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)     

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     

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.     

Applications of modelling for bioprocess design and control in industrial production

The on-line measurement of the relevant parameters and the control conception for three production processes for fine chemicals by fermentation and biotransformation at the 15 m³ scale were developed. The models describe the bioprocesses which successfully result in fully automated manufacturing steps. Modelling also proved to be a valuable tool for a better insight into biochemical fundamentals of the processes. Moreover, proper use of data logging, modelling and process control was important for quality, since two processes were controlled on-line and quality relevant deviations were registered early. Finally, combining modelling with simulation, we could drastically reduce both development time and cost.List of Symbols F l/h flux - V l volume - U ₀ g/l nicotinonitrile concentration influx - U g/l actual nicotinonitrile concentration - q _ug/gh specific educt (=nicotinonitrile) transformation rate - x g/l biocatalyst concentration - p ₀ g/l nicotinamide concentration influx - p g/l actual nicotinamide concentration - q _pg/gh specific product (=nicotinamide) formation rate - k parameter loss of activity - q _{u, max}g/gh max. specific educt transformation rate - K _ug/l saturation constant for nicotinonitrile - K _ig/l inhibition constant for nicotinonitrile - K _iig/l inhibition constant for nicotinamide - MW _Ag/mol molecular weight for nicotinonitrile - MW _Bg/mol molecular weight for nicotinamide - NS Nicotinic acid - 6-HNS 6-Hydroxynicotinic acid - r _{NS, 6HNS} g/lh 6-HNS production rate - r _{6HNS, X} g/lh biomass production rate - r _{NS, 6HNS, max} g/lh max. 6-HNS production rate - S _NS g/l actual NS concentration - K _{S, NS} g/l saturation constant for NS - K _{i, 6HNS} g/l inhibition constant for 6-HNS - K _o2 g/l saturation constant for oxygen - r _{6HNS, X, max} g/lh max. biomass production rate - S _6HNS g/l actual 6-HNS concentration - K _{ii, NS} g/l inhibition constant for NS - RQ mol/mol respiration quotient - S _xylg/l actual xylene concentration - K _{i, xyl}g/ inhibition constant for xylene - K _{i, DMPY}g/ inhibition constant for 2,5-dimethylpyrazine - r _Xg/lh biomass production rate - r _{X, max}g/lh max. biomass production rate - K _{s, xyl}g/l saturation constant for xylene - S _DMPYg/l actual concentration of DMPY - K _{i, MPCA}g/ inhibition constant for MPCA - K _O2g/ saturation constant for oxygen - S _MPCAg/l actual MPCA concentration - S _O2g/l actual oxygen concentration - r _MPCAg/lh MPCA production rate - r _{MPCA, max}g/lh max. MPCA production rate - k _lgl inhibition constant for the intermediates - k _{s, DMPY}gl saturation constant for DMPY     

Metabolic changes during substrate shifts in continuous cultures of the yeast Candida boidinii variant 60

Summary Substrate shift experiments in chemostat cultures with either methanol or glucose as carbon source were performed with the yeast Candida boidinii variant 60. At low dilution rates of 0.064 h^–1 the culture may be easily shifted from methanol to glucose medium and back again to methanol. From these experiments it can be seen that glucose does not give rise to any catabolite inhibition of alcohol oxidase. Alcohol oxidase and formaldehyde dehydrogenase seem to be regulated by a repression-derepression mechanism, as small basal activities of both these enzymes can still be measured during growth on glucose. On the other hand, formate dehydrogenase activity is completely absent in the presence of glucose. This kind of regulation seems to favor the smooth switch from growth on glucose to methanol metabolism.With methanol or glucose, growth yields (Y_S) of 0.3 and 0.35, respectively may be obtained, and oxygen consumption (Q_{O 2}) is much higher in methanol cultures than in glucose-grown cells. Accordingly, the RQ values during growth on methanol decrease to about 0.5. Based on the yield coefficient of 0.3, it is possible to calculate that 38% of the methanol consumed must be incorporated into biomass, whereas 62% of the methanol is oxidized to CO₂. The corresponding RQ of 0.56 could not be experimentally ascertained.The activities of three mitochondrial enzymes were found to be higher in methanol-grown cells than in cells from glucose cultures. The low activites of enzymes for the phosphogluconate route in methanol-grown cells indicates that a cyclic oxidation of formaldehyde via hexose phosphate to CO₂ cannot be of great importance for methanol metabolism.List of Symbols D 1/h Dilution rate - 1/h Specific growth rate - Q_{CO 2} mmol/g·h Specific CO₂ production rate - Q_{O 2} mmol/g·h Specific O₂ comsumption rate - Q_S g/g·h Specific substrate consumption rate - RQ ./. Respiratory quotient (Q_{CO 2}/Q_{O 2}) - S_O g/l Substrate concentration in the feeding medium - $#x0073;$#x0304 g/l Substrate concentration in the fermentor - $#x0078;$#x0304 g/l Biomass in the fermentor - Y_{O 2} g/mmol O₂ Biomass yield on oxygen - Y_S g/g Biomass yield on carbon source     

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.     

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)     

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)     

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     

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     

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     

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]     

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     

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     

Performance,kinetics, and substrate utilization in a continuous yeast fermentation with cell recycle by ultrafiltration membranes

Summary A continuous single stage yeast fermentation with cell recycle by ultrafiltration membranes was operated at various recycle ratios. Cell concentration was increased 10.6 times, and ethanol concentration and fermentor productivity both 5.3 times with 97% recycle as compared to no recycle. Both specific growth rate and specific ethanol productivity followed the exponential ethanol inhibition form (specific productivity was constant up to 37.5 g/l of ethanol before decreasing), similar to that obtained without recycle, but with greater inhibition constants most likely due to toxins retained in the system at hight recycle ratios.By analyzing steady state data, the fractions of substrate used for cell growth, ethanol formation, and what which were wasted were accounted for. Yeast metabolism varied from mostly aerobic at low recycle ratios to mostly anaerobic at high recycle ratios at a constant dissolved oxygen concentration of 0.8 mg/kg. By increasing the cell recycle ratio, wasted substrate was reduced. When applied to ethanol fermentation, the familiar terminology of substrate used for Maintenance must be used with caution: it is not the same as the wasted substrate reported here.A general method for determining the best recycle ratio is presented; a balance among fermentor productivity, specific productivity, and wasted substrate needs to be made in recycle systems to approach an optimal design.Nomenclature B Bleed flow rate, l/h - C _T Concentration of toxins, arbitrary units - D Dilution rate, h^-1 - F Filtrate or permeate flow rate, removed from system, l/h - F _o Total feed flow rate to system, l/h - K _s Monod form constant, g/l - P Product (ethanol) concentration, g/l - P _o Ethanol concentration in feed, g/l - PP} Adjusted product concentration, g/l - PD Fermentor productivity, g/l-h - R Recycle ratio, F/F _o - S Substrate concentration in fermentor, g/l - S _o Substrate concentration in feed, g/l - V Working volume of fermentor, l - V _MB Viability based on methylene blue test - X Cell concentration, g dry cell/l - X _o Cell concentration in feed, g/l - Y _ATP Cellular yield from ATP, g cells/mol ATP - Y _ATPS Yield of ATP from substrate, mole ATP/mole glucose - Y _G True growth yield or maximum yield of cells from substrate, g cell/g glucose - Y _P Maximum theoretical yield of ethanol from glucose, 0.511 g ethanol/g glucose - Y _P/S Experimental yield of product from substrate, g ethanol/g glucose - Y _x/s Experimental yield of cells from substrate, g cell/g glucose - S _NP/X Non-product associated substrate utilization, g glucose/g cell - k ₁, k₂, k₃, k₄ Constants - k ₁ ^APP , k ₂ ^APP Apparent k ₁, k₃ - k ₁ ^TRUE True k ₁ - m Maintenance coefficient, g glucose/g cell-h - m ^* Coefficient of substrate not used for growth nor for ethanol formation, g glucose/g cell-h - Specific growth rate, g cells/g cells-h, reported as h^-1 - _m Maximum specific growth rate, h^-1 - v Specific productivity, g ethanol/g cell-h, reported as h^-1 - v _m Maximum specific productivity, h^-1     

Continuous production of itaconic acid by Aspergillus terreus immobilized in a porous disk bioreactor

Summary Aspergillus terreus NRRL 1960 was grown on porous disks rotating intermittently in and out of the liquid phase. This immobilized fungal cell bioreactor was used to produce itaconic acid from glucose in a continuous operation. The effect of temperature, pH, disk rotation speed, and feed rate on the itaconic acid concentration and volumetric productivity were studied. The highest itaconic acid concentration and volumetric productivity obtained were 18.2 g/l and 0.73 g/l·h, respectively, under the following conditions: temperature at 36°C, pH 3.0, disk rotation speed at 8 rpm, and feed rate at 60 ml/h. These results are better than those by conventional fermentation or by other immobilized method.Nomenclature F feed rate (l/h) - K _1s saturation constant for immobilized cells (g/l) - K _2s saturation constant for suspended cells (g/l) - M ₁ increased mass of immobilized cells (g) - M ₂ total mass of immobilized cells (g) - P concentration of itaconic acid (g/l) - S substrate concentration in and out of the reactor (g/l) - S ₀ substrate concentration in the feed (g/l) - V liquid volume of the reactor (1) - X concentration of the suspended cells (g/l) - Y ₁ apparent yield of the immobilized cells (g cells/g substrate) - Y ₂ apparent yield of the suspended cells (g cell/g substrate) - Y ₃ apparent yield of itaconic acid (g itaconic acid/g substrate) - m ₁ maintenance and by-products coefficient of the immobilized cells (g substrate/g cell·h) - m ₂ maintenance and by-products coefficient of the suspended cells (g substrate/g cell·h) - µ_1max maximum specific growth rate of the immobilized cells (h^-1) - µ_2max maximum specific growth rate of the suspended cells (h^-1)     

Influence of the ratio of the initial substrate concentration to biomass concentration on the performance of a sequencing batch reactor

Biomass behaviour and COD removal in a benchscale activated sludge reactor have been studied alternating anaerobic and aerobic conditions. Particular attention has been paid to the influence of the ratio of the initial substrate concentration (S ₀) to the initial biomass concentration (X ₀) on the reactor performance. Tests at very low ratios (S ₀/X ₀<2) demonstrate the existence of a threshold below which the reactor performance is seriously affected (S ₀/X ₀=0.5). Under conditions of total suppression of cell duplication, substrate maintenance requirements have also been calculated for the microbial consortium present in the activated sludges. The results obtained show that stressed biomass can survive conditions of substrate lack better than unstressed biomass.List of Symbols b h^–1 specific death rate - COD g/l chemical oxygen demand - DO g/l dissolved oxygen concentration - K _s g/l Monod saturation constant - MLSS g/l mixed liquor suspended solid concentration - P g/l phosphorus concentration - S g/l substrate concentration - S ₀ g/l initial substrate concentration - SS g/l suspended solid concentration - t h time - X g/l biomass concentration - X ₀ g/l initial biomass concentration - Y _SX g/g yield of growth on substrate - _max h^–1 maximum specific growth rate     

Kinetics of bio-oxidation of a medium comprising phenol and a mixture of organic contaminants

The kinetics of bio-oxidation by a microbial ensemble of a model mixture of contaminants that mimicked the ground-water pollution plume at an existing contaminated site was investigated. Phenol at 50 mg/l and a mixture of ten organic contaminants (MOC) (benzene, tetrachloromethane, trichloroethylene, toluene, o-xylene, 1,4-dichlorobenzene, o-cresol, nitrobenzene, naphthalene and 2,6-dichlorophenol) at individual concentrations ranging from 150 g/l to 600 g/l were the components of the model mixture. The microbial ensemble consisted of at least three Pseudomonas spp. isolated from the polluted site. Patterns of oxygen uptake rate (OUR) for the oxidation of phenol alone and with added MOC were treated mathematically. The values for kinetic parameters that gave the best fit to the data were respectively 11.29 and 15.03 ml O₂ h^–1 (mg protein)^–1 for the OUR maximum (OUR_max), 75.89 mg/l and 33.66 mg/l for the saturation constant (K _s), 105.92 mg/l and 36.44 mg/l for the inhibitor constant (K _i), and 89.66 mg/l and 35.02 mg/l the substrate minimum inhibitory concentration (S _mic). This study also scrutinised interference between the two components of the model mixture of contaminants (phenol and MOC) on the basis of variations in kinetic patterns. MOC was shown to be toxic at milligram per litre levels. The microbial ensemble increased phenol oxidation in response to MOC, possibly to obtain the energy to overcome this toxic effect. This was indicated by an acceleration of phenol oxidation in response to increasing concentrations of MOC and higher OUR_max for oxidation of phenol in the presence of MOC. The toxicity of MOC also resulted in enhanced vulnerability of the microbial ensemble to a phenol inhibitory effect, indicated by the diminution of K _i and S _mic. The microbial ensemble showed high resistance to inhibition by the sole presence of phenol possibly because of adaptation to toxic features of MOC during the processes of enrichment and cultivation.     

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     

Observer design for differential-algebraic model of an aerobic culture of a recombinant yeast

The mathematical model of an aerobic culture of recombinant yeast presented in work by Zhang et al. (1997) is given by a differential-algebraic system. The classical nonlinear observer algorithms are generally based on ordinary differential equations. In this paper, first we extend the nonlinear observer synthesis to differential-algebraic dynamical systems. Next, we apply this observer theory to the mathematical model proposed in Zhang et al. (1997). More precisely, based on the total cell concentration and the recombinant protein concentration, the observer gives the online estimation of the glucose, the ethanol, the plasmid-bearing cell concentration and a parameter that represents the probability of plasmid loss of plasmid-bearing cells. Numerical simulations are given to show the good performances of the designed observer.Symbols C ₁ activity of pacing enzyme pool for glucose fermentation (dimensionless) - C ₂ activity of pacing enzyme pool for glucose oxidation (dimensionless) - C ₃ activity of pacing enzyme pool for ethanol oxidation (dimensionless) - E ethanol concentration (g/l) - G glucose concentration (g/l) - k _a regulation constant for (g glucose/g cell h^–1) - k _b regulation constant for (dimensionless) - k _c regulation constant for (g glucose/g cell h^–1) - k _d regulation constant for (dimensionless) - K _m1 saturation constant for glucose fermentation (g/l) - K _m2 saturation constant for glucose oxidation (g/l) - K _m3 saturation constant for ethanol oxidation (g/l) - L ( t) time lag function (dimensionless) - p probability of plasmid loss of plasmid-bearing cells (dimensionless) - P recombinant protein concentration (mg/g cell) - q _G total glucose flux culture time (g glucose/g cell h) - t culture time (h) - t _lag lag time (h) - X total cell concentration (g/l) - X ⁺ plasmid-bearing cell concentration (g/l) - Y ^F _{X / G} cell yield for glucose fermentation pathway (g cell/g glucose) - Y ^O _{X / G} cell yield for glucose oxidation pathway (g cell/g glucose) - Y _{X / E} cell yield for ethanol oxidation pathway (g cell/g ethanol) - Y _{E / X} ethanol yield for fermentation pathway based on cell mass (g ethanol·g cell) - ₂ glucoamylase yield for glucose oxidation (units/g cell) - ₃ glucoamylase yield for ethanol oxidation (units/g cell) - µ₁ specific growth rate for glucose fermentation (h^–1) - µ₂ specific growth rate for glucose oxidation (h^–1) - µ₃ specific growth rate for ethanol oxidation (h^–1) - µ_1max maximum specific growth rate for glucose fermentation (h^–1) - µ_2max maximum specific growth rate for glucose oxidation (h^–1) - µ_3max maximum specific growth rate for ethanol oxidation (h^–1)