A pulsing device for packed-bed bioreactors: II. Application to alcoholic fermentation

When the immobilized cells are employed in packed-bed bioreactors several problems appear. To overcome these drawbacks, a new bioreactor based on the use of pulsed systems was developed [1]. In this work, we study the glucose fermentation by immobilized Saccharomyces cerevisiae in a packed-bed bioreactor. A comparative study was then carried out for continuous fermentation in two packed-bed bioreactors, one of them with pulsed flow. The determination of the axial dispersion coefficients indicates that by introducing the pulsation, the hydraulic behaviour is closer to the plug flow model. In both cases, the residence time tested varied from 0.8 to 2.6 h. A higher ethanol concentration and productivity (increases up to 16%) were achieved with the pulsated reactors. The volumes occupied by the CO₂ were 5.22% and 9.45% for fermentation with/without pulsation respectively. An activity test of the particles from the different sections revealed that the concentration and viability of bioparticles from the two bioreactors are similar. From the results we conclude that the improvements of the process are attributable to a mechanical effect rather than to physiological changes of microorganisms.List of Symbols D m²/s dispersion coefficient - K _is l/g inhibition substrate constant - K _ip l/g inhibition ethanol constant - K _s g/l Apparent affinity constant - P g/l ethanol concentration - q _p g/(gh) specific ethanol productivity - Q _p g/(lh) overall ethanol productivity - q _s g/(gh) specific glucose consumption rate - Q _s g/(lh) glucose consumption rate - S g/l residual glucose concentration - S(in0) g/l initial glucose concentration - V _max g/(lh) maximum rate - Y _p/s g/g yield in product     

Updated model of the batch acetone-butanol fermentation

Summary The recent models of the Acetone-Butanol fermentation did not adequately describe the culture inhibition by the accumulating metabolites and were unable to simulate the acidogenic culture dynamics at elevated pH levels. The present updated modification of the model features a generalised inhibition term and a pH dependent terms for intracellular conversion of undissociated acids into solvent products. The culture dynamics predictions by the developed model compared well with experimental results from an unconventional acidogenic fermentation ofC. acetobutylicum.Nomenclature A acetone concentration in the fermentation broth, [g/L] - AA total concentration of dissociated and undissociated acetic acid, [g/L] - AA _undiss concentration of undissociated acetic acid, [g/L] - APS Absolute Parameter Sensitivity - AT acetoin concentration in the fermentation broth, [g/L] - B butanol concentration in the fermentation broth, [g/L] - BA total concentration of dissociated and undissociated butyric acid, [g/L] - BA _undiss concentration of undissociated butyric acid, [g/L] - E ethanol concentration in the fermentation broth, [g/L] - f(T) inhibition function as defined in Equation (2) - k ₁ constant in Equation (4), [g substrate/g biomass] - k ₂ constant in Equation (4), [g substrate/(g biomass.h)] - k ₁ constant in Equation (5), [g substrate/(g biomass] - k ₂ constant in Equation (5), [g substrate/(g biomass.h)] - k ₃ constant in Equation (6), [g butyric acid/g substrate] - k ₄ constant in Equation (6), [g butyric acid/(g biomass.h)] - k ₅ constant in Equation (7), [g butanol/g substrate] - k ₆ constant in Equation (8), [g acetic acid/g substrate] - k ₇ constant in Equation (8), [g acetic acid/(g biomass.h)] - k ₈ constant in Equation (9), [g acetone/g substrate] - k ₉ constant in Equation (10), [g ethanol/g substrate] - k ₁₀ constant in Equation (11), [g acetoin/g substrate] - k ₁₁ constant in Equation (12), [g lactic acid/g substrate] - K _I Inhibition constant, [g inhibitory products/L] - ke maintenance energy requirement for the cell, [g substrate/(g biomass.h)] - K _AA acetic acid saturation constant, [g acetic acid/L] - K _BA butyric acid saturation constant, [g butyric acid/L] - K _S Monod's saturation constant, [g substrate/L] - LA lactic acid concentration in the fermentation broth, [g/L] - m _i ,n _i constants in Equation (14) - n empirical constant, dependent on degree of inhibition. - P concentration of inhibitory products (B+BA+AA), [g/L] - P _max maximum value of product concentration to inhibit the fermentation, [g/L] - pK_a equilibrium constant - r _A rate of acetone production, [g acetone/L.h] - r _AA rate of acetic acid production, [g acetic acid/L.h] - r _AT rate of acetoin production, [g acetoin/L.h] - r _B rate of butanol production, [g butanol/L.h] - r _BA rate of butyric acid production, [g butyric acid/L.h] - r _E rate of ethanol production, [g ethanol/L.h] - RPS Relative Parameter Sensitivity - r _LA rate of lactic acid production, [g lactic acid/L.h] - r _S dS/dt=total substrate consumption rate, [g substrate/L.h] - r _S substrate utilization rate, [g substrate/L.h] - S substrate concentration in the fermentation broth, [g substrate/L] - S ₀ initial substrate concentration, [substrate/L] - t time, [h] - X biomass concentration, [g/L] - Y _X yield of biomass with respect to substrate, [g biomass/g substrate] - Y _{P i} yield of metabolic product with respect to substrate, [g product/g substrate] Derivatives dX/dt rate of biomass production, [g biomass/L.h] - dP _i /dt rate of product formation, [g product/L.h] Greek letters specific growth rate of the culture, [h^–1] - I specific growth rate of the culture in the presence of the inhibitory products, [h^–1] - µ_max maximum specific growth rate of the culture, [h^–1]     

Enzyme production in a cell recycle fermentation system evaluated by computer simulations

Enzyme production in a cell recycle fermentation system was studied by computer simulations, using a mathematical model of -amylase production by Bacillus amyloliquefaciens. The model was modified so as to enable simulation of enzyme production by hypothetical organisms having different production kinetics at different fermentation conditions important for growth and production. The simulations were designed as a two-level factorial assay, the factor studied being fermentation with or without cell recycling, repression of product synthesis by glucose, kinetic production constants, product degradation by a protease, mode of fermentation, and starch versus glucose as the substrate carbon source.The main factor of importance for ensuring high enzyme production was cell recycling. Product formation kinetics related to the stationary growth phase combined with continuous fermentation with cell recycling also had a positive impact. The effect was greatest when two or more of these three factors were present in combinations, none of them alone guaranteeing a good result. Product degradation by a protease decreased the amount of product obtained; however, when combined with cell recycling, the protease effect was overshadowed by the increased production. Simulation of this type should prove a useful tool for analyzing troublesome fermentations and for identifying production organisms for further study in integrated fermentation systems.List of Symbols a proportionality constant relating the specific growth rate to the logarithm of G (h) - a ₁ reaction order with respect to starch concentration - a ₂ reaction order with respect to glucose concentration - c starch concentration (g/l) - c ₀ starch concentration in the feed (g/l) - D dilution rate (h^–1) - e intrinsic intracellular amylase concentration (g product/g cell mass) - E extracellular amylase concentration (g/l) - F volumetric flow rate (l/h) - G average number of genome equivalents of DNA/cell - K ₁ intracellular repression constant - K ₂ intracellular repression constant - K _s Monod saturation constant (g/l) - k ₃ product excretion rate constant (h^–1) - k _I translation constant (g product/g mRNA/h) - k _d first order decay constant (h^–1) - k _dw first order decay constant (h^–1) - k _gl rate constant for glucose production (g/l/h) - k _{m, dgr} saturation constant for product degradation (g/l) - k _st rate constant for starch hydrolysis (g/l/h) - k _t1 proportionality constant for amylase production (g mRNA/g substrate) - k _t2 proportionality constant for amylase production (g mRNA *h/g substrate) - k _w protease excretion rate constant (h^–1) - k _wt1 proportionality constant for protease production (g mRNA/g substrate) - k _wt2 proportionality constant for protease production (g mRNA *h/g substrate) - k _wI translation constant (g protease/g mRNA/h) - m maintenance coefficient (g substrate/g cell mass/h) - n number of binding sites for the co-repressor on the cytoplasmic repressor - Q repression function, K₁/K₂ less than or equal to 1.0 - Q _w repression function, K₁/K₂ less than or equal to 1.0 - r intrinsic amylase mRNA concentration (g mRNA/g cell mass) - r _m intrinsic protease mRNA concentration (g mRNA/g cell mass) - R _ex retention by the filter of the compounds x=: C starch, E amylase, or S glucose - R _t amylase transport rate (g product/g cell mass/h) - R _wt protease transport rate (g protease/g cell mass/h) - R _s rate of glucose production (g/l/h) - R _c rate of starch hydrolysis (g/l/h) - S ₀ feed concentration of free reducing sugar (g/l) - s extracellular concentration of reducing sugar (g/l) - t time (h) - V volume (1) - w intracellular protease concentration (g/l) - W extracellular protease concentration (g/l) - X cell mass concentration (dry weight) (g/l) - Y yield coefficient (g cell mass/g substrate) - substrate uptake (g substrate/g cell mass/h) - specific growth rate of cell mass (h^–1) - _d specific death rate of cells (h^–1) - _m maximum specific growth rate of cell mass (h^–1) - _m,dgr maximum specific rate of amylase degradation (h^–1) This study was supported by the Nordic Industrial Foundation Bioprocess Engineering Programme and the Center for Process Biotechnology, The Technical University of Denmark.     

Carbon dioxide desorption from fermentation broth by use of oxygen vectors

The ability of oxygen vector to extract produced carbon dioxide has been tested in an anaerobic fermentation. During the continuous culture of Clostridium acetobutylicum at pH 4.6 and at a dilution rate of 0.124 h^–1, a feed composed of an emulsion of 18.5% by volume of Forane F66E was able to extract about 9% of the total CO₂ produced under CO₂ partial pressure equal to 0.42 atm. A theoretical evaluation of the extracted amount, based on the hypothesis of total saturation of the vector by carbon dioxide, has lead to very good agreement.List of Symbols [AA] g/l acetic acid concentration - [BA] g/l butyric acid concentration - D 1/h Q _w /V dilution rate - [ETH] g/l ethanol concentration - H _w Henry constant of CO₂ for water at 37°C (=23.91 mmol/(l atm)) - H _F Henry constant of CO₂ for Forane at 37°C (=83.4 mmol/(l atm)) - H _i g/mol molar mass of componenti - P _i atm partial pressure of gasi - W _w l/h aqueous flow - Q_f 1/h Forane flow - mmol/(lh) dissolved CO₂ flow in aqueous effluent - mmol/(lh) CO₂ gas flow - mmol/(lh) CO₂ gas flow without Forane - mmol/(lh) CO₂ gas flow with Forane - mmol/(lh) total CO₂ production - r _X g/(lh) biomass production rate - r _G mmol/(lh) total gas flow - mmol/(lh) hydrogen production - mmol/(lh) nitrogen flow - r _S mmol/(lh) glucose input - V 1 fermentor volume     

A mathematical model of kinetics of the biosynthesis of tetracyclines

Summary A mathematical model simulating the behaviour or Streptomyces aureofaciens in batch culture under conditions when tetracyclines are synthesized in excessive amounts has been formulated. The response of the mathematical model to the experimental conditions applied corresponds with data obtained in the experiments. The mathematical model demonstrated that the level of tetracycline production is determined during the period of culture growth beginning with exhaustion of inorganic phosphate from the medium and ending with inhibition of the synthesis of enzymes caused by the synthesized tetracyclines. Further tetracycline synthesis is then proportional to the amount of enzymes synthesized in this interval.List of symbols E Activity of ACT-oxygenase (10×nkat/g) - P Product concentration (mg/l) - k ₁-k ₆ Rate constants - K _S Saturation constant (g sugar/l) - K _I1 Inhibition constant (mg product/l) - K _I2 Inhibition constant (mM phosphate/l) - K _I3 Inhibition constant (mg product/l) - S ₁ Substrate sucrose (g sugar/l) - S ₂ Substrate concentration — phosphate (mM/l) - r _P Specific rate of product formation (mg product/g · h) - r _E Specific rate of enzyme synthesis (10×nkat/g² · h), Expressed by activity units - t Cultivation time (hour) - X Biomass dry weight (g/l) - Y _S/X Yield coefficient - Specific growth rate (h^-1)     

Influence of substrate transport on the activity of immobilized Papaver somniferum cells

Summary Intraparticle diffusion resistance was studied for Papaver somniferum cells immobilized by Ca alginate gel. In callus tissue, these plant cells convert codeinone to codeine. First, the diffusion rates of substrates in the gel were measured, followed by investigation of the consumption rates of the substrates by free cells. The consumption rate of sucrose was zero order in relation to sucrose concentration, whereas that of codeinone was first order in relation to its concentration. The oxygen consumption rate obeyed Michaelis-Menten type kinetics with respect to dissolved oxygen concentration. Combining the reaction rates and diffusion rates allows calculation of the extent of the effect of diffusion limitation on the overall reaction rates. The analysis showed that the effectiveness factor for each substrate was about unity and that the influence of diffusion resistance was negligible. However, the oxygen concentration decreased considerably inside the particle, and this may affect the activity of the plant cell for repeated use over a long time period. Thus, deactivation proceeds due to the oxygen deficit although the temporal reaction rate is not affected.Abbreviations C _c cell concentration (g/l) - C _cod codeinone concentration (g/l) - c _{O 2} dissolved oxygen concentration (g/l) - K _m constant in Eq. (3) (g/l) - K _cod rate constant in Eq. (1) (l/g of cells per second) - k _suc rate constant in Eq. (2) (g sucrose/g of cells per second) - R radius of particles (mm) - r distance from the centre of the particle (mm) - r _cod consumption rate of codeinone (g codeinone/g of cells per second) - r _{O 2} consumption rate of O₂ (g oxygen/g of cells per second) - r _suc consumption rate of sucrose (g sucrose/g of cells per second) - V _m maximum respiration rate (g oxygen/g of cells per second) T. Nozawa is now with the Department of Agricultural Chemistry, University of TokyoT. Isohara is now with the Nippon Steel Corporation     

Anaerobic digestion of palm oil mill effluent and condensation water waste: an overall kinetic model for methane production and substrate utilization

The process of anaerobic digestion is viewed as a series of reactions which can be described kinetically both in terms of substrate utilization and methane production. It is considered that the rate limiting factor in the digestion of complex wastewaters is hydrolysis and this cannot be adequately described using a Monod equation. In contrast readily assimilable wastewaters conform well to this approach. A generalized equation has thus been derived, based on both the Monod and Contois equations, which serves extreme cases. The model was verified experimentally using continuous feed anaerobic digesters treating palm oil mill effluent (POME) and condensation water from a thermal concentration process. POME represents a complex substrate comprising of unhydrolyzed materials whereas the condensation water is predominantly short chain volatile fatty acids. Substrate removal and methane production in both cases could be predicted accurately using the generalized equation presented.List of Symbols A (=K_skY/K_h) Kinetic parameter - B Specific methane yield, 1 of CH₄/g of substrate added B₀ Maximum specific methane yield, 1 of CH₄/g of substrate added at infinity - C Empirical constant in Contois equation - F Volumetric substrate removal rate, g/l day - k Hydrolysed substrate transport rate coefficient, 1/days - K (=YC) Kinetic parameter in Chen-Hashimoto equation - K _h Substrate hydrolysis rate coefficient, 1/days - K _s Half-saturation constant for hydrolysed substrate, g/l - M _v Volumetric methane production rate, 1 of CH₄/l day - MS Mineral solids, g/l - MSS Mineral suspended soilds, g/l - POME Palm oil mill effluent - R (=S_r/S_T0) Refractory coefficient - S _h Concentration of hydrolysed substrate, g/l - S _u Intracellular concentration of hydrolysed substrate, g/l - S ₀ Input biodegradable substrate concentration, g/l - S Biodegradable substrate concentration in the effluent or in the digester, g/l - S _r Refractory feed substrate concentration, g/l - S _T0 (=S₀+S_r) Total feed substrate concentration, g/l - S _T (S+S_r) Total substrate concentration in the effluent, g/l - TS Total solids, g/l - TSS Total suspended solids, g/l - VFA Total volatile fatty acids, g/l - VS Volatile solids, g/l - VSS Volatile suspended solids, g/l - X Biomass concentration, g/l - Y Biomass yield coefficient, biomass/substrate mass - Hydraulic retention time, days. - Specific growth rate of microorganisms, l/days - _m Maximum specific growth rate of microorganisms, l/days The authors wish to express their gratitude to the Departamento de Postgrado y Especialización del CSIC and to the Consejería de Educación y Ciencia de la Junta de Andalucia for their financial support of this work.     

A kinetic model and simulation of starch saccharification and simultaneous ethanol fermentation by amyloglucosidase and Zymomonas mobilis

A mathematical model is described for the simultaneous saccharification and ethanol fermentation (SSF) of sago starch using amyloglucosidase (AMG) and Zymomonas mobilis. By introducing the degree of polymerization (DP) of oligosaccharides produced from sago starch treated with -amylase, a series of Michaelis-Menten equations were obtained. After determining kinetic parameters from the results of simple experiments carried out at various substrate and enzyme concentrations and from the subsite mapping theory, this model was adapted to simulate the SSF process. The results of simulation for SSF are in good agreement with experimental results.List of Symbols g/g rate coefficient of production - _max 1/h maximum specific growth rate - E %, v/w AMG concentration - G ₁ mmol/l glucose concentration - G _c mmol/l glucose concentration consumed - G _f mmol/l glucose concentration formed - G _n mmol/l n-mer maltooligosaccharide concentration - K _i g/l ethanol inhibition constant for ethanol production - K _g mmol/l glucose inhibition constant for glucose production - K _p mmol/l glucose limitation constant for ethanol production - K _x mmol/l glucose limitation constant for cell growth - K _m,n mmol/l Michaelis-Menten constant for n-mer oligosaccharide - k _e %, v/w enzyme limitation constant - k _es proportional constant - k _{max, n} 1/s maximal velocity for n-mer digestion - k _s g/l substrate limitation constant - m _s g/g maintenance energy - MW _n g/mol molecular weight of n-mer oligosaccharide - P g/l ethanol concentration - P ₀ g/l initial ethanol concentration - P _m g/l maximal ethanol concentration - Q _pm g/(g · h) maximum specific ethanol production rate - S _n mmol/h branched n-mer oligosaccharide concentration - S ₀ g/l initial starch concentration - S _sta g/l starch concentration - S _tot g/l total sugar concentration - V _{max, n} 1/h maximum digestion rate of n-mer oligosaccharide - V ₀ g/(l · h) initial glucose formation rate - X g/l cell mass - X ₀ g/l initial cell mass - Y _p/s g/g ethanol yield - Y _x/s g/g cell mass yield     

Kinetic behavior of penicillin acylase immobilized on acrylic carrier

The usefulness of Lilly's kinetic equation to describe penicillin G hydrolysis performed by immobilized penicillin acylase onto the acrylic carrier has been shown. Based on the experimental results characteristic kinetic constants have been estimated. The effect of noncompetitive inhibition of 6-amino penicillanic acid has not been found. Five components of reaction resistance have been defined. These components were also estimated for the reaction of the native enzyme as well as the Boehringer preparation.List of Symbols C _E g/m³ enzyme concentration - C _P,C _Q mol/m³ product concentrations - C _S mol/m³ substrate concentration - C _SO mol/m³ initial substrate concentration - K _A mol/m³ constant which defines the affinity of a substrate to the enzyme - K _iS mol/m³ substrate inhibitory constant - K _iP mol/m³ PhAA inhibitory constant - K _iQ mol/m³ 6-APA inhibitory constant - k ₃ mol/g/min constant rate of dissociation of the active complex - R(1) concentrational component of reaction resistance - R(2) resistance component derived from substrate affinity - R(3) resistance component due to the inhibition of the enzyme by substrate - R(4) resistance component due to the inhibition of the enzyme by PhAA - R(5) resistance component due to inhibition of the enzyme by 6-APA - r = dC_s/dt mol/m³ min rate of reaction - t min reaction time - (i) relative resistance of reaction     

Lactic acid production by batch fermentation of whey permeate: A mathematical model

Summary The batch fermentation of whey permeate to lactic acid was improved by supplementing the broth with enzyme-hydrolyzed whey protein. A mathematical model based on laboratory results predicts to a 99% confidence limit the kinetics of this fermentation. Cell growth, acid production and protein and sugar use rates are defined in quantifiable terms related to the state of cell metabolism. The model shows that the constants of the Leudeking-Piret model are not true constants, but must vary with the medium composition, and especially the peptide average molecular weight. The kinetic mechanism on which the model is based also is presented.Nomenclature K _i lactic acid inhibition constant (g/l) - K _pr protein saturation constant during cell growth (g/l) - K _pr protein saturation constant during maintenance (g/l) - K _s lactose saturation constant (g/l) - [LA] lactic acid concentration (g/l) - [PR] protein concentration (g/l) - [S] lactose concentration (g/l) - t time (h) - [X] cell mass concentration (g/l) - , fermentation constants of Leudeking and Piret - specific growth rate (l/h) - Y _{g, LA/S} acid yield during cell growth (g acid/g sugar) - Y _{m, LA/S} acid yield during maintenance (g acid/g sugar) - Y _x/pr yield (g cells/g protein) - specific sugar use rate during cell growth (g sugar/h·g cell) - specific sugar use rate during maintenance (g sugar/h·cell)     

On-line monitoring and modelling based process control of high rate nitrification — lab scale experimental results

This paper presents a new concept for the control of nitrification in highly polluted waste waters. The approach is based on mathematical modelling. To determine the substrate degradation rates of the microorganisms involved, a mathematical model using gas measurement is used. A fuzzy-controller maximises the capacity utilisation efficiencies. The experiments carried out in a lab-scale reactor demonstrate that even with highly varying ammonia concentrations in the influent, the nitrogen concentrations in the effluent can be kept within legal limits.List of Symbols c mg/l concentration - c mg/l gas concentration - H ₂ Henry-coefficient - k _L a 1/h mass transfer coefficient - mol/l dissociation constant - K _iS mg/l substrate inhibitor constant - k _iH mg/l inhibitor constant - k _S mg/l saturation constant - K _O2 mg/l oxygen saturation constant - r(B) mg/lh growth rate - r(S) mg/lh degradation reaction rate - t _v h retention time - T °C temperature - V 1 volume - V 1/h flow rate - Y g/g yield coefficient - k _b capacity utilisation efficiency - 1/h specific growth rate     

Interrelation between penicillin productivity and growth rate

Summary Fermentations were carried out in an 801 tower-loop reactor with pellets of Penicillium chrysogenum. The development of the inner structure of the pellets with regard to various fermentation conditions was observed by means of histological preparations of the pellets. Under conditions of energy-source-limitation mycelial tip growth and lysis of other mycelial parts exist simultaneously. Thus the net growth rate (formation rate of cell mass) is higher than the gross growth rate (multiplication rate of cell mass). Under conditions of nitrogen limitation, gross growth rate and net growth rate are identical. A very strict correlation between gross growth rate and penicillin production rate was found as long as sufficient oxygen supply could be maintained and carbon catabolite repression was avoided. The energy source requirement of the biomass can be described with the sum of three terms that correspond to gross growth, lysis compensation growth and maintenance.Symbols a Constant 1/l h - b Constant - K Decay rate constant for product 1/h - K ₁ Substrate inhibition constant g/l - K _op Controls saturation constant for oxygen g/l - K _p Saturation constant for substrate g/l - m Maintenance coefficient 1/h - ms Apparent maintenance coefficient 1/h - O Dissolved oxygen concentration g/l - P Product concentration g/l - p Exponent of O - q Specific productivity 1/h - S Substrate concentration g/l - t Time h - t ₁ Beginning of production phase h - t ₂ Time of pellet dissolution h - V Liquid volume of fermentation broth l - X Dry cell mass concentration g/l - Y Yield of dry cell mass from energy substrate - g Specific gross growth rate of biomass 1/h - l Specific lysis rate of cell mass 1/h - n Specific net growth rate of cell mass 1/h - p Maximum specific rate of product formation 1/h     

Product formation during batch fermentation with recombinant Escherichia coli containing a runaway plasmid

The product formation during batch fermentation with recombinant E. coli containing a runaway replication plasmid has been examined. Theoretical modelling is combined with experimental work to study the effect of operating conditions. In particular the influence of induction profile has been investigated. High sensitivity to operating conditions is observed, and both model and experimental data illustrate the presence of very narrow limits for an optimal induction profile.List of Symbols f _i function for allocation of energy to the i'th reaction in the one substrate model - g _i function for allocation of energy to the i'th reaction in the two substrate model - h function for inhibition by plasmid material - K _i (h^–1) kinetic rate constant for the i'th reaction - k _i (g/l) saturation constants - K _p (g P/g biomass) saturation constant for recombinant protein synthesis - K _s (g/l) inhibition constant of glucose on acetate metabolism - K _p,i (g P/g biomass) inhibition constant of plasmid material on cellular activity - p (g/l) extracellular acetic acid concentration - r _i (h^–1) specific rate of i'th reaction - s (g/l) extracellular glucose concentration - X _i (g i/g biomass) intracellular concentration of the i'th component - _ij stoichiometric coefficients for the i'th metabolic product in the j'th reaction - _ij stochiometric coefficients for the i'th component in the biotic phase in the j'th reaction - _i relative allocation of energy to the i'th reaction with growth on acetate compared with growth on glucose     

Physiological control and process kinetics of clavine alkaloid production byClaviceps purpurea

Summary Kinetic parameters of production of clavine alkaloids were evaluated in twoClaviceps purpurea strains. Mutagenesis brought about enhanced resistance of the biosynthetic system towards alkaloids. Addition of glucose into the fermentation medium altered the zero order kinetics of production to activation-inhibition kinetics. The glucose treatment allowed performance of both elymoclavine-inhibitionless and clavine alkaloid-decompositionless fermentations if a combination of fermentation and separation units in a closed loop was used.Nomenlacture k ₁ rate constant of agroclavine synthesis (mg Agro · mg Elymo/l·g DW·day for stage 1, mg Agro/g DW·day for stage 2) - k ₂ parameter describing inhibition of agroclavine formation rate by elymoclavine (mg Elymo/l) - k ₃ specific rate of agroclavine decay (l/g DW·day) - k ₄ maximal specific rate of elymoclavine synthesis (stage 1, 1/g DW·day, stage 2, mg Elymo/g DW·day) - k ₄ ^– maximal specific rate of elymoclavine synthesis in stage 1 (inhibition-activation mechanism) (mg Elymo/g DW·day) - k ₅ physiological constant describing the elymoclavine decay rate (l²/g DW·day·mg Elymo) - k ₅ ^– physiological constant describing the activation of elymoclavine biosynthesis by elymoclavine (mg Elymo/l) - k ₆ physiological constant describing the repression of elymoclavine biosynthesis by elymoclavine (mg Elymo/l) - k ₇ maximal specific growth rate (1/day) - k ₈ specific rate of biomass decay (l/g DW·day) - A agroclavine concentration (mg/l) - E elymoclavine concentration (mg/l) - r _A specific rate of agroclavine biosynthesis (mg Agro/g DW·day) - r _E specific rate of elymoclavine biosynthesis (mg Elymo/g DW·day) - r _i specific rate of alkaloid biosynthesis (mg alkaloid/g DW·day) - X dry biomass concentration (g/l) - specific growth rate (1/day) Abbreviations Agro agroclavine - Elymo elymoclavine - Chano chanoclavine - DW dry weight of biomass     

Fed-batch culture of hybridoma cells: comparison of optimal control approach and closed loop strategies

Control of fed-batch culture of hybridoma cells was investigated based on two approaches optimal control theory and feedback control. Experiments were conducted for both approaches-with a feed enriched in glutamine. The optimal feed trajectory, a decreasing one, yielded a final monoclonal antibody (MAb) concentration of 170 mg/l, a three-fold increase compared to a typical batch operation.The feedback strategy relied on the on-line estimation of the net specific growth rate of cells from the measurement of the CO₂ production rate with a mass-spectrometer. A PI controller was then used to maintain the growth rate at a desired value by adjusting the dilution rate to the reactor. For the chosen set-point (0.1 d^–1), the final MAb concentration achieved was about 100 mg/1. It was found that there was a delay in the assimilation of the glutamine that should be included in the model to explain the lower MAb production in feedback mode. A higher production can be expected also for a lower set-point in feedback operation.List of Symbols Amm mM ammonia concentration - CPR l/(ld) carbon dioxide production rate - D _t l/d dilution rate - e _t l/d control error - F L/d feed flow rate - Glc mM glucose concentration - Gln mM glutamine concentration - Lac mM lactate concentration - I mg performance index - k _d l/d specific death rate - K _damm l/(mM · d) kinetic parameter for death rate - K _dgln mM kinetic parameter for death rate - K _dlac l/(mM·d) kinetic parameter for death rate - K _c l controller gain - K _glc mM kinetic parameter for growth rate - K _gln mM kinetic parameter for growth rate - K _tr L/(cell·d) transport coefficient - K l/d kinetic parameter for Mab production - m _glc mM/(cell·d) maintenance coefficient - M _Ab mg/l monoclonal antibody concentration - P _t covariance matrix - q _glc l/(l·cell·d) specific CO₂ production rate - q _glc mM/(cell·d) specific glucose uptake rate - q _gln mM/(cell·d) specific glutamine uptake rate - q _Mab mg/(l·cell·d) specific monoclonal antibody production - t _f d final culture time - T d sampling rate - u control input - V l reactor volume - X cell/l total cells concentration - X _v cell/l viable cells concentration - Y yield coefficient Greek mg/cell variable yield coefficient - ₀ mg/(cell·d) growth-associated kinetic parameter - mg/(cell·d) non growth-associated kinetic parameter - _t+1 defined by Eq. (19) - forgetting factor - l/d specific growth rate - _max l/d specific growth rate - _i d controller integral time constant     

Modeling of the pyruvate production with<Emphasis Type="Italic"> Escherichia coli</Emphasis> in a fed-batch bioreactor

A family of 10 competing, unstructured models has been developed to model cell growth, substrate consumption, and product formation of the pyruvate producing strain Escherichia coli YYC202 ldhA::Kan strain used in fed-batch processes. The strain is completely blocked in its ability to convert pyruvate into acetyl-CoA or acetate (using glucose as the carbon source) resulting in an acetate auxotrophy during growth in glucose minimal medium. Parameter estimation was carried out using data from fed-batch fermentation performed at constant glucose feed rates of q_VG=10 mL h^–1. Acetate was fed according to the previously developed feeding strategy. While the model identification was realized by least-square fit, the model discrimination was based on the model selection criterion (MSC). The validation of model parameters was performed applying data from two different fed-batch experiments with glucose feed rate q_VG=20 and 30 mL h^–1, respectively. Consequently, the most suitable model was identified that reflected the pyruvate and biomass curves adequately by considering a pyruvate inhibited growth (Jerusalimsky approach) and pyruvate inhibited product formation (described by modified Luedeking–Piret/Levenspiel term).List of symbols c_A acetate concentration (g L^–1) - c_A,0 acetate concentration in the feed (g L^–1) - c_G glucose concentration (g L^–1) - c_G,0 glucose concentration in the feed (g L^–1) - c_P pyruvate concentration (g L^–1) - c_P,max critical pyruvate concentration above which reaction cannot proceed (g L^–1) - c_X biomass concentration (g L^–1) - K_I inhibition constant for pyruvate production (g L^–1) - K_I^A inhibition constant for biomass growth on acetate (g L^–1) - K_P saturation constant for pyruvate production (g L^–1) - K_P inhibition constant of Jerusalimsky (g L^–1) - K_S^A Monod growth constant for acetate (g L^–1) - K_S^G Monod growth constant for glucose (g L^–1) - m_A maintenance coefficient for growth on acetate (g g^–1 h^–1) - m_G maintenance coefficient for growth on glucose (g g^–1 h^–1) - n constant of extended Monod kinetics (Levenspiel) (–) - q_V volumetric flow rate (L h^–1) - q_VA volumetric flow rate of acetate (L h^–1) - q_VG volumetric flow rate of glucose (L h^–1) - r_A specific rate of acetate consumption (g g^–1 h^–1) - r_G specific rate of glucose consumption (g g^–1 h^–1) - r_P specific rate of pyruvate production (g g^–1 h^–1) - r_P,max maximum specific rate of pyruvate production (g g^–1 h^–1) - t time (h) - V reaction (broth) volume (L) - Y_P/G yield coefficient pyruvate from glucose (g g^–1) - Y_X/A yield coefficient biomass from acetate (g g^–1) - Y_X/A,max maximum yield coefficient biomass from acetate (g g^–1) - Y_X/G yield coefficient biomass from glucose (g g^–1) - Y_X/G,max maximum yield coefficient biomass from glucose (g g^–1) - growth associated product formation coefficient (g g^–1) - non-growth associated product formation coefficient (g g^–1 h^–1) - specific growth rate (h^–1) - _max maximum specific growth rate (h^–1)     

Inhibitory effect of dihydroxyacetone onGluconobacter oxydans: Kinetic aspects and expression by mathematical equations

Summary Microbial conversion of glycerol into dihydroxyacetone (DHA) byGluconobacter oxydans was subjected to inhibition by excess substrate. Comparison of cultures containing increasing initial DHA contents (0 to 100 g l^–1) demonstrated that DHA also inhibited this fermentation process. The first effect was on bacterial growth (cellular development stopped when DHA concentration reached 67 gl^–1), and then on oxidation of glycerol (DHA synthesis only occurred when the DHA concentration in the culture medium was lower than 85 g l^–1). Productivity, specific rates and, to a lesser extent, conversion yields decreased as initial concentrations of DHA increased. The changes in the specific parameters according to increasing initial DHA contents were described by general equations. These formulae satisfactorily express the concave aspect of the curves and the reduction in biological activity when the cells were in contact with DHA concentrations of up to 96 g l^–1.Abbreviations X, S, P biomass, substrate, product concentrations - r _x,r _s,r _p rates of growth, consumption and production - ,q _s,q _p specific rates of growth, glycerol consumption and DHA production - Y _x/s, Y_p/s conversion yields of substrate into biomass and product - K _s constant of affinity of cells to the substrate - K _ip product inhibition constant - P _m threshold concentration of DHA in substrate     

Lactose continuous fermentation with cells recycled by ultrafiltration and lactate separation by electrodialysis: model identification

Summary An off-line parameter estimation method has been developed to predict the dynamic behaviour of a continuous lactose fermentation system. The model used is an unstructured model taking into account cell growth, substrate consumption, and metabolite production (lactic acid). This method, based on the Hooke-Jeeves non-linear-programming technique, results in a good estimation of the biological parameters of the model, and so gives a better understanding of the different phenomena involved in lactose fermentation.Nomenclature Cp, Cs, Cz, Dp, Ds, Dz coefficients in system (A) - Fe bioreactor influent flow rate (1/h) - I current in the ED unit (A) - J lactate flux in the ED unit (g/h) - Kd mortality constant (h^-1) - Kp product inhibition constant (g/l) - Ks strbstrate saturation constant (g/l) - P ₀ product concentration in the bioreactor (g/l) - P ₁ product concentration in the D tank (g/l) - P _0r estimation of P ₀ (g/l) - Q ₀ retentate flow rate (UF influent) (1/h) - Q ₁ permeate flow rate (1/h) - Q ₂₂ cell bleed flow rate (1/h) - Q ₃ recycling flow rate in the ED (influent) (1/h) - Se substrate concentration in the influent (g/l) - S ₀ supstrate concentration in the bioreactor (g/l) - S ₁ substrate concentration in tank D (g/l) - S _0r estimation of S ₀ (g/l) - t time (h) - V ₀ fermentation broth volume (1) - V ₁ tank D volume (1) - X ₀ biomass concentration in the bioreactor (g/l) - Y _P/S (=1/Y _S/P) lactic acid yield coefficient (g lactic acid/g lactose consumed) - Y _X/S (=1/Y _S/X) cell yield coefficient (g cells produced/g lactose consumed) - Y _X/Z (=1/Y _Z/X) second cell yield coefficient (g cells produced/g nitrogen consumed) - Y _x, Y _m input mathematical parameters of the linear system (M ₂) - Ze nitrogen concentration in the influent (g/l) - Z ₀ nitrogen concentration in the bioreactor (g/l) - Z ₁ nitrogen concentration in tank D (g/l) - Z _0r estimation of Z ₀ (g/l) - , constants of the Luedeking and Piret's model - specific growth rate (h^-1) - _max maximum specific growth rate (h^-1)     

Circadian rhythmicity in a fermentation process?

Summary An idea is proposed for the role of the circadian rhythmicity in the control of the oscillatory behavior observed in the growth and product formation during the cell-retention continuous culture of Clostridium acetobutylicum. C. acetobutylicum is highly sensitive to the permeability of the cell membrane. A physical mechanism for the variability of the cytoplasmic membrane has been proposed suggesting that the performance of the cell membrane, due to its liquid crystalline structure, is influenced by the external forces (e.g. earth's magnetic field). A previously developed Physiological State Model was extended by incorporating the effect of external forces on the cell membrane permeability. The new mathematical model could simulate the observed oscillatory behavior of the microbial culture. Some experimental results in support of the theoretical predictions have been presented.Nomenclature a Anisotropy - B Butanol concentration in the fermentation broth (g/l) - B _i Intracellular butanol concentration (g/l) - B _ex Extracellular butanol concentration (g/l) - Mean value of the butyric acid solution concentration (g/l) - BA _i Intracellular butyric acid concentration (g/l) - BA _ex Extracellular butyric acid concentration (g/l) - D Dilution rate (l/h) - H Magnetizing force (oersted) - K Constant in Equation (1) - k B Constant in Equation (15) - K _BA Saturation constant - k _{BA 1} Constant in Equation (13) - k _{BA 2} Constant in Equation (13) - K _D Constant in Equation (13) - k _{G 1} Constant in Equation (8) - k _{G 2} Constant in Equation (8) - k _{G 3} Constant in Equation (9) - K _I Inhibition Constant - k _p Constant in Eq. (11) - K _S Monod constant - n Number of the active sugar transport sites - P Cellular membrane permeability (l/g wet cell·h) - q _S Specific rate of substrate utilization (g substrate/g biomass·h) - S Substrate concentration in the fermentation broth (g/l) - S _O Substrate concentration in the feed solution (g/l) - t Time (h) - X Total biomass concentration (g/l) - X ₁ Active biomass concentration (g/l) - X ₂ Non-active biomass concentration (g/l) Greek Letters Ratio of the dry to wet cell weight (g dry cell/g wet cell) - ₁ Constant in Equation (6) - ₂ Constant in Equation (6) - ₃ Constant in Equation (6) - Specific culture growth rate (1/h)     

External factors involved in the regulation of an extracellular proteinase synthesis in Bacillus megaterium

Summary A mathematical model was formulated to describe the kinetics and stoichiometry of growth and proteinase production in Bacillus megaterium. Synthesis of the extracellular proteinase in a batch culture is repressed by amino acids. The specific rate of formation of the enzyme (r _E) can be described by the formula {ie373-1}, where k ₂ and k ₃ stand for the non-repressible and repressible part of enzyme synthesis respectively, k _{S 2} is a repression coefficient and S ₂ indicates the concentration of amono acids; the values of k ₂ and k _{S 2} depend on the composition of the mixture of amino acids. Even in a high concentration, a single amino acid is less effective than a mixture of amino acids. The dependence of the proteinase repression on the concentration of an external amino acid (leucine) follows the same course as its rate of incorporation into proteins, approaching saturation at concentrations higher than 50 M (half saturation approximately 10 M). However, the total uptake of leucine did not exhibit any saturation even at 500 M external concentration.Symbols X biomass concentration, g/l - E proteinase concentration, unit/l - t time, h - S ₁ concentration of glucose, g/l - S ₂ concentration of amino acids, g/l - specific growth rate, l/h - rE specific rate of enzyme production, unit/g/h - k ₁ growth kinetic constant, l/h - k ₂ product formation kinetic constant (for non-repressible part of enzyme synthesis), unit/g - k ₃ product formation kinetic constant (for repressible portion of enzyme synthesis), unit/g - k _{S 1} saturation constant, g/l - k _{S 2} repression coefficient for a certain amino acid or amino acids mixture, g/l