Kinetics of protein aggregation. Quantitative estimation of the chaperone-like activity in test-systems based on suppression of protein aggregation

The experimental data on the kinetics of irreversible aggregation of proteins caused by exposure to elevated temperatures or the action of denaturing agents (guanidine hydrochloride, urea) have been analyzed. It was shown that the terminal phase of aggregation followed, as a rule, first order kinetics. For the kinetic curves registered by an increase in the apparent absorbance (A) in time (t) the methods of estimation of the corresponding kinetic parameters A _lim and k _I (A _lim is the limiting value of A at t and k _I is the rate constant of the first order) have been proposed. Cases are revealed when the reaction rate constant k _I calculated from the kinetic curve of aggregation of the enzymes coincides with the rate constant for enzyme inactivation. Such a situation is interpreted as a case when the rate of aggregation is limited by the stage of denaturation of the enzyme. A conclusion has been made that, in order to establish the mechanism of protein aggregation, the kinetic investigations of aggregation should be carried out over a wide range of protein concentrations. The refolding experiments after denaturation of proteins by guanidine hydrochloride or urea have been also analyzed. It was shown that aggregation accompanying refolding follows first order kinetics at the final phase of the process. The model of protein refolding explaining such a kinetic regularity has been proposed. When aggregation of protein substrate follows first order kinetics, parameters A _lim and k _I may be used for the quantitative characterization of the chaperone-like activity in the test-systems based on suppression of protein aggregation.     

The study of amorphous aggregation of tobacco mosaic virus coat protein by dynamic light scattering

The kinetics of heat-induced and cetyltrimethylammonium bromide induced amorphous aggregation of tobacco mosaic virus coat protein in Na(+)/Na(+) phosphate buffer, pH 8.0, have been studied using dynamic light scattering. In the case of thermal aggregation (52 degrees C) the character of the dependence of the hydrodynamic radius (R(h)) on time indicates that at certain instant the population of aggregates is split into two components. The size of the aggregates of one kind remains practically constant in time, whereas the size of aggregates of other kind increases monotonously in time reaching the values characteristic of aggregates prone to precipitation (R(h)=900-1500 nm). The construction of the light scattering intensity versus R(h) plots shows that the large aggregates (the start aggregates) exist in the system at the instant the initial increase in the light scattering intensity is observed. For thermal aggregation the R(h) value for the start aggregates is independent of the protein concentration and equal to 21.6 nm. In the case of the surfactant-induced aggregation (at 25 degrees C) no splitting of the aggregates into two components is observed and the size of the start aggregates turns out to be much larger (107 nm) than on the thermal aggregation. The dependence of R(h) on time for both heat-induced aggregation and surfactant-induced aggregation after a lapse of time follows the power law indicating that the aggregation process proceeds in the kinetic regime of diffusion-limited cluster-cluster aggregation. Fractal dimension is close to 1.8. The molecular chaperone alpha-crystallin does not affect the kinetics of tobacco mosaic virus coat protein thermal aggregation.     

Kinetics of thermal aggregation of tobacco mosaic virus coat protein

The kinetics of thermal aggregation of coat protein (CP) of tobacco mosaic virus (TMV) have been studied at 42 and 52°C in a wide range of protein concentrations, [P]₀. The kinetics of aggregation were followed by monitoring the increase in the apparent absorbance (A) at 320 nm. At 52°C the kinetic curves may be approximated by the exponential law in the range of TMV CP concentrations from 0.02 to 0.30 mg/ml, the first order rate constant being linearly proportional to [P]₀ (50 mM phosphate buffer, pH 8.0). The analogous picture was observed at 42°C in the range of TMV CP concentrations from 0.01 to 0.04 mg/ml (100 mM phosphate buffer, pH 8.0). At higher TMV CP concentrations the time of half-conversion approaches a limiting value with increasing [P]₀ and at sufficiently high protein concentrations the kinetic curves fall on a common curve in the coordinates {A/A _lim; t} (t is time and A _lim is the limiting value of A at t ). According to a mechanism of aggregation of TMV CP proposed by the authors at rather low protein concentrations the rate of aggregation is limited by the stage of growth of aggregate, which proceeds as a reaction of the pseudo-first order, whereas at rather high protein concentrations the rate-limiting stage is the stage of protein molecule unfolding.     

Characterization of Oligomers of Heterogeneous Size as Precursors of Amyloid Fibril Nucleation of an SH3 Domain: An Experimental Kinetics Study

Understanding the earliest molecular events during nucleation of the amyloid aggregation cascade is of fundamental significance to prevent amyloid related disorders. We report here an experimental kinetic analysis of the amyloid aggregation of the N47A mutant of the α-spectrin SH3 domain (N47A Spc-SH3) under mild acid conditions, where it is governed by rapid formation of amyloid nuclei. The initial rates of formation of amyloid structures, monitored by thioflavine T fluorescence at different protein concentrations, agree quantitatively with high-order kinetics, suggesting an oligomerization pre-equilibrium preceding the rate-limiting step of amyloid nucleation. The curves of native state depletion also follow high-order irreversible kinetics. The analysis is consistent with the existence of low-populated and heterogeneous oligomeric precursors of fibrillation that form by association of partially unfolded protein monomers. An increase in NaCl concentration accelerates fibrillation but reduces the apparent order of the nucleation kinetics; and a double mutant (K43A, N47A) Spc-SH3 domain, largely unfolded under native conditions and prone to oligomerize, fibrillates with apparent first order kinetics. On the light of these observations, we propose a simple kinetic model for the nucleation event, in which the monomer conformational unfolding and the oligomerization of an amyloidogenic intermediate are rapidly pre-equilibrated. A conformational change of the polypeptide chains within any of the oligomers, irrespective of their size, is the rate-limiting step leading to the amyloid nuclei. This model is able to explain quantitatively the initial rates of aggregation and the observed variations in the apparent order of the kinetics and, more importantly, provides crucial thermodynamic magnitudes of the processes preceding the nucleation. This kinetic approach is simple to use and may be of general applicability to characterize the amyloidogenic intermediates and oligomeric precursors of other disease-related proteins.     

Kinetics of thermal aggregation of glycogen phosphorylase b from rabbit skeletal muscle: mechanism of protective action of alpha-crystallin

The kinetics of thermal aggregation of glycogen phosphorylase b (Phb) from rabbit skeletal muscle have been studied by dynamic light scattering (0.08M Hepes, pH 6.8, containing 0.1M NaCl; 48 degrees C). The hydrodynamic radius of the start aggregates determined from the initial linear parts of the dependences of the hydrodynamic radius (R(h)) on time was found to be 16.7 +/- 1.0 nm. At rather high values of time, the R(h) value for the protein aggregates becomes proportional to t(1/1.8) = t(0.56) suggesting that the aggregation process proceeds in the regime of diffusion-limited cluster-cluster aggregation. In the presence of alpha-crystallin, a protein possessing the chaperone-like activity, the process of protein aggregation switches to the regime of reaction-limited cluster-cluster aggregation as indicated by the exponential dependence of the R(h) value on time. It was shown that the addition of alpha-crystallin raises the rate of thermal inactivation of Phb. These data in combination with the results of the study of interaction of Phb with alpha-crystallin by analytical ultracentrifugation suggest that alpha-crystallin interacts with the intermediates of unfolding of the Phb molecule.     

Change in kinetic regime of protein aggregation with temperature increase. Thermal aggregation of rabbit muscle creatine kinase

Creatine kinase thermal aggregation kinetics has been studied in 30 mM Hepes-NaOH buffer, pH 8.0, at two temperatures: 50.6 and 60°C. Aggregation kinetics was analyzed by measuring the growth of apparent absorption (A) at 400 nm. It was found that the limiting value of apparent absorption (A _lim) is proportional to protein concentration at both temperatures. The first order rate constant (k _I) does not depend on protein concentration in the range 0.05–0.2 mg/ml at temperature 50.6°C, but at temperature 60°C it increases with the growth of protein concentration in the range 0.1–0.4 mg/ml. Kinetic curves, shown in coordinates {A/A _lim; t}, in experiments at 50.6°C fuse to a common curve, which coincides with the theoretical curve of creatine kinase denaturation calculated using the denaturation rate constant determined from differential scanning calorimetry. At temperature 60°C, half-transformation time t _1/2 = ln2/k _I decreases when protein concentration grows. We conclude that when temperature increased from 50.6 to 60°C, change in the kinetic regime of thermal creatine kinase aggregation took place: at 50.6°C aggregation rate is limited by the stage of protein molecule denaturation, but at 60°C it is limited by the stage of protein aggregate growth, which proceeds as a reaction of pseudo-first order. Small heat shock protein Hsp 16.3 Mycobacterium tuberculosis suppresses the creatine kinase aggregation. Published in Russian in Biokhimiya, 2006, Vol. 71, No. 3, pp. 408–416.     

Kinetics of cold-set diffusion-limited aggregations of denatured whey protein isolate colloids

The CaCl2-induced cold-set aggregation kinetics of the denatured whey protein isolate (WPI) colloids has been investigated under dilute diffusion-limited cluster aggregation (DLCA) conditions, using small-angle light scattering. In particular, the structure factor, the scattered intensity at zero angle and the average radius of gyration have been measured for the aggregating system as a function of time. It is found that the fractal dimension of the clusters is df= 1.85, in the range typical of clusters aggregated under DLCA conditions. The aggregation kinetics in this transition region can be described by a power law relation in the initial stage of the aggregation, but the exponent of the power law is equal to 0.7, i.e., significantly larger than 1/df= 0.54, which is the typical value of the DLCA kinetics. Since it is found that the average gyration radius of the clusters has reached a value of 80 microm, leading to a cumulative volume fraction of clusters equal to 0.25, it is legitimate to expect that the process is in the region of transition from aggregation to gelation. This confirmed by the fact that, at the later stage of the aggregation, the growth of the average cluster size further accelerates with time and eventually becomes explosive, leading to gelation. The observed aggregation kinetics has been compared with that reported in the literature from DLCA Monte Carlo simulations, and a good agreement has been found with the data corresponding to the transition region from aggregation to gelation. Numerical simulations using the Smoluchowski kinetic model have also been carried out in order to support the experimental findings.     

Estimation of protein aggregation propensity with a melting point apparatus

A method for studying protein aggregation with an automated melting point apparatus is described. The method employs thermal ramping and can generate a series of protein aggregation curves. The midpoint aggregation curve-associated temperature (T_a) is used to evaluate the difference between the curves where the lower T_a value corresponds to a higher aggregation propensity. The applicability of the method was demonstrated with human interleukin-1 receptor antagonist (IL-1ra) as a protein aggregation model. The method could be employed for rapid evaluation of various factors such as mutations, buffers, and excipients influencing protein aggregation propensity under the thermal stress.     

Comparative Analysis of the Effects of α-Crystallin and GroEL on the Kinetics of Thermal Aggregation of Rabbit Muscle Glyceraldehyde-3-Phosphate Dehydrogenase

Effects of α-crystallin and GroEL on the kinetics of thermal aggregation of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase (GAPDH) have been studied using dynamic light scattering and analytical ultracentrifugation. The analysis of the initial parts of the dependences of the hydrodynamic radius of protein aggregates on time shows that in the presence of α-crystallin or GroEL the kinetic regime of GAPDH aggregation is changed from the regime of diffusion-limited cluster–cluster aggregation to the regime of reaction-limited cluster–cluster aggregation, wherein the sticking probability for the colliding particles becomes lower the unity. In contrast to α-crystallin, GroEL does not interfere with formation of the start aggregates which include denatured GAPDH molecules. On the basis of the analytical ultracentrifugation data the conclusion has been made that the products of dissociation of GAPDH and α-crystallin or GroEL play an important role in the interactions of GAPDH and chaperones at elevated temperatures.     

Kinetics of Denaturation of Rabbit Skeletal Muscle Glycogen Phosphorylase b by Guanidine Hydrochloride

The kinetics of denaturation and aggregation of rabbit muscle glycogen phosphorylase b in the presence of guanidine hydrochloride (GuHCl) have been studied. The curve of inactivation of phosphorylase b in time includes a region of the fast decline in the enzymatic activity,an intermediate plateau,and a part with subsequent decrease in the enzymatic activity. The fact that the shape of the inactivation curves is dependent on the enzyme concentration testifies to the dissociative mechanism of inactivation. The dissociation of phosphorylase b dimers into monomers in the presence of GuHCl is supported by sedimentation data. The rate of phosphorylase b aggregation in the presence of GuHCl rises as the denaturant concentration increases to 1.12 M; at higher concentration of GuHCl, suppression of aggregation occurs. At rather low concentration of the protein (0.25 mg/ml), the terminal phase of aggregation follows the kinetics of a monomolecular reaction (the reaction rate constant is equal to 0.082 min^–1;1 M GuHCl, 25°C). At higher concentration of phosphorylase b (0.75 mg/ml), aggregation proceeds as a trimolecular reaction.     

Model Discrimination and Mechanistic Interpretation of Kinetic Data in Protein Aggregation Studies

Given the importance of protein aggregation in amyloid diseases and in the manufacture of protein pharmaceuticals, there has been increased interest in measuring and modeling the kinetics of protein aggregation. Several groups have analyzed aggregation data quantitatively, typically measuring aggregation kinetics by following the loss of protein monomer over time and invoking a nucleated growth mechanism. Such analysis has led to mechanistic conclusions about the size and nature of the nucleus, the aggregation pathway, and/or the physicochemical properties of aggregation-prone proteins. We have examined some of the difficulties that arise when extracting mechanistic meaning from monomer-loss kinetic data. Using literature data on the aggregation of polyglutamine, a mutant β-clam protein, and protein L, we determined parameter values for 18 different kinetic models. We developed a statistical model discrimination method to analyze protein aggregation data in light of competing mechanisms; a key feature of the method is that it penalizes overparameterization. We show that, for typical monomer-loss kinetic data, multiple models provide equivalent fits, making mechanistic determination impossible. We also define the type and quality of experimental data needed to make more definitive conclusions about the mechanism of aggregation. Specifically, we demonstrate how direct measurement of fibril size provides robust discrimination.     

Formation kinetics of insulin-based amyloid gels and the effect of added metalloporphyrins

The kinetics of insulin-based amyloid gel formation has been studied using extinction and fluorescence detection. The process is treated as autocatalytic, and the kinetic profiles are fit using a nonconventional analysis involving a time-dependent rate constant (factor): k(t) = k(o) + k(c)(k(c)t)(n). The dependence of the kinetic parameters on initial solution conditions of concentration, pH, and ionic strength has been investigated. A mechanism is proposed in which the rate-determining step involves the activation of insulin solute species into partially unfolded, structurally modified monomers, which then aggregate. The influence of added metalloporphyrins on the rate and extent of gel formation is described. Metal derivatives of tetrakis(4-sulfonatophenyl)porphine prove effective at inhibiting the aggregation of insulin via pathways that depend on concentration and identity of the incorporated metal.     

Kinetic and titration methods for determination of active site contents of enzyme and catalytic antibody preparations

Kinetic characterization of enzymes and analogous catalysts such as catalytic antibodies requires knowledge of the molarity of functional sites. Various stoichiometric titration methods are available for the determination of active-site concentrations of some enzymes and these are exemplified in the second part of this article. Most of these are not general in that they require the existence of certain types of either intermediate or active-site residues that are susceptible to specific covalent modification. Thus they are not readily applicable to many enzymes and they are rarely available currently for titration of catalytic antibody active sites. In the first part of the article we discuss a general kinetic method for the investigation of active-site availability in preparations of macromolecular catalysts. The method involves steady-state kinetics to provide Vmax and Km and single-turnover first-order kinetics using excess of catalyst over substrate to provide the analogous parameters k(obs)lim and K(m)app. The active-site contents of preparations that contain only active catalyst (Ea) and inert material (Ei) may be calculated as [Ea](T) = Vmax)/k(obs)lim. This is true even if nonproductive binding to E(a) occurs. For polyclonal catalytic antibody preparations, which may contain binding but noncatalytic material (Eb) in addition to Ea and Ei, the significance of Vmax/k(obs)lim is more complex but provides an upper limit to E(a). This can be refined by consideration of the relative values of Km and the equilibrium dissociation constant of EbS. Analysis of the Ea, Eb, Ei system requires the separate determination of Ei. For catalytic antibodies this may be achieved by analytical affinity chromatography using an immobilized hapten or hapten analog and an ELISA procedure to ensure the clean separation of Ei from the Ea + Eb mixture.     

大黄酸和大黄素的热分析及其动力学研究

本文采用热重法(TG)和差热分析法(DTA)测定了大黄酸和大黄素的DTA,TG-DTG曲线。两者的DTA曲线中皆有两个较为明显的吸热峰,第一个在熔化过程中出现,第二个发生在热分解过程中并伴随有明显的失重现象。TG曲线均有一个失重平台,失重率在90%以上。用TG-DTG法对两者在非等温条件下进行热分解动力学研究,把从TG-DTG曲线中取得的数据和31个不同的方程采用Achar微分法和Madhusudanan-Krishnan-Ni-nan(MKN)积分法对其进行非等温分解动力学研究,得到动力学参数活化能(E和指前因子A)和分解动力学机理及方程。得出结论:大黄酸和大黄素的动力学方程为dα/dt=Aexp(-E/RT)3/2(1-α)4/3[1/(1-α)1/3-1]-1和dα/dt=Aexp(-E/RT)3/2(1-α)2/3[1/(1-α)1/3]-1,其分解等合3D抗理。二者的活化能E(kJ/mol)分别为117.6和86.79,lnA/s-1分别是36.72和27.44。     

Interrelationships of glycosylation and aggregation kinetics for Peniophora lycii phytase

The kinetics of thermally induced aggregation of the glycoprotein Peniophora lycii phytase (Phy) and a deglycosylated form (dgPhy) was studied by dynamic (DLS) and static (SLS) light scattering. This provided a detailed insight into the time course of the formation of small aggregates ( approximately 10-100 molecules) of the enzyme. The thermodynamic stability of the two forms was also investigated using scanning calorimetry (DSC). It was found that the glycans strongly promoted kinetic stability (i.e., reduced the rate of irreversible denaturation) while leaving the equilibrium denaturation temperature, T(d), defined by DSC, largely unaltered. At pH 4.5-5.0, for example, dgPhy aggregated approximately 200 times faster than Phy, even though the difference in T(d) was only 1-3 degrees C. To elucidate the mechanism by which the glycans promote kinetic stability, we measured the effect of ionic strength and temperature on the aggregation rate. Also, the second virial coefficients (B(22)) for the two forms were measured by SLS. These results showed that the aggregation rate of Phy scaled with the concentration of thermally denatured protein. This suggested first-order kinetics with respect to the concentration of the thermally denatured state. A similar but less pronounced correlation was found for dgPhy, and it was suggested that while the aggregation process for the deglycosylated form is dominated by denatured protein, it also involves a smaller contribution from associating molecules in the native state. The measurements of B(22) revealed that dgPhy had slightly higher values than Phy. This suggests that dgPhy interacts more favorably with the buffer than Phy and hence rules out strong hydration of the glycans as the origin of their effect on the kinetic stability. On the basis of this and the effects of pH and ionic strength, we suggest that the inhibition of aggregation is more likely to depend on steric hindrance of the glycans in the aggregated form of the protein.     

The pH Dependence of Violaxanthin Deepoxidation in Isolated Pea Chloroplasts

The absorbance change at 505 nm was used to monitor the kinetics of violaxanthin deepoxidation in isolated pea (Pisum sativum) chloroplasts under dark conditions at various pH values. In long-term measurements (65 min) a fast and a slow exponential component of the 505-nm absorbance change could be resolved. The fast rate constant was up to 10 times higher than the slow rate constant. The asymptote value of the fast kinetic component was twice that of the slow component. The pH dependency of the parameters of the fast kinetic component was analyzed from pH 5.2 to pH 7.0. It was found that the asymptote value dropped slightly with increasing pH. The rate constant was zero at pH values greater than 6.3 and showed maximum values at pH values less than 5.8. Hill plot analysis revealed a strong positive cooperativity for the pH dependency of the fast rate constant (Hill coefficient nH = 5.3). The results are discussed with respect to published activity curves of violaxanthin deepoxidation.     

Kinetic studies of recA protein binding to a fluorescent single-stranded polynucleotide

Fluorescence spectroscopy was used to investigate the binding of Escherichia coli recA protein to a single-stranded polynucleotide. Poly(deoxy-1,N6-ethenoadenylic acid) was prepared by reaction of chloroacetaldehyde with poly(deoxyadenylic acid). The fluorescence of poly(deoxy-1,N6-ethenoadenylic acid) was enhanced upon recA protein binding. The kinetics of the binding process were studied as a function of several parameters: ionic concentration (KCl and MgCl2), pH, nature of the nucleoside triphosphate [adenosine 5'-triphosphate or adenosine 5'-O-(gamma-thiotriphosphate)], protein and polynucleotide concentrations, polynucleotide chain length, and order of sequential additions. The observed kinetic curves exhibited a lag phase followed by a slow binding process characteristic of a nucleation-elongation mechanism with an additional slow step governing the rate of the association process. The lag phase reflecting the nucleation step was not observed when the protein was first bound to the polynucleotide before addition of adenosine 5'-triphosphate. Adenosine 5'-triphosphate induced a dissociation of the recA protein, which was immediately followed by binding of the recA-adenosine 5'-triphosphate-Mg2+ ternary complex. The origin of this "mnemonic effect" and of the different kinetic steps is discussed with respect to protein conformational changes and aggregation phenomena.     

Antiaggregation activity of chaperones and its quantification

Methods for the quantitative estimation of the antiaggregation activity of protein chaperones (first of all, small heat shock proteins) and chemical chaperones including amino acids, carbohydrates, polyamines, and cyclodextrins are discussed. Based on analysis of the plots of light scattering intensity or apparent optical absorption versus time, formulas for calculation of initial rate of aggregation of protein substrate and lag period on kinetic curves of aggregation were derived. Possible determination of the stoichiometry of chaperone-protein substrate complex from the dependence of the initial rate of aggregation on the ratio of protein chaperone/protein substrate concentrations is discussed. To characterize efficiency of the protective action of chemical chaperones, the [L]_0.5 value can be used ([L]_0.5 is the concentration of a chemical chaperone at which twofold decrease in the initial rate of aggregation occurs). Methods for quantitative estimation of the combined protective action of chaperones are discussed.     

Kinetic manifestations of slow conformation rearrangements of lactate dehydrogenase. An experiment and a mathematical model

Non-steady-state kinetics of lactate dehydrogenase (LDH) catalyzed reaction was investigated for a wide time interval (from 100 msec to 1-3 min) by using stopped-flow methods. A two-stage character of LDH reaction, slow changes like a lag-period on kinetic curves at pH 8.0, flexions on kinetic curves after pre-mixing LDH with NAD+ and pyruvate have been revealed. The graph theory for mathematical analysis of experimental data was applied, which has been developed for the non-steady-state kinetics. An enzyme model of the two-conformer LDH structure was used. The reaction scheme with a preferential inhibition of one of the conformers (pH 8.0) is suggested. The obtained values of kinetic constants prove that transitions between LDH conformers must be slow.     

Heat-induced denaturation and aggregation of ovalbumin at neutral pH described by irreversible first-order kinetics

The heat-induced denaturation kinetics of two different sources of ovalbumin at pH 7 was studied by chromatography and differential scanning calorimetry. The kinetics was found to be independent of protein concentration and salt concentration, but was strongly dependent on temperature. For highly pure ovalbumin, the decrease in nondenatured native protein showed first-order dependence. The activation energy obtained with different techniques varied between 430 and 490 kJ*mole(-1). First-order behavior was studied in detail using differential scanning calorimetry. The calorimetric traces were irreversible and highly scan rate-dependent. The shape of the thermograms as well as the scan rate dependence can be explained by assuming that the thermal denaturation takes place according to a simplified kinetic process where N is the native state, D is denatured (or another final state) and k a first-order kinetic constant that changes with temperature, according to the Arrhenius equation. A kinetic model for the temperature-induced denaturation and aggregation of ovalbumin is presented. Commercially obtained ovalbumin was found to contain an intermediate-stable fraction (IS) of about 20% that was unable to form aggregates. The denaturation of this fraction did not satisfy first-order kinetics.