, (6) 25 and (7) 40 mM.
cr
(B) The dependence of the initial rate (v) of DTT-induced aggregation of α-lactalbumin on DTT
us
concentration in logarithmic coordinates. (C) Dependence of the lag period (t0) on the reciprocal value of DΤΤ concentration. (D) Relationship between the initial rate (v) of DTT-induced
an
aggregation of α-lactalbumin and the lag period (t0). The experimental data are represented in
M
coordinates {1/v1/n; t0}.
Fig. 7. Relationship between the relative initial rate (v/v0) of DTT-induced aggregation of BSA
d
and the lag period (t0). The changes in v/v0 and t0 values are due to suppression of DTT-induced
te
aggregation of BSA by chemical chaperones, namely, arginine (Arg), arginine ethylester
Ac ce p
(ArgEE), arginine amide (ArgAd) and proline (Pro). (A) The dependence of the relative initial rate (v/v0) of DTT-induced aggregation of BSA on t0 value (v0 is the initial rate of aggregation in the absence of chemical chaperones). The plot was constructed from the experimental data represented in [29]. The dotted vertical line corresponds to t0 = t0,in. The solid curve was calculated from Eq. (11) at t0,in = 4.5 min and β = 5.6 min. (B) The (v0 − v)/v versus t0 plot. Solid curve was calculated from Eq. (10) at t0,in = 4.5 min and β = 5.6 min.
Fig. 8. Relationship between the relative initial rate of aggregation (v/v0) and the lag period (t0)
for thermal aggregation of GAPDH (0.4 mg mL-1) at 45 °C (10 mM Na-phosphate buffer, pH 7.5, containing 0.1 M NaCl). The changes in v/v0 and t0 values are due to acceleration of GAPDH aggregation in the presence of HP-β-CD [32]. The dependence of the lag period (t0) on 24
Page 24 of 35
the reciprocal value of HP-β-CD concentration. (B) The v/v0 versus t0 plot (v0 is the initial rate of GAPDH aggregation in the absence of HP-β-CD). Solid curve was calculated from Eq. (12) at
Ac ce p
te
d
M
an
us
cr
ip t
t0,in = 3.03 min and t0,lim = 1.56 min. The dotted vertical line corresponds to t0 = t0,lim.
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us
cr
ip t
Table 1 Parameters of DTT-induced aggregation of α-lactalbumin at 37 °C in 0.1 N Na-phosphate buffer, pH 6.8. α-Lactalbumin, v × 104, t0, min Rh,0, nm t2R, min mg mL-1 (counts/s) min-2 0.4 36 ± 3 5.7 ± 0.4 0.0024 ± 0.0002 27.0 ± 0.2 0.45 0.0048 ± 0.0003 25.2 ± 0.1 38 ± 5 4.9 ± 0.4 0.5 0.014 ± 0.001 21.7 ± 0.1 32 ± 3 3.0 ± 0.1 0.55 0.24 ± 0.02 19.8 ± 0.1 26 ± 3 2.0 ± 0.1 0.6 0.15 ± 0.01 21.5 ± 0.1 30 ± 5 2.8 ± 0.2 0.65 0.26 ± 0.02 20.9 ± 0.1 39 ± 3 2.7 ± 0.2 0.7 0.63 ± 0.06 17.3 ± 0.1 28 ± 5 1.5 ± 0.1 0.8 1.5 ± 0.2 16.0 ± 0.1 32 ± 5 1.2 ± 0.1 0.9 14.8 ± 0.1 26 ± 2 0.97 ± 0.06 2.2 ± 0.3 1.0 15.0 ± 0.1 24 ± 4 0.92 ± 0.06 2.0 ± 0.3
Ac ce p
te
d
M
an
Parameter v characterizes the initial rate of aggregation; t0 is the duration of the lag period on the dependences of the light scattering intensity on time (v and t0 were calculated from Eq. (3)). Rh,0 is the hydrodynamic radius of the start aggregates; t2R is the time interval, over which the Rh value increases from Rh,0 to 2Rh,0 (Rh,0 and t2R were calculated from Eq. (6)).
26
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