The dynamics of single-substrate continuous cultures: the role of transport enzymes

A chemostat limited by a single growth-limiting substrate displays a rich spectrum of dynamics. Depending on the flow rate and feed concentration, the chemostat settles into a steady state or executes sustained oscillations. The transients in response to abrupt increases in the flow rate or the feed concentration are also quite complex. For example, if the increase in the flow rate is small, there is no perceptible change in the substrate concentration. If the increase in the flow rate is large, there is a large increase in the substrate concentration lasting several hours or days before the culture adjusts to a new steady state. In the latter case, the substrate concentration and cell density frequently undergo damped oscillations during their approach to the steady state. In this work, we formulate a simple structured model containing the inducible transport enzyme as the key intracellular variable. The model displays the foregoing dynamics under conditions similar to those employed in the experiments. The model suggests that long recovery times (on the order of several hours to several days) can occur because the initial transport enzyme level is too small to cope with the increased substrate supply. The substrate concentration, therefore, increases until the enzyme level is built up to a sufficiently high level by the slow process of enzyme induction. Damped and sustained oscillations can occur because transport enzyme synthesis is autocatalytic, and hence, destabilizing. At low dilution rates, the response of stabilizing processes, such as enzyme dilution and substrate consumption, becomes very slow, leading to damped and sustained oscillations.     

Perspectives in the modeling and optimization of PHB production by pure and mixed cultures

Poly(beta-hydroxybutyrate) or PHB is an important member of the family of polyhydroxyalkanoates with properties that make it potentially competitive with synthetic polymers. In addition, PHB is biodegradable. While the biochemistry of PHB synthesis by microorganisms is well known, improvement of large-scale productivity requires good fermentation modeling and optimization. The latter aspect is reviewed here. Current models are of two types: (i) mechanistic and (ii) cybernetic. The models may be unstructured or structured, and they have been applied to single cultures and co-cultures. However, neither class of models expresses adequately all the important features of large-scale non-ideal fermentations. Model-independent neural networks provide faithful representations of observations, but they can be difficult to design. So hybrid models, combining mechanistic, cybernetic and neural models, offer a useful compromise. All three kinds of basic models are discussed with applications and directions toward hybrid model development.     

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.     

Kinetic analysis of template-instructed and de novo RNA synthesis by Q beta replicase

The kinetics of template-free and template-instructed RNA synthesis by Q_β replicase were investigated. Template-instructed RNA synthesis has different growth rates in the exponential (excess enzyme) and the linear (excess template) phase of growth. In the absence of exogenous template, Q_β replicase synthesizes self-replicating RNA after an initial lag phase (“template-free” synthesis). The lag time can be determined by extrapolating the growth curve to the time of appearance of the first self-replicating strand. Growth rates in the exponential and linear phase, and especially the times of the lag phase for nucleotide incorporations under identical template-free conditions, show considerable scattering in contrast to the deterministic behavior of template-instructed synthesis. Evaluation of the kinetic data reveals that the time lag of template-free synthesis is strongly dependent on the concentration of the nucleoside triphosphate and the enzyme. The lag time is approximately inversely proportional to the powers 2.75 of the nucleotide and 2.5 of the enzyme concentration, respectively, both being lower limit values. The rate of template-instructed RNA synthesis is linearly proportional to the enzyme concentration and less than linearly proportional to the triphosphate concentration, in accordance with a substrate dependence of a Michaelis-Menten type of mechanism. The kinetic data cannot be reconciled with the proposition that template-free synthesis is due to low concentrations of templates present as impurities in the incorporation mixture and giving rise to autocatalytic RNA synthesis by a template-instructed mechanism. The data strongly favor the de novo mechanism proposed by Sumper &; Luce (1975).     

Perspectives in the Modeling and Optimization of PHB Production by Pure and Mixed Cultures

ABSTRACT

Poly(β-hydroxybutyrate) or PHB is an important member of the family of polyhydroxyalkanoates with properties that make it potentially competitive with synthetic polymers. In addition, PHB is biodegradable. While the biochemistry of PHB synthesis by microorganisms is well known, improvement of large-scale productivity requires good fermentation modeling and optimization. The latter aspect is reviewed here.

Current models are of two types: (i) mechanistic and (ii) cybernetic. The models may be unstructured or structured, and they have been applied to single cultures and co-cultures. However, neither class of models expresses adequately all the important features of large-scale non-ideal fermentations. Model-independent neural networks provide faithful representations of observations, but they can be difficult to design. So hybrid models, combining mechanistic, cybernetic and neural models, offer a useful compromise. All three kinds of basic models are discussed with applications and directions toward hybrid model development.     

Macrokinetic model for Gluconobacter oxydans in 2-keto-L-gulonic acid mixed culture

A set of kinetic models have been developed for the production of 2-keto-L-gulonic acid from L-sorbose by a mixed culture of Gluconobacter oxydans and Bacillus megaterium. A metabolic pathway is proposed for Gluconobacter oxydans, and a macrokinetic model has been developed for Gluconobacter oxydans, where the balances of some key metabolites, ATP and NADH are taken into account. An unstructured model is proposed for concomitant bacterium Bacillus megaterium. In the macrokinetic model and unstructured model, the mechanism of interaction between Gluconobacter oxydans and Bacillus megaterium is investigated and modeled. The specific substrate uptake rate and the specific growth rate obtained from the macrokinetic model are then coupled into a bioreactor model such that the relationship between the substrate feeding rate and the main state variables, such as the medium volume, the biomass concentrations, the substrate, and the is set up. A closed loop regulator model is introduced to approximate the induction of enzyme pool during lag phase after inoculation. Experimental results demonstrate that the model is able to describe 2-keto-L-gulonic acid fermentation process with reasonable accuracy.     

Hierarchical amino acid utilization and its influence on fermentation dynamics: rifamycin B fermentation using Amycolatopsis mediterranei S699, a case study

Background  

Industrial fermentation typically uses complex nitrogen substrates which consist of mixture of amino acids. The uptake of amino acids is known to be mediated by several amino acid transporters with certain preferences. However, models to predict this preferential uptake are not available. We present the stoichiometry for the utilization of amino acids as a sole carbon and nitrogen substrate or along with glucose as an additional carbon source. In the former case, the excess nitrogen provided by the amino acids is excreted by the organism in the form of ammonia. We have developed a cybernetic model to predict the sequence and kinetics of uptake of amino acids. The model is based on the assumption that the growth on a specific substrate is dependent on key enzyme(s) responsible for the uptake and assimilation of the substrates. These enzymes may be regulated by mechanisms of nitrogen catabolite repression. The model hypothesizes that the organism is an optimal strategist and invests resources for the uptake of a substrate that are proportional to the returns.     

Stochastic and deterministic models for the kinetic behavior of certain structured enzyme systems II: consecutive two enzyme systems.

This paper contains extensions of results from a previous paper regarding structured one enzyme systems to a more complicated structured two enzyme system. A stochastic model and a deterministic model are developed for such systems and their steady state reaction kinetics are compared. These comparisons are in the form of graphs of the reaction kinetics versus substrate concentration. Two quantities are proposed as indications of lack of agreement between the two models. This lack of agreement corresponds to situations in which the model systems are more highly non-linear, in accord with Jensen's inequalities. Implications of these results, relative to experimental procedures are briefly discussed.     

Unstructured models for suspension cultures of Taxus media cells in a bioreactor under substrate-sufficient conditions

For a better understanding of the simulation, optimization, and process control in cell cultures, good kinetic models are necessary for large scale plant cell culture. In this paper, the systematic kinetics of taxol production by Taxus media cell suspension cultures in a stirred 15-L bioreactor under substrate-sufficient conditions and the absence of inducer intervention were studied. A kinetic model of cell growth was established by logistic equation, and kinetic unstructured models of substrate consumption, product synthesis and rheological behavior were constituted, which incorporated energy spilling. These models were verified by comparing the simulation results with those obtained experimentally. These results showed that energy spilling was a key factor that must be considered in constructing unstructured kinetic models of Taxus media cell suspension cultures in a stirred bioreactor under substrate-sufficient conditions. Besides, an optimized operation measure of decreasing energy spilling was proposed. An increase of 17.64% in cell biomass and 14.88% in taxol concentration were obtained when the strategy of limiting added carbon several times was experimentally implemented in a 15-L bioreactor. Results demonstrated that these established models should be helpful in the process prediction and operation optimization to guide the production and amplification of Taxus media cell suspension cultures in a bioreactor.     

Metabolic regulation in bacterial continuous cultures: II

The transient behavior of a continuous culture of Klebsiella pneumoniae with mixed feed of glucose and xylose arising from step-up and step-down in dilution rates and from a feed-switching experiment is presented. he organism gradually switches from simultaneous utilization of the substrates at low growth rates to preferred utilization of the faster substrate (i.e, supporting a higher growth rate) at high dilution rates. The metabolic lags following a step increase in dilution rate and a significant accumulation of the slower substrate during the transient period result from the effects of metabolic regulation. The cybernetic modeling approach that successfully described the foregoing situations with single-substrate feeds is employed to describe mixed substrate behavior. The parameters in the mixed-substrate (glucose and xylose) model are the same as those in the single-substrate models with the singular exception of the rate constant for the xylose growth enzyme synthesis. The reason for this discrepancy is discussed in detail. It appears that the constitutive rate of enzyme synthesis for growth on a given substrate may be related to the past history of the organism in regard to whether or not the organism has been exposed to the particular substrate. Thus, the results further demonstrate the ability of the framework to effectively describe metabolic regulation in batch, fedbatch, and continuous microbial cultures.     

Structured kinetic model to represent the utilization of multiple substrates in complex media during rifamycin B fermentation

Industrial fermentations typically use media that are balanced with multiple substitutable substrates including complex carbon and nitrogen source. Yet, much of the modeling effort to date has mainly focused on defined media. Here, we present a structured model that accounts for growth and product formation kinetics of rifamycin B fermentation in a multi-substrate complex medium. The phenomenological model considers the organism to be an optimal strategist with an in-built mechanism that regulates the sequential and simultaneous uptake of the substrate combinations. This regulatory process is modeled by assuming that the uptake of a substrate depends on the level of a key enzyme or a set of enzymes, which may be inducible. Further, the fraction of flux through a given metabolic branch is estimated using a simple multi-variable constrained optimization. The model has the typical form of Monod equation with terms incorporating multiple limiting substrates and substrate inhibition. Several batch runs were set up with varying initial substrate concentrations to estimate the kinetic parameters for the rifamycin overproducer strain Amycolatopsis mediterranei S699. Glucose and ammonium sulfate (AMS) demonstrated significant substrate inhibition toward growth as well as product formation. The model correctly predicts the experimentally observed regulated simultaneous uptake of the substitutable substrate combinations under different fermentation conditions. The modeling results may have applications in the optimization and control of rifamycin B fermentation while the modeling strategy presented here would be applicable to other industrially important fermentations.     

Evaluation of Various Unstructured Kinetic Models for the Production of Protease by Bacillus sphaericus MTTC511

Bacillus sphaericus MTCC511 was used for the production of protease in submerged batch fermentation. Maximum protease activity of 1010 U/L was obtained during a fermentation period of 24 h under optimized conditions of 30 °C in a medium with an initial pH of 7 and at a shaking rate of 120 rpm. The maximum biomass obtained in the batch fermentation was 2.55 g/L after 16 h. Various unstructured models were analyzed to simulate the experimental values of microbial growth, protease activity and substrate concentration. The unstructured models, i.e. the Monod model for microbial growth, the Monod incorporated Luedeking‐Piret model for the production of protease and the Monod‐incorporated modified Luedeking‐Piret model for the utilization of substrate were capable of predicting the fermentation profile with high coefficient of determination (R²) values of 0.9967, 0.9402 and 0.9729, respectively. The results indicated that the unstructured models were able to describe the fermentation kinetics more effectively.     

Mathematical model of cell growth and phosphatase biosynthesis in Saccharomyces carlsbergensis under phosphate limitation.

The rate kinetics of growth and acid phosphate formation in the batch culture of Saccharomyces carlsbergensis LAM 1068 was studied under varying degrees of phosphate limitation. The mathematical model that was developed is concerned with the time lag for exponential growth, the biphasic growth on a substrate (glucose) and its product (ethanol), sustained growth on conservative phosphate, and the derepression of acid phosphatase. The numerical calculations using appropriate parametric constants successfully described the variation in the cell mass, glucose, ethanol, and inorganic phosphate concentrations, and the enzyme activity of acid phosphatase during aerobic growth of S. carlsbergensis under five different conditions of phosphate starvation. A simulation study revealed that the optimum initial phosphate concentration in the medium giving a high productivity of acid phosphatase was 2.0 mg phosphorus/g glucose liter.     

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.     

Structured model for denitrifier diauxic growth

We present a model for diauxic growth of denitrifying bacteria in which nitrate reductase synthesis kinetics dominate the overall growth kinetics. The model is based on the assumption of the existence of a nitrate respiration operon, thereby linking the rate of nitrate uptake to the activity of nitrate reductase. We show that this approach can model diauxic growth of Pseudomonas denitrificans by conducting experiments in which nitrate reductase activity was measured during both lag and ensuing exponential growth phases. We consistently observed the pattern of low nitrate reductase enzyme activity during the lag phase, increasing before the onset of growth. By fitting model parameters we were able to successfully match experimental data for growth, nitrate uptake, and enzyme activity level.     

Kinetic study of the velum formation by Saccharomyces cerevisiae (beticus ssp.) during the biological aging of wines

The main objetive of this work was to evaluate and model the biofilm growth of the Saccharomyces cerevisiae (beticus ssp.) yeast during the biological aging of some types of wines. Thus, we have study how the biofilm growth, the glycerine is consumed and the acetaldehyde is produced, and how this phenomena are affected by the media ethanol concentration (0–17%, v/v), under experimental conditions similar to the industrial ones. In consequence, the growth of the S. cerevisiae (beticus ssp.) biofilm on the surface of the liquid was studied and kinetically modelled. Growth curves were fitted by using general kinetic models that include biomass and substrate inhibition factors. The alcohol content of the medium for the fastest growth rate of biofilm was found to be 4.3%, v/v. The proposed kinetic models for biomass growth, glycerine consumption and acetaldehyde formation fit well with the experimental data.The growth kinetics of S. cerevisiae beticus ssp. in biofilm phase presents a typical discontinuous microbial growth profile (with lag, exponential and stationary phases). The glycerine consumption is directly related to the substrate concentrations (ethanol and glycerine). Finally, the rate of acetaldehyde formation suggests a model associated with the rate of microbial growth, which is modified by a substrate-dependent factor. The suggested model can be used for optimization and control processes of biological aging of wines.