Effect of time delay in specific growth rate on the periodic operation of bioreactors with input multiplicities

The effect of time delay in specific growth rate () on the periodic operation of bioreactors with input multiplicities is theoretically analyzed for productivity improvement. A periodic rectangular pulse is applied either in feed substrate concentration (S_f) or in dilution rate (D). Periodic operation under feed substrate concentration cycling gives improvement in productivity at lower value of ¯S_f of the two steady-state multiplicities of S_f only when the time delay in is larger. Whereas the larger value of ¯S_f gives improvement in average productivity for all values of time delay. Dilution rate (D) cycling gives an improvement in average productivity particularly for larger time delay in . This improvement in average productivity is obtained only at smaller value of dilution rate out of the two steady-state input multiplicities of D.List of Symbols D 1/h dilution rate - F memory function - g dummy variable - K_i g/l substrate inhibition constant - K_m g/l substrate saturation constant - P g/l product concentration - P_m g/l product saturation constant - Q g/(hl) product cell produced per unit time - S g/l substrate concentration - S_f g/l feed substrate concentration - S_f,p g/l feed substrate concentration during fraction of a period - X g/l biomass concentration - Y_X/S g/g cell mass yield - w variable either S or Z - Z g/l weighted average of substrate concentration Greek Letters 1/h time delay parameter - ₁ , ₂ product yield parameters, g/g and 1/h - pulse width expressed as a fraction of a period - 1/h specific growth rate - _m 1/h maximum specific growth rate - h period of oscillation - – average value     

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.     

Diagnosing lactic acid fermentation based on specific rates of growth,substrate consumption and product formation

The on-line calculated specific rates of growth, substrate consumption and product formation were used to diagnose microbial activities during a lactic acid fermentation. The specific rates were calculated from on-line measured cell mass, and substrate and product concentrations. The specific rates were more sensitive indicators of slight changes in fermentation conditions than such monitored data as cell mass or product concentrations.List of Symbols 1/h specific rate of cell growth - 1/h specific rate of substrate consumption - 1/h specific rate of product formation - ^* dimensionless specific rate of cell growth - ^* dimensionless specific rate of substrate consumption - ^* dimensionless specific rate of product formation - _max 1/h maximum specific rate of cell growth - _max 1/h maximum specific rate of substrate consumption - _max 1/h maximum specific rate of product formation - X g/l cell mass concentration - S g/l substrate concentration - S ^* dimensionless substrate concentration - S ₀ g/l initial substrate concentration - P g/l product concentration     

Phosphate-limited growth of Chromatium vinosum in continuous culture

Chromatium vinosum DSM 185 was grown in continuous culture at a constant dilution rate of 0.071 h^-1 with sulfide as the only electron donor. The organism was subjected to conditions ranging from phosphate limitation (S _R-phosphate=2.7 M and S _R-sulfide=1.8 mM) to sulfide limitation (S _R-phosphate=86 M and S _R-sulfide=1.8 mM). At values of S _R-phosphate below 7.5 M the culture was washed out, whereas S _R-phosphate above this value resulted in steady states. The saturation constant (K ) for growth on phosphate was estimated to be between 2.6 and 4.1 M. The specific phosphorus content of the cells increased from 0.30 to 0.85 mol P mg^-1 protein with increasing S _R-phosphate. The specific rate of phosphate uptake increased with increasing S _R-phosphate, and displayed a non-hyperbolic saturation relationship with respect to the concentration of phosphate in the inflowing medium. Approximation of a hyperbolic saturation function yielded a maximum uptake rate (V _max) of 85 nmol P mg^-1 protein h^-1, and a saturation constant for uptake (K _t) of 0.7 M. When phosphate was supplied in excess 8.5% of the phosphate taken up by the cells was excreted as organic phosphorus at a specific rate of 8 nmol P mg^-1 protein h^-1.Non-standard abbreviations BChla bacteriochlorophyll a - D dilution rate; _max, maximum specific growth rate - maximum specific growth rate if the substrate were not inhibitory - K saturation constant for growth on phosphate - V _max maximum rate of phosphate uptake - K _i saturation constant for phosphate uptake - K _i inhibition constant for growth in the presence of sulfide - S _R concentration of substrate in the inflowing medium     

The induction and repression of benzene and catechol oxidizing capacity of Pseudomonas putida ML2 studied in perturbed chemostat culture

The oxidation of catechol, an intermediate in benzene catabolism, was studied using transient variations in dissolved oxygen tension (DOT) when a succinate limited steady state culture of Pseudomonas putida ML2 was perturbed with a pulse of another substrate. A model was developed and tested for the effect of fluctuations in oxidizing enzyme activity on DOT. It was found that the rate of induction of catechol oxidizing enzymes was independent of dilution rate up to a relative growth rate /_max of 0.75. Only at higher dilution rates was catabolite repression observed.Abbreviations DOT dissolved oxygen tension - K _L a gas transfer coefficient - specific growth rate - _max maximum specific growth rate - K_s substrate saturation constant     

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.     

Product inhibition during the feeding phasein fed-batch ethanol fermentation of sugar-cane blackstrap molasses

Summary The following equations represent the influence of the ethanol concentration (E) on the specific growth rate of the yeast cells () and on the specific production rate of ethanol () during the reactor filling phase in fed-batch fermentation of sugar-cane blackstrap molasses: = ₀ - k · E and v = v ₀ · K/(K +E) Nomenclature E ethanol concentration in the aqueous phase of the fermenting medium (g.L^–1) - E_m value of E when = 0 or = 0 (g.L^–1) - F medium feeding rate (L.h^–1) - k empirical constant (L.g^–1.h^–1) - K empirical constant (g.L^–1) - M_as mass of TRS added to the, reactor (g) - M_cs mass of consumed TRS (g) - M_e mass of ethanol in the aqueous phase of the fermenting medium (g) - M_s mass of TRS in the aqueous phase of the fermenting medium (g) - M_x mass of yeast cells (dry matter) in the fermenting medium (g) - r correlation coefficient - S TRS concentration in the aqueous phase of the fermenting medium (g.L^–1) - S_m TRS concentration of the feeding medium (g.L^–1) - t time (h) - T temperature (° C) - TRS total reducing sugars calculated as glucose - V volume of the fermenting medium (L) - V₀ volume of the inoculum (L) - X yeast cells concentration (dry matter) in the fermenting medium (g.L^–1) - filling-up time (h) - specific growth rate of the yeast cells (h^–1) - ₀ value of when E=0 - specific production rate of ethanol (h^–1) - ₀ value of when E=0 - density of the yeast cells (g.L^–1) - dry matter content of the yeast cells     

Phenol degradation by a psychrotrophic strain of Pseudomonas putida

Summary Cell growth and phenol degradation kinetics were studied at 10°C for a psychrotrophic bacterium, Pseudomonas putida Q5. The batch studies were conducted for initial phenol concentrations, S_o, ranging from 14 to 1000 mg/1. The experimental data for 14<=S_o<=200 mg/1 were fitted by non-linear regression to the integrated Haldane substrate inhibition growth rate model. The values of the kinetic parameters were found to be: _m=0.119 h^–1, K _S=5.27 mg/1 and K _I=377 mg/1. The yield factor of dry biomass from substrate consumed was Y=0.55. Compared to mesophilic pseudomonads previously studied, the psychrotrophic strain grows on and degrades phenol at rates that are ca. 65–80% lower. However, use of the psychrotrophic microorganism may still be economically advantageous for waste-water treatment processes installed in cold climatic regions, and in cases where influent waste-water temperatures exhibit seasonal variation in the range 10–30°C.Nomenclature K _S saturation constant (mg/l) - K _I substrate inhibition constant (mg/l) - specific growth rate (h^–1) - _m maximum specific growth rate without substrate inhibition (h^–1) - _max maximum achievable specific growth rate with substrate inhibition (h^–1) - S substrate (phenol) concentration (mg/l) - S_o initial substrate concentration (mg/l) - S_max substrate concentration corresponding to _max (mg/l) - t time (h) - X cell concentration, dry basis (mg DW/l) - X_f final cell concentration, dry basis (mg DW/l) - X_o initial cell concentration, dry basis (mg DW/l) - Y yield factor (mg DW cell produced/mg substrate consumed)     

Polysulfide utilization by Thiocapsa roseopersicina

The purple sulfur bacterium Thiocapsa roseopersicina, being the dominant anoxygenic phototroph in microbial mats, was tested for growth on polysulfide as the electron donor for carbon dioxide fixation. Data collected in continuous cultures revealed _max to be 0.065 h^-1 and the saturation affinity constant K _s to be 6.7 M. The value of the inhibition constant K _i was estimated in batch cultures and was found to be approximately 1100 M. When grown on monosulfide, the organism was capable of trisulfide utilization without lag. Monosulfide-limited growth was established to have a _max of 0.091 h^-1 and K _s of 8.0 M. Field observations revealed polysulfide, present at supra-optimal concentrations, as a major pool of reduced sulfur in a laminated marine sediment ecosystem.Non-standard abbreviations DLP Direct Linear Plot - TS Total Sugar - SS Structural Sugar - P Protein - R _R concentration of growth limiting nutrient in reservoir vessel - S _nutrient residual concentration of growth-limiting nutrient in the culture vessel - S _{sulfur compound} concentration of sulfur in the corresponding compound - D dilution rate - _max maximum specific growth rate - K _s saturation constant - K _i inhibition constant Dedicated to Prof. Dr. Norbert Pfennig on the occasion of his 65th birthday     

Effect of minerals on the production of the delta endotoxin byBacillus thuringiensis subsp.israelensis

Summary A study has been made of the mineral requirements ofBacillus thuringiensis subsp.israelensis for production of the mosquitocide delta endotoxin. The optimum concentrations of K₂HOP₄, MgSO₄.7H₂O and CaCO₃ for toxin production are 1g/l, 0.3g/l and 1g/l respectively while the elements Fe, Mn, Cu are required at levels of 2 g/ml, 5 g/ml and 0.25 g/ml respectively.     

A mathematical model for solid state fermentation in tray bioreactors

A simple mathematical model for the interaction of mass transport with biochemical reaction in solid state fermentations (SSF) in static tray type bioreactors under isothermal conditions has been developed. The analysis has enabled scientific explanations to a number of practical observations, through the concept of critical substrate bed thickness. The model will be most useful in the prediction of the concentration gradients as also in efficient design of these bioreactors.List of Symbols C g/cm³ Oxygen concentration in the bed - C _g g/cm³ Atmospheric oxygen concentration - C ^* Dimensionless oxygen concentration, C/C _g - D _e cm²/h Effective diffusivity - H cm Bed thickness or height - H _c cm Critical bed thickness or height - H _m cm Maximum height of zone of zero oxygen concentration - p _i mg/(g · h) Productivity (Eq. 13) - R g/(cm³ · h) Biochemical reaction rate - t h Fermentation time - t ^* Dimensionless time, D _e t/H² - X mg/cm³ Biomass concentration - X _max mg/cm³ Maximum biomass concentration - y Dimensionless thickness or height, (y = z/H) - y cm Thickness of zone of zero oxygen concentration (Eq. 12) - Y Yield coefficient - z cm Bed thickness or height along tray axis - Bed void fraction - _max h^–1 Specific growth rate - Thiele modulus      

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)     

A model for lipase production by Candida rugosa

A model adequately describing the lipase production by Candida rugosa has been developed, calibrated and validated using new experimental data. Process modelling has been done using CAMBIO software (Computer Aided Modelling of BIOprocesses), allowing to easy and interactively test various hypothesis and reaction schemes.Olive oil, oleic acid and glycerol has been used as substrates. The model satisfactorily describes the time evolution of biomass growth as well as lipase production in all cases. In particular diauxic behavior is successfully characterized.Model development process has helped in obtaining a 3-fold increase in lipase production when using oleic acid as substrate instead of the original olive oil used.List of Symbols Oil g/l Oil concentration - Fa g/l Fatty acids concentration - Gly g/l Glycerol concentration - Cr g/l Biomass (dry weight) - Lp U/ml Lipase - _p Oil hydrolysis rate - _gly Uptake rate on glycerol - _fa Uptake rate on fatty acids - _lp Increase rate of lipase - Y _ca Biomass/Fatty acids yield - Y _cg Biomass/Glycerol yield - Y _la Lipase/Fatty acids yield - k _l Specific growth rate on fatty acids - K _c Saturation constant - K _I Inhibition constant for lipase - k11 Specific growth rate on glycerol - k ₃ Oil hydrolysis parameter     

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     

Development of high frequency multiple shoot formation in Persian clover (<Emphasis Type="Italic">Trifolium resupinatum</Emphasis> L.)

An efficient and reliable micropropagation system for Persian clover (Trifolium resupinatum L.) was developed using different explants and media. Node, hypocotyl and cotyledonary node explants were cultured on Murashige and Skoog (MS) medium supplemented with combinations of either 6-benzyladenine (BA) and indole-3-butyric acid (IBA) or BA, Kinetin (KIN) and IBA. Direct multiple shoots developed within 6weeks in all explants in most media tested. The best shoot multiplication capacity was obtained from cotyledonary node explants on MS medium containing 7.1M BA and 1M IBA or 14.1M BA and 1M IBA. Elongated shoots were rooted on either MS medium alone or combination with different concentrations of indole-3-butyric acid (IBA), indole-3-acetic acid (IAA) and -naphthaleneacetic acid (NAA). High rooting was achieved in half strength MS medium containing 8M IBA.     

Feeding in the rotifer Brachionus calyciflorus

Summary The laboratory feeding behavior of Brachionus calyciflorus varies depending upon the type of food cell available in suspension. When feeding on the yeast Rhodotorula glutinis, rotifers show a continuous increase in ingestion with increased cell density between 0.01 and 1000 g dry weight ml^-1. Effective clearance rates drop from ca. 50 l animal^-1 h^-1 to less than 0.5 l animal^-1 h^-1 over this food density range. When feeding on Englena gracilis, B. calyciflorus ingestion rates are constant between 1.0 and 100 g ml^-1 of available food, averaging close to 25 ng animal^-1 h^-1. The decrease in clearance rate is more striking than with R. glutinis, dropping from 45 l animal^-1 h^-1 at 0.1 g ml^-1 to 0.13 l animal^-1 h^-1 at 100 g ml^-1. Differences between the patterns obtained with the two food types indicate fundamental dissimilarities in the feeding behavior of this rotifer species when presented with these different foods.     

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)     

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     

A modified unstructured mathemathical model for the penicillin G fed-batch fermentation

Summary In this paper, an updated unstructured mathematical model for the penicillin G fed-batch fermentation is proposed, in order to correct some physical and biochemical shortcomings in the model of Heijnen et al. (1979,Biotechnol. Bioeng.,21, 2175–2201) and the model of Bajpai and Reuß (1980,J. Chem. Tech. Biotechnol.,30, 332–344). Its main features are the consistency for all values of the variables, and the ability to adequately describe different metabolic conditions of the mould. The model presented here can be considered as the translation of the latest advances in the biochemical knowledge of the penicillin biosynthesis.Nomenclature t time (h) - S amount of substrate in broth (g) - X amount of cell mass in broth (g) - P amount of product in broth (g) - V fermentor volume (L) - F input substrate feed rate (L/hr) - C _s S/V substrate concentration in broth (g/L) - C _x X/V cell mass concentration in broth (g/L) - C _P P/V product concentration in broth (g/L) - s _F substrate concentration in feed stream (g/L) - E _m parameter related to the endogenous fraction of maintenance (g/L) - E _p parameter related to the endogenous fraction of production (g/L) - K _x Contois saturation constant for substrate limitation of biomass production (g/g DM) - K _s Monod saturation constant for substrate limitation of biomss production (g/L) - K _p saturation constant for substrate limitation of product formation (g/L) - K _i substrate inhibition constant for product formation (g/L) - m _s maintenance constant (g/g DM hr) - k _h penicillin hydrolysis or degradation constant (hr^–1) - Y _x/s cell mass on substrate yield (g DM/g) - Y _p/s product on substrate yield (g/g) - specific substrate consumption rate (g/g DM hr) - specific growth rate (hr^–1) - _substr specific substrate to biomass conversion rate (hr^–1) - _x maximum specific substrate to biomass conversion rate (hr^–1) - specific production rate (g/g DM hr) - _p specific production constant (g/g DM hr)     

Biodegradation of phenol by arthrobacter and modelling of the kinetics

The toxic effects of phenol, a common constituent of many industrial effluents, necessitates treatment of the polluted streams. Biodegradation is a popular technique and enjoys many advantages. The degradation of phenol with Arthrobacter species is studied in batch cultures and it is observed that the substrate is inhibiting. The fit of various models, including the model proposed earlier by us [17], to the experimental data is studied. The model is used to fit available data in literature, which unfortunately is very sparse. In all the cases the present model fits the data best.List of Symbols S mg/l substrate concentration - S ₀ mg/l threshold substrate concentration - K _I mg/l inhibition constant - K _m , K _s mg/l half saturation constant of growth kinetics - m, n constants - 1/h specific growth rate - _m 1/h maximal specific growth rate - X mg/l biomass concentration at time t - X ₀ mg/l initial biomass concentration Abbreviations MTCC Microbial Type Culture Collection - IMTECH Institute of Microbial Technology The cooperation of the staff of the Biosciences and Biotechnology Center, I.I.T. Madras is greatly appreciated.