Non-native protein aggregation kinetics

Experimental kinetics of non-native protein aggregation are of practical importance in that they help dictate viable processing, formulation, and storage conditions for biotechnology products, and appear to play a role in determining the onset of a number of diseases. Fundamentally, aggregation kinetics provide insights into the identity of key intermediates in the process, and quantitative tests of available models of aggregation. Although aggregation kinetics often display seemingly disparate behaviors across different proteins and sample conditions, this review illustrates how many of these can be understood within a general framework that treats aggregation as a multi-stage process, and how most available kinetic models of aggregation can be grouped hierarchically in terms of which stage(s) they include. This provides an aid for workers seeking a mechanistic interpretation of in vitro aggregation kinetics, for discriminating among competing models, and in designing experiments to assess in vitro protein stability. Limitations and the utility of purely kinetic approaches to studying aggregation, clarifications of common misperceptions regarding experimental aggregation kinetics, and some outstanding challenges in the field are briefly discussed.     

Sorptive removal of Methylene blue from aqueous solution using palm kernel fibre: Effect of fibre dose

The use of palm kernel fibre, a readily available agricultural waste product for the sorption of Methylene blue from aqueous solution and the possible mechanism of sorption has been investigated at various fibre doses. The extent of dye removal and the rate of sorption were analyzed using two kinetic rate models (pseudo-first and pseudo-second-order kinetic models) and two diffusion models (intraparticle and external mass transfer models).

Analysis of the kinetic data at different sorbent dose revealed that the pseudo-first order kinetics fitted to the kinetic data only in the first 5 min of sorption and then deviated from the experimental data. The pseudo-second-order kinetic model was found to better fit the experimental data with high correlation coefficients at the various fibre dose used. The dye sorption was confirmed to follow the pseudo-second-order model by investigating the relationship between the amount of dye sorbed and the change in hydrogen ion concentration of the dye solution and also the dependence of dye uptake with solution temperature. It was found that the change in hydrogen ion concentration and increase in sorption temperature were directly related to the amount of dye sorbed, and activation energy was calculated to be −39.57 kJ/mol, indicating that the dye uptake is chemisorption, involving valence forces through sharing or exchange of electrons between sorbent and sorbate as covalent forces.

The intraparticle diffusion plots showed three sections indicating that intraparticle diffusion is not solely rate controlling. The intraparticle diffusion and mass transfer rate constants where observed to be well correlated with sorbent dose in the first 5 min of sorption, indicating sorption process is complex. It was found that at low sorbent dose the mass transfer is the main rate controlling parameter. However at high sorbent dose, intraparticle diffusion becomes rate controlling.     

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.     

叶绿素铜钠盐染色蚕丝织物动力学研究

为提高植物染料叶绿素铜钠盐对蚕丝织物上染过程的控制,提供染色工艺优化的理论指导,本文研究了叶绿素铜钠盐上染蚕丝织物的动力学吸附过程,探讨了染色机理,并运用准一级和准二级动力学模型对叶绿素铜钠盐染色蚕丝织物的实验数据进行模拟,计算叶绿素铜钠盐染色蚕丝织物的动力学参数.结果表明:叶绿素铜钠盐在蚕丝织物上的染色符合准二级动力学模型,且在染色温度70～90℃范围内,随着染色温度的升高,染色平衡吸附量降低,染色速率常数增大,半染时间减小,扩散系数增大.     

Novel kinetics in the sodium conductance system predicted by the aggregation model of channel gating.

Special voltage-clamp pulse protocols are given that make differential predictions for the kinetics of models based on a simple sequential, simple cyclic, and an aggregation scheme. Detailed kinetic time-courses for the discriminating pulse protocols are numerically derived from the differential equation system that describes the aggregation model.     

Rapid microtubule self-assembly kinetics

Microtubule assembly is vital for many fundamental cellular processes. Current models for microtubule assembly kinetics assume that the subunit dissociation rate from a microtubule tip is independent of free subunit concentration. Total-Internal-Reflection-Fluorescence (TIRF) microscopy experiments and data from a laser tweezers assay that measures in vitro microtubule assembly with nanometer resolution, provides evidence that the subunit dissociation rate from a microtubule tip increases as the free subunit concentration increases. These data are consistent with a two-dimensional model for microtubule assembly, and are explained by a shift in microtubule tip structure from a relatively blunt shape at low free concentrations to relatively tapered at high free concentrations. We find that because both the association and the dissociation rates increase at higher free subunit concentrations, the kinetics of microtubule assembly are an order-of-magnitude higher than currently estimated in the literature.     

Kinetics and mechanism of methylene blue sorption onto palm kernel fibre

The kinetics and mechanism of the sorptive removal of methylene blue dye from aqueous solution using palm kernel fibre as adsorbent have been investigated. Batch kinetic experiments were performed and system variables investigated includes pH and initial dye concentration. The kinetic data were fitted to the pseudo-first, pseudo-second, intraparticle diffusion and mass transfer models. The pseudo-first order reaction kinetics fitted to the experimental data only in the first 5 min of sorption and then deviated, while the pseudo-second order kinetic model was found to fit the experimental data for the entire sorption period with high coefficient of determination. Equations were developed using the pseudo-second order model, which predicts the amounts of methylene blue at any contact time and initial concentration within the given range. This suggests that the sorption of methylene blue onto palm kernel fibre follows a chemical activation mechanism. A mathematical relationship was also drawn between the equilibrium sorption capacity and the change in pH (ΔH⁺) at the end of the kinetic experiments with varying initial dye concentration, supporting the fact that chemical reaction (ion exchange) occurred and is important in the rate determining step. Mass transfer was found to be favoured at high concentrations while intraparticle diffusion was favoured at low concentrations.     

Applying Molecular Crowding Models to Simulations of Virus Capsid Assembly In Vitro

Virus capsid assembly has been widely studied as a biophysical system, both for its biological and medical significance and as an important model for complex self-assembly processes. No current technology can monitor assembly in detail and what information we have on assembly kinetics comes exclusively from in vitro studies. There are many differences between the intracellular environment and that of an in vitro assembly assay, however, that might be expected to alter assembly pathways. Here, we explore one specific feature characteristic of the intracellular environment and known to have large effects on macromolecular assembly processes: molecular crowding. We combine prior particle simulation methods for estimating crowding effects with coarse-grained stochastic models of capsid assembly, using the crowding models to adjust kinetics of capsid simulations to examine possible effects of crowding on assembly pathways. Simulations suggest a striking difference depending on whether or not a system uses nucleation-limited assembly, with crowding tending to promote off-pathway growth in a nonnucleation-limited model but often enhancing assembly efficiency at high crowding levels even while impeding it at lower crowding levels in a nucleation-limited model. These models may help us understand how complicated assembly systems may have evolved to function with high efficiency and fidelity in the densely crowded environment of the cell.     

Competitive cooperative bindings of a small ligand to a linear polymer. II. Investigations on the mechanisms of proflavine binding to poly (A) and DNA.

Experimental binding isotherms relative to the interactions between proflavine and poly(A) or DNA are analyzed by comparison with theoretical models dealing with competitive cooperative bindings. In the case of poly(A), there are apparently no specific binding sites for the positive co-operative binding (complex I) leading to dye aggregation along the polyanionic chain. The second complex (complex II) seems to involve specific base-dye interactions, but it cannot be said whether this binding displays negative cooperativity or noncooperativity. None of the two simpler theoretical models agree quantitatively with all experimental data. A plausible interpretation can be given if it is assumed that (i) the electrostatic binding of one isolated bound dye molecule (nucleus of complex I) involves a definite interaction between a phosphate group and the positive charge of the dye; (ii) the structure of complex II is such that a dye–phosphate ionic interaction is maintained. In the case of DNA, our model of monoexclusive interactions fits the data more closely than does the model of biexclusive interactions. This gives experimental support for structural models in which the intercalated molecule interacts preferentially with one strand of the double helix and blocks only one phosphate for electrostatic binding. In order to propose a mechanism consistent with equilibrium and relaxation kinetic data, a modified reaction scheme is considered which takes account of the cooperativity effects in external binding and extends previous models.     

Applying Molecular Crowding Models to Simulations of Virus Capsid Assembly In?Vitro

Virus capsid assembly has been widely studied as a biophysical system, both for its biological and medical significance and as an important model for complex self-assembly processes. No current technology can monitor assembly in detail and what information we have on assembly kinetics comes exclusively from in vitro studies. There are many differences between the intracellular environment and that of an in vitro assembly assay, however, that might be expected to alter assembly pathways. Here, we explore one specific feature characteristic of the intracellular environment and known to have large effects on macromolecular assembly processes: molecular crowding. We combine prior particle simulation methods for estimating crowding effects with coarse-grained stochastic models of capsid assembly, using the crowding models to adjust kinetics of capsid simulations to examine possible effects of crowding on assembly pathways. Simulations suggest a striking difference depending on whether or not a system uses nucleation-limited assembly, with crowding tending to promote off-pathway growth in a nonnucleation-limited model but often enhancing assembly efficiency at high crowding levels even while impeding it at lower crowding levels in a nucleation-limited model. These models may help us understand how complicated assembly systems may have evolved to function with high efficiency and fidelity in the densely crowded environment of the cell.     

Competition between Primary Nucleation and Autocatalysis in Amyloid Fibril Self-Assembly

Kinetic measurements of the self-assembly of proteins into amyloid fibrils are often used to make inferences about molecular mechanisms. In particular, the lag time—the quiescent period before aggregates are detected—is often found to scale with the protein concentration as a power law, whose exponent has been used to infer the presence or absence of autocatalytic growth processes such as fibril fragmentation. Here we show that experimental data for lag time versus protein concentration can show signs of kinks: clear changes in scaling exponent, indicating changes in the dominant molecular mechanism determining the lag time. Classical models for the kinetics of fibril assembly suggest that at least two mechanisms are at play during the lag time: primary nucleation and autocatalytic growth. Using computer simulations and theoretical calculations, we investigate whether the competition between these two processes can account for the kinks which we observe in our and others’ experimental data. We derive theoretical conditions for the crossover between nucleation-dominated and growth-dominated regimes, and analyze their dependence on system volume and autocatalysis mechanism. Comparing these predictions to the data, we find that the experimentally observed kinks cannot be explained by a simple crossover between nucleation-dominated and autocatalytic growth regimes. Our results show that existing kinetic models fail to explain detailed features of lag time versus concentration curves, suggesting that new mechanistic understanding is needed. More broadly, our work demonstrates that care is needed in interpreting lag-time scaling exponents from protein assembly data.     

Kinetics and thermodynamics of basic dye sorption on phosphoric acid esterifying soybean hull with solid phase preparation technique

In this paper, the solid phase preparation method of a cationic sorbent, which bears hydroxyl groups of phosphoric acid derived from esterified soybean hull (ESH), was reported. The sorption kinetics and thermodynamics of two basic dyes, acridine orange (AO) and malachite green (MG), from aqueous solution onto ESH were investigated with a batch system. The isothermal data of dye sorptions followed the Langmuir model better than the Freundlich model. The maximum sorption capacity (Q(m)) of ESH for AO and MG was 238.1 mg/g and 178.57 mg/g, respectively. The dye sorption processes could be described by the pseudo-second-order kinetic model. The thermodynamic study indicated that the dye sorptions were spontaneous and exothermic. Lower temperatures were favorable for the sorption processes.     

Successive openings of the same acetylcholine receptor channel are correlated in open time.

Previous analysis of single-channel current records has shown that both the opening and closing transitions of chemically activated ion channels are operated by fast and slow kinetic processes. The fast component in the kinetics of channel opening has been interpreted as the reopening of a channel that has just closed. The fast component in the kinetics of channel closure has many possible explanations and is therefore more difficult to interpret. We can gain insight into the closing process by asking whether the lifetimes of successive openings of an acetylcholine receptor channel are correlated in open-state lifetime. Five kinetic models of channel closure are considered. Two of these models predict uncorrelated open-state lifetimes, one predicts correlated open-state lifetimes, and for two others a range of behavior is possible. Acetylcholine receptor channel data from cultured rat muscle are analyzed to show that open-state lifetimes are correlated, eliminating two models of channel gating.     

Exploring protein aggregation and self-propagation using lattice models: phase diagram and kinetics

Many seemingly unrelated neurodegenerative disorders, such as amyloid and prion diseases, are associated with propagating fibrils whose structures are dramatically different from the native states of the corresponding monomers. This observation, along with the experimental demonstration that any protein can aggregate to form either fibrils or amorphous structures (inclusion bodies) under appropriate external conditions, suggest that there must be general principles that govern aggregation mechanisms. To probe generic aspects of prion-like behavior we use the model of Harrison, Chan, Prusiner, and Cohen. In this model, aggregation of a structure, that is conformationally distinct from the native state of the monomer, occurs by three parallel routes. Kinetic partitioning, which leads to parallel assembly pathways, occurs early in the aggregation process. In all pathways transient unfolding precedes polymerization and self-propagation. Chain polymerization is consistent with templated assembly, with the dimer being the minimal nucleus. The kinetic effciency of R(n-1) + G --> R(n) (R is the aggregation prone state and G is either U, the unfolded state, or N, the native state of the monomer) is increased when polymerization occurs in the presence of a "seed" (a dimer). These results support the seeded nucleated-polymerization model of fibril formation in amyloid peptides. To probe generic aspects of aggregation in two-state proteins, we use lattice models with side chains. The phase diagram in the (T,C) plane (T is the temperature and C is the polypeptide concentration) reveals a bewildering array of "phases" or structures. Explicit computations for dimers show that there are at least six phases including ordered structures and amorphous aggregates. In the ordered region of the phase diagram there are three distinct structures. We find ordered dimers (OD) in which each monomer is in the folded state and the interaction between the monomers occurs via a well-defined interface. In the domain-swapped structures a certain fraction of intrachain contacts are replaced by interchain contacts. In the parallel dimers the interface is stabilized by favorable intermolecular hydrophobic interactions. The kinetics of folding to OD shows that aggregation proceeds directly from U in a dynamically cooperative manner without populating partially structured intermediates. These results support the experimental observation that ordered aggregation in the two-state folders U1A and CI2 takes place from U. The contrasting aggregation processes in the two models suggest that there are several distinct mechanisms for polymerization that depend not only on the polypeptide sequence but also on external conditions (such as C, T, pH, and salt concentration).     

Reconsidering the mechanism of polyglutamine peptide aggregation

There are at least nine neurodegenerative diseases associated with proteins that contain an unusually expanded polyglutamine domain, the best known of which is Huntington's disease. In all of these diseases, the mutant protein aggregates into neuronal inclusions; it is generally, although not universally, believed that protein aggregation is an underlying cause of the observed neuronal degeneration. In an effort to examine the role of polyglutamine in facilitating protein aggregation, investigators have used synthetic polyglutamine peptides as model systems. Analysis of kinetic data led to the conclusions that aggregation follows a simple nucleation-elongation mechanism characterized by a significant lag time, during which the peptide is monomeric, and that the nucleus is a monomer in a thermodynamically unfavorable conformation [Chen, S. M., et al. (2002) Proc. Natl. Acad. Sci. U.S.A. 99, 11884-11889]. We re-examined this hypothesis by measuring the aggregation kinetics of the polyglutamine peptide K2Q23K2, using sedimentation, static and dynamic light scattering, and size exclusion chromatography. Our data show that during the lag time in sedimentation kinetics, there is substantial organization of the peptide into soluble linear aggregates. These aggregates have no regular secondary structure as measured by circular dichroism but have particle dimensions and morphologies similar to those of mature insoluble aggregates. The soluble aggregates constitute approximately 30% of the total peptide mass, form rapidly, and continue to grow over a period of hours to days, eventually precipitating. Once insoluble aggregates form, loss of monomer from the solution phase continues. Our data support an assembly mechanism for polyglutamine peptide more complex than that previously proposed.     

Modeling Multivalent Ligand-Receptor Interactions with Steric Constraints on Configurations of Cell-Surface Receptor Aggregates

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcεRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.     

Modeling the discoloration of a mixture of reactive textile dyes by commercial laccase

Degradation of a mixture of three reactive textile dyes (Reactive Black 5, Reactive Yellow 15 and Reactive Red 239), simulating a real textile effluent, by commercial laccase, was investigated in a batch reactor. The discoloration was appraised as a percentage of the absorbance reduction at the wavelength of maximum absorbance for each dye and as total color removal based in all visible spectrum. A significantly high discoloration was achieved in both cases, indicating the applicability of this method for textile wastewater treatment. Mathematical models were developed to simulate the kinetics of laccase catalyzed degradation of reactive dyes in mixtures. Like in single dye degradation, some of the reactions present an unusual kinetic behavior, corresponding to the activation of the laccase-mediator system. The kinetic constants of the models were estimated by minimizing the difference between the predicted and the experimental time courses. Although not perfect, the ability of the models in representing the experimental results suggests that they could be used in design and simulation applications.     

Mathematical modeling of nucleotide excision repair reveals efficiency of sequential assembly strategies

Nucleotide excision repair (NER) requires the concerted action of many different proteins that assemble at sites of damaged DNA in a sequential fashion. We have constructed a mathematical model delineating hallmarks and general characteristics for NER. We measured the assembly kinetics of the putative damage-recognition factor XPC-HR23B at sites of DNA damage in the nuclei of living cells. These and other in vivo kinetic data allowed us to scrutinize the dynamic behavior of the nucleotide excision repair process in detail. A sequential assembly mechanism appears remarkably advantageous in terms of repair efficiency. Alternative mechanisms for repairosome formation, including random assembly and preassembly, can readily become kinetically unfavorable. Based on the model, new experiments can be defined to gain further insight into this complex process and to critically test model predictions. Our work provides a kinetic framework for NER and rationalizes why many multiprotein processes within the cell nucleus show sequential assembly strategy.     

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.