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      

Performance characteristics of yeast growth in a modified airlift fermenter

Two types of airlift fermenters, conventional (UT-ALF) and modified (CDT-ALF) were investigated to evaluate their performance with respect to baker's yeast growth. The riser tube of conventional external loop airlift fermenter is replaced by a converging-diverging tube, which is named as modified airlift fermenter having downcomer to riser cross-sectional area ratio A _d /A _r =1.8.The results were compared for the two types of airlift fermenter. A modified growth kinetics model for baker's yeast with oxygen as limiting substrate, has been proposed. The values of K _s and K _d of the growth model were determined from experimental data. The proposed model represented better for CDT-ALF system compared to UT-ALF. Compared to UT-ALF, CDT-ALF always showed higher cell mass concentration and low residual sugar concentration irrespective of the operating conditions. At optimum operating condition (initial glucose concentration 30 g/l, air flow rate 0.5 vvm and fermentation time 8 hrs.) 16.7% higher cell mass was observed in CDT-ALF compared to that in UT-ALF and yield (Y _x/s ) was found to be 0.51 which was theoretically very near to maximum achievable value.Symbols ALF Airlift fermenter - UT Uniform tube - CDT Converging-diverging tube - A _r Cross sectional area of riser - A _d Cross sectional area of downcomer - C _s Glucose cone, at any time, g/l - C _l Dissolved oxygen conc, at any time, g/l - _max Max. sp. growth rate, hr^–1 - Sp. growth rate, hr^–1 - X ₀ Initial cell mass cone. (dry wt.), g/l - X Cell mass conc. at any time t, g/l - C _s0 Initial glucose conc., g/l - C _s Glucose conc. at any time t, g/l - C _l Equilibrium conc. of oxygen, 0.0076 g/l - y _x/s Yield coefficient (dimensionless) - y _x/s gm cell mass produced/gm glucose consumed - Y _O2 gm cell produced/gm oxygen consumed - k _d maintenance coefficient, hr^–1 - K _L a volumetric mass transfer coefficient, hr^–1 - k _s saturation constant for the substrate, g/l - K _O2 saturation constant for the substrate of dissolved oxygen, g/l. This work was supported by a research grant from the Department of Biotechnology Govt. of India.     

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)     

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

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

The effect of carbon dioxide on the growth kinetics of fructose-limited chemostat cultures of Acetobacterium woodii DSM 1030

The growth of the anaerobic acetogenic bacterium Acetobacterium woodii DSM 1030 was investigated in fructose-limited chemostat cultures. A defined medium was developed which contained fructose, mineral salts, cysteine · HCl and Ca pantothenate (1 mg · 1^–1) supplied in a vitamin supplement. Growth at high dilution rates was dependent on the presence of CO₂ in the gas phase. The ^max was found to be 0.16 h^–1 and the fructose maintenance requirement was 0.1 to 0.13 mmol fructose · (g dry wt)^–1 · h^–1. A growth yield of 61 g dry wt · (mol fructose)^–1, corrected for the cell maintenance requirement and for incorporation of fructose carbon into cell biomass, was determined from the fructose consumption. A corresponding growth yield of 69 g dry wt · (mol fructose)^–1 was calculated from the acetate production assuming that fructose fermentation was homoacetogenic. A Y_ATP of 12.2 to 13.8 g dry wt · (mol ATP)^–1 was calculated from these growth yields using a value of 5 mol ATP · (mol fructose)^–1 as an estimate of the amount of ATP synthesised from fructose fermentation. The addition of yeast extract (0.5 g · 1^–1) to the medium did not influence the ^max or cell yield. After prolonged growth under fructose-limited conditions the requirement of the culture for CO₂ in the gas phase was reduced.Abbreviations YE yeast extract - IC inorganic carbon - D fermenter dilution rate : h^–1 - M_X maintenance requirement for X: mmol X · (g dry wt)^–1 · h^–1 - X may be fructose (Fruct), fructose consumed in energy metabolism (Fruct [E]), acetate (Ac) - ATP CO₂, NH _inf4 ^sup+ or Pi - qX specific rate of utilisation or consumption of X: mmol X · (g dry wt)^–1 · h^–1 - V fermenter volume: litre - rC · Cell, fermenter cell carbon production: mmol C · h^–1 - Y_X yield of cells on X: g dry wt · (mol X)^–1 - Y _infx ^supmax the yield corrected for cell maintenance: g dry wt · (mol X)^–1 - S_ATP stoichiometry of ATP synthesis from fructose: mol ATP · (mol frucose)^–1 - x cell concentration: g dry wt · 1^–1 - specific growth rate : h^–1 - ^max maximum specific growth rate: h^–1     

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

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

Phenol degradation by a psychrotrophic strain of Pseudomonas putida

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

Induction effect of PO 2 during continuous yeast production from ethanol in a multistage tower fermentor

Summary The effect of the periodic variation of the partial pressure of oxygen in the aeration gas on biomass concentrations, ethanol conversion, yield and productivity during continuous cultivations of the yeast Candida utilis in a multistage tower fermentor was studied. The results were compared with those obtained under aeration conditions with a constant P_{O 2} in the aeration gas. The results demonstrated that, with the optimum P_{O 2} in the aeration gas, the aeration procedure with the periodic variation of P_{O 2} in the gas phase permitted achievement of the same process parameters as those under constant P_{O 2}. Using this new aeration procedure, the consumption of pure oxygen can be lowered by 55% to 60%. In addition, the significance of the induction effect of P_{O 2} on growth characteristics in the individual stages of the fermentor was proved.Symbols Ac Concentration of acetic acid (g/l) - i Number of stage - P_{O 2} Partial pressure of oxygen in the aeration gas (torr) - P_R Productivity of the fermentor (g cell dwt/l/h) - S_R Ethanol concentration in the feed (g/l) - S Ethanol concentration in the cultivation broth (g/l) - t Time of continuous cultivation (h) - X Cell dry weight concentration (g/l) - (Y_X/S)_W Yield of cell dry weight from ethanol for the whole fermentor (g cell dwt/g ethanol) - Concentration interval in which parameters varied during the long-term cultivation at constant constant P_{O 2}=263.5 torr in the aeration gas - ₁ Concentration interval in which parameters varied during the long-term cultivation before the increase of P_{O 2} in the aeration gas - ₂ Concentration interval in which parameters varied during the long-term cultivation immediately after the decrtease of P_{O 2} in the aeration gas - ₃ Concentration interval in which parameters varied during the long-term cultivation about 24 h after the decrease of P_{O 2} in the aeration gas - ₄ Concentration interval in which parameters varied during the long-term cultivation about 48 h after the decrease of P_{O 2} in the aeration gas     

Fermentation ofd-xylose,d-glucose andl-arabinose mixture byPichia stipitis Y 7124: sugar tolerance

Summary The effect of substrate concentration (S ₀) on the fermentation parameters of a sugar mixture byPichia stipitis Y 7124 was investigated under anaerobic and microaerobic conditions. Under microaerobiosisP. stipitis maintained high ethanol yield and productivity when initial substrate concentration did not exceed 150 g/l; ethanol yield of about 0.40 g/g and volumetric productivity up to 0.39 g/l per hour were obtained. Optimal specific ethanol productivity (0.2 g/g per hour) was observed withS ₀=110 g/l. Under anaerobic conditionsP. stipitis exhibited the highest fermentative performances atS ₀=20 g/l; it produced ethanol with a yield of 0.42 g/g, with a specific rate of 1.1 g/g per day. When the initial substrate level increased, specific ethanol productivity declined gradually and ethanol yield was dependent on the degree of utilization of each sugar in the mixture.Abbreviations E _m maximum produced ethanol (g/l) - E ₀ initial ethanol (g/l) - E _v evaporated ethanol (g/l) - Q _p volumetric productivity of ethanol (g ethanol/l per hour or g/l per day) - q _p specific productivity of ethanol (g ethanol/g cells per hour) - q _pm maximum specific productivity of ethanol (g/l per hour) - S ₀ initial substrate concentration (g/l) - t _f time at which produced ethanol is maximum (h) - Y _p/s ethanol yield (g ethanol produced/g substrate utilized) - Y _x/s cell yeild (g cells produced/g substrate utilized) - Y _xo/xy xylitol yield (g xylitol produced/g xylose utilized) - probability coefficient - specific growth rate coefficient (h^-1 or d^-1)     

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     

L-lactate production from xylose employingLactococcus lactis IO-1

Summary The growth, substrate utilisation and L-lactate production ofLactococcus lactis IO-1 were examined on xylose, and glucose and xylose media. The yield of lactate on xylose was 0.47 g lactate/g xylose at an initial xylose concentration of 51.2 g/l and the _max was 0.72 h^–1. Xylose cultures were more susceptible to lactate inhibition than were glucose cultures but showed similar kinetic behaviour. The organism was capable of complete sugar utilisation when grown on a mixture of 20 g/l xylose and 20 g/l glucose and synthesised 0.66 g lactate/g sugar.     

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     

On-line parameter and state estimation of continuous cultivation by extended Kalman filter

Summary The on-line estimation of biomass concentration and of three variable parameters of the non-linear model of continuous cultivation by an extended Kalman filter is demonstrated. Yeast growth in aerobic conditions on an ethanol substrate is represented by an unstructured non-linear stochastic t-variant dynamic model. The filter algorithm uses easily accessible data concerning the input substrate concentration, its concentration in the fermentor and dilution rate, and estimates the biomass concentration, maximum specific growth rate, saturation constant and substrate yield coefficient. The microorganismCandida utilis, strain Vratimov, was cultivated on the ethanol substrate. The filter results obtained with the real data from one cultivation experiment are presented. The practical possibility of using this method for on-line estimation of biomass concentration, which is difficult to measure, is discussed.Nomenclature D dilution rate (h^-1) - DO₂ dissolved oxygen concentration (%) - E identity matrix - F Jacobi matrix of the deterministic part of the system equations g - g continuousn-vector non-linear real function - h m-vector non-linear real function - K Kalman filter gain matrix - K _S saturation constant (kgm^-3) - K_S expectation of the saturation constant estimate - M Jacobi matrix of the deterministic part of the measurement equations h - P(t₀) co-variance matrix of the initial values of the state - P(t_k/t_k) c-variance matrix of the error in (t _k|t _k) - P(t_k+1/t_k) co-variance matrix of the error in (t _k+1|t _k - Q co-variance matrix of the state noise - R co-variance matrix of the output noise - S substrate concentration (kgm^-3) - S _i input substrate concentration - t time - t _k discrete time instant with indexk=0, 1, 2,... - u(t) input vector - v(t_k) measurement (output) noise sequence - w(t) n-vector white Gaussian random process - x(t₀) initial state of the system - (t₀) expectation of the initial state values - x(t) n-dimensional state vector - x(t_k) state vector at the time instantt _k - (t_k|t_k) expectation of the state estimate at timet _k when measurements are known to the timet _k - (t_k+1|t_k) expectation of the state prediction - X biomass concentration (kgm^-3) - expectation of the biomass concentration estimate - y(t_k) m-dimensional output vector at the time instantt _k - Y _XIS substrate yield coefficient - _X|S expectation of the substrate yield coefficient estimate - specific growth rate (h^-1) - _M maximum specific growth rate (h^-1) - expectation of the maximum specific growth rate estimate - state transition matrix     

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     

Optimisation of agitation and aeration in fermenters

The problem of optimising agitation and aeration in a given fermenter is addressed. The objective function is total electric power consumed for agitation, compression and refrigeration. The major constraint considered is to ensure that the dissolved oxygen concentration is above the critical value. It is shown that it is possible to analytically calculate the optimal pair (air flowrate, stirrer speed) and that, at least for the industrial antibiotics fermentation used as case-study, the optimum lies within a window for satisfactory operation, limited by other possible constraints to the problem. Savings achievable by optimal operation as compared with current industrial procedure were found to be around 10% at pilot plant scale (0.26 m³) and 20% at full scale (85 m³).List of Symbols A fermenter cross sectional area (m²) - C dissolved oxygen concentration (mole m^–3) - C ^* DO concentration in equilibrium with the gas (mole m^–3) - C _crit critical DO concentration (mole m^–3) - C _p specific heat of air at constant pressure (J kg^–1 K^–1) - C _sp dissolved oxygen set point (mole m^–3) - C _v specific heat of air at constant volume (J kg^–1 K^–1) - D agitator diameter (m) - f pressure correction of air flow-rate - (Fl _g)_F aeration number at flooding - (Fr _g)_F froude number at flooding - k coefficient in expression for mass transfer coefficient - K _La volumetric oxygen transfer coefficient (s^–1) - m power exponent in expression for mass transfer coefficient - n gas flow rate exponent in expression for mass transfer coefficient - n ^* number of impellers - N rotation speed (s^–1) - N _F rotation speed at flooding (s^–1) - N _p unaerated power number - N _pg aerated power number - OUR Oxygen Uptake Rate (mole m^–3 s^–1) - p ₀ atmospheric pressure (N m^–2) - p ₁ compressor exit pressure (N m^–2) - p ₂ pressure at the bottom of the fermenter (N m^–2) - p ₃ pressure at the top of the fermenter (N m^–2) - P _c compression power (W) - P _d power added by expansion (W) - P _ev power removed by evaporation (W) - P _g agitation power (W) - P _m power added by metabolism (W) - P _r power removed by refrigeration (W) - P _t total power (W) - Q air flow-rate at atmospheric conditions (m³ s^–1) - Q _f air flow-rate at average fermenter conditions (m³ s^–1) - s ₀ absolute humidity at atmospheric conditions - s ₃ absolute humidity at fermenter exit - T tank diameter (m) - V liquid volume (m³) - v _s gas superficial velocity (m s^–1) - _i parameter defined in the text - safety margin for dissolved oxygen (mole m^–3) - ratio of specific heats of air - _g agitation efficiency - _c compression efficiency - _r refrigeration efficiency - liquid density (kg m^–3) - _g air density (kg m^–3) - latent heat of vaporisation of water (J kg^–1) The authors are grateful to Elsa Silva, Carlos Lopes, Carlos Aguiar, Fernando Mendes, and Alexandre Cardoso, who helped with parts of this work, and to CIPAN for permission to publish these data.     

Fluidized bed biomethanation of acetic acid

Summary The kinetics of acetate biomethanation was studied in a high recycle ratio biological fluidized bed reactor behaving in practice as a completely mixed reactor. The active biofilm consisted of bacteria from a methane fermenter that after spontaneous immobilization on the bed particles (sand) were adapted to acetate as the only carbon source. The effects of temperature (13°, 20°, 25° and 35°C), substrate concentration (500, 1000 and 1500 mg chemical oxygen demand (COD) l^-1) and hydraulic retention time (1 to 8 h) on substrate consumption were studied. Maximum substrate consumption (as % COD reduction) amounted from 25% (13°C, 1500 mg COD l^-1) to 93% (35°C, 500 mg COD l^-1). At 35°C the concentration of attached biomass presented a weakly increase with reactor substrate concentration (from 3.10 g VS l^-1 to 4.54 g VS l^-1 for 32 and 1150 mg COD l^-1 respectively). On the other hand when reducing , a sharp incrase in biomass loss coefficient was observed showing that excess biofilm growth was continuously removed by shearing forces. Thus in the assayed conditions the attached biomass concentration was basically determined by the bed superficial velocity. Result show that diffusional resistances are negligible. Data are fairly well correlated by a variable order kinetic model. The apparent reaction order is a function of temperature and increases from 0.27 to 0.7 when temperature decreases from 35° C to 13°C.Nomenclature b Total biomass loss coefficient (T^-1) - J Flux of substrate removal into the biofilm surface (ML^-2 T^-1) - J _d Flux of substrate removed into the biofilm surface in deep conditions (ML^-2 T^-1) - k Maximum specific rate of substrate utilization (T^-1) - K Variable order kinetic constant (T^-1 M^n-1 L^3n-3) - K _s9 Hall saturation constant (ML^-3) - n Reaction order - q Feed flow rate (L³ T^-1) - S Substrate concentration (ML^-3) - Se Effluent substrate concentration (ML^-3) - So Influent substrate concentration (ML^-3) - Se_min Minimum substrate concentration able to sustain a steady-state biofilm (ML^-3) - T Temperature - t Time(T) - V Bed volume (L³) - VS Volatile solids (M) - VSS Volatile suspended solids - X Attached biomass concentration (ML^-3) - X _c Effluent volatile suspended solids (ML^-3) - Y Yield coefficient - Hydraulic retention time (T) This work forms part of a Doctoral Thesis of senior author     

Batch xylitol production by<Emphasis Type="Italic"> Candida guilliermondii</Emphasis> FTI 20037 from sugarcane bagasse hemicellulosic hydrolyzate at controlled pH values

Batch fermentation of sugarcane bagasse hemicellulosic hydrolyzate by the yeast Candida guilliermondii FTI 20037 was performed using controlled pH values (3.5, 5.5, 7.5). The maximum values of xylitol volumetric productivity (Q _p=0.76 g/l h) and xylose volumetric consumption (Q _s=1.19 g/l h) were attained at pH 5.5. At pH 3.5 and 7.5 the Q _p value decreased by 66 and 72%, respectively. Independently of the pH value, Y _x/s decreased with the increase in Y _p/s suggesting that the xylitol bioconversion improves when the cellular growth is limited. At the highest pH value (7.5), the maximum specific xylitol production value was the lowest (q _pmax=0.085 g/l h.), indicating that the xylose metabolism of the yeast was diverted from xylitol formation to cell growth.List of symbols P _max xylitol concentration (g/l) - Q _x volumetric cell production rate (g/l h) - Q _s volumetric xylose uptake rate (g/l h) - Q _p volumetric xylitol production rate (g/l h) - q _pmax specific xylitol production (g/g h) - q _smax specific xylose uptake rate (g/g h) - _max specific cell growth rate (h^–1) - Y _p/s xylitol yield coefficient, g xylitol per g xylose consumed (g/g) - Y _p/x xylitol yield coefficient, g xylitol per g dry cell mass produced (g/g) - Y _x/s cell yield coefficient, g dry cell mass per g xylose consumed (g/g) - _cell percentage of the cell yield from the theoretical value (%) - _xylitol percentage of xylitol yield from the theoretical value (%)     

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)     

The growth of Pseudomonas putida on m-toluic acid and on toluene in batch and in chemostat cultures

Summary The present study describes the growth of Pseudomonas putida cells (ATCC 33015) in batch and continuous cultures on two toxic substrates; toluene and m-toluic acid as sole carbon and energy sources. In fed-batch cultures on m-toluic acid up to 3.55 g cell dry weight/1 were achieved with a maximal specific growth rate (_max) of 0.1 h^-1. The average cellular yield was 1.42 g cell dry weight/g m-toluic acid utilized. When liquid toluene was added to shake-flask cultures in the presence of 0.7 g/1 m-toluic acid, the average cellular yield obtained was 1.3 g cell dry weight/g toluene utilized and the _max was 0.13 h^-1. Growth on toluene vapour in the presence of 0.7 g/l m-toluic acid in batch cultures resulted in a cellular yield of 1.28 g cell dry weight/g toluene utilized, with growth kinetics almost identical to those with liquid toluene (_max liquid=0.13 h^-1, _max vapour=0.12 h^-1). The maximal biomass concentration was 3.8 g cell dry weight/l, obtained in both cases after 100 h of incubation. Pseudomonas putida was grown in a chemostat initially on 0.7 g/l m-toluic acid and vapour toluene and then in the steady state on toluene as the sole source of carbon and energy. Toluene was added continuously to the culture as vapour with the inflowing airstream. Chemostat cultures could be maintained at steady state for several months on toluene. The maximal biomass concentration obtained in the chemostat culture was 3.2 g cell dry weight/l. The maximum specific growth rate was 0.13 h^-1, with a cellular yield of 1.05 g cell dry weight/g toluene utilized. Approximately 70% of the toluene consumed was converted into biomass, and the remainder was converted to CO₂ and unidentified byproducts.     

Influence of the initial glycerol concentration on the specific growth rate of Candida utilis cultivated on a synthetic medium containing glycerol as the main carbon source

Summary The following equation correlates the specific growth rate () and the initial concentration of glycerol (S) in batch cultivation of Candida utilis IZ 1840 when S varies from 15 to 75 g L^-1 µ 0 273 - 0.00193 S