Non-photochemical quenching kinetics during the dark to light transition in relation to the formation of antheraxanthin and zeaxanthin

Nonlinear regression analysis (NLR) is applied to quantify the dynamic response of non-photochemical fluorescence quenching (NPQ) of Trifolium repens cv. Regal upon dark to light transition. Commonly, only steady-state levels of NPQ are evaluated, ignoring transient kinetics. Experimental NPQ kinetics are fitted best with a sum of two functions: a sigmoidal Hill function plus a transient logarithmic normal function. It is shown that not only steady-state level of NPQ, but also the speed at which steady state is reached, increased with light intensity. The question is raised which biological processes cause the induction of the components of NPQ kinetics. The NPQ kinetics are found to resemble the kinetics of antheraxanthin and zeaxanthin formation during a dark to light transition. Furthermore, both molecules are known to induce NPQ. The hypothesis is put forward that a transient phase of NPQ (0-2 min after transition) is dependent upon concentrations of antheraxanthin, whereas the saturating phase corresponds with the production of zeaxanthin. A mathematical model, based on the presented hypothesis, predicts the effect of increasing light intensity on concentrations of antheraxanthin and zeaxanthin which correspond with experimental results. Implications of the hypothesis are discussed as well as the role of NLR in evaluating chlorophyll a fluorescence kinetics.     

Kinetics of protein subunit interactions: simulation of a polymerization overshoot

Theoretical calculations of the kinetics of a polymerization reaction have been carried out for a scheme in which there is a nucleation step that is slow relative to subsequent propagation steps. A transient maximum (overshoot) in molecular weight can be expected in such reversibly self-associating systems when polymerization is initiated suddenly. The extent of overshoot decreases with increasing initial concentration of true equilibrium is strongly dependent on the rate of nucleus formation and the rate of depolymerization when the absolute values of both are small relative to the rate of propagation.     

A biochemically structured model for Saccharomyces cerevisiae.

A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S(f), as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations.     

Temperature-dependent growth kinetics of Escherichia coli ML 30 in glucose-limited continuous culture.

Detailed comparison of growth kinetics at temperatures below and above the optimal temperature was carried out with Escherichia coli ML 30 (DSM 1329) in continuous culture. The culture was grown with glucose as the sole limiting source of carbon and energy (100 mg liter(-1) in feed medium), and the resulting steady-state concentrations of glucose were measured as a function of the dilution rate at 17.4, 28.4, 37, and 40 degrees C. The experimental data could not be described by the conventional Monod equation over the entire temperature range, but an extended form of the Monod model [mu = mu(max) x (s - s(min))/(Ks + s - s(min))], which predicts a finite substrate concentration at 0 growth rate (s(min)), provided a good fit. The two parameters mu(max) and s(min) were temperature dependent, whereas, surprisingly, fitting the model to the experimental data yielded virtually identical Ks values (approximately 33 microg liter(-1)) at all temperatures. A model that describes steady-state glucose concentrations as a function of temperature at constant growth rates is presented. In similar experiments with mixtures of glucose and galactose (1:1 mixture), the two sugars were utilized simultaneously at all temperatures examined, and their steady-state concentrations were reduced compared with to growth with either glucose or galactose alone. The results of laboratory-scale kinetic experiments are discussed with respect to the concentrations observed in natural environments.     

A kinetic model for the impact of packaging signal mimics on genome encapsulation

Inspired by recent experiments on the spontaneous assembly of virus-like particles from a solution containing a synthetic coat protein and double-stranded DNA, we put forward a kinetic model that has as main ingredients a stochastic nucleation and a deterministic growth process. The efficiency and rate of DNA packaging strongly increase after tiling the DNA with CRISPR-Cas proteins at predesignated locations, mimicking assembly signals in viruses. Our model shows that treating these proteins as nucleation-inducing diffusion barriers is sufficient to explain the experimentally observed increase in encapsulation efficiency, but only if the nucleation rate is sufficiently high. We find an optimum in the encapsulation kinetics for conditions where the number of packaging signal mimics is equal to the number of nucleation events that can occur during the time required to fully encapsulate the DNA template, presuming that the nucleation events can only take place adjacent to a packaging signal. Our theory is in satisfactory agreement with the available experimental data.     

An autocatalytic reaction as a model for the kinetics of the aggregation of beta-amyloid

Alzheimer's disease is the commonest form of senile dementia, affecting almost 20 million people worldwide. This neurodegenerative disorder is characterized by amyloid deposition in senile plaques, composed primarily of fibrils of an aggregated peptide, beta-amyloid. Fibrillation of beta-amyloid is a nucleation-dependent polymerization process, which is controlled by two kinetics parameters: the nucleation rate and the elongation or growth rate. As the kinetics of fibrillation is strongly dependent on the presence of trace amounts of fibrils, we suggest that the aggregation of beta-amyloid is a model of autocatalytic reaction. A mathematical analysis, permitting quantitative monitoring of the kinetics of fibrillogenesis of beta-amyloid, nucleation, and elongation constants, is presented. The model was checked by applying it to the aggregation of the fragment 1-40 of the beta-amyloid. Understanding of these rate constants may facilitate the study of the effect of substances used for controlling fibril creation and growth. The disaggregating effect of dodecyl trimethylammonium bromide, a cationic surfactant, was easily quantified by means of the model.     

The effect of mono- and divalent salts on the rise and decay kinetics of EPR signal II in Photosystem II preparations from spinach

The rise and decay kinetics of EPR signal II have been used to probe the organization of the donor side of Photosystem II (PS II) before and after extraction of PS II preparations with high concentrations of salt. 800 mM NaCl or 500-800 mM NaBr substantially depletes the preparations of the 16 and 24 kDa proteins and decreases the steady-state rate of O2-evolution by 70-80% from control rates. These treatments do not largely alter the decay kinetics of Signal II; the rise kinetics remain in the instrument limited time range (2 microseconds or less) during the first 8-12 flashes. Treating PS II preparations with 800 mM CaCl2 removes the 16, 24 and 33 kDa proteins with at least 95% inhibition of the steady-state rates of O2 evolution. The additional removal of the 33 kDa polypeptide decreases the rates of oxidation and rereduction of Z, the species responsible for Signal II. Preparations treated with either mono- or divalent salts show a steady-state light-induced increase in Signal II similar to that seen in Tris-washed samples. Such a steady-state increase indicates that the rate of electron transport from water to Z is greatly decreased or blocked. The data are interpreted within a model in which there is an intermediate electron carrier between the O2 evolving complex and Z.     

Kinetic studies on photolysis-induced gelation of sickle cell hemoglobin suggest a new mechanism.

The kinetics of deoxyhemoglobin S gelation have been investigated using photolytic dissociation of the carbon monoxide complex to initiate the process. Measurements over a wide range of times, 10(-3)-10(4) show that both the concentration dependence of the tenth-time (i.e., the time required to complete one-tenth the reaction) and the time dependence of the process decrease as gelation speeds up. In slowly gelling samples, where single domains of polymers are formed in the small sample volumes employed with this technique (1-2 x 10(-9) cm3), there is a marked increase in the variability of the tenth-times. These results are explained by a mechanism in which gelation is initiated by homogeneous nucleation of polymers in the bulk solution phase, followed by heterogeneous nucleation on the surface of existing polymers. At the lowest concentrations, homogeneous nucleation is so improbable that stochastic behavior is observed in the small sample volumes, and heterogeneous nucleation is the dominant pathway for polymer formation, thereby accounting for the high time dependence. At the highest concentrations homogeneous nucleation becomes much more probable, and the time dependence decreases. The decrease in concentration dependence of the tenth-time with increasing concentration results from a decrease in size of both the homogeneous and heterogeneous critical nuclei. The model rationalizes the major observations on the kinetics of gelation of deoxyhemoglobin S, and is readily testable by further experiments.     

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.     

Interpretation of the renaturation kinetics of gelatin solutions

Renaturation kinetics of dilute gelatin solutions are studied by optical rotation and u.v. absorption. Comparing initial slopes of renaturation curves for concentrations below 10 mg.ml-1, the rate limiting process appears as the sum of a constant rate intramolecular nucleation and a bimolecular nucleation. To fit the whole renaturation curves, a kinetic model using Monte Carlo calculations was tested, consisting of random nucleation, rapid total propagation and slow reversion depending on the size of helical segment. Mismatch on the final renaturation extent indicates that propagation is more limited than proposed.     

Transient growth- and product-formation kinetics of acetic acid bacteria

Rates of growth and product formation under non-stationary conditions were measured in fermentations of industrial acetic acid bacteria. A repeated-batch process, where conditions change rapidly, and a slower shift experiment in CSTR culture were examined. Significant deviations from the steady-state kinetics determined in continuous fermentations were found for cell growth as well as for the formation of acetic acid. Algebraic functions of the inhibiting acid concentration were identified to describe the rates of reaction under stationary conditions. Transient kinetics are modeled by phenomenological differential equations. The data from both the repeated-batch experiments and the CSTR shift is consistently reproduced. Measurements and simulation results are presented in phase diagrams of the reaction rates over the concentration of acetic acid. Due to the dynamic effects, which enhance the transient rates of both growth and product formation, the repeated-batch process is superior to a continuous fermentation in terms of total volumetric productivity and final acid concentration.     

Osmolyte controlled fibrillation kinetics of insulin: New insight into fibrillation using the preferential exclusion principle

Amyloid proteins are converted from their native‐fold to long β‐sheet‐rich fibrils in a typical sigmoidal time‐dependent protein aggregation curve. This reaction process from monomer or dimer to oligomer to nuclei and then to fibrils is the subject of intense study. The main results of this work are based on the use of a well‐studied model amyloid protein, insulin, which has been used in vitro by others. Nine osmolyte molecules, added during the protein aggregation process for the production of amyloid fibrils, slow‐down or speed up the process depending on the molecular structure of each osmolyte. Of these, all stabilizing osmolytes (sugars) slow down the aggregation process in the following order: tri > di > monosaccharides, whereas destabilizing osmolytes (urea, guanidium hydrochloride) speed up the aggregation process in a predictable way that fits the trend of all osmolytes. With respect to kinetics, we illustrate, by adapting our earlier reaction model to the insulin system, that the intermediates (trimers, tetramers, pentamers, etc.) are at very low concentrations and that nucleation is orders of magnitude slower than fibril growth. The results are then collated into a cogent explanation using the preferential exclusion and accumulation of osmolytes away from and at the protein surface during nucleation, respectively. Both the heat of solution and the neutral molecular surface area of the osmolytes correlate linearly with two fitting parameters of the kinetic rate model, that is, the lag time and the nucleation rate prior to fibril formation. These kinetic and thermodynamic results support the preferential exclusion model and the existence of oligomers including nuclei and larger structures that could induce toxicity. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

An appraisal of the role of biliary phospholipases in the pathogenesis of gallstone disease

Human bile contains proteins that influence nucleation of cholesterol. Recently, it has been suggested that activity of phospholipases in bile may play a role in this process. To study the influence of phospholipase on nucleation we have determined the effect of phospholipases A2, C and D on the nucleation time of model bile. Phospholipase C decreased the nucleation time, whereas phospholipase A2 inhibited nucleation. The phospholipases were effective only at relatively high concentrations. Phospholipase D was strongly inhibited in model bile and probably only influenced the nucleation time by an aspecific protein effect. The cleavage products of the different phospholipases were determined in native bile samples of 14 cholesterol gallstone patients, 6 patients without stones and 4 patients with pigment stones. In all samples, choline, phosphorylcholine and free fatty acids (FFA) could be detected. However, there was no significant difference between the three groups of patients. The rate of production of choline, phosphorylcholine and FFA was measured in bile incubated at 37 degrees C. Again, there was no significant difference between the three groups of patients. We conclude that phospholipase activity in bile does not play an important role in the pathogenesis of gallstone disease.     

Kinetic study of hybridoma cell growth in continuous culture. I. A model for non-producing cells

The kinetic behavior of a nonproducing hybridoma clone AFP-27-NP was investigated in continuous culture under glucose-limited conditions. A total of more than 21, 000 h of cultures were operated at dilution rates ranging from 0.01 to 0.06 h(-1). The viable cell concentrations, dead cell concentrations, and cell volumes all varied with the dilution rate. A steady-state model was developed based on the biomass concentration and the glucose concentration. The specific growth rate as a function of glucose concentration is described by a model similar to the Monod model with a threshold glucose concentration and a minimum specific growth rate incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. A death rate is included in the model which is described by an inverted Monod-type function of glucose concentration. The yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper region of specific growth rates. No maintenance term for glucose consumption was needed; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepted the specific growth rate axis at a value close to the minimum growth rate. The values for the model parameters were determined from regression analysis of the steady-state data. The model predictions and experimental results fit very well.     

The relationship between kinetics of substrate-limited transitions and steady-state growth in continuous cultures ofAquaspirillum autotrophicum limited by pyruvate

Heterotrophic growth at steady state and during transient states caused by the sudden change of the concentration of the limiting factor in the feed medium was investigated experimentally for continuous cultures ofAquaspirillum autotrophicum limited by pyruvate. A model for describing the growth at steady state was selected from three unstructured models after statistical tests of the data. This model postulates that the growth yield increases linearly with the growth rate. Growth during transitions where the substrate remained limiting at all times was fitted with first-order kinetics. Theoretical predictions of these kinetics were derived from the unstructured models used to describe steady state. The predicted rate coefficients of the transients were compared to the experimental coefficients. It appeared that the model which best described steady-state growth also provided the best predictions for growth during the transient state. It is a widespread opinion that unstructured models are adequate to describe growth under steady-state conditions but not to predict transitions in continuous culture. However, for the particular case studied here, no higher degree of complexity was required to describe transitions, provided the growth of the culture was always limited by the substrate.     

Kinetics of sickle hemoglobin polymerization. III. Nucleation rates determined from stochastic fluctuations in polymerization progress curves

The polymerization kinetics of sickle cell hemoglobin are found to exhibit stochastic variations when observed in very small volumes (approximately 10(-10) cm3). The distribution of progress curves has been measured at several temperatures for a 4.50 mM-hemoglobin S sample using a laser-photolysis, light-scattering technique. The progress curves at a given temperature are superimposable when translated along the time axis, showing that the variability of the kinetic progress curves results primarily from fluctuations in the time at which polymerization is initiated. The shapes of the initial part of the progress curves are well-fitted using the functional form I(t) = Io + As exp (Bt), derived from a dual nucleation model. When the distribution of the measured tenth times is broad, the rate of homogeneous nucleation can be obtained by fitting the exponential tail of the distribution. As the distribution sharpen, the rate of homogeneous nucleation can be estimated by modelling the width of the distribution function using a simple Monte-Carlo simulation of the polymerization kinetics. Using the rates of homogeneous nucleation obtained from the distributions, the rates of heterogeneous nucleation and polymer growth can be obtained from the experimental parameters As and B. The resulting nucleation rates are roughly 1000 times greater than those obtained from an analysis of bulk kinetic data. The results provide strong support for the dual-nucleation mechanism and show that the distribution of progress curves provides a powerful independent method for measuring the rate of homogeneous nucleation and thereby obtaining values for the other principal rates of the mechanism.     

A simple model to describe transient differences between cell number and biomass growth rates of Escherichia coli

Information on the response of a microbial culture to dynamic environmental conditions is necessary for the design of transient operation processes. However, most attempts at modelling culture response have been directed at describing the steady-state behavior. Thus, there is a need for adequate dynamic models for process design. Simulations of nutrient shifts were completed using a "single-cell" model for Escherichia coli. It was discovered that the specific mass growth rate and the specific number of cells growth rate were different under transient conditions, whereas at steady state (balanced growth) these rates are equivalent. Using these observations, a simple delay model to describe the transient behavior of the two growth rates is formulated and tested. The model contains as state variables only the readily measurable macroscopic quantities (biomass, cell number, and limiting nutrient). This model agreed well with the predictions of the single-cell model.     

Non-native aggregation of alpha-chymotrypsinogen occurs through nucleation and growth with competing nucleus sizes and negative activation energies

The kinetics and structural transitions of non-native aggregation of alpha-chymotrypsinogen (aCgn) were investigated over a wide range of temperature and initial protein concentration at pH 3.5, where high molecular weight aggregates remained soluble throughout the reaction. A comparison of thermodynamic, kinetic, and spectroscopic data shows that aggregation under non-native-favoring conditions proceeds through a molten globule unfolded monomer state, with a nucleation and growth mechanism. Formation of irreversible aggregates and conversion to beta-sheet secondary structures occur simultaneously without detectable intermediates, suggesting that beta-sheet formation may be a commitment step during the nucleation and growth stages. Analysis of the kinetics using a Lumry-Eyring with nucleated polymerization (LENP) model provides the predominant nucleus size and the product of the intrinsic nucleation and intrinsic growth time scales at each state point. We find that the nucleus size depends on both temperature and protein concentration, and in some cases there is competition between two distinct nucleus sizes. The observed rate coefficient (kobs) for aggregation displays a maximum as a function of temperature because of the competition between folding-unfolding thermodynamics and the intrinsic growth and nucleation rates; the latter contribution has a large, negative activation enthalpy that dominates kobs at elevated temperatures. Temperature-jump experiments reveal that aggregates depolymerize at high temperatures, indicating that they are lower in enthalpy than the free monomer. Overall, the results suggest more generally that non-native aggregation may proceed through more than one nucleus size and that intrinsic kinetics of nucleation and growth may have significant entropic barriers.     

On the utility of a compartmental population kinetics model of intestinal epithelial stem cell proliferation and differentiation

Background

The small intestinal epithelium is a dynamic system with specialized cell types. The various cell populations of this tissue are continually renewed and replenished from stem cells that reside in the small intestinal crypt. The cell types and their locations in the crypt and villus are well known, but the details of the kinetics of stem cell division, and precursor cell proliferation and differentiation into mature enterocytes and secretory cells are still being studied. These proliferation and differentiation events have been extensively modeled with a variety of computational approaches in the past.

Methods

A compartmental population kinetics model, incorporating experimentally measured proliferation rates for various intestinal epithelial cell types, is implemented for a previously reported scheme for the intestinal cell dynamics. A sensitivity analysis is performed to determine the effect that varying the model parameters has upon the model outputs, the steady-state cell populations.

Results

The model is unable to reproduce the experimentally known timescale of renewal of the intestinal epithelium if literature values for the proliferation rates of stem cells and transit amplifying cells are employed. Unphysically large rates of proliferation result when these parameters are allowed to vary to reproduce this timescale and the steady-state populations of terminally differentiated intestinal epithelial cells. Sensitivity analysis reveals that the strongest contributor to the steady-state populations is the transit amplifying cell proliferation rate when literature values are used, but that the differentiation rate of transit amplifying cells to secretory progenitor cells dominates when all parameters are allowed to vary.

Conclusions

A compartmental population kinetics model of proliferation and differentiation of cells of the intestinal epithelium can provide a simplifying means of understanding a complicated multistep process. However, when literature values for proliferation rates of the crypt based columnar and transit amplifying cell populations are employed in the model, it cannot reproduce the experimentally known timescale of intestinal epithelial renewal. Nevertheless, it remains a valuable conceptual tool, and its sensitivity analysis provides important clues for which events in the process are the most important in controlling the steady-state populations of specialized intestinal epithelial cells.

     

Mass-transfer and kinetics of microencapsulated alpha-chymotrypsin action]

A theoretical model for transient and steady-state kinetics of microencapsulated enzymes action has been developed. The model is meant to overcome the diffusional limitations, caused by a microcapsulated membrane. The effects of various parameters (enzymatic reaction rate constants, enzyme concentration in microcapsules, membrane permeability, substrate concentration, and bulk pH values) on the overall apparent reaction rate have been analyzed using esters hydrolysis catalyzed by alpha-chymotrypsin encapsulated into polycarbonate membranes as an example.