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.     

A kLa identification technique for a dynamic model of the coupled system: Air-lift fermenter — oxygen probes

The time delay of oxygen probe response to the signal from a fermenter makes identification of the volumetric oxygen transfer coefficient k_La by the dynamic method more complicated. A coupled model involving the transient-state oxygen balance of the fermenter together with the dynamic model of the oxygen probe must be then formulated, solved and identified. In this paper two simple models of air-lift loop fermenters have been proposed and a coupled mathematical model of the fermenter – oxygen probe system has been developed. The identification procedure was used to estimate k_La values in the fermenter with internal circulation flow on the basis of experimental measurements. A comparison of evaluated and experimental indications of the probes placed at various heights of the column proves that the model presented gives a possibility of the first-step approximation of k_La in loop fermenters.     

Kinetic analysis of biphasic protein modification reactions cooperative effects

A mathematical treatment of protein modification reactions is presented, and it is shown thai in these cases protein modification is described by a summation of exponential functions of reaction time, the number of exponentials being equal to the number of modified protein species. It is shown that in cases of protein modification cooperativity, there is a strict dependence of the coefficients of the multiexponential modification equation on the constants of the same equation. The conditions necessary for a reduction of a multiexponential protein modification equation to one of a summation of two exponentials only are examined. The possible formulae for the coefficients of a two-exponential-summation equation, used to describe the modification of protein models with two, three or four modifiable residues (as well as some aspects of models with five and six modifiable residues) per protein molecule are derived. It is seen that the number of such coefficients is severely limited. The most frequently obtained formula for the lower stoichiomelric coefficient of a 'wo-exponential-summation equation is Ak_a/(k_a-k_b). where k_b and k_b are the constants of the two exponentials of the equation, and A is a constant. The value most frequently arrived at for A is (n?1)/n, where n is the number of modifiable residues per protein molecule, while values such as 1/n, or a/n (where a is an integer, and also where a < n) are also possible. In most of the cooperative protein modification models worked out, k_a is identical with k_n, viz., k_a is identical with the rate constant for the first stoichiometric protein modification.     

Predicting kinetic constants of protein-protein interactions based on structural properties

Elucidating kinetic processes of protein–protein interactions (PPI) helps to understand how basic building blocks affect overall behavior of living systems. In this study, we used structure‐based properties to build predictive models for kinetic constants of PPI. A highly diverse PPI dataset, protein–protein kinetic interaction data and structures (PPKIDS), was built. PPKIDS contains 62 PPI with complex structures and kinetic constants measured experimentally. The influence of structural properties on kinetics of PPI was studied using 35 structure‐based features, describing different aspects of complex structures. Linear models for the prediction of kinetic constants were built by fitting with selected subsets of structure‐based features. The models gave correlation coefficients of 0.801, 0.732, and 0.770 for k_off, k_on, and K_d, respectively, in leave‐one‐out cross validations. The predictive models reported here use only protein complex structures as input and can be generally applied in PPI studies as well as systems biology modeling. Our study confirmed that different properties play different roles in the kinetic process of PPI. For example, k_on was affected by overall structural features of complexes, such as the composition of secondary structures, the change of translational and rotational entropy, and the electrostatic interaction; while k_off was determined by interfacial properties, such as number of contacted atom pairs per 100 Ų. This information provides useful hints for PPI design. Proteins 2010;79:720–734. © 2010 Wiley‐Liss, Inc.     

A new dynamic model for highly efficient mass transfer in aerated bioreactors and consequences for kLa identification

Gas–liquid mass transfer is often rate‐limiting in laboratory and industrial cultures of aerobic or autotrophic organisms. The volumetric mass transfer coefficient k_La is a crucial characteristic for comparing, optimizing, and upscaling mass transfer efficiency of bioreactors. Reliable dynamic models and resulting methods for parameter identification are needed for quantitative modeling of microbial growth dynamics. We describe a laboratory‐scale stirred tank reactor (STR) with a highly efficient aeration system (k_La ≈ 570 h^?1). The reactor can sustain yeast culture with high cell density and high oxygen uptake rate, leading to a significant drop in gas concentration from inflow to outflow (by 21%). Standard models fail to predict the observed mass transfer dynamics and to identify k_La correctly. In order to capture the concentration gradient in the gas phase, we refine a standard ordinary differential equation (ODE) model and obtain a system of partial integro‐differential equations (PIDE), for which we derive an approximate analytical solution. Specific reactor configurations, in particular a relatively short bubble residence time, allow a quasi steady‐state approximation of the PIDE system by a simpler ODE model which still accounts for the concentration gradient. Moreover, we perform an appropriate scaling of all variables and parameters. In particular, we introduce the dimensionless overall efficiency κ, which is more informative than k_La since it combines the effects of gas inflow, exchange, and solution. Current standard models of mass transfer in laboratory‐scale aerated STRs neglect the gradient in the gas concentration, which arises from highly efficient bubbling systems and high cellular exchange rates. The resulting error in the identification of κ (and hence k_La) increases dramatically with increasing mass transfer efficiency. Notably, the error differs between cell‐free and culture‐based methods of parameter identification, potentially confounding the determination of the “biological enhancement” of mass transfer. Our new model provides an improved theoretical framework that can be readily applied to aerated bioreactors in research and biotechnology. Biotechnol. Bioeng. 2012; 109: 2997–3006. © 2012 Wiley Periodicals, Inc.     

Use of glucose oxidase system in measuring aeration capacity of fermentors. Comparison of the dynamic and steady-state methods of kla measurement

A steady-state method for k_la determination has been presented using the Michaelis–Menten two-substrate kinetic equation for oxidation of glucose in the presence of the enzymes glucose oxidase and excess catalase. The conditions have been specified where spontaneous hydrolysis of lactone is sufficiently rapid, thus eliminating inhibitory action of lactone on the oxidation. In glucose oxidase-free batches, the k_la values were determined using various modification of the dynamic method. The dynamic methods in which gas interchange was effected without interrupting aeration and agitation of the batch yielded erroneously lower k_la values as compared to the results of steady-state methods if the measured k_la value was higher than 0.03 s^?1. The values yielded by the dynamic method in which the gas interchange was effected at the same time with turning on aeration and agitation of the batch agreed with values resulting from the steady-state method provided that the measured k_la values were lower than 0.08^?1 and the simultaneous interfacial transport of nitrogen and oxygen had been taken into account in the evaluation. At k_la values higher than 0.08 ^?1, this modification of the dynamic method also yielded lower k_la values as compared with the outcome of the steady-state method. The experiments performed do not, however, allow one to decide unambiguously on the whether these lower k_la values are due to failure of the adopted model to describe adequately the dynamic behavior of the system or whether they are true values differing from those yielded by the steady-state method on account of different physical properties of compared batches.     

Kinetic behavior of heterogeneous populations in completely mixed reactors

The kinetic behavior of heterogeneous microbial populations was studied in a continuous flow completely mixed reactor operated at various dilution rates. Glucose was used as the growth-limiting nutrient. The physiological growth parameters for cells harvested from continuous flow reactors were determined using batch experiments. It, was found that the growth parameters, maximum growth rate (μ_m), saturation constant (k_s), and cell yield (Y) vary for each dilution rate, and cannot be considered as precise constants in depicting the kinetic behavior of heterogeneous populations. In addition, it was found that the yield coefficients obtained from batch experiments were always lower than those obtained from continuous flow experiments. Levels of substrate and biological solids calculated for different dilution rates using growth constants from batch experiments did not agree with the experimental values observed in steady-state experiments. However, when the yield values from, the continuous flow experiments were used in conjunction with batch values for μ_m and k_s the theoretical and experimental dilute-out curves agreed fairly closely (within the range needed for engineering prediction) until the culture began to wash out of the unit. In general, the data substantiated the use of the single phase relationship between growth rate and substrate concentration described by the Monod equation, μ = μ_mS/(k_s + s).     

A joint experimental and theoretical investigation of kinetics and mechanistic study in a synthesis reaction between triphenylphosphine and dialkyl acetylenedicarboxylates in the presence of benzhydrazide

Stable crystalline phosphorus ylides were obtained in excellent yields from the 1:1:1 addition reaction between triphenylphosphine (TPP) and dialkyl acetylenedicarboxylates, in the presence of NH-acids, such as benzhydrazide. To determine the kinetic parameters of the reactions, they were monitored by UV spectrophotometery. The second order fits were automatically drawn and the values of the second order rate constant (k₂) were calculated using standard equations within the program. At the temperature range studied the dependence of the second order rate constant (Ln k₂) on reciprocal temperature was compatible with Arrhenius equation. This provided the relevant plots to calculate the activation energy of all reactions. Furthermore, useful information were obtained from studies of the effect of solvent, structure of reactants (different alkyl groups within the dialkyl acetylenedicarboxylates) and also concentration of reactants on the rate of reactions. On the basis of experimental data the proposed mechanism was confirmed according to the obtained results and a steady state approximation and the first step (k₂) and third (k₃) steps of the reactions were recognized as the rate determining steps, respectively. In addition, three speculative proposed mechanisms were theoretically investigated using quantum mechanical calculation. The results, arising from the second and third speculative mechanisms, were far from the experimental data. Nevertheless, there was a good agreement between the theoretical kinetic data, emerge from the first speculative mechanism, and experimental kinetic data of proposed mechanism.

Using CFD simulations and statistical analysis to correlate oxygen mass transfer coefficient to both geometrical parameters and operating conditions in a stirred-tank bioreactor

Optimization of a bioreactor design can be an especially challenging process. For instance, testing different bioreactor vessel geometries and different impeller and sparger types, locations, and dimensions can lead to an exceedingly large number of configurations and necessary experiments. Computational fluid dynamics (CFD), therefore, has been widely used to model multiphase flow in stirred-tank bioreactors to minimize the number of optimization experiments. In this study, a multiphase CFD model with population balance equations are used to model gas–liquid mixing, as well as gas bubble distribution, in a 50 L single-use bioreactor vessel. The vessel is the larger chamber in an early prototype of a multichamber bioreactor for mammalian cell culture. The model results are validated with oxygen mass transfer coefficient (k_La) measurements within the prototype. The validated model is projected to predict the effect of using ring or pipe spargers of different sizes and the effect of varying the impeller diameter on k_La. The simulations show that ring spargers result in a superior k_La compared to pipe spargers, with an optimum sparger-to-impeller diameter ratio of 0.8. In addition, larger impellers are shown to improve k_La. A correlation of k_La is presented as a function of both the reactor geometry (i.e., sparger-to-impeller diameter ratio and impeller-to-vessel diameter ratio) and operating conditions (i.e., Reynolds number and gas flow rate). The resulting correlation can be used to predict k_La in a bioreactor and to optimize its design, geometry, and operating conditions.     

Study of the thermal stability of D-amino acid oxidase from Trigonopsis variabilis reveals enzyme inactivation via multiple steps

The thermal stability of a highly purified preparation of D-amino acid oxidase from Trigonopsis variabilis (TvDAO), which does not show microheterogeneity due to the partial oxidation of Cys-108, was studied based on dependence of temperature (20–60°C) and protein concentration (5–100 µmol L^?1). The time courses of loss of enzyme activity in 100 mmol L^?1 potassium phosphate buffer, pH 8.0, are well described by a formal kinetic mechanism in which two parallel denaturation processes, partial thermal unfolding and dissociation of the FAD cofactor, combine to yield the overall inactivation rate. Estimates from global fitting of the data revealed that the first-order rate constant of the unfolding reaction (k_a) increased 10⁴-fold in response to an increase in temperature from 20 to 60°C. The rate constants of FAD release (k_b) and binding (k_?b) as well as the irreversible aggregation of the apo-enzyme (k_agg) were less sensitive to changes in temperature, their activation energy (E_a) being about 52 kJ mol^?1 in comparison with an E_a value of 185 kJ mol^?1 for k_a. The rate-determining step of TvDAO inactivation switched from FAD dissociation to unfolding at high temperatures. The model adequately described the effect of protein concentration on inactivation kinetics. Its predictions regarding the extent of FAD release and aggregation during thermal denaturation were confirmed by experiments. TvDAO is shown to contain two highly reactive cysteines per protein subunit whose modification with 5,5′-dithio-bis (2-nitrobenzoic acid) was accompanied by inactivation. Dithiothreitol (1 mmol L^?1) enhanced up to 10-fold the recovery of enzyme activity during ion exchange chromatography of technical-grade TvDAO. However, it did not stabilize TvDAO at all temperatures and protein concentrations, suggesting that deactivation of cysteines was not responsible for thermal denaturation.     

Prey capture tactics of spiders: An analysis based on a simulation model for spider's growth

The prey capture tactics of spiders was analyzed, considering the energy gained by the capture of prey and that required for it. For the purpose of it, a growth model of spiders was constructed, expressing the flow rate of prey biomass to the spider's body by differential equations. Solving these equations under the differing values of three parameters, growth curves of spiders was obtained. These three parameters are the amount of prey biomass supplied daily to spiders, x₀, the rate of prey capture of spiders, α, and a coefficient of the respiration rate required for the capture of prey, k. When the value of k increased, spiders could grow only at high value of x₀. These results suggest that habitats with small prey biomass are preferred by spiders adopting a sit-and-wait tactics for prey capture, which requires small values of k. Wolf spiders are one of these spiders showing that tactics. On the other hand, web-builders which require large amount of energy for spinning webs (namely, take large value of k), are able to grow only in the habitats with large prey biomass. Each species of spiders are considered to locate in a certain point between both extremes of these tactics for the capture of prey.     

On-line estimation of kLa by an analog computer

A new method was developed for estimating the volumetric oxygen transfer coefficient, k_La, in a fermentor. Various methods were investigated for the on-line estimation of k_La with an analog computer employing a steepest-descent calculation technique. The method by which k_La is estimated (by minimizing the error residue of the model) was found to be very applicable. A method for the simultaneous estimation of the volumetric oxygen transfer coefficient and respiration rate in biological systems is also presented.     

Analytical method for simultaneously measuring ex vivo drug receptor occupancy and dissociation rate: Application to (R)-dimethindene occupancy of central histamine H1 receptors

We introduce a novel experimental method to determine both the extent of ex vivo receptor occupancy of administered compound and its dissociation rate constant (k₄). [Here, we reference k₄ as the rate of offset of unlabeled ligand in convention with Motulsky and Mahan ()]. We derived a kinetic rate equation based on the dissociation rate constant for an unlabeled compound competing for the same site as a labeled compound and describe a model to simulate fractional occupancy. To validate our model, we performed in vitro kinetics and ex vivo occupancy experiments in rat cortex with varying concentrations of (R)-dimethindene, a sedating antihistamine. Brain tissue was removed at various times post oral administration, and histamine H1 receptor ligand [³H]-doxepin binding to homogenates from drug-treated or vehicle-treated rats was measured at multiple time points at room temperature. Fractional occupancy and k₄ for (R)-dimethindene binding to H1 receptors were calculated by using our proposed model. Rats dosed with 30 and 60?mg/kg (R)-dimethindene showed 42% and 67% occupancy of central H1 receptors, respectively. These results were comparable to occupancy data determined by equilibrium radioligand binding. In addition, drug k₄ rate determined by using our ex vivo method was equivalent to k₄determined by in vitro competition kinetics (dissociation half-life t_1/2 ~ 30?min). The outlined method can be used to assess, by simulation and experiment, occupancy for compounds based on dissociation rate constants and contributes to current efforts in drug optimization to profile antagonist efficacy in terms of its kinetic drug-target binding parameters. Data described by the method may be analyzed with commercially available software. Suggested fitting procedures are given in the appendix.     

A mathematical model for the vertical distribution of chlorophyllA in estuarine intertidal sediments

Coastal and estuarine intertidal sediments are commonly colonized by dense populations of microphytobenthos. Due to wind and tides, important fractions of microphytobenthic populations may be buried. A mathematical model describing the depth variation of chlorophyll a in intertidal sediments was developed and experimentally tested. The model assumed first-order chlorophylla degradation and a constant mean burial velocity which resulted in a negative exponential variationC _Z =C _O exp{-k/vz} (C _Z andC _O =chlorophylla concentration at depth zand at the surface;k=specific degradation rate of chlorophyll a to pheopigments;V=mean burial velocity). Chlorophylla concentration depth profiles in different sediment types measured at the Tagus estuary and Ria Formosa (Portugal) were used to validate the model. The model was adjusted to field data. The chlorophyll a degradation rate was measured in a microcosm experiment under total darkness and no tidal action, and sampled during three months. This rate was shown to be independent of time and depth for the upper 0–15 mm depth interval. This result allowed the estimation ofV for each sampling site. Comparison of predicted and observed temporal data further confirmed the validity of the model andk andV values. Despite its simplicity, the proposed model adequately described the depth distribution of chlorophylla in different types of intertidal sediments. The model allowed the quantitative characterization of the buried microphytobenthic biomass (depth-integrated biomass) and the assessment of its importance as potentially productive stock of cells.     

怀槐细胞悬浮培养的结构化动力学模型

为探明怀槐细胞生长、异黄酮染料木素合成与底物消耗间的关系,建立了怀槐细胞悬浮培养的结构化动力学模型。模型预测分析了胞内外的蔗糖代谢、胞内结构组分变化、胞内中间组分的变化、细胞呼吸损失以及胞内外异黄酮染料木素的合成情况。模型各参数灵敏度的分析表明kM_b1、k_b2 和k_p是最为灵敏的参数,其调节10%时,目标函数变化的最大比例分别达12.8%、4.61%和2.54%,其它参数对目标函数变化的影响均小于0.5%。该模型预测值与实验值具有较好的吻合性。     

Determination of charge,stoichiometry and reaction constants fromI–V curve studies on a K+ transporter inNitella

Summary InNitella cells with low pump activity, the electrical characteristics of membrane transport are mainly determined by K⁺ transport. Current-voltage curves were measured at outside K⁺ concentrations ranging from 0.1 to 100 mol m^–3. Above 1 mol m^–3, current saturated at positive and at very negative potentials. It was found that theseI–V curves could be fitted by a Class 1, case 1 reaction kinetic model, which is a cyclic reaction scheme with one pair of rate constants sensitive to membrane potential (Class I) and neutral transporter (or electrically charged substrate-transporter complex, case I). The analysis revealed the relative rate constants of a 3-state model. From the linear dependence of the rate constant of substrate binding (k ₃₂) on [K⁺] _a the stoichiometry of 1 K⁺/cycle was obtained. The complex transporter substrate is very unstable (very high value ofK ₂₃) resulting in a very low density of this state and in what can be called Mitchellian behavior; namely, the driving forces resulting from the electrical and from the concentration gradient can hardly be distinguished.     

The volumetric oxygen mass transfer coefficient in antibiotic biosynthesis liquids

This paper approaches the problem of oxygen mass transfer. This transfer is in antibiotic biosynthesis liquids produced by microorganisms belonging to the actinomycete and fungi classes, which exhibit a shear thinning non-Newtonian rheological behaviour. The volumetric oxygen mass transfer coefficients in these liquids (k_L a_b) change during biosynthesis processes. The change is mainly due to rheological parameter modifications, such as increasing the consistency index (K) and decreasing the flow behaviour index (n). The values of k_L a_b were 3.0–6.5 times lower than those recorded in water, and their decreasing depended on the k_L a values obtained without biological liquid and on the nature of fermentation broths, as well. Starting from experimental data, two correlations were established between k_L a_b and P/V,υ_SG and P/V,υ_SG, N, respectively. These correlations contain a dimensionless factor (η_am/η_g), which takes into account the rheological properties of the liquid phase and offers the possibility for a fast and sufficiently accurate estimation of k_L a_b. The empirical correlations developed in the paper correspond reasonably well with the relatively wide variety of experimental data, as in the model proposed by PEREZ and SANDALL , and allow for the comparison of the fermentation batches of the same or different microorganisms; also, they may be applied to the workings of design, scale-up, control and monitoring of bioreactors.     

The ionic environment determines ribozyme cleavage rate by modulation of nucleobase pK a

Several small ribozymes employ general acid–base catalysis as a mechanism to enhance site-specific RNA cleavage, even though the functional groups on the ribonucleoside building blocks of RNA have pK_a values far removed from physiological pH. The rate of the cleavage reaction is strongly affected by the identity of the metal cation present in the reaction solution; however, the mechanism(s) by which different cations contribute to rate enhancement has not been determined. Using the Neurospora VS ribozyme, we provide evidence that different cations confer particular shifts in the apparent pK_a values of the catalytic nucleobases, which in turn determines the fraction of RNA in the protonation state competent for general acid–base catalysis at a given pH, which determines the observed rate of the cleavage reaction. Despite large differences in observed rates of cleavage in different cations, mathematical models of general acid–base catalysis indicate that k₁, the intrinsic rate of the bond-breaking step, is essentially constant irrespective of the identity of the cation(s) in the reaction solution. Thus, in contrast to models that invoke unique roles for metal ions in ribozyme chemical mechanisms, we find that most, and possibly all, of the ion-specific rate enhancement in the VS ribozyme can be explained solely by the effect of the ions on nucleobase pK_a. The inference that k₁ is essentially constant suggests a resolution of the problem of kinetic ambiguity in favor of a model in which the lower pK_a is that of the general acid and the higher pK_a is that of the general base.