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)     

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.     

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     

Ethanol fermentation using a glucose negative mutant ofZymomonas mobilis

Summary The fermentation of an equimolar mixture of glucose and fructose into ethanol and sorbitol by a glucose negative mutant ofZymomonas mobilis was monitored. The results were analyzed using a recently described method based on polynomial fitting and calculation of intantaneous and overall parameters. These parameters described well the physiology of this mixed-substrate mixed-product fermentation. Growth of the mutant was greatly inhibited on this medium. Fructose was quantitatively converted into sorbitol while glucose was oxidized into gluconic acid .This latter product was utilized as substrate for cell growth and ethanol production.Nomenclature X biomass concentration, g/l - S total sugar concentration, g/l - Glu glucose concentration, g/l - Fru fructose concentration, g/l - Sor sorbitol concentration, g/l - P ethanol concentration, g/l - t fermentation time, h - specific growth rate, h^-1 - q_s specific sugar uptake rate, g/g.h - q_G specific glucose uptake rate, g/g.h - q_F specific fructose uptake rate, g/g.h - q_P specific ethanol productivity, g/g.h - q_Sor specific sorbitol productivity, g/g.h - Y_X/S biomass yield on total sugar, g/g - Y_P/S ethanol yield on total sugar, g/g - Y_Sor/S sorbitol yield on total sugar, g/g - y_Sor/f sorbitol yield on fructose, g/g - Y_P/G ethanol yield on glucose, g/g     

Start-up sensitivity to the initial state of a batch bioreactor for a recombinant Escherichia coli in a complex medium

The sensitivities with respect to the initial state of five key variables describing the performance of a batch bioreactor have been computed from an experimentally validated kinetic model. The system has a recombinant Escherichia coli strain containing the plasmid pBR Eco gap, which codes for glyceraldehyde-3-phosphate dehydrogenase (GAPDH) in a complex medium. Since previous studies have shown the start-up sensitivities to be particularly important, the initial 10% of the duration of fermentation was chosen as the time span. The sensitivities of the cell mass, GAPDH and acetate increased with time while those of glucose and yeast extract remained practically constant.Acetate has a crucial role as it functions as both a product and a reactant. With no acetate in the inoculum, the sensitivities of acetate increased an order of magnitude faster than other sensitivities. However, upon addition of acetate through the inoculum, its sensitivities decreased the fastest and stabilised beyond a starting concentration of about 1 g/l whereas other sensitivities stabilised after 5 to 6 g/l of initial acetate. A three-dimensional envelope in the space of acetate concentration-time-relative sensitivity shows a locus of concentrations for minimum time-dependent acetate sensitivity; this may be maintained through fed-batch operation.List of Symbols a A/A₀ - A g/l initial concentration at any time - A ₀ g/l initial acetate concentration - e E/E₀ - E g/l yeast extract concentration at any time - E ₀ g/l initial yeast extract concentration - g G/G₀ - G g/l glucose concentration at any time - G ₀ g/l initial glucose concentration - k _A ^A g/l inhibition constant for acetate-dependent growth during the acetate phase - k _A ^G g/l inhibition constant for acetate-dependent growth during the glucose phase - k _M ^A 1/h rate constant for acetate phase - k _M ^G 1/h rate constant for glucose phase - K _A g/1 affinity constant for acetate - K _G g/1 affinity constant for glucose - m ^A 1/h coefficient of maintenance in acetate - m _m ^A 1/h maximum value of m ^A - m ^G 1/h coefficient of maintenance in glucose - m _m ^G 1/h maximum value of m ^G - n empirical constant - P P/P₀ - P U/ml GAPDH concentration at any time - P ₀ U/ml initial GAPDH concentration - s _c (i,j) sensitivity of y _i to y _j(0) for A ₀=c - t h time - x X/X₀ - X g/l cell mass concentration at any time - X ₀ g/l initial cell mass concentration - y ₁ x - y₂ g - y₃ a - y₄ e - y ₅ p - y _x/A ^A g/g yield coefficient for cell mass per unit mass of acetate during acetate phase - y _x/A ^G g/g yield coefficient for cell mass per unit mass of acetate during glucose phase - y _x/G g/g yield coefficient for cell mass per unit mass of glucose - y _E/x ^A g/g yield coefficient for yeast extract per unit cell mass during acetate phase - y _P/x ^A g/g yield coefficient for yeast extract per unit cell mass during glucose phase - y _P/x ^A U/g yield coefficient for GAPDH per unit cell mass during acetate phase - y _P/x ^G U/g yield coefficient for GAPDH per unit cell mass during glucose phase Greek Letters ₀ proportionality constant for plasmid loss probability - ₁ 1/h maximum rate of plasmid replication - ₂ 1/h saturation constant of the host component of plasmid replication - regulation function (0 or 1) - regulation function (0 or 1) - exponent of growth inhibition term for acetate during the acetate phase - exponent of growth inhibition term for acetate during the glucose phase - ^A 1/h specific growth rate during acetate phase - _m ^A 1/h maximum value of ^A - ^G 1/h specific growth rate during glucose phase - _m ^G 1/h maximum value of ^G - _c (i,j) ratio of sensitivities, s _c (i,j)/s ₀(i,j) - nondimensional time, t _m ^G      

Ethanol fermentation using a fructose-negative mutant of Zymomonas mobilis

Summary The fermentation of an equimolar mixture of glucose and fructose into ethanol and sorbitol by a fructose negative mutant of Zymomonas mobilis is analysed using a recently described methodology (Ait-Abdelkader and Baratti, Biotechnol. Tech. 1993,329–334) based on polynomial fitting and calculation of instantaneous and overall parameters. These parameters are utilized to describe this mixed-substrate mixed-product fermentation.Nomenclature X biomass concentration, g/l - S total sugar concentration, g/l - Glu glucose concentration, g/l - Fru fructose concentration, g/l - Sor sorbitol concentration, g/l - P ethanol concentration, g/l - t fermentation time, h - specific growth rate, h^-1 - q_s specific sugar uptake rate, g/g.h - q_g specific glucose uptake rate, g/g.h - q_F specific fructose uptake rate, g/g.h - q_P specific ethanol productivity, g/g.h - q_Sor specific sorbitol productivity, g/g.h - Y_X/S biomass yield on total sugar, g/g - Y_P/S ethanol yield on total sugar, g/g - Y_Sor/S sorbitol yield on total sugar, g/g - Y_Sor/F sorbitol yield on fructose, (g/g) - Y_P/G ethanol yield on glucose, (g/g)     

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)     

Integral kinetics of the cleavage of maltose catalysed by α-glucosidase fromSaccharomyces carlsbergensis

Summary A new, sensitive and continuous assay for -glucosidase is described exploiting the different angles of rotation for the substrate maltose and the product glucose. Kinetic experiments revealed a very pronounced product inhibition of -glucosidase fromSaccharomyces carlsbergensis with a K_i of 4.85·10^–3 M for glucose.The K_M of maltose was found to be 37.8·10^–3 M. Taking these values, an integral kinetic curve for the enzymatic hydrolysis of maltose was calculated, which is shown to fit the experimental data.Symbols used k₁ (min^–1) pseudo first-order rate constant (for enzymatic cleavage) - k₂ (min^–1) rate constant (for mutarotation reaction) - I, P (mol/1) inhibitor (product) concentration - k_i (mmol/1) inhibitor constant - K_M (mmol/l) Michaelis constant - [M] ₅₈₉ ³⁰ (degree/m · l/mol) molecular rotation at 30°C and 589 nm - s (mmol/l) substrate concentration - R (mmol/mg · min) reaction rate - V_max (mmol/mg · min) maximal rate - U (mol/min) activity unit (here at 30°C and pH=6.8) Indices O initial value - max maximal value     

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 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     

Effect of substrate concentration on ethanol production by Zymomonas mobilis on cellulose hydrolysate

Summary A cellulose hydrolysate from Aspen wood, containing mainly glucose, was fermented into ethanol by a thermotolerant strain MSN77 of Zymomonas mobilis. The effect of the hydrolysate concentration on fermentation parameters was investigated. Growth parameters (specific growth rate and biomass yield) were inhibited at high hydrolysate concentrations. Catabolic parameters (specific glucose uptake rate, specific ethanol productivity and ethanol yield) were not affected. These effects could be explained by the increase in medium osmolality. The results are similar to those described for molasses based media. Strain MSN77 could efficiently ferment glucose from Aspen wood up to a concentration of 60 g/l. At higher concentration, growth was inhibited.Nomenclature S glucose concentration (g/l) - X biomass concentration (g/l) - P ethanol concentration (g/l) - C conversion of glucose (%) - t fermentation time (h) - q_S specific glucose uptake rate (g/g.h) - q_p specific ethanol productivity (g/g.h) - YINX/S biomass yield (g/g) - Y_p/S ethanol yield (g/g) - specific growth rate (h^-1)     

Batch kinetic studies of glucose isomerization to fructose by Arthrobacter species

Glucose can be isomerized to fructose by the catalytic action of the enzyme, glucose isomerase. This enzyme is synthesized by a variety of micro-organisms, predominantly by bacteria. Arthrobacter species cells are grown in a medium standardized specifically to synthesize the enzyme and are then used to isomerize glucose under conditions of no further cell growth. Effect of metal ions on the isomerization is studied and it is found that magnesium promoted the reaction, sodium had no effect and calcium and manganese inhibited the reaction. Rate of reaction per unit of catalyst is found to be constant. Michaelis-Menten model modified for the reversibility of the reaction is suitable to describe the isomerization kinetics and the kinetic parameters are determined and reported.List of Symbols k ₁ rate constant (Glucose to intermediate complex) - k _–1 rate constant (Intermediate complex to glucose) - k ₂ rate constant (Intermediate complex to fructose) - k _–2 rate constant (Fructose to intermediate complex) - v _mf maximum reaction velocity of the forward (GF) reaction - v _mb maximum reaction velocity of the reverse (FG) reaction - K _f Michaelis-Menten constant for the forward (GF) reaction - K _b Michaelis-Menten constant for the reverse (FG) reaction - K _eq equilibrium constant - r _G rate of glucose consumption     

Interrelation between penicillin productivity and growth rate

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

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

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

Effect of growth temperature on the morphology and performance ofZymomonas mobilis ATCC 29 191 in batch and continuous culture

Summary Increasing the temperature in chemostat culture ofZymomonas mobilis ATCC 29 191 with low and high glucose concentrations was found to result in a decreasing frequency of septation leading to the formation of long filaments and in increasing outer membrane blebbing. Whether this effect is strain specific or universal inZymomonas is, unknown. Improvements in the fermentation kinetics could be achieved at elevated temperatures, with an optimum at 33°C. Temperatures >30°C induced uncoupled growth in chemostat cultures ofZ. mobilis ATCC 29 191. The results of this study emphasize the importance of temperature regulation in optimizing the performance of continuous fermentations withZymomonas.Nomenclature D Dilution rate, 1/h - _max Maximum specific growth rate, 1/h - S _R Initial substrate concentration, g glucose/1 - S Amount of glucose consumed, g glucose/1 - S ₀ Effluent substrate concentration, g glucose/1 - X Biomass concentration - g cells/1 - [P] Amount of product formed, g ethanol/1 - [P] Product concentrations, g ethanol/l - Y _x/s Growth yield, g cells/g glucose used - Y _p/s Product yield, g ethanol/g glucose used - O _s Specific rate of glucose uptake, g glucose/g cells/h - Q _p Specific rate of ethanol formation, g ethanol/g cells/h - VP Volumetric productivity, g ethanol/1/h - t Fermentation time, h Corresponding author     

Carbon dioxide desorption from fermentation broth by use of oxygen vectors

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

Development of a structured model for biopolymer synthesis in the fungus Aureobasidium pullulans

Previous modelling of the pullulan fermentation is discussed and found to lack any mechanistic basis. It is concluded that predictive ability can only be conferred by a structured model with at least two compartments, based upon the best available knowledge of the physiology of the microorganism. Such a model is constructed and compared with experimental data.List of Symbols A (gdm^–3)(g/l) Ammonium ion concentration - B (gdm^–3)(g/l) Concentration of balanced growth compartment of biomass - G (gdm^–3)(g/l) Glucose concentration - k _A (gdm^–3)(g/l) Saturation constant for ammonium - k _G (gdm^–3)(g/l) Saturation constant for glucose - k _S (gdm^–3)(g/l) Saturation constant for sucrose - P (gdm^–3)(g/l) Pullulan concentration - Q Quality of biomass=U/(U+B) - r _G (gdm^–1h^–1)(g/l/h) Rate of removal of glucose from broth - r _GB (gdm^–3h^–1)(g/l/h) Rate of incorporation of glucose into balanced compartment - r _GB (gdm^–3h^–1)(g/l/h) Rate of utilisation of glucose for energy production and cell maintenance - r _GP (gdm^–3h^–1)(g/l/h) Rate of conversion of glucose to pullulan - r _GU (gdm^–3h^–1)(g/l/h) Rate of incorporation of glucose into unbalanced compartment - r _s (gdm^–3h^–1)(g/l/h) Rate of conversion of sucrose to glucose - S (gdm^–3)(g/l) Concentration of sucrose - U (gdm^–3)(g/l) Concentration of unbalanced growth compartment of biomass - X (gdm^–3)(g/l) Biomass concentration - Y _G/A Grams of glucose consumed per gram of ammonium consumed - Y _G/B Grams of glucose consumed per gram of balanced biomass produced - Y _G/U Grams of glucose consumed per gram of unbalanced biomass produced - Y _G/P Grams of glucose consumed per gram of pullulan produced - Rate constant for conversion of sucrose to glucose - Rate constant for uptake of glucose by the cells - Model parameter governing inhibition of sucrose conversion and glucose utilisation - Model parameter denoting fraction of glucose uptake devoted to cell maintenance and energy production - Model parameter governing apportionment of glucose between pseudo-growth and pullulan production This work was funded by the National Engineering Laboratory (NEL) through the Bioreactor Design Club. The authors would like to express their gratitude to the NEL for this generous support.     

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.     

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]     

Regulation of intracellular H+ balance in Zymomonas mobilis 113 during the shift from anaerobic to aerobic conditions

Summary The energetics, enzyme activities and end-product synthesis of Zymomonas mobilis 113 in continuous culture were studied after the shift from an anaerobic to an aerobic environment. Aeration diminished ethanol yield and lactic acid concentration, but increased glucose consumption rate and production of acetic acid. After the shift to aerobic conditions reduced nicotinamide adenine dinucleotide (phosphate) [NAD(P)H]-oxidase activity was stimulated. Washed cell suspensions consumed oxygen with glucose, lactate and ethanol as substrates. The aerobic Z. mobilis 113 regulated their intracellular redox balance by production and reoxidation of the end products, coupled with the formation of NAD(P)H. An increase in transmembrane pH gradient (pH) and a decrease in intracellular ATP concentration were observed after the shift to aerobic conditions. At low medium redox potential (Eh) values the H⁺ balance was regulated in an energy-independent way via end-product excretion. Under aerobic conditions this was supplemented by ATP-dependent H⁺ excretion by the membrane H⁺-ATPase.Abbreviations D dilution rate (h^-1) - S ₀ initial glucose concentration (g/l) - Y _x/s growth yield (g/mol) - Y _p/s product yield (g/g) - q _s specific rate of substrate utilization (g/g per hour) - q _p specific rate of ethanol formation (g/g per hour) - qo ₂ specific rate of CO₂ production (mmol/g per hour) - specific growth rate (h^-1) - X dry biomass concentration (g/l) - Eh redox potential of culture medium (mV) - pH transmembrane pH gradient (pH units) - pH_in intracellular pH - SASE sum of activities of specific enmymes of Entner-Doudoroff pathway