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.     

酵母菌转化人参皂苷Rb1的动力学

在分批发酵中,对酵母菌转化人参皂苷的动力学进行了研究。应用Logistic方程和Luedeking-Piret方程,得到了描述分批发酵过程中,酵母菌体生长、底物消耗和产物合成的动力学模型及模型参数,并对实验数据与模型进行了验证比较,模型计算值与实验值拟合良好,所建模型能很好地描述酵母菌转化人参皂苷的动力学特征。为进一步研究和预测酵母菌生物转化过程奠定理论基础。     

Biochemical basis for whole-cell uptake kinetics: specific affinity, oligotrophic capacity, and the meaning of the michaelis constant

Formulations are presented that describe the concentration dependency of nutrient-limited transport and growth in molecular terms. They relate the rate of transport at steady state through a two-sequence process, transport and metabolism, to ambient concentrations according to the amounts and kinetic characteristics of the two rate-limiting proteins in these sequences. Sequences are separated by a metabolic pool. A novel feature of these formulations is the translation coefficient, which relates the transport rate attained at given ambient nutrient concentrations and membrane transporter characteristics to the nutrient concentrations sustained in the metabolic pools. The formulations, termed janusian kinetics, show that hyperbolic kinetics are retained during independent changes in transporter and enzyme contents or characteristics. Specific affinity (a degrees (A)) depends strongly on the amount and kinetic characteristics of the transporters; it is also mildly affected by the amount and characteristics of the rate-limiting enzyme. This kinetic constant best describes the ability to accumulate substrate from limiting concentrations. Maximal velocity (V(max)) describes uptake from concentrated solutions and can depend strongly on either limiting enzyme content or the associated content of transporters. The whole-cell Michaelis constant (K(T)), which depends on the ratio of rate-limiting enzyme to transporter, can be relatively independent of change in a degrees (A) and is best used to describe the concentration at which saturation begins to occur. Theory specifies that good oligotrophs have a large a degrees (A) for nutrient collection and a small V(max) for economy of enzyme, giving a small K(T). The product of the two constants is universally rather constant so that oligotrophy is scaled on a plot of a degrees (A) versus K(T), with better oligotrophs toward one end. This idea is borne out by experimental data, and therefore typical small difficult-to-culture aquatic bacteria may be classified as oligobacteria.     

根茎型植物扁秆荆三棱对光照强度和养分水平的生长响应及资源分配策略

自然界中光照和养分因子常存在时空变化,对植物造成选择压力。克隆植物可通过克隆生长和生物量分配的可塑性来适应环境变化。尽管一些研究关注了克隆植物对光照和养分因子的生长响应,但尚未深入全面了解克隆植物对光照和养分资源投资的分配策略。以根茎型草本克隆植物扁秆荆三棱(Bolboschoenus planiculmis)为研究对象,在温室实验中,将其独立分株种植于由2种光照强度(光照和遮阴)和4种养分水平(对照、低养分、中养分和高养分)交叉组成的8种处理组合中,研究了光照和养分对其生长繁殖及资源贮存策略的影响。结果表明,扁秆荆三棱的生长、无性繁殖及资源贮存性状均受到光照强度的显著影响,在遮阴条件下各生长繁殖性状指标被抑制。且构件的数目、长度等特征对养分差异的可塑性响应先于其生物量积累特征。在光照条件下,高养分处理的总生物量、叶片数、总根茎分株数、长根茎分株数、总根茎长、芽长度、芽数量等指标大于其他养分处理,而在遮阴条件下,其在不同养分处理间无显著差异,表明光照条件可影响养分对扁秆荆三棱可塑性的作用,且高营养水平不能补偿由于光照不足而导致的生长能力下降。光照强度显著影响了总根茎、总球茎及大、中、小球茎的生物量分配,遮阴条件下,总生物量减少了对地下部分根茎和球茎的分配,并将有限的生物量优先分配给小球茎。总根茎的生物量分配未对养分发生可塑性反应,而随着养分增加,总球茎分配下降,说明在养分受限的环境中球茎的贮存功能可缓冲资源缺乏对植物生长的影响。在相同条件下,根茎生物量对长根茎的分配显著大于短根茎,以保持较高的繁殖能力;而总球茎对有分株球茎的生物量分配小于无分株球茎,表明扁秆荆三棱总球茎对贮存功能的分配优先于繁殖功能。研究为进一步理解根茎型克隆植物对光强及基质养分环境变化的生态适应提供了依据。     

Circadian and infradian aspects of the cell cycle: from past to future

A review of some aspects of circadian and infradian rhythms of the cell cycle is given. The background is that the research of the last decade has given entirely new insights into the cell cycle as a dynamic process which occurs in waves. After some short historical notes on the development of methodology for study of cell kinetics, it is reviewed how the strong variability of this function was recognized from the 1960's. This again led to an increasing understanding of the rhythmic pattern of cell renewal in various tissues of the body. Conventional methods for studying cell population kinetics gave general insights into both circadian and infradian rhythms, but were hampered by several shortcomings. The techniques were time consuming, and usually one and only one parameter could be studied at a time. However, this general knowledge both had a strong impact on the understanding of cell kinetics and provided a basis for designing cancer chemotherapy. Today we are facing a new area in the study of cell population kinetics. New, rapid and automated methods for multiparameter studies of both cell kinetics and other biological properties of cell populations have given entirely new possibilities for cell kinetic research. Methods, mainly connected to analytical cytology, can discriminate subpopulations with varying kinetic properties, and also enable monitoring of cell proliferation in normal and malignant tissues of patients. Chronobiology has had a strong impact on the understanding of cell population kinetics in the body. In the light of the new developments in the fields of growth factors and their regulatory influences on the cell cycle, important and fundamental aspects of biological rhythms are now being elucidated.     

On the mechanistic origin of damped oscillations in biochemical reaction systems

A generalized reaction scheme for the kinetic interaction of two reactants in a metabolic pathway has been examined in order to establish what minimal mechanistic patterns are required to support a damped oscillatory transient-state kinetic behaviour of such a two-component system when operating near a steady state. All potentially oscillating sub-systems inherent in this scheme are listed and briefly characterized. The list includes several mechanistic patterns that may be frequently encountered in biological system (e.g. involving feedback inhibition, feed-forward activation, substrate inhibition or product activation), but also draw attention to some hitherto unforeseen mechanisms by which the kinetic interaction of two metabolites may trigger damped oscillations. The results can be used to identify possible sources of oscillations in metabolic pathways without detailed knowledge about the explicit rate equations that apply.     

Kinetics of light emission by photosynthetic systems: Second order light decay kinetics means elovich kinetics in a solid state reaction; 1.5 order light decay kinetics means second order reaction kinetics

Kinetics of biological light emission processes do not mean what they seem to mean, because measured light intensity is not proportional to reactant concentration but to reaction rate. Therefore, the differential equation for light decay is usually different from that of concentration decay, so that mass action interpretations cannot be applied directly to light intensity decay. An observed second order light decay for Chlorella at 6.5°C, implies Elovich solid state reaction kinetics, which agrees with other evidence for solid state processes in photosynthesis. An observed 1.5 order light decay for Cholorella at 28°C implies second order liquid or solid state reaction kinetics. First ordere light decay implies first order reaction kinetics.     

Kinetics of reactive azo-dye decolorization by Pseudomonas luteola in a biological activated carbon process

A laboratory-scale biological activated carbon (BAC) process was conducted to treat a reactive azo-dye (reactive red 22) by Pseudomonas luteola and the kinetics of azo-dye decolorization was investigated. The BAC-reactor removed 89% of reactive red 22 while P. luteola biofilm and suspended P. luteola reached a maximum growth rate at a steady-state condition. The azo-dye effluent from BAC-reactor met a discharge standard required by Taiwan government. The kinetic BAC-model, based on fundamental mechanisms, including surface diffusion, liquid-film mass transfer, Monod kinetics, growth of biofilm and suspended cells as well as shear loss of biofilm, was developed to describe the performance of biofilm attached on activated carbon in the azo-dye treatment process. The kinetic BAC-model predictions and experimental results for simultaneous adsorption and biodegradation of azo-dye contaminants were compared. It is shown that the fundamental mechanisms of BAC-process for azo-dye decolorization are not the simple addition but the synergetic combination of carbon adsorption and biodegradation of P. luteola strain. The major aspects of such synergism are the bioregeneration of the adsorbent and the reduction of the toxic effect of azo-dye contaminants in textile wastewater on P. luteola strain. The kinetic BAC-model not only provides insights into underlying mechanisms of adsorption and biodegradation but also can be used as a powerful tool to assist the design of a pilot-scale or full-scale BAC-process to treat azo-dye contaminants by P. luteola cells in textile wastewater.     

Herbivorous animals can mitigate unfavourable ratios of energy and material supplies by enhancing nutrient recycling

Recent evidence shows that high supply ratios of light and nutrients limit planktonic herbivore growth by lowering the nutritional quality of algae. Over longer time scales, however, grazers may ameliorate this effect by their impact on nutrient cycling. We examine this possibility using two species of the herbivorous zooplankter Daphnia and its algal prey under different light intensities and low phosphorus supply in laboratory microcosms. At high light, Daphnia biomass was limited for a substantial period because of low P content of algal cells. However, a gradual increase in Daphnia density eventually improved food quality through grazing and nutrient cycling and via a novel process involving positive density dependence. Competitive exclusion of one of the two Daphnia species occurred under low light but not under high light when algae were nutritionally unsuitable. Such stoichiometrically mediated interactions among herbivorous animals may represent important mechanisms that affect community structure and material flows in ecosystems.     

A cell-based approach to characterize antimicrobial compounds through kinetic dose response

The rapid spread of antibiotic resistance has created a pressing need for the development of novel drug screening platforms. Herein, we report on the use of cell-based kinetic dose response curves for small molecule characterization in antibiotic discovery efforts. Kinetically monitoring bacterial growth at sub-inhibitory concentrations of antimicrobial small molecules generates unique dose response profiles. We show that clustering of profiles by growth characteristics can classify antibiotics by mechanism of action. Furthermore, changes in growth kinetics have the potential to offer insight into the mechanistic action of novel molecules and can be used to predict off-target effects generated through structure–activity relationship studies. Kinetic dose response also allows for detection of unstable compounds early in the lead development process. We propose that this kinetic approach is a rapid and cost-effective means to gather critical information on antimicrobial small molecules during the hit selection and lead development pipeline.     

Kinetics of indole acetic acid-induced growth in hypocotyl sections of Vigna mdiata

The kinetics of auxin-induced elongation of segments from Vigna radiata (L.) Wilczek hypocotyls have been investigated using auxanometer measurements. Doseresponse curves were established for several well-defined parameters of the growth response. The experimental data revealed that different kinetic parameters were affected differently by increasing auxin concentrations. The dose-response curves are slightly sigmoid for fresh weight, nearly bell-shaped for total elongation or maximal elongation rate, and nearly linear for maximal growth acceleration. The effects of auxin concentration on regulation of growth orientation are discussed.
A biphasic response is observed mainly with segments taken from the middle of the hypocotyl ('C') which exhibit maximal growth rates. Segments from other levels, with lesser growth potentials, exhibit a very weak response. The two successive phases may then require different maturation states. Kinetics of the acceleration curves are very similar all along the hypocotyl and remain very homogeneous with increasing IAA concentrations.     

Kinetic model for the process of aerobic biodegradation of organic fraction of municipal solid waste

The kinetic model of biological oxidation of the organic fraction of municipal solid waste suspension is presented in this paper. The whole process of the aerobic biodegradation consists of three phases: the hydrolysis and intensive biodegradation phase, the limited biodegradation phase and the terminal phase. The first two phases play the most important role and the unstructured model is applied to successfully describe them. Kinetics of microbial decomposition of organic substances is described by the Monod equation. Also, a strong influence of temperature on the process kinetics is observed. The relation between a maximum specific growth rate and temperature is mathematically described.     

The impact of thiol peroxidases on redox regulation

The biology of glutathione peroxidases and peroxiredoxins is reviewed with emphasis on their role in metabolic regulation. Apart from their obvious function in balancing oxidative challenge, these thiol peroxidases are not only implicated in orchestrating the adaptive response to oxidative stress, but also in regulating signaling triggered by hormones, growth factors and cytokines. The mechanisms presently discussed comprise dampening of redox-sensitive regulatory processes by elimination of hydroperoxides, suppression of lipoxygenase activity, committing suicide to save H₂O₂ for signaling, direct binding to receptors or regulatory proteins in a peroxidase activity-independent manner, or acting as sensors for hydroperoxides and as transducers of oxidant signals. The various mechanistic proposals are discussed in the light of kinetic data, which unfortunately are scarce. Taking into account pivotal criteria of a meaningful regulatory circuit, kinetic plausibility and specificity, the mechanistic concepts implying a direct sensor/transducer function of the thiol peroxidases appear most appealing. With rate constants for the reaction with hydroperoxide of 10⁵–10⁸ M^{? 1} s^{? 1}, thiol peroxidases are qualified as kinetically preferred hydroperoxide sensors, and the ability of the oxidized enzymes to react with defined protein thiols lends specificity to the transduction process. The versatility of thiol peroxidases, however, allows multiple ways of interaction with regulatory pathways.     

Application of the Kinetic Triplets and Geometrical Characteristics of Thermal Analysis Curves in Identifying the Main Bioactive Compounds (BC) that Govern the Thermal and Thermo-Oxidative Degradation Mechanism of <Emphasis Type="Italic">Aronia melanocarpa</Emphasis> (Black Chokeberry)

Thermal and thermo-oxidative kinetics of Aronia melanocarpa fresh samples was investigated. The current investigation was based on the application of kinetic triplets and geometrical characteristics of thermal analysis curves in identifying the main bioactive compounds that govern the thermal and thermo-oxidative degradation mechanisms. From established kinetic model in an argon atmosphere, it was found that released products arise from decomposition of phenolic compounds where autocatalysis may occurs from the inevitable presence of water already in the early stages of the process through the hydrolysis reaction pathway. In the case of thermo-oxidative degradation, it was found that the main mechanistic scheme can be presented with two different forms of reaction mechanism function, such as: nth order reaction model (with n > 1) (in lower heating mode) and ?esták-Berggren autocatalytic model (in higher heating mode). Isoconversional analysis has been shown that neochlorogenic acid represents the governed bioactive compound which has a strong hydrogen-donating activity. Based on the mechanistic conclusions, it was established that in an air atmosphere, the cyanidin-3-glucosylrutinoside (Cy-3-GR) degradation significantly participates in overall complex mechanism.     

Effects of spatial variation of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold.

The effects of spatial variation of cells and nutrient and product concentration, in combination with product inhibition in cell growth kinetics on chondrocyte generation in a polymer scaffold, are analyzed. Experimental studies reported previously have demonstrated spatial dependence in the cultivation of chondrocytes. In the present study, the cell-polymer system is assumed to consist of two distinct phases. The cells, fluid, polymer matrix, and extracellular matrix comprise one phase, and the other phase consists of a fluid and polymer matrix. The only two species in the fluid considered to affect cell growth are the nutrient and product. The multiphase transport process of these two species in the cell-polymer system is described by the species continuity equations and corresponding boundary conditions for each individual phase. A volume-averaging approach is utilized for this system to derive averaged species continuity equations for the nutrient and product concentrations. The volume-averaging approach allows for a single species in a two-phase system to be represented by a single averaged continuity equation. Competitive product inhibition, saturation kinetics of substrate, and cell population control are assumed to affect the cell growth kinetics. A modified Contois growth kinetic model is used to represent the three factors that affect cell growth. A parameter analysis is performed and the results are compared qualitatively with experimental data found in the literature.     

Intraparticle diffusional effects in immobilized cell particles

Summary Immobilized cell technology frequently relies on the entrapment of the biomass in a gel particle, and it is generally observed that mass transfer limitations within the gel particle lead to nonuniform cell distribution. This note addresses the consequence of maintaining a very high cell mass density within a biopolymer particle. We illustrate that conventional effectiveness factor calculations can be used to determine particle sizes which would avoid nonuniform cell growth. The analysis is based on simple Monod kinetics. Special attention is given to near zero order kinetic systems in which the effectiveness factor remains high although the limiting nutrient may be depleted near the center of the particle. Mina Dalili is at the Department of Chemical Engineering, North Carolina State University     

Repulsive expansion dynamics in colony growth and gene expression

Spatial expansion of a population of cells can arise from growth of microorganisms, plant cells, and mammalian cells. It underlies normal or dysfunctional tissue development, and it can be exploited as the foundation for programming spatial patterns. This expansion is often driven by continuous growth and division of cells within a colony, which in turn pushes the peripheral cells outward. This process generates a repulsion velocity field at each location within the colony. Here we show that this process can be approximated as coarse-grained repulsive-expansion kinetics. This framework enables accurate and efficient simulation of growth and gene expression dynamics in radially symmetric colonies with homogenous z-directional distribution. It is robust even if cells are not spherical and vary in size. The simplicity of the resulting mathematical framework also greatly facilitates generation of mechanistic insights.     

The Good,the Bad,and the Tiny: A Simple,Mechanistic-Probabilistic Model of Virus-Nutrient Colimitation in Microbes

For phytoplankton and other microbes, nutrient receptors are often the passages through which viruses invade. This presents a bottom-up vs. top-down, co-limitation scenario; how do these would-be-hosts balance minimizing viral susceptibility with maximizing uptake of limiting nutrient(s)? This question has been addressed in the biological literature on evolutionary timescales for populations, but a shorter timescale, mechanistic perspective is lacking, and marine viral literature suggests the strong influence of additional factors, e.g. host size; while the literature on both nutrient uptake and host-virus interactions is expansive, their intersection, of ubiquitous relevance to marine environments, is understudied. I present a simple, mechanistic model from first principles to analyze the effect of this co-limitation scenario on individual growth, which suggests that in environments with high risk of viral invasion or spatial/temporal heterogeneity, an individual host’s growth rate may be optimized with respect to receptor coverage, producing top-down selective pressure on short timescales. The model has general applicability, is suggestive of hypotheses for empirical exploration, and can be extended to theoretical studies of more complex behaviors and systems.     

Chloroperoxidase-catalyzed oxidation of 4,6-dimethyldibenzothiophene as dimer complexes: evidence for kinetic cooperativity

A sigmoidal kinetic behavior of chloroperoxidase for the oxidation of 4,6-dimethyldibenzothiophene (4,6-DMDBT) in water-miscible organic solvent is for the first time reported. Kinetics of 4,6-DMDBT oxidation showed a cooperative profile probably due to the capacity of chloroperoxidase to recognize a substrate dimer (pi-pi dimer) in its active site. Experimental evidence is given for dimer formation and its presence in the active site of chloroperoxidase. The kinetic data were adjusted for a binding site able to interact with either monomer or dimer substrates, producing a cooperative model describing a one-site binding of two related species. Determination of kinetics constants by iterative calculations of possible oxidation paths of 4,6-DMDBT suggests that kinetics oxidation of dimer substrate is preferred when compared to monomer oxidation. Steady-state fluorometry of substrate in the absence and presence of chloroperoxidase, described by the spectral center of mass, supports this last conclusion.