The use of automated parameter searches to improve ion channel kinetics for neural modeling

The voltage and time dependence of ion channels can be regulated, notably by phosphorylation, interaction with phospholipids, and binding to auxiliary subunits. Many parameter variation studies have set conductance densities free while leaving kinetic channel properties fixed as the experimental constraints on the latter are usually better than on the former. Because individual cells can tightly regulate their ion channel properties, we suggest that kinetic parameters may be profitably set free during model optimization in order to both improve matches to data and refine kinetic parameters. To this end, we analyzed the parameter optimization of reduced models of three electrophysiologically characterized and morphologically reconstructed globus pallidus neurons. We performed two automated searches with different types of free parameters. First, conductance density parameters were set free. Even the best resulting models exhibited unavoidable problems which were due to limitations in our channel kinetics. We next set channel kinetics free for the optimized density matches and obtained significantly improved model performance. Some kinetic parameters consistently shifted to similar new values in multiple runs across three models, suggesting the possibility for tailored improvements to channel models. These results suggest that optimized channel kinetics can improve model matches to experimental voltage traces, particularly for channels characterized under different experimental conditions than recorded data to be matched by a model. The resulting shifts in channel kinetics from the original template provide valuable guidance for future experimental efforts to determine the detailed kinetics of channel isoforms and possible modulated states in particular types of neurons.     

Study of kinetic parameters in a mechanistic model for enzymatic hydrolysis of sugarcane bagasse subjected to different pretreatments

The goal of this work is to evaluate the influence of different pretreatments in the kinetics of enzymatic hydrolysis of sugarcane bagasse and to propose a reliable methodology to easily perform sensitivity analysis and updating kinetic parameters whenever necessary. A kinetic model was modified to represent the experimental data of the batch enzymatic hydrolysis of sugarcane bagasse pretreated with alkaline hydrogen peroxide. The simultaneous estimation of kinetic parameters of the mathematical model was performed using the Pikaia genetic algorithm using batch hydrolysis experimental data obtained with different enzymatic loads. Subsequently, Plackett–Burman designs were used to identify the kinetic parameters with the higher influence on the dynamic behavior of the process variables, which were re-estimated to describe experimental data of the hydrolysis of bagasse pretreated with phosphoric acid + sodium hydroxide. The methodology was accurate and straightforward and can be used whenever there are changes in pretreatment conditions and/or fluctuations in biomass composition in different harvests.     

Kinetics of phenol biodegradation in the presence of glucose

The kinetics of utilization of glucose, phenol, and their mixtures by Pseudomonas putida (ATCC 17514) were studied with a continuously aerated, jacketed batch reactor operating at 28 degrees C and pH 7.2. It was found that when glucose is the sole carbon and energy source, the culture utilizes it following Monod kinetics. When phenol is the sole carbon and energy source, the culture biodegrades it following Andrews (inhibitory) kinetics. When both glucose and phenol are present in the medium, the culture uses them simultaneously but with lower specific rates. Reduction of the specific substrate utilization rates indicates that the two substances are involved in a cross-inhibitory pattern which can be classified as uncompetitive. The values of the kinetic interaction constants suggest that glucose inhibits the specific rate of phenol removal much more than phenol inhibits the specific rate of glucose utilization. The results suggest that substitutable substrates which are dissimilar in origin and molecular structure may be involved in an uncompetitive cross-inhibitory interaction when they are simultaneously removed. It is also concluded that the use of easily degradable substrates may not enhance the per-unit amount of biomass removal of compounds which are classified as toxic. A general classification of kinetic interactions between substitutable resources is proposed. (c) 1996 John Wiley & Sons, Inc.     

Effects of Different PER Translational Kinetics on the Dynamics of a Core Circadian Clock Model

Living beings display self-sustained daily rhythms in multiple biological processes, which persist in the absence of external cues since they are generated by endogenous circadian clocks. The period (per) gene is a central player within the core molecular mechanism for keeping circadian time in most animals. Recently, the modulation PER translation has been reported, both in mammals and flies, suggesting that translational regulation of clock components is important for the proper clock gene expression and molecular clock performance. Because translational regulation ultimately implies changes in the kinetics of translation and, therefore, in the circadian clock dynamics, we sought to study how and to what extent the molecular clock dynamics is affected by the kinetics of PER translation. With this objective, we used a minimal mathematical model of the molecular circadian clock to qualitatively characterize the dynamical changes derived from kinetically different PER translational mechanisms. We found that the emergence of self-sustained oscillations with characteristic period, amplitude, and phase lag (time delays) between per mRNA and protein expression depends on the kinetic parameters related to PER translation. Interestingly, under certain conditions, a PER translation mechanism with saturable kinetics introduces longer time delays than a mechanism ruled by a first-order kinetics. In addition, the kinetic laws of PER translation significantly changed the sensitivity of our model to parameters related to the synthesis and degradation of per mRNA and PER degradation. Lastly, we found a set of parameters, with realistic values, for which our model reproduces some experimental results reported recently for Drosophila melanogaster and we present some predictions derived from our analysis.     

Simulation of sequential batch reactor (SBR) operation for simultaneous removal of nitrogen and phosphorus

Modeling of the operation of sequential batch reactor (SBR) was performed to find out optimum design parameters for simultaneous removal of nitrogen and phosphorus in a small-scale wastewater treatment plant. The models were set up with material balances on SBR operation and Monod kinetics. The model parameters were obtained to best fit the experimental results in a small scale SBR. The models were useful in optimizing hydraulic retention time (HRT) and successfully simulated operations of SBR in a larger scale. Especially the model predicted well the reactions occurring in the filling period as well as the effect of dilution, and evaluated the performance of SBR process under diverse operating conditions.     

Modelling of oligosaccharide synthesis by dextransucrase

Dextransucrase catalyses the formation of dextran, but also of numerous oligosaccharides from sucrose and different acceptors, if appropriate conditions are chosen. Much experimental work has been carried out and a scheme of reactions and a mathematical model have been developed to describe the complex kinetic behaviour of the enzyme. A computer program was used to calculate the parameters of the model from a broad range of experimental data, investigating a large number of kinetic tests with the acceptors maltose and fructose. The results lead to design considerations for a continuous reactor system with immobilized dextransucrase to produce leucrose, a disaccharide of industrial interest.     

A kinetic study of lipase-catalyzed reversible kinetic resolution involving verification at miniplant-scale

Lipase-catalyzed kinetic resolution of racemates is a popular method for synthesis of chiral synthons. Most of these resolutions are reversible equilibrium limited reactions. For the first time, an extensive kinetic model is proposed for kinetic resolution reactions, which takes into account the full reversibility of the reaction, substrate inhibition by an acyl donor and an acyl acceptor as well as alternative substrate inhibition by each enantiomer. For this purpose, the reversible enantioselective transesterification of (R/S)-1-methoxy-2-propanol with ethyl acetate catalyzed by Candida antarctica lipase B (CAL-B) is investigated. The detailed model presented here is valid for a wide range of substrate and product concentrations. Following model discrimination and the application of Haldane equations to reduce the degree of freedom in parameter estimation, the 11 free parameters are successfully identified. All parameters are fitted to the complete data set simultaneously. Six types of independent initial rate studies provide a solid data basis for the model. The effect of changes in substrate and product concentration on reaction kinetics is discussed. The developed model is used for simulations to study the behavior of reaction kinetics in a fixed bed reactor. The typical plot of enantiomeric excess versus conversion of substrate and product is evaluated at various initial substrate mixtures. The model is validated by comparison with experimental results obtained with a fixed bed reactor, which is part of a fully automated state-of-the-art miniplant.     

A comprehensive kinetic model of laccase‐catalyzed oxidation of aqueous phenol

A comprehensive model was developed to describe the kinetics of the laccase‐catalyzed oxidation of phenol that incorporates enzyme kinetics, enzyme inactivation, variable reaction stoichiometry between substrate and oxygen, and oxygen mass‐transfer. The model was calibrated and validated against data obtained from experiments conducted in an open system, which allowed oxygen to transfer from air to the reacting mixture and phenol conversion to approach completion. Inactivation of laccase was observed over the course of the reaction and was found to be dependent on the rate of substrate transformation. A single kinetic expression was sufficient to describe laccase inactivation arising from interaction with reacting species over time. Excellent agreement was found between model predictions of phenol and oxygen concentrations and experimental data over time for a wide range of initial substrate concentrations and enzyme activities. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Kinetic cutinase-catalyzed esterification of caproic acid in organic solvent system

Practical application of any chemical reaction requires the knowledge of its kinetics; in particular if one wishes to be able to describe a chemical reactor over an extended range of reaction conditions or if one intends to optimize the reaction conditions, a suitable kinetic model must be obtained. In order to ensure that the model is applicable over a wide range of experimental conditions it should be based on a mechanistic scheme describing the fundamental steps involved in the reaction; the development of these kind of models can also be used to provide insight into the processes that are taking place.A kinetic study, using experiments carried out in a batch stirred reactor, has been made for the enzymatic esterification of caproic acid with ethyl alcohol catalyzed by Fusarium solani pisi cutinase. Different acid and alcohol concentrations (whilst also varying the acid/alcohol molar ratio) were tested and the results were used to identify the best reaction scheme to describe the results obtained over an extended range of conditions. Several different approaches were used to identify the most adequate mechanistic model, namely by resorting to the quasi stationary state and the rate-limiting hypothesis. The main kinetic characteristics observed in esterification reaction were found to follow an ordered Ping-Pong Bi–Bi mechanism but different modifications were used o ensure that the kinetic model was applicable over the entire range of experimental conditions that were covered.     

Seeded isothermal batch crystallization of lysozyme

The kinetics of lysozyme crystallization under seeded isothermal batch conditions was followed by measurement of the decline in solution concentration versus time. Kinetics were measured for five different values of the seed crystal mass. The data were analyzed using a recently proposed mathematical model. For each seed mass, the model fit the kinetic data well. Growth rate constants determined using the model were approximately constant over a sixfold increase in the seed crystal mass, and fell well within the range of values reported in the literature, but obtained using entirely different experimental techniques. These results confirmed the utility of the proposed model. The proposed model can be used to analyze crystallization kinetics using absorbance measurements only, without the need to characterize the crystal size, thus avoiding the need for expensive laser light scattering and digital microscopy instrumentation. Thus, the model offers a low-cost straightforward method to analyze and simulate the effects of changes in operating parameters such as the seed crystal mass, solution volume, initial protein concentration, pH, temperature, salt concentration, and time.     

Modeling of a Catalyzed Reaction Using Lipase Immobilized in a Poly(vinyl alcohol) Membrane

A mathematical model for the hydrolysis reaction of p‐nitro phenol laurate catalyzed by a lipase immobilized in a membrane was developed. In an earlier study this model reaction was found to show very different reaction rates when it was performed in aqueous micellar solution with free enzyme and with membrane immobilized enzyme. It was assumed that a local accumulation of substrate in the membrane is responsible for the observed rate enhancement. The conversion of p‐nitro phenol ester within the membrane was modeled by considering a combination of the convective flow through poly(vinyl alcohol) membrane pores, concentration polarization of substrate containing micelles at the membrane surface and the kinetics of the reaction with free enzymes. It was demonstrated that the model offered a comprehensive understanding of the interaction of the involved phenomena. The modeling results are in good agreement with the experimental data from 10 runs with different enzyme and substrate concentrations. The substrate concentration at the membrane surface increased by up to a factor of 3 compared to the feed concentration. This effect explains the observed rate enhancement. Moreover, the model was used to determine the unknown parameters, i.e., the intrinsic retention and the mass transfer coefficient, by fitting the model to the experimental data. The model may also be used to calculate the optimum operating conditions and design parameters of such a reactor.     

Kinetics of Mixed Microbial Assemblages Enhance Removal of Highly Dilute Organic Substrates

Our experiments with selected organic substrates reveal that the rate-limiting process governing microbial degradation rates changes with substrate concentration, S, in such a manner that substrate removal is enhanced at lower values of S. This enhancement is the result of the dominance of very efficient systems for substrate removal at low substrate concentrations. The variability of dominant kinetic parameters over a range of S causes the kinetics of complex assemblages to be profoundly dissimilar to those of systems possessing a single set of kinetic parameters; these findings necessitate taking a new approach to predicting substrate removal rates over wide ranges of S.     

Kinetic Modeling of cometabolic degradation of ethanethiol and phenol by Ralstonia eutropha

Cometabolism, as a complex phenomenon in microbial world, is a special mechanism for transformation of many compounds of environmental and toxicological significance. Several models have been proposed to describe the cometabolic transformations of non-growth substrates in the absence or presence of growth substrates. In this study, a model was proposed to simulate the degradation kinetics of phenol and ethanethiol (ET) by a pure culture of Ralstonia eutropha, including the effects of cell growth, endogenous cell decay, loss of transformation activity, competitive inhibition between growth and non-growth substrates, and self-inhibition of non-growth substrate. The model parameters were determined independently and were then used for evaluating the applicability of the model by comparing experimental data with model predictions. The model successfully predicted ET transformation and phenol utilization for a wide range of concentrations of ET (0 ～ 40 mg/L) and phenol (0 ～ 100 mg/L).     

Horseradish peroxidase catalyzed hydroxylation of phenol: II. Kinetic model

A numeric kinetic model of the horseradish peroxidase catalyzed hydroxylation of phenol is proposed to complete the previous thermodynamic analysis. As previously stated, the basic role of HRP is to catalyze the production of DHF* radicals. These further form hydroxyl radicals that hydroxylate phenol via noncatalyzed reactions. The transient differential equations of the model are solved numerically. Several kinetic constants are adjusted to fit basic experimental data. This set of values is then kept constant to simulate additive experiments carried out under different conditions. Predictions of the model concerning the effects of HRP concentration, temperature variation, and presence of catalase and superoxide dismutase are consistent with the experimental results. The quantitative kinetic approach consequently fully confirmed the previous thermodynamic conclusions.     

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.     

Investigations of reaction kinetics for immobilized enzymes--identification of parameters in the presence of diffusion limitation

A method is proposed for identification of kinetic parameters when diffusion of substrates is limiting in reactions catalyzed by immobilized enzymes. This method overcomes conventional sequential procedures, which assume immobilization does not affect the conformation of the enzyme and, thus, consider intrinsic and inherent kinetics to be the same. The coupled equations describing intraparticle mass transport are solved simultaneously using numerical methods and are used for direct estimation of kinetic parameters by fitting modeling results to time-course measurements in a stirred tank reactor. While most traditional procedures were based on Michaelis-Menten kinetics, the method presented here is applicable to more complex kinetic mechanisms involving multiple state variables, such as ping-pong bi-bi. The method is applied to the kinetic resolution of (R/S)-1-methoxy-2-propanol with vinyl acetate catalyzed by Candida antarctica lipase B. A mathematical model is developed consisting of irreversible ping-pong bi-bi kinetics, including competitive inhibition of both enantiomers. The kinetic model, which fits to experimental data over a wide range of both substrates (5-95%) and temperatures (5-56 degrees C), is used for simulations to study typical behavior of immobilized enzyme systems.     

Kinetic modeling of the photosynthetic growth of Chlamydomonas reinhardtii in a photobioreactor

The aim of this study was to establish and validate a model for the photosynthetic growth of Chlamydomonas reinhardtii in photobioreactors (PBRs). The proposed model is based on an energetic analysis of the excitation energy transfer in the photosynthesis apparatus (the Z-scheme for photosynthesis). This approach has already been validated in cyanobacteria (Arthorspira platensis) and is extended here to predict the volumetric biomass productivity for the microalga C. reinhardtii in autotrophic conditions, taking into consideration the two metabolic processes taking place in this eukaryotic microorganism, namely photosynthesis and respiration. The kinetic growth model obtained was then coupled to a radiative transfer model (the two-flux model) to determine the local kinetics, and thereby the volumetric biomass productivity, in a torus PBR. The model was found to predict PBR performances accurately for a broad set of operating conditions, including both light-limited and kinetic growth regimes, with a variance of less than 10% between experimental results and simulations.     

Macro-kinetic investigation on phenol uptake from air by biofiltration: Influence of superficial gas flow rate and inlet pollutant concentration

The macro-kinetic behavior of phenol removal from a synthetic exhaust gas was investigated theoretically as well as experimentally by means of two identical continuously operating laboratory-scale biological filter bed columns. A mixture of peat and glass beads was used as filter material. After sterilization it was inoculated with a pure strain of Pseudomonas putida, as employed in previous experimental studies. To determine the influence of the superficial gas flow rate on biofilter performance and to evaluate the phenol concentration profiles along the column, two series of continuous tests were carried out varying either the inlet phenol concentration, up to 1650 mg . m(-3), or the superficial gas flow rate, from 30 to 460 m(3) . m(-2) . h(-1). The elimination capacity of the biofilter is proved by a maximum volumetric phenol removal rate of 0.73 kg . m(-3) . h(-1). The experimental results are consistent with a biofilm model incorporating first-order substrate elimination kinetics. The model may be considered a useful tool in scaling-up a biofiltration system. Furthermore, the deodorization capacity of the biofilter was investigated, at inlet phenol concentrations up to 280 mg . m(-3) and superficial gas flow rates ranging from 30 to 92 m(3) . m(-2) . h(-1). The deodorization of the gas was achieved at a maximum inlet phenol concentration of about 255 mg . m(-3), operating at a superficial gas flow rate of 30 m(3) . m(-2) . h(-1). (c) 1996 John Wiley & Sons, Inc.