Determination of kinetic parameters of 1,3-propanediol fermentation by Clostridium diolis using statistically optimized medium

1,3-propanediol (1,3-PD) is a chemical compound of immense importance primarily used as a raw material for fiber and textile industry. It can be produced by the fermentation of glycerol available abundantly as a by-product from the biodiesel plant. The present study was aimed at determination of key kinetic parameters of 1,3-PD fermentation by Clostridium diolis. Initial experiments on microbial growth inhibition were followed by optimization of nutrient medium recipe by statistical means. Batch kinetic data from studies in bioreactor using optimum concentration of variables obtained from statistical medium design was used for estimation of kinetic parameters of 1,3-PD production. Direct use of raw glycerol from biodiesel plant without any pre-treatment for 1,3-PD production using this strain investigated for the first time in this work gave results comparable to commercial glycerol. The parameter values obtained in this study would be used to develop a mathematical model for 1,3-PD to be used as a guide for designing various reactor operating strategies for further improving 1,3-PD production. An outline of protocol for model development has been discussed in the present work.     

Detection and kinetics of mucosal pathogenic bacteria binding with polysaccharides

The detection and kinetics of mucosal pathogenic bacteria binding on polysaccharide ligands were studied using a surface plasmon resonance biosensor. The kinetic model applied curve-fitting to the experimental surface plasmon resonance sensorgrams to evaluate the binding interactions. The kinetic parameters for the mucosal pathogenic bacteria (Pseudomonas aeruginosa, Pseudomonasfluorescens, Serratia marcescens) with the alginate ligand were determined from a kinetic model. In addition, the binding interactions of the mucosal pathogenic bacteria with polysaccharide binding pairs (Pseudomonas aeruginosa/alginate, Streptococcus pneumoniae/pneumococcal polysaccharide, Staphylococcus aureus/pectin) were also compared with their kinetic parameters. The rate constants of association for Pseudomonas aeruginosa with the alginate ligand were higher than those for Pseudomonas fluorescens. Serratia marcescens had no detectable interaction with the alginate ligand. The adhesion affinity of Pseudomonas aeruginosa with alginate was higher than that for the other binding pairs. The binding affinities of the pathogenic bacteria with their own polysaccharide were higher than that of Staphylococcus aureus with pectin. Measuring the contact angle was found to be a feasible method for detecting binding interactions between analytes and ligands.     

Application of response surface methodology to cell immobilization for the production of palatinose

Response surface methodology (RSM), based on multivariate non-linear model, was applied to study the interactions and optimization of the immobilization parameters for cell entrapment, namely alginate concentration, cell loading and bead diameter using Erwinia rhapontici NCPPB 1578 that produced palatinose. ANOVA analysis and statistical parameters calculations showed that RSM could be used effectively to model and improve a complex system like cell immobilization. Palatinose yield was increased by 40%. The maximum yield of 140 mg/ml was achieved in a batch of 1h at alginate concentration of 5% w/v, cell loading of 5 g l(-1) and 2.25 mm bead diameter. Thus, the E. rhapontici NCPPB 1578 immobilization in alginate bead and subsequent palatinose yield was successfully improved by application of RSM technique.     

An image analysis and statistical evaluation program for the assessment of tumour cell invasion in vitro.

Tumour cell invasion is a complex process, which is essential for the formation of metastasis and is therefore of critical clinical importance. For detailed investigations of the invasive process, quantifiable in vitro models of invasion are necessary. In this study we describe an image analysis procedure and a statistical program which facilitate an objective analysis of experiments carried out using the embryonic chick heart invasion model of Mareel. Tumour multicellular spheroids are confronted with embryonic chick heart fragments in culture and are sampled after different time intervals for up to 7 days. Immunohistological sections are then evaluated by an image analysis procedure which provides 9 parameters indicating invasion, proliferation and destruction taking place in the confrontation cultures. The data obtained by image analysis are further evaluated by a statistical program which describes the change with time of each parameter by means of linear regression analysis. Thus the data obtained at various time intervals serve as the source data for a single statistic, namely the slope of the regression line. Confidence intervals and statistical differences between various experiments can be calculated. In order to make the procedure more comprehensible in biological terms, the program provides a full text interpretation of the experimental results. The image analysis procedure in conjunction with statistical evaluation and text interpretation provides a comprehensive tool for the quantitative assessment of experimental invasion in vitro.     

Estimation of kinetic parameters in a structured yeast model using regularisation.

In this work, a procedure for estimating kinetic parameters in biochemically structured models was developed. The approach is applicable when the structure of a kinetic model has been set up and the kinetic parameters should be estimated. The procedure consists of five steps. First, initial values were found in or calculated from literature. Hereafter using sensitivity analysis the most sensitive parameters were identified. In the third step physiological knowledge was combined with the parameter sensitivities to manually tune the most sensitive parameters. In step four, a global optimisation routine was applied for simultaneous estimation of the most sensitive parameters identified during the sensitivity analysis. Regularisation was included in the simultaneous estimation to reduce the effect of insensitive parameters. Finally, confidence intervals for the estimated parameters were calculated. This parameter estimation approach was demonstrated on a biochemically structured yeast model containing 11 reactions and 37 kinetic constants as a case study.     

Empirical modeling of batch fermentation kinetics for poly(glutamic acid) production and other microbial biopolymers

An empirical kinetic model is proposed for the batch production of poly(glutamic acid) from Bacillus subtilis IFO 3335. In addition, the proposed model was used to fit the kinetic data of poly(glutamic acid) production from other bacterial strains using different media, as well as kinetic data from different strains for the production of the exocellular biopolymers dextran, hyaluronic acid, xanthan, alginate, and the endocellular biopolymer polyhydroxybutyrate. The empirical model treats the biopolymer as a component of the biomass and fits the experimental biomass data using a sigmoidal relationship that includes the maximum specific growth rate, mu(max), and the substrate saturation parameter, K(S). An empirical parameter, the relative coefficient (r), quantifies, in relative terms, the degree of nongrowth-associated biopolymer formation.     

Data analysis problems in the area of pharmacokinetics research.

Of interest in compartment analysis is the estimation of kinetic first order rate constants and quantification of the amount of drug present in each compartment at every point in time. From the data pertaining to only one compartment, it is not always possible to estimate all the first order rate parameters of linear and non-linear compartment systems. When multiple varying doses are administered at different intervals of time, the equations quantifying the maximum and minimum amount of drug accumulated in each interval may be used. To obtain estimates of kinetic parameters, statistical adjustments may be used in the kinetic equations.     

Development of a compartmental model of human zinc metabolism: identifiability and multiple studies analyses

A compartmental model of zinc metabolism has been developed from stable isotope tracer studies of five healthy adults. Multiple isotope tracers were administered orally and intravenously, and the resulting enrichment was measured in plasma, erythrocytes, urine, and feces for as long as 3 wk. Data from total zinc measurements and model-independent calculations of various steady-state parameters were also modeled with the kinetic data. A structure comprised of 14 compartments and as many as 25 unknown kinetic parameters was developed to adequately model the data from each of the individual studies. The structural identifiability of the model was established using the GLOBI2 identifiability analysis software. Numerical identifiability of parameter estimates was evaluated using statistical data provided by SAAM. A majority of the model parameters was estimated with sufficient statistical certainty to be considered well determined. After the fitting of the model and data from the individual studies using SAAM/CONSAM, results were submitted to SAAM extended multiple studies analysis for aggregation into a single set of population parameters and statistics. The model was judged to be valid based on criteria described elsewhere.     

A simple computer program with statistical tests for the analysis of enzyme kinetics.

A simple computer program that calculates the kinetic parameters of enzyme reactions is described. Parameters are determined by nonlinear, least-squares regression using either Marquardt-Levenberg or Gauss-Newton algorithms to find the minimum sum of squares. Three types of enzyme reactions can be analyzed: single substrate reactions (Michaelis-Menten and sigmoidal kinetics), enzyme activation at a fixed substrate value or enzyme inhibition at a fixed substrate value. The user can monitor goodness of fit through nonparametric statistical tests (performed automatically by the computer) and through visual examination of the pattern of residuals. The program is unique in providing equations for activator and inhibition analysis as well as in enabling the user to fix some of the parameters before regression analysis. The simplicity of the program makes it extremely useful for quickly determining kinetic parameters during the data-gathering process.     

Confidence intervals of evolutionary distances between sequences and comparison with usual approaches including the bootstrap method

Two methods are commonly employed for evaluating the extent of the uncertainty of evolutionary distances between sequences: either some estimator of the variance of the distance estimator, or the bootstrap method. However, both approaches can be misleading, particularly when the evolutionary distance is small. We propose using another statistical method which does not have the same defect: interval estimation. We show how confidence intervals may be constructed for the Jukes and Cantor (1969) and Kimura two-parameter (1980) estimators. We compare the exact confidence intervals thus obtained with the approximate intervals derived by the two previous methods, using artificial and biological data. The results show that the usual methods clearly underestimate the variability when the substitution rate is low and when sequences are short. Moreover, our analysis suggests that similar results may be expected for other evolutionary distance estimators.      

Identification of Growth Phases and Influencing Factors in Cultivations with AGE1.HN Cells Using Set-Based Methods

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty.     

Software for dynamic analysis of tracer-based metabolomic data: estimation of metabolic fluxes and their statistical analysis

MOTIVATION: Metabolic flux analysis of biochemical reaction networks using isotope tracers requires software tools that can analyze the dynamics of isotopic isomer (isotopomer) accumulation in metabolites and reveal the underlying kinetic mechanisms of metabolism regulation. Since existing tools are restricted by the isotopic steady state and remain disconnected from the underlying kinetic mechanisms, we have recently developed a novel approach for the analysis of tracer-based metabolomic data that meets these requirements. The present contribution describes the last step of this development: implementation of (i) the algorithms for the determination of the kinetic parameters and respective metabolic fluxes consistent with the experimental data and (ii) statistical analysis of both fluxes and parameters, thereby lending it a practical application. RESULTS: The C++ applications package for dynamic isotopomer distribution data analysis was supplemented by (i) five distinct methods for resolving a large system of differential equations; (ii) the 'simulated annealing' algorithm adopted to estimate the set of parameters and metabolic fluxes, which corresponds to the global minimum of the difference between the computed and measured isotopomer distributions; and (iii) the algorithms for statistical analysis of the estimated parameters and fluxes, which use the covariance matrix evaluation, as well as Monte Carlo simulations. An example of using this tool for the analysis of (13)C distribution in the metabolites of glucose degradation pathways has demonstrated the evaluation of optimal set of parameters and fluxes consistent with the experimental pattern, their range and statistical significance, and also the advantages of using dynamic rather than the usual steady-state method of analysis. AVAILABILITY: Software is available free from http://www.bq.ub.es/bioqint/selivanov.htm     

Calcium and phosphate effects on growth and alkaloid production in Coffea arabica: experimental results and mathematical model

Plant, mammalian, and microbial cells are commonly immobilized in calcium alginate gels for the production of valuable secondary metabolites. However, calcium ions are known to inhibit growth in various types of cells, and calcium is an integral part of such gels. Therefore, an investigation was conducted to evaluate the effect of calcium on the growth and alkaloid production of a model cell-line, Coffea arabica, in suspension culture before, attempting to immobilize such cells in alginate. A kinetic model was then developed from the results to describe cell growth and alkaloid production and the mechanism by which calcium influences these variables. In addition, it was observed that there was a characteristic relationship between the concentration of calcium in the external medium and the concentration of extra cellular and intracellular phosphate. The intracellular phosphate level was, in turn, related to the production of alkaloids. Using these results, a dynamic mathematical model of cell growth and alkaloid production was developed based on the proposed roles of calcium and phosphate. The model showed satisfactory agreement with three sets of experiments at different calcium concentrations. A possible linkage between the calcium and phosphate results is postulated based on the limited solubility of calcium phosphate.     

Waste biomass of Nostoc linckia as adsorbent of crystal violet dye: Optimization based on statistical model

The potential of spent biomass of a hydrogen producing cyanobacterial strain Nostoc linckia from a hydrogen fermentor was studied for decolorization of a tri-phenylmethane dye, crystal violet. The waste cyanobacterial biomass immobilized in calcium alginate was used as a biosorbent and the process variables were optimized for maximum dye removal using the statistical response surface methodology (RSM). Batch mode experiments were performed to determine the kinetic behavior of the dye in aqueous solution allowing the computation of kinetic parameters. Influence of interacting parameters like temperature (25-35 °C), pH (4-8), initial dye concentration (100-200 mg/L) and cyanobacterial dose (0.2-0.4 g) on dye removal were examined using central composite design (CCD) which included two additional levels for each parameter. Second-order polynomial regression model, was applied which was statistically validated using analysis of variance. Ability of the immobilized biomass to decolorize the dye was maximum (72%) at pH 8.0, temperature 35 °C, 200 mg/L initial dye concentration and 0.2 g cyanobacterial dose. Adsorption of the dye on cell surface was further confirmed by scanning electron micrographs of the biomass before and after dye loading. FT-IR studies revealed that decolorization was due to biosorption mediated mainly by functional groups like hydroxyl, amide, carboxylate, methyl and methylene groups present on the cell surface.     

Macro approach and fuzzy modeling of entrapped biocatalyst

The interactions between a strain of Saccharomyces cerevisiae and an alginate matrix are investigated to ascertain the main factors affecting the bioreaction evolution. During the tests several parameters (glucose, ethanol, calcium ion and biomass concentration, pH, and alginate bed diameter) were evaluated, coupled with microscopic investigation inside the beads to determine the spatial biomass distribution. A detailed analysis of macro parameters and a correlation among them are proposed using a fuzzy algorithm. A global two-step fuzzy model results in which biomass distribution inside the beads is represented as a hidden parameter.     

Effect of ammonium sulphate concentration and agitation speed on the kinetics of alginate production by Azotobacter vinelandii DSM576 in batch fermentation

Growth and alginate production by Azotobacter vinelandii DSM576 as a function of initial ammonium sulphate concentration (0.45–1.05 g l⁻¹) and agitation speed (300–700 rpm) were studied in batch fermentations at controlled pH. The time course of growth, alginate production and substrate consumption and the effect of nitrogen concentration and agitation speed on kinetic parameters and on maximum alginate molecular weight (MW) was modelled using empirical equations. The kinetics of growth, alginate production and polymerization were deeply affected by agitation speed and, to a lesser extent, by inorganic nitrogen concentration. Average and maximum specific growth rate and maximum alginate MW all increased with agitation speed, and were higher at intermediate ammonium sulphate concentration. Maximum alginate MW (>250,000) was obtained at high agitation speed (600–700 rpm) and alginate depolymerization was limited or did not occur at all when the agitation speed was higher than 500 rpm, while at 400 rpm depolymerization significantly reduced the alginate. However, alginate yield was negatively affected by increasing agitation speed. A good compromise between alginate yield (>2 g l⁻¹) and quality (MW>250,000) was obtained with agitation speed of 500–600 rpm and 0.75–0.90 g l⁻¹ of ammonium sulphate. Journal of Industrial Microbiology & Biotechnology (2000) 25, 242–248. Received 23 February 2000/ Accepted in revised form 04 August 2000     

Kinetic Model Development for Accelerated Stability Studies

Accelerated stability coupled with modeling to predict the stability of compounds, blends, and products at long-term storage conditions provides significant benefits in science-based decision-making throughout drug substance and drug product development. The study can often be completed, including data analysis in the space of three working weeks, and the information gathered and learning made in this time period can rival years of traditional analysis. The speed of the studies allows an earlier assessment of risk to quality enabling appropriate risk mitigation strategies to be implemented in a timely manner. The scientific foundation is based upon Arrhenius kinetic equations that can be linear or nonlinear in time, and can be based upon water vapor pressure or liquid water activity (relative humidity). A variety of kinetic models are evaluated, and the best model is chosen based upon both Bayesian information criteria and an automated assessment of kinetic model parameters fitting within acceptable ranges. Confidence intervals are estimated based upon a bootstrapping approach. Moisture vapor transmission rate models are applied on top of the resulting kinetic models in order to simulate different packaging types and the use of desiccant. The kinetic models are integrated with the prediction of packaging humidity over time to create a long-term prediction of impurities and other phenomena. The resulting models have been shown to be useful for not only the prediction of drug product impurities in long-term storage but other physical phenomena as well such as hydrate development and solvate loss.     

Modeling, simulation, and kinetic analysis of a heterogeneous reaction system for the enzymatic conversion of poorly soluble substrate.

We developed a kinetic model that describes a heterogeneous reaction system consisting of a solid substrate suspension for the production of D-amino acid using D-hydantoinase. As a biocatalyst, mass-produced free and whole cell enzymes were used. The heterogeneous reaction system involves dissolution of a solid substrate, enzymatic conversion of the dissolved D-form substrate, spontaneous racemization of an L-form substrate to D-form, and deactivation of the enzyme. In the case of using whole cell enzymes, transfer of the dissolved substrate and product through the cell membrane was considered. The kinetic parameters were determined from experiments, literature data, and by using Marquardt's method of nonlinear regression analysis. The model was simulated using the kinetic parameters and compared with experimental data, and a good agreement was observed between the experimental results and the simulation ones. Factors affecting the kinetics of the heterogeneous reaction system were analyzed on the basis of the kinetic model, and the efficiency of the reaction systems using free and whole cell enzymes was also compared.     

Evaluation of Medium Components by Plackett-Burman Statistical Design for Lipase Production by Candida rugosa and Kinetic Modeling

Lipase production by Candida rugosa was carried out in submerged fermentation. Plackett-Burman statistical experimental design was applied to evaluate the fermentation medium components. The effect of twelve medium components was studied in sixteen experimental trials. Glucose, olive oil, peptone and FeCl3?6H2O were found to have more significance on lipase production by Candida rugosa. Maximum lipase activity of 3.8 u mL-1 was obtained at 50 h of fermentation period. The fermentation was carried out at optimized temperature of 30oC, initial pH of 6.8 and shaking speed of 120 r/min. Unstructured kinetic models were used to simulate the experimental data. Logistic model, Luedeking-Piret model and modified Luedeking-Piret model were found suitable to efficiently predict the cell mass, lipase production and glucose consumption respectively with high determination coefficient(R2). From the estimated values of the Luedeking-Piret kinetic model parameters, α and β, it was found that the lipase production by Candida rugosa is growth associated.