The production of lactic acid from whey permeate byLactobacillus helveticus

Summary The effect of pH on growth and lactic acid production ofLactobacillus helveticus was investigated in a continuous culture using supplemented whey ultrafiltrate. Maximum lactate productivity of 5 gl^–1h^–1 occurred at pH 5.5. Whey permeates concentrated up to four times were fermented using batch cultures. Maximum lactic acid concentration of 95 gl^–1 was attained, but residual sugars indicated a possible limitation in growth factors.Nomenclature D Dilution rate [h^–1] - X Biomass [gl^–1] - Glu Glucose consentration [gl^–1] - Gal Galactose consentration [gl^–1] - S Substrate, Lactose consentration [gl^–1] - P Product, Lactate consentration [gl^–1] - Y_p/s Yield, defined as P/S [gg^–1] - r_i Rate of synthesis or consumption of i [gl^–1h^–1]     

Factors which influence the sedimentation characteristics of Torulopsis glabrata after growth in a recirculation system

Summary Some environmental affects on cell aggregation described in the literature are briefly summarized. By means of a biomass recirculation culture (Contact system), using the yeast Torulopsis glabrata, the aggregation behavior of cells in static and in dynamic test systems is described. Sedimentation times required to obtain 50 g · l^–1 yeast dry matter in static systems were always higher than in dynamic ones.In addition to, influencing the biomass yield, the specific growth rate of the yeast also affected cell aggregation. The specific growth rate and therefore the aggregation could be regulated by the biomass recirculation rate as well as by the sedimenter volume.Abbreviations f_o Overflow flow rate (l·h^–1) - f_R Recycle flow rate (l·h^–1) - f_t0t Total flow rate through the fermenter (l·h^–1) - g Gram - h Hour - D_R Fermenter dilution rate due to recycle (h^–1) - D_S Fermeter dilution rate due to substrate (h^–1) - D_tot Total fermenter dilution rate (h^–1) - l Liter - Specific growth rate (h^–1) - P_F Fermenter productivity (g·l^–1·h^–1) - P_FS Overall productivity (g·l^–1·h^–1) - R_pM Rates per minute - RS Residual sugar content in the effluent with respect to the substrate concentration (%) - Y Yield of biomass with respect to sugar concentration (%) - Sed 50 Sedimentation time to reach a YDM of 50 g·l^–1 (min) - V Volume (l) - V_F Fermenter volume (l) - V_Sed Sedimenter volume (l) - VVM Volumes per volume and minute - X_F YDM in the fermenter (g·l^–1) - X_F YDM in the recycle (g·l^–1) - X_S Yeast dry matter due to substrate concentration (g·l^–1) - YDM Yeast dry matter (g·l^–1)     

Linear growth in microbial cultures limited by accumulated substrate

Summary The linear growth phase in cultures limited by intracellular (conservative) substrate is represented by a flat exponential curve. Within the range of experimental errors, the presented model fits well the data from both batch and continuous cultures ofEscherichia coli, whose growth is limited in that way.List of symbols D dilution rate, h^–1 - K_S saturation constant, g.L^–1 - S concentration of the limiting substrate, g.L^–1 - S_i concentration of the limiting substrate accumulated in the cells, g.g^–1 - S_o initial concentration of the limiting substrate, g.L^–1 - t time of cultivation, h - t₁ time of exhaustion of the limiting substrate from medium, h - t_o beginning of exponential phase, h - X biomass concentration, g.L^–1 - X₁ biomass concentration at the time of exhaustion of the limiting substrate from the medium, g.L^–1 - X_o biomass concn. at the beginning of exponential phase, g.L^–1 - biomass concn. at steady-state, g.L^–1 - Y growth yield coefficient (biomass/substrate) - specific growth rate, h^–1 - _m maximum specific growth rate, h^–1     

Fed-batch production of baker's yeast using millet (Pennisetum typhoides) flour hydrolysate as the carbon source

A fermentation medium based on millet (Pennisetum typhoides) flour hydrolysate and a four-phase feeding strategy for fed-batch production of baker's yeast,Saccharomyces cerevisiae, are presented. Millet flour was prepared by dry-milling and sieving of whole grain. A 25% (w/v) flour mash was liquefied with a thermostable 1,4--d-glucanohydrolase (EC 3.2.1.1) in the presence of 100 ppm Ca²⁺, at 80°C, pH 6.1–6.3, for 1 h. The liquefied mash was saccharified with 1,4--d-glucan glucohydrolase (EC 3.2.1.3) at 55°C, pH 5.5, for 2 h. An average of 75% of the flour was hydrolysed and about 82% of the hydrolysate was glucose. The feeding profile, which was based on a model with desired specific growth rate range of 0.18–0.23 h^–1, biomass yield coefficient of 0.5 g g^–1 and feed substrate concentration of 200 g L^–1, was implemented manually using the millet flour hydrolysate in test experiments and glucose feed in control experiments. The fermentation off-gas was analyzed on-line by mass spectrometry for the calculation of carbon dioxide production rate, oxygen up-take rate and the respiratory quotient. Off-line determination of biomass, ethanol and glucose were done, respectively, by dry weight, gas chromatography and spectrophotometry. Cell mass concentrations of 49.9–51.9 g L^–1 were achieved in all experiments within 27 h of which the last 15 h were in the fedbatch mode. The average biomass yields for the millet flour and glucose media were 0.48 and 0.49 g g^–1, respectively. No significant differences were observed between the dough-leavening activities of the products of the test and the control media and a commercial preparation of instant active dry yeast. Millet flour hydrolysate was established to be a satisfactory low cost replacement for glucose in the production of baking quality yeast.Nomenclature C _ox Dissolved oxygen concentration (mg L^–1) - CPR Carbon dioxide production rate (mmol h^–1) - C _s0 Glucose concentration in the feed (g L^–1) - C _s Substrate concentration in the fermenter (g L^–1) - C _s.crit Critical substrate concentration (g L^–1) - E Ethanol concentration (g L^–1) - F _s Substrate flow rate (g h^–1) - i Sample number (–) - K _e Constant in Equation 6 (g L^–1) - K _o Constant in Equation 7 (mg L^–1) - K _s Constant in Equation 5 (g L^–1) - m Specific maintenance term (h^–1) - OUR Oxygen up-take rate (mmol h^–1) - q _ox Specific oxygen up-take rate (h^–1) - q _ox.max Maximum specific oxygen up-take rate (h^–1) - q _p Specific product formation rate (h^–1) - q _s Specific substrate up-take rate (g g^–1 h^–1) - q _s.max Maximum specific substrate up-take rate (g g^–1 h^–1) - RQ Respiratory quotient (–) - S Total substrate in the fermenter at timet (g) - S ₀ Substrate mass fraction in the feed (g g^–1) - t Fermentation time (h) - V Instantaneous volume of the broth in the fermenter (L) - V ₀ Starting volume in the fermenter (L) - V _si Volume of samplei (L) - x Biomass concentration in the fermenter (g L^–1) - X ₀ Total amount of initial biomass (g) - X _t Total amount of biomass at timet (g) - Y _p/s Product yield coefficient on substrate (–) - Y _x/e Biomass yield coefficient on ethanol (–) - Y _x/s Biomass yield coefficient on substrate (–) Greek letters Moles of carbon per mole of yeast (–) - Moles of hydrogen atom per mole of yeast (–) - Moles of oxygen atom per mole of yeast (–) - Moles of nitrogen atom per mole of yeast (–) - Specific growth rate (h^–1) - _crit Critical specific growth rate (h^–1) - _E Specific ethanol up-take rate (h^–1) - _max.E Maximum specific ethanol up-take rate (h^–1)     

Influence of operational parameters in the flocculation and production ofLactobacillus plantarum

Summary The influence of different operational parameters, such as the dilution rate (D) and the bleeding rate (B), in the production of a flocculent strain ofLactobacillus plantarum was studied. The effect of the dilution rate was demonstrated to be related to the lactic acid concentration inside the reactor. The effect of the bleeding rate was shown to be critical in the stabilization of the operation (due to a better pH control). It also allowed a continuous recovery of cells outside the reactor. Viability testing of the lactic starter cultures showed that operation with cell purge increased the viability of the starter cultures obtained.Nomenclature B Bleeding rate, h^–1 - D Dilution rate, h^–1 - F Feed flow rate, L h^–1 - I Feed velocity, m h^–1 - Specific growth rate, h^–1 - v Lactic acid specific productivity, g g^–1 h^–1 - P Product concentration (lactic acid), g L^–1 - P _out Product concentration leaving the system, g L^–1 - Q _b Bleeding flow rate, L h^–1 - R Recirculation velocity, m h^–1 - S Substract concentration, g L^–1 - t Time, h - T _p Time of ascensional flow (length of the column/total ascensional velocity), h - T _r Residence time (1/D), h - V Volume of the reactor, L - X Cell concentration, g L^–1 - X _out Cell concentration leaving the system, g L^–1     

Model aided design of repeated fed-batch penicillin fermentation

Structured models of antibiotic fermentation that quantify maturation and aging of product forming biomass are fitted to experimental data. Conditions of superiority of repeated fed batch cultivation are characterized on the basis of a performance criterion that includes penicillin productivity and costs of operation. Emphasis is placed on the relevance of such research to the model aided design of optimal cyclic operation.List of Symbols c IU/mg cost factor - D s^–1 dilution rate - J IU · cm^–3 · h^–1 net productivity - k _p IU · mg^–11 · h^–1 specific product formation rate - k _pm IU · mg^–1 · h^–1 maximum specific product formation rate - p IU/cm³ concentration of penicillin - T s final time of fermentation - t s fermentation time - X kg/m³ concentration of biomass dry weight - X ₁kg/m³ concentration of young, immature biomass - X ₂ kg/m³ concentration of mature product forming biomass - X _c kg/m³ biomass concentration of the end of growth phase - X _mkg/m³ maximum biomass concentration Greek Letters s^–1 specific maturation rate - s^–1 specific aging rate - s^–1 specific growth rate - _m s^–1 maximum specific growth rate - _p s^–1 specific growth rate during the product formation phase - s cycle time - % volume fraction of draw-off Abbreviations CC chemostat culture - RFBC repeated fed batch culture - RBC repeated batch culture     

Kinetics of inhibition in propionic acid fermentation

The inhibitory effect of propionic acid P and biomass concentration X is studied in batch and continuous fermentations with cell recycle.In batch fermentations, the specific growth rate decreases and cancels out at a critical propionic acid concentration Pc ₁; the formerly decreasing specific production rate becomes constant after Pc ₁ and cancels out when a second critical propionic acid concentration Pc ₂ is reached.In continuous fermentation with cell recycle, a similar inhibition is observed with biomass. The specific rates decrease and become constant at a critical biomass concentration Xc. They cancel out at different high biomass concentrations.In both cases, the specific production rate can be related to the specific growth rate by the Luedeking and Piret expression: =+, [1], where the constants and are determined by the fermentation parameters.List of Symbols t h time - X kg/m³ biomass concentration - P kg/m³ propionic acid concentration - A kg/m³ acetic acid concentration - S kg/m³ lactose concentration - dX/dt kg/(m³h) instantaneous rate of cell growth - dP/dt kg/(m³h) instantaneous rate of propionic acid production - h^–1 specific growth rate - h^–1 specific propionic acid production rate - D h^–1 dilution rate     

Protein production from whey usingPenicillium cyclopium; growth parameters and cellular composition

Summary The growth parameters ofPenicillium cyclopium have been evaluated in a continuous culture system for the production of fungal protein from whey. Dilution rates varied from 0.05 to 0.20 h^–1 under constant conditions of temperature (28°C) and pH (3.5). The saturation coefficients in the Monod equation were 0.74 g l^–1 for lactose and 0.14 mg l^–1 for oxygen, respectively. For a wide range of dilution rates, the yield was 0.68 g g^–1 biomass per lactose and the maintenance coefficient 0.005 g g^–1 h^–1 lactose per biomass, respectively. The maximum biomass productivity achieved was 2 g l^–1 h^–1 biomass at dilution rates of 0.16–0.17 h^–1 with a lactose concentration of 20 g l^–1 in the feed. The crude protein and total nucleic acid contents increased with a dilution rate, crude protein content varied from 43% to 54% and total nucleic acids from 6 to 9% in the range of dilution rates from 0.05 to 0.2 h^–1, while the Lowry protein content was almost constant at approximately 37.5% of dry matter.Nomenclature (mg l^–1) C_o initial concentration of dissolved oxygen - (h^–1) D dilution rate - (mg l^–1) K₀₂ saturation coefficient for oxygen - (g l^–1) K_s saturation coefficient for substrate - (g g^–1 h^–1) lactose per biomass) m maintenance energy coefficient - (mM g^–1 h^–1O₂ per biomass) Q₀₂ specific oxygen uptake rate - (g l^–1) S residual substrate concentration at steady state - (g l^–1) S_o initial substrate concentration in feed - (min) t_1/2 time when C_o is equal to C_o/2 - (g l^–1) X biomass concentration - (g l^–1) X biomass concentration at steady state - (g g^–1 biomass per lactose) Y_G yield coefficient for cell growth - (g g^–1 biomass per lactose) Y_x/s overall yield coefficient - (h^–1) specific growth rate     

Effects of growth temperature on maximal specific growth rate,yield, maintenance,and death rate in glucose-limited continuous culture of the thermophilic Bacillus caldotenax

Summary The influence of temperature on the growth of the theromophilic Bacillus caldotenax was investigated using chemostat techniques and a chemically defined minimal medium. All determined growth constants, that is maximal specific growth rate, yield and maintenance, were temperature dependent. It was striking that the very large maintenance requirement was about 10 times higher than for mesophilic cells under equivalent conditions. A death rate, which was very substantial at optimal and supraoptimal growth temperatures, was estimated by comparing the maintenance for substrate and oxygen. There was no indication for a thermoadaptation as postulated by Haberstich and Zuber (1974).Symbols D Dilution rate (h^–1) - D_c=_max Critical dilution rate (h^–1) - E Temperature characteristic (J mol^–1) - k Organism constant - k_d Death rate coefficient (h^–1) - k_m Maintenance substrate coefficient estimated from M_O (h^–1) - M_O Maintenance respiration, mmol O₂ per g dry biomass and h (mmol g^–1h^–1) - M_O Maintenance respiration, taking k_d into account - m_S Maintenance substrate coefficient, g glucose per g dry biomass and h (h^–1) - OD Optical density at 546 nm - QO₂ Specific O₂-uptake rate (mmol g^–1h^–1) - Q _O2 ^V Specific O₂-uptake rate for viable portion of biomass (mmol g^–1 h^–1) - Q_S Specific glucose uptake rate (h^–1) - Q _S ^V Specific glucose uptake rate for viable portion of biomass (h^–1) - R Gas constant 8.28 J mol^–1K^–1 - S Substrate concentration in reactor (g l^–1) - S_O Influent substrate concentration (g l^–1) - T_max Maximal growth temperature (°C) - T_min Minimal growth temperature (°C) - X Dry biomass (g l^–1) - X_tOt=X Dry biomass containing dead and viable cells - X_v Viable portion of biomass - Y _O ^m Potential yield for O₂ corrected for maintenance respiration (g mol^–1) - Y _S ^m Potential yield for substrate corrected for maintenance requirement, g biomass per g glucose (–) - Specific growth rate (h^–1) - _max Maximal specific growth rate (h^–1)     

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)     

Mathematical modeling of production of microbial lipids

As a part of the investigations on the microbial lipid production using the yeast Rhodotorula gracilis, CFR-1, kinetics of the biomass synthesis has been studied using shake flask experiments. Using a medium containing a carbon to nitrogen ratio of 701, the rates of biomass production were followed at different initial substrate concentrations in the range of 20–100 kg/m³. A logistic model was found to be reasonably adequate to describe the kinetics of the growth of biomass; the maximum specific growth rate of 0.105 h^–1 was applicable for substrate concentrations less than 60 kg/m³, which gave reasonable agreement between predicted and actual biomass concentration values.List of Symbols S ₀, X ₀ kg/m³ Initial concentrations of sugar, non lipid biomass respectively - X, X(t) kg/m³ Concentrations of non lipid biomass at any time t - dX/dt kg/(m³ · h) Rate of biomass growth - h^–1 Specific growth rate - _max h^–1 Maximum specific growth rate - K _s mol/dm³ Monods constant - X _max kg/m³ Maximum biomass reached in a run     

Conversion of cellulose into fungal cell mass

Summary Chaetomium cellulolyticum (ATCC 32319) was cultivated on glucose, Avicel and/or Sigmacell in a 20-1 stirred tank batch reactor. The substrate (cellulose) concentration, the cell mass concentration (through protein and/or nitrogen content), reducing sugar concentration, the enzyme activity, the alkali consumption rate, the dissolved O₂ and CO₂ concentrations in the outlet gas were measured. The specific growth rate, the substrate yield coefficient, cell productivity, the oxygen consumption rate, the CO₂ production rate and the volumetric mass transfer coefficient were determined. At the beginning of the growth phase the oxygen utilization rate exhibits a sharp maximum. This maximum could be used to start process control. Because of the long lag phase periodic batch operation is recommended.Symbols CP cell protein concentration (g l^–1) - FPA FP enzyme activity (IU l^–1) - GP dissolved protein concentration (g l^–1) - IU international unit of enzyme activity - k_La volumetric mass tranfer coefficient (h^–1) - LG alkali (1 n NaOH) consumption (ml) - LGX specific alkali consumption rate per cell mass (ml g^–1 h^–1) - P cell mass productivity (g l^–1 h^–1) - specific oxygen consumption rate per cell mass (g g^–1 h^–1) - Q aeration rate (volumetric gas flow rate per volume of medium, vvm) (min^–1) - N impeller speed (revolution per minute, rpm) (min^–1) - S substrate concentration (g l^–1) - S⁰ S at t_F=0 (g l^–1) - S₀ S in feed (g l^–1) - SR acid consumption (ml) - TDW total dry weight (g l^–1) - T temperature (° C) - t_F cultivation time (h) - U substrate conversion - X cell mass concentration (g l^–1) - Y_X/S vield coefficient - specific growth rate (h^–1) - _m maximum specific growth rate (h^–1)     

Lactic acid productivity of a continuous culture of Lactobacillus delbreuckii

Summary Maximum volumetric productivities of biomass (1.40 gl^–1h^–1) and lactic acid (8.93 gl^–1h^–1) for a continuous culture ofLactobacillus delbreuckii occurred between dilution rates 0.35h^–1 and 0.40h^–1. All major nutrients were in excess in these cultures. Glucose utilisation was complete at dilution rates of 0.1h^–1 and lower. Product and biomass yields were constant in the dilution rate range studied (0.05h^–1 to 0.50h^–1).     

Influence of pH,lactose and lactic acid on the growth of Streptococcus cremoris: a kinetic study

Summary The effect of various culture conditions on growth kinetics of an homofermentative strain of the lactic acid bacterium Streptococcus cremoris were investigated in batch cultures, in order to facilitate the production of this organism as a starter culture for the dairy industry. An optimal pH range of 6.3–6.9 was found and a lactose concentration of 37 g·l^-1 was shown to be sufficient to cover the energetic demand for biomass formation, using the recommended medium. The study of the effect of lactic acid concentration on growth kinetics revealed that the end-product was not the sole factor affecting growth. The strain was characterized for its tolerance towards lactic acid and a critical concentration of 70 g·l^-1 demonstrated. With the product yield of 0.9 g·g^-1 at non-lactose limiting conditions the lactic acid concentration of 33 g·l^-1 could not explain the low growth rates obtained, implicating a nutritional limitation.Symbols t _f fermentation duration (h) - X Biomass concentration (g·l^-1) - X _m maximum biomass concentration (g·l^-1) - S lactose concentration (g·l^-1) - S _r residual lactose concentration (g·l^-1) - P produced lactic acid concentration (g·l^-1) - P _a added lactic acid concentration (g·l^-1) - P _c critical lactic acid concentration (g·l^-1) - specific growth rate (h^-1) - _max maximum specific growth rate (h^-1) - R _x/S biomass yield (g·g^-1) calculated when =0 - R _P/S product yield (g·g^-1)     

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)     

Two mathematical models for the development of a single microbial pellet

A mathematical model for pellet development of filamentous microorganisms is presented, which simulates in detail location and growth of single hyphal elements. The basic model for growth, septation and branching of discrete hyphae is adopted from Yang et al. [2, 23]. Exact solutions to the intracellular mass-balance equations of a growth-limiting key component is given for two types of either branched or unbranched cellular compartments. Furthermore, the growth model was extended in regard to the external mass-balance equations of limiting substrates (oxygen, glucose) under the assumption that the substrates can enter the denser regions of the pellet only diffusively. Penetration of the substrates into the more porous outer regions of the pellet occurs more easily due to microeddies in the surrounding fluid. Chipping of hyphae from the pellet surface by shear forces was included in the model as well. The application of shear forces leads to a marked smoothing of the simulated pellet surface. The development of pellets from spore germination up to late stages with cell-lysis due to shortage of substrates in the pellet centre can be described. The effects of various model parameters are discussed.List of Symbols A _i algebraic coefficient (i = 1, 2,..., 6) - B _i algebraic coefficient (i = 1, 2,..., 6) - C _i mass-concentration of component i (i = O₂, S) (gl^–1) - C _i,crit concentration of substance i critical for lysis (i=O₂, S) (gl^–1) - C _i,stop concentration of substance i below which cells are inactivated (gl^–1) - C(l _i,t) intracellular concentration of the key component at site l _i and time t (gl^–1) - C _m maximal intracellular concentration of the key component (gl^–1) - C _X Concentration of dry biomass (gl^–1) - D intracellular diffusion coefficient of the key component (m² h^–1) - D _max,i maximal molecular diffusion coefficient of substrate i (i = O₂, S) (m² h^–1) - D _eff,i effective diffusion coefficient of component i (i = O₂) (m² h^–1) - d _h cross-sectional diameter of hyphae (m) - k production coefficient for the key component (h^–1) - K _s Monod coefficient for glucose (gl^–1) - k ₀ Monod coefficient for oxygen (gl^–1) - L _c total length of a compartment (m) - L _i total length of branch i (i=1, 2, 3) (m) - l _i position on branch i (i=1, 2, 3) - L _m maximal length of a segment (m) - m _i maintenance coefficient of substrate i (h^–1) - N _m maximal number of segments in a compartment - n _iR number of tips of type i in layer R, i=1, 2 - p auxiliary variable (see Eq. (7)) - P _Br probability that a hypha is chipped off (%h^–1) - pO ₂ partial pressure of oxygen in the liquid phase (%) - Q auxiliary variable (see Eq. (8)) - Q _i uptake rate of substrate i (i = O₂, S) (gl^–1 h^–1) - q auxiliary variable (see Eq. (7)) - R index of radial layer (R=1, 2, 3,..., R _max) - r radius (m) - r _crit critical radius, Eq. (15) (m) - r _max pellet radius (m) - r _tip distance from the pellet centre to the tip position (m) - r _thr threshold radius (m) - s auxiliary variable (see Eq. (7)) - S index for glucose - t time (h) - v _R volume of layer R (1) - Y _Mi observable yield coefficient of biomass on substrate i (gg^–1) - Y _Xi yield coefficient of biomass on substrate i (gg^–1) Greek Letters _i actual tip expansion rate (m h^–1) - _i,m actual maximal extension rate of tip i (i=1, 2) (m h^–1) - _1y lysis rate (h^–1) - _m maximal tip extension rate (m h^–1) - auxiliary variable in Eq. (2) - auxiliary variable in Eq. (3) - auxiliary variable defined in Eq. (4) (m^–1) - _shear shear force parameter - _R overall specific growth rate in layer R (h^–1) - _m maximal specific hyphal growth rate (h^–1) - cell volume density (l cell volume per 1) - _crit critical cell volume density in Eq. (15) - _S shear force parameter - _X cell mass density (g dry weight per 1 wet cells) - (C _i) growth kinetics on substrate i - proportional factor in Eq. (34) (l g^–1) We thank the Deutsche Forschungsgemeinschaft (DFG) for financially supporting parts of this work.We thank the Deutsche Forschungsgemeinschaft (DFG) for financially supporting parts of this work.     

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.     

Application of a membrane recycle bioreactor for continuous ethanol production

Summary A series of continuous fermentations were carried out with a production strain of the yeast Saccharomyces cerevisiae in a membrane bioreactor. A membrane separation module composed of ultrafiltration tubular membranes retained all biomass in a fermentation zone of the bioreactor and allowed continuous removal of fermentation products into a cell-free permeate. In a system with total (100%) cell recycle the impact of fermentation conditions [dilution rate (0.03–0.3 h^–1); substrate concentration in the feed (50–300 g·1^–1); biomass concentration (depending on the experimental conditions)] was studied on the behaviour of the immobilized cell population and on ethanol formation. Maximum ethanol productivity (15 g·1^–1·h^–1) was attained at an ethanol concentration of 81 g·1^–1. The highest demands of cells for maintenance energy were found at the maximum feed substrate concentration (300 g·1^–1) and at very low concentrations of cells in the broth.     

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)     

Modeling the cucumber fermentation: Growth ofLactobacillus plantarum

Summary Specific growth rate models of product-inhibited cell growth exist but are rarely applied to fermentations beyond ethanol and large-scale antibiotic production. The present paper summarizes experimental data and the development of a model for growth of the commercially important bacterium,Lactobacillus plantarum, in cucumber juice. The model provides an excellent correlation of data for the influence on bacterial growth rate of NaCl, protons (H⁺), and the neutral, inhibitory forms of acetic acid and the fermentation product, lactic acid. The effects of each of the variables are first modeled separately using established functional forms and then combined in the final model formulation.Nomenclature [C] inhibitory component concentration, mM - [C]_max concentration of the inhibitory component where the specific growth rate is zero, mM, determined by model fitting - [H⁺] hydrogen ion concentration, mM - [HLa] undissociated lactic acid concentration, mM - [La^–] dissociated lactic acid concentration, mM - [La_t] total lactic acid ([HLa]+[La^–]) concentration, mM - [HAc] undissociated acetic acid concentration, mM - [Ac^–] dissociated acetic acid concentration, mM - [Ac_t] total acetic acid ([HAc]+[Ac^–]) concentration, mM - [NaCl] sodium chloride concentration, %, w/v - specific growth rate, h^–1 - _max maximum specific growth rate, h^–1 - ₀ specific growth rate, h^–1, at 0 concentration of additive - K _ij inhibition coefficient - , ,K _m coefficients determined by model fitting Mention of a trademark or proprietary product does not constitute a guarantee or warranty of the product by the US Department of Agriculture or North Carolina Agricultural Research Service, nor does it imply approval to the exclusion of other products that may be suitable.