Intraparticle mass-transfer resistance and apparent time stability of immobilized yeast alcohol dehydrogenase

The stability and, consequently, the lifetime of immobilized enzymes (IME) are important factors in practical applications of IME, especially so far as design and operation of the enzyme reactors are concerned. In this paper a model is presented which describes the effect of intraparticle diffusion on time stability behaviour of IME, and which has been verified experimentally by the two-substrate enzymic reaction. As a model reaction the ethanol oxidation catalysed by immobilized yeast alcohol dehydrogenase was chosen. The reaction was performed in the batch-recycle reactor at 303 K and pH-value 8.9, under the conditions of high ethanol concentration and low coenzyme (NAD⁺) concentration, so that NAD⁺ was the limiting substrate. The values of the apparent and intrinsic deactivation constant as well as the apparent relative lifetime of the enzyme were calculated.The results show that the diffusional resistance influences the time stability of the IME catalyst and that IME appears to be more stabilized under the larger diffusion resistance.List of Symbols C _A, C_B, C_E mol · m^–3 concentration of coenzyme NAD⁺, ethanol and enzyme, respectively - C _p mol · m³ concentration of reaction product NADH - d _p mm particle diameter - D _eff m² · s^–1 effective volume diffusivity of NAD⁺ within porous matrix - k _d s^–1 intrinsic deactivation constant - K _A, K_A, K_B mol · m^–3 kinetic constant defined by Eq. (1) - K _A ^x mol · m^–3 kinetic constant defined by Eq. (5) - r _A mol · m^–3 · s^–1 intrinsic reaction rate - R m particle radius - R _v mol · m^–3 · s^–1 observed reaction rate per unit volume of immobilized enzyme - t _E s enzyme deactivation time - t _r s reaction time - V mol · m^–3 · s^–1 maximum reaction rate in Eq. (1) - V ^x mol · m^–3 · s^–1 parameter defined by Eq. (4) - V _f m³ total volume of fluid in reactor - w _s kg mass of immobilized enzyme bed - factor defined by Eqs. (19) and (20) - kg · m^–3 density of immobilized enzyme bed - unstableness factor - effectiveness factor - Thiele modulus - relative half-lifetime of immobilized enzyme Index o values obtained with fresh immobilized enzyme     

Immobilization of lactase for the continuous hydrolysis of whey permaete

The production of lactose-based sweeteners is considered very promising. Fungal lactase has been immobilized on crosslinked chitin to develop a process for the continuous hydrolysis of demineralized whey permaete. The optimization of lactase immobilization on chitin and chitosan was performed, activities of 4 · 10⁵ and 2.2 · 10⁵ u/kg at yields of 33 and 23% were obtained for both supports, respectively. The chitin based catalyst was selected for further studies and a procedure was developed for in-situ enzyme immobilization. The kinetic behaviour of the catalyst was determined to propose a kinetic model for the initial rate of lactose hydrolysis. Pseudo steady-state and long term operation of packed bed reactors with chitin-immobilized lactase ranging from small laboratory to pre-pilot unit was carried out. The results are discussed and compared with commercial immobilized lactases. Preliminary economic evaluation for the production of ultrafiltered whey protein and hydrolyzed lactose syrup, within a dairy industry in Chile, was satisfactory in terms of profitability, both for the chitin immobilized lactase developed and for a commercial immobilized lactase.List of Symbols a moles/m³ glucose concentration in Eq. (1) - C _i US$ total annual cost (without considering plant depreciation) - D US$ annual depreciation - F m³/h flowrate - h m³/h volumetric mass transfer coefficient - i moles/m³ galactose concentration in Eqs. (1) and (2) - K _A moles/m³ dissociation constant for glucose in Eq. (1) - K _A moles/m³ dissociation constant for glucose in Eq. (1) - K _I moles/m³ inhibition constant for galactose in Eqs. (1) and (2) - K _m moles/m³ Michaelis constant for substrate in Eqs. (1) and (2) - k _D h^–1 first-order thermal deactivation constant - P kg dry weight of catalyst - PV US$ net present value - R % discounted cash-flow rate of return - s moles/m³ substrate concentration - s₀ moles/m³ feed substrate concentration - S _n US$ annual sales income - TC US$ total capital income - t _1/2 h catalyst half-life - v moles/h · kg initial rate of reaction - V _MAX moles/h · kg maximum reaction rate in Eqs. (1) and (2) - V _MAX moles/h · kg maximum reaction rate in Eq. (1) - ¯V _max moles/h initial rate of reaction - V _R m³ reaction volume free of catalyst particles - X substrate degree of conversion = s₀–s/s₀ - Damkoehler number = ¯V _MAX /h k _m - moles/(m³ · h) reactor productivity in Eq. (3)     

Two mathematical models for the development of a single microbial pellet

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

Packed-bed immobilized enzyme reactors for complex processes

Utilization of enzymic reactors for biotechnological-biomedical applications is currently developing at a sustained pace.Our present study concentrates on development of procedures for describing the performance of devices where enzyme-catalyzed reactions between two substrates take place, and for the rational design and optimization of the reactors considered. Within this context, an analytical model was developed for immobilized enzyme packed-bed reactors; it takes into account internal diffusion limitations for the cosubstrates, and hydrodynamic backmixing effects. In order to overcome the complex mathematical problems involved, the compartmental analysis approach was employed.Using this model, performance was simulated for various configurations of the enzymic unit, i.e. from a continuously operated stirred tank reactor (CSTR) to an essentially plug flow type. In addition, an experimental method is described for quantitatively assessing the backmixing effects prevailing in the reactor.The procedures established also provide the ground for further developments, particularly for systems where, in parallel to the enzymic reaction, additional processes (e. g. complexation) take place.List of Symbols C _j,i mM Concentration of substrate j in the pores of stage - iD _j cm²/s Internal (pore) diffusion coefficient of substrate j; defined in Eq. (7) - D _e cm²/s Axial dispersion diffusion coefficient - D _j, cm²/s cm²/s Bulk diffusion coefficient for substrate j - E mM Enzyme concentration inside the catalytic pores - J _j,immol/s/cm² Net flux of substrate j taking place from the bulk of stage i into the corresponding pores; defined in Eq. (6) - K _m,1, K _m,2 mM Michaelis-Menten constants for cosubstrates 1 and 2, respectively - k s ^–1 Catalytic constant - k _s cm/s Catalytic constant - n Total number of elementary stages in the reactor - Q cm³/s Volumetric flow rate throught the reactor - r cm Radius of the pore - R _j,i mM/s Reaction rate of substrate j in stage i, in terms of volumetric units - S cm² Internal surface of a pore - S _j,0 mM Concentration of substrate j in the reactor feed - S _j,i–1, S _j,i mM Concentration of substrate j in the bulk phase leaving stages i — 1 and i, respectivley - V _i cm³ Total volume of stage i (bulk phase + pore phase + inert solid carrier) - V cm³ Total volume of the reactor - V _m ^* mmol/s/cm² Maximal reaction rate in terms of surface units; defined in Eq. (8) - V _m mM/s Maximal reaction rate in terms of volumetric units; defined in Eq. (8) - V _p cm³ Volume of one pore - y cm Axial coordinate of the pores - y ₀ cm Depth of the pores - Z cm Axial coordinate of the reactor - Z ₀ cm Length of the reactor - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - Ratio between the radius of the enzyme molecule and the radius of the pore (dimensionless) - V₁ Dimensionless parameter; defined in Eq. (21) - v₂ Dimensionless parameter; defined in Eq. (21) - Q Volumetric packing density of catalytic particles (dimensionless) - Ø Porosity of the catalytic particles (dimensionless) - Ø Dimensionless concentration of substrate j in pores of stage i; defined in Eq. (16) - _j,i-1,_j,i Dimensionless concentration of substrate j in the bulk phase of stage i; defined in Eq. (18) - Dimensionless position; defined in Eq. (16) - ² s² Variance; defined in Eq. (33) - Mean residence time in the reactor; defined in Eq. (33)     

Production studies on protozoa

Summary In the river Saale and in the terrestrial moss Mnium cuspidatum Leyss. in 1974/75 the annual production of Testacea and loricate ciliated protozoa were investigated.The production was estimated in the Saale-Aufwuchs on a -meso ... oligosaprobic (Kaulsdorf, Thuringia, GDR) and on a -mesosaprobic (Rothenstein, Thuringia, GDR) area of the river. The mosses were investigated in a forest near Jena.The production was estimated on slides and in special productionchambers; the time of exposure was 2 weeks. Investigations concerned annual production of individuals and biomass, the ratio of annual production/standing crop (P/B), numbers of generations per year (G) and mortality (M%/d). In the mosses, the rainfall modified the production and dislocation of the protozoa.The values for production are: Aufwuchs Saale (-meso... oligosaprobic): 24·10⁶ i/m²·a (=1,0 g/m²·a=79·10³ i/m²·d); P/B: 12.6. Aufwuchs Saale (-mesosaprobic): 3.2·10⁶ i/m²·a (=0.35 g/m²·a=81·10³ i/m²·d); P/B: 34.9; G: 22; M: 5%/d. Moss: 145·10⁶ i/m²·a (=0.11 g/m²·a=40.6·10³ i/m²·d); P/B: 8.1; G: 16.5; M: 3.0%/d.     

Inhibition of the acidogenic dissimilation of glucose in anaerobic continuous cultures by free butyric acid

Summary In anaerobic wastewater treatment the separation of fermentative and methanogenic bacteria is aimed at an increased performance of the total digestion process. It is known that the attainable growth rate of the acidogenic population in continuous culture decreases at increasing influent concentrations of glucose. To account for this phenomenon, a new kinetic model was developed that combines substrate and product inhibition. In the present research product inhibition was investigated quantitatively in a continuous culture fermenting 50 mmol/l glucose. Extra acetate and butyrate were added up to 200 mmol/l at different pH values, and it turned out that only free butyric acid inhibited growth. The lower attainable growth rates of cultures producing comparable amounts of butyrate when fed with concentrated influents, strongly indicated substrate inhibition. Evidence is presented that transitions to low-conversion steady states predicted by the kinetic model, play a role and decrease the stability of the culture.Nomenclature D dilution rate, h^-1 - D_att highest D using certain experimental procedure h^-1 - K_i substrate inhibition constant, mol·m^-3 - K_p product inhibition constant mol·m^-3 - K_s substrate saturation constant, mol·m^-3 - P concentration inhibitory product mol·m^-3 - S substrate concentration, mol·m^-3 - S_o influent substrate concentration, mol·m^-3 - S _max ^c substrate concentration at _max ^c , mol·m^-3 - S _max ^h substrate concentration at _max ^h , mol·m^-3 - specific growth rate, h^-1 - experimental realization of at D_att, h^-1 - _max maximum specific growth rate, h^-1 - _max ^c maximum attainable specific growth rate according to combined substrate/product inhibition model, h^-1 - _h ⁰ specific growth rate at S₀ according to Haldane kinetics, h^-1 - _max ^c maximum attainable specific growth rate according to Haldane kinetics, h^-1 - Y_p yield inhibitory product, mol·mol^-1 - Y_x yield biomass, kg dry weight·kg^-1 - bio biomass - EtOH ethanol - gluc glucose - HAc acetate - HBt butyrate - HCap caproate - HFo formate - HPr propionate - HVal valerate - prod produced - lact lactate     

Optimal temperature and concentration profiles in a cascade of CSTR's performing Michaelis-Menten reactions with first order enzyme deactivation

A necessary condition is found for the intermediate temperatures and substrate concentrations in a series of CSTR's performing an enzyme-catalyzed reaction which leads to the minimum overall volume of the cascade for given initial and final temperatures and substrate concentrations. The reaction is assumed to occur in a single phase under steady state conditions. The common case of Michaelis-Menten kinetics coupled with first order deactivation of the enzyme is considered. This analysis shows that intermediate stream temperatures play as important a role as intermediate substrate concentrations when optimizing in the presence of nonisothermal conditions. The general procedure is applied to a practical example involving a series of two reactors with reasonable values for the relevant five operating parameters. These parameters are defined as dimensionless ratios involving activation energies (or enthalpy changes of reaction), preexponential factors, and initial temperature and substrate concentration. For negligible rate of deactivation, the qptimality condition corresponds to having the ratio of any two consecutive concentrations as a single-parameter increasing function of the previous ratio of consecutive concentrations.List of Symbols C _E,0 mol.m^–3 Initial concentration of active enzyme - C _E,i mol.m^–3 Concentration of active enzyme at the outlet of the i-th reactor - C _S,0 mol.m^–3 Initial concentration of substrate - C _S,i mol.m^–3 Concentration of substrate at the outlet of the i-th reactor - Da _i Damköhler number associated with the i-th reactor ((V _i.k_v,0.C_E,0)/(Q.C_S,0)) - Da _min Minimum value of the overall Damköhler number - Da _tot Overall Damköhler number - E _d J.mol^–1 Activation energy of the step of deactivation of the enzyme - E _m J.mol^–1 Standard enthalpy change of the step of binding of substrate to the enzyme - E _v J.mol^–1 Activation energy of the step of enzymatic transformation of substrate - i Integer variable - j Dummy integer variable - k Dummy integer variable - k _d,i s^–1 Kinetic constant associated with the deactivation of enzyme in the i-th reactor (k _d,o·exp{–E _d/(R.T _i}) - k _d,0 s^–1 Preexponential factor of the kinetic constant associated with the deactivation of the enzyme - K _m,i mol.m^–3 Equilibrium constant associated with the binding of substrate to the enzyme in the i-th reactor, (k _m,o·exp{–E _m}(R.T _i}) - K _m,0 mol.m^–3 Preexponential factor of the Michaelis-Menten constant associated with the binding of substrate to the enzyme - k _v,i s^–1 Kinetic constant associated with the transformation of the substrate by the enzyme in the i-th reactor (k _v,o·exp{–E _v/(R.T _i})) - k _v,0 s^–1 Preexponential factor of the kinetic constant associated with the transformation of the substrate by the enzyme - N Number of reactors in the series - Q m³.s^–1 Volumetric flow rate of reacting liquid through the reactor network - R J.K^–1.mol^–1 Ideal gas constant - T _i K Absolute temperature at the outlet of the i-th reactor - T ₀ K Initial absolute temperature - V _i m³ Volume of the i-th reactor - v _max mol.m^–3.s^–1 Maximum rate of reaction under saturation conditions of substrate - x _i Normalized concentration of substrate (C_S,i/C_{S, 0}) - x _i,opt Optimum value of the normalized concentration of substrate - y _i Dimensionless temperature (exp{–T ₀/T _i}) - y _i,opt Optimum value of the dimensionless temperature Greek Symbols Dimensionless preexponential factor associated with the Michaelis-Menten constant (K _m,0/C_s,0) - Dimensionless activation energy of the step of enzymatic transformation of substrate (E _v/R.T₀)) - Dimensionless standard enthalpy change of the step of binding of substrate to the enzyme (E _m/(R.T₀)) - Dimensionless activation energy of the step of deactivation of the enzyme (E _d/(R.T₀)) - Dimensionless deactivation preexponential factor ((k _d,0.C_S,0)/(k_v,0.C_E,0)     

Changes in carp myosin ATPase induced by temperature acclimation

Summary Myosins were isolated from dorsal ordinary muscles of carp acclimated to 10°C and 30°C for a minimum of 5 weeks and examined for their ATPase activities. Ca²⁺-ATPase activity was different between myosins from cold-and warm-acclimated carp, especially at KCl concentrations ranging from 0.1 to 0.2 M, when measured at pH 7.0. The highest activity was 0.32 mol P_i·min^-1·mg^-1 at 0.2 M KCl for cold-acclimated carp and 0.47 mol P_i·min^-1·mg^-1 at 0.1 M KCl for warm-acclimated fish. The pH-dependency of Ca²⁺-ATPase activity at 0.5 M KCl for both carp was, however, similar exhibiting two maxima around 0.3 mol P_i·min^-1·mg^-1 at pH 6 and 0.4 mol P_i·min^-1·mg^-1 at pH 9. K⁺(EDTA)-ATPase activity at pH 7.0 neither exhibited differences between both myosins. It increased with increasing KCl concentration showing the highest value of about 0.4 mol P_i·min^-1·mg^-1 at 0.6–0.7 M KCl. Actin-activated myosin Mg²⁺-ATPase activity was markedly different between cold-and warm-acclimated carp. The maximum initial velocity was 0.53 mol P_i·min^-1·mg^-1 myosin at pH 7.0 and 0.05 M KCl for cold-acclimated carp, which was 1.6 times as high as that for warm-acclimated carp. These differences were in good agreement with those obtained with myofibrillar Mg²⁺-ATPase activity between both carp. No differences were, however, observed in myosin affinity to actin. Differences in myosin properties between cold- and warm-acclimated carp were further evidenced by its thermal stability. The inactivation rate constant of myosin Ca²⁺-ATPase was 25·10^-4·s^-1 at 30°C and pH 7.0 for cold-acclimated carp, which was about 4 times as high as that for warm-acclimated carp. Light chain composition did not differ between both carp myosins. The differences in a primary structure of the heavy chain subunit was, however, clearly demonstrated between both myosins by peptide mapping.Abbreviations ATPase adenosine 5-triphosphatase - DTNB 5,5 dithio-bis-2-nitrobenzoic acid - DTT dithiothreitol - EGTA ethyleneglycol bis (-aminoethylether)-N,N,N,N-tetraacetic acid - K _D inactivation rate constant - SDS sodium dodecyl sulfate - SDS-PAGE SDS-polyacrylamide gel electrophoresis     

Effects of dissolved oxygen concentration on lipase production by Rhizopus delemar

Summary The influence of the concentration of oxygen on lipase production by the fungus Rhizopus delemar was studied in different fermenters. The effect of oxygen limitation ( 47 mol/l) on lipase production by R. delemar is large as could be demonstrated in pellet and filamentous cultures. A model is proposed to describe the extent of oxygen limitation in pellet cultures. Model estimates indicate that oxygen is the limiting substrate in shake flask cultures and that an optimal inoculum size for oxygen-dependent processes can occur.Low oxygen concentrations greatly negatively affect the metabolism of R. delemar, which could be shown by cultivation in continuous cultures in filamentous growth form (D_optimal=0.086 h^-1). Continuous cultivations of R. delemar at constant, low-oxygen concentrations are a useful tool to scale down fermentation processes in cases where a transient or local oxygen limitation occurs.Symbols and Abbreviations CO Oxygen concentration in the gas phase at time = 0 (kg·m^-3) - C_{O 2i} Oxygen concentration at the pellet liquid interface (kg·m^-3) - C_{O 2i} Oxygen concentration in the bulk (kg·m^-3) - D Dilution rate (h^-1) - ID_{O 2} Diffusion coefficient for oxygen (m²·s^-1) - dw Dry weight of biomass (kg) - f Conversion factor (rs _{O 2} to oxygen consumption rate per m³) (-) - k Radial growth rate (m·s^-1) - K Constant - kla Volumetric mass transfer coefficient (s^-1) - klA Oxygen transfer rate (m^-3·s^-1) - kl Mass transfer coefficient (m·s^-1) - K _{O 2} Affinity constant for oxygen (mol·m^-3) - K _w Cotton plug resistance (m^-3·s^-1) - M Henry coefficient (-) - NV Number of pellets per volume (m^-3) - R Radius (m) - RO Radius of oxygen-deficient core (m) - RQ Respiration quotient (mol CO₂/mol O₂) - rs _{O 2} Specific oxygen consumption rate per dry weight biomass (kg O₂·s^-1[kg dw]^-1) - rX Biomass production rate (kg·m^-3·s^-1) - SG Soytone glucose medium (for shake flask experiments) - SG ₄ Soytone glucose medium (for tower fermenter and continuous culture experiments) - V Volume of medium (m^-3) - X Biomass (dry weight) concentration (kg·m^-3) - XR _o Biomass concentration within RO for a given X (kg·m^-3) - Y _{O 2} Biomass yield calculated on oxygen (kg dw/kg O₂) - Thiele modulus - Efficiency factor =1-(RO/R)³ (-) - Growth rate (m^-1·s^-1·kg^1/3) - Dry weight per volume of pellet (kg·m^-3)     

Optimizing control of a continuous stirred tank fermenter using a neural network

Feedforward neural networks are a general class of nonlinear models that can be used advantageously to model dynamic processes. In this investigation, a neural network was used to model the dynamic behaviour of a continuous stirred tank fermenter in view of using this model for predictive control. In this system, the control setpoint is not known explicitly but it is calculated in such a way to optimize an objective criterion. The results presented show that neural networks can model very accurately the dynamics of a continuous stirred tank fermenter and, the neural model, when used recursively, can predict the state variables over a long prediction horizon with sufficient accuracy. In addition, neural networks can adapt rapidly to changes in fermentation dynamics.List of Symbols F Dimensionless flow rate (F/ V₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective cost function - K _i Dimensionless constant in Eq. (3) (k _i /s₀) - k _i kg/m³ Substrate inhibition constant in Haldane model - k _m Dimensionless constant in Eq. (3) (k _s /s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - n prediction horizon - S Dimensionless substrate concentration (s/s₀) - s kg/m³ Substrate concentration - t h Time - v Dimensionless volume (V/V₀) - V m³ Liquid volume in fermenter - W _ij , W _jk Weight matrices in neural network - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ) - 1/h Maximum specific growth rate - 1/h Specific growth rate - Dimensionless time ( t)     

Biotransformation of cephalosporin C to 7-aminocephalosporanic acid with coimmobilized biocatalyst in a batch bioreactor

Biotransformation of cephalosporin C (CPS-C) to 7-aminocephalosporanic acid (7-ACA) was carried out with coimmobilized permeabilized cells of Trigonopsis variabilis and Pseudomonas species entrapped in Ca-pectate gel beads. Good aeration and stirring during the process was assured. The analysis of this complicated biochemical process in a heterogeneous system was based on the identification of individual effects (internal diffusion, reaction) running simultaneously. A spectrophotometric method was proposed for the determination of 7-(-ketoadipyl amido) cephalosporanic acid (CO-GL-7-ACA) and 7-ACA. The reaction-diffusion model containing dimensionless partial differential equations was solved by using the orthogonal collocation method. A good agreement between experimental values and values predicted by the mathematical model was obtained. Numerical simulations were performed on the basis of following the two assumptions:- several times higher activity of both cells,- hydrogen peroxide was continuously supplied in the bioreactor.List of Symbols A m² surface of the bead - c _i mol/dm³ concentration of component in the bead and/or in the solution - c _i0 mol/dm³ initial concentration of component in the solution - c _l0 mol/dm³ initial concentration of CPS-C in the solution - C _jl orthogonal collocation weights of the first derivation - D _ei m²/s effective diffusion coefficient of the components - D _jl orthogonal collocation weights of the second derivation - k ₅ dm³/(mol · s) kinetic parameter of non-enzyme reaction - K _inh mol/dm³ inhibition parameter for the first enzyme reaction - K _i dimensionless Michaelis constant for the first and second enzyme reaction, defined in Eq. (7) - K _l dimensionless inhibition parameter for the first enzyme reaction, defined in Eq. (7) - K _mi mol/dm³ Michaelis constant for the first and second enzyme reaction - n number of beads - P( _i ) symbol of dimensionless reaction rate, defined in Eq. (13) - r m radial coordinate inside the bead - R m radius of the bead - R(c _i ) mol/(dm³ · s) symbol for reaction rate, defined in Eq. (6) - t s time - V _max mol/(dm³ · s) max. reaction rate for the first and second enzyme reaction - V _L dm³ volume of solution excluding the space occupied by beads - voidage in batch bioreactor - _P porosity of the bead - i dimensionless effective diffusion coefficient of the components, defined in Eq. (7) - dimensionless time, defined in Eq. (7) - _mi Thiele modulus, defined in Eq. (7) - _i dimensionless concentration, defined in Eq. (7) - dimensionless radial position inside the bead, defined in Eq. (7) - _l0 initial dimension concentration of CPS-C, defined in Eq. (9), (10) - _i0 initial dimension concentration of component, defined in Eq. (9), (10) The authors wish to thank Dr. P. Gemeiner of Slovak Academy of Sciences for rendering of pectate gel. This work is supported by Ministry of Education (Grant No. 1/990 935/93).     

Flight of the honey bee VI: energetics of wind tunnel exhaustion flights at defined fuel content,speed adaptation and aerodynamics

To gain information on extended flight energetics, quasi-natural flight conditions imitating steady horizontal flight were set by combining the tetheredflight wind-tunnel method with the exhaustion-flight method. The bees were suspended from a two-component aerodynamic balance at different, near optimum body angle of attack and were allowed to choose their own speed: their body mass and body weight was determined before and after a flight; their speed, lift, wingbeat frequency and total flight time were measured throughout a flight. These values were used to determine thrust, resultant aerodynamic force (magnitude and tilting angle), Reynolds number, total flight distance and total flight impulse. Flights in which lift was body weight were mostly obtained. Bees, flown to complete exhausion, were refed with 5, 10, 15 or 20 l of a 1.28-mol·l^-1 glucose solution (energy content w=18.5, 37.0, 55.5 or 74.0 J) and again flown to complete exhaustion at an ambient temperature of 25±1.5°C by a flight of known duration such that the calculation of absolute and relative metabolic power was possible. Mean body mass after exhaustion was 76.49±3.52 mg. During long term flights of 7.47–31.30 min similar changes in flight velocity, lift, thrust, aerodynamic force, wingbeat frequency and tilting angle took place, independent of the volume of feeding solution. After increasing rapidly within 15 s a more or less steady phase of 60–80% of total flight time, showing only a slight decrease, was followed by a steeper, more irregular decrease, finally reaching 0 within 20–30 s. In steady phases lift was nearly equal to resultant aerodynamic force; tilting angle was 79.8±4.0°, thrust to lift radio did not vary, thrust was 18.0±7.4% of lift, lift was somewhat higher/equal/lower than body mass in 61.3%, 16.1%, 22.6% of all totally analysable flights (n=31). The following parameters were varied as functions of volume of feeding solution (5–20 l in steps of 5 l) and energy content. (18.5–74.0 J in steps of 18.5 J): total flight time, velocity, total flight distance, mean lift, thrust, mean resultant aerodynamic force, tilting angle, total flight impulse, wingbeat frequency, metabolic power and metabolic power related to body mass, the latter related to empty, full and mean (=100 mg) body mass. The following positive correlations were found: L=1.069·10^-9 f ^2.538; R=1.629·10^-9 f ^2.464; P _m=7.079·10^-8 f ^2.456; P _m=0.008v+0.008; P _m=18.996L+0.022; P _m=19.782R+0.021; P _m=82.143T+0.028; P _m=1.245·bm _f ^1.424 ; P _{mrel e}=6.471·bm _f ^1.040 ; =83.248+0.385. The following negative correlations were found: V=3.939–0.032; T=1.324·10^-4–0.038·10^-4. Statistically significant correlations were not found in T(f), L(), R(), f(), P _m(bm _e), P _{m rel e}(bm _e), P _{m rel f}(bm _e), P _{m rel f}(bm _f).Abbreviations A(m²) frontal area - bl(m) body length - bm(mg) body mass - c(mol·1^-1) glucose concentration of feeding solution - c _D (dimensionless) drag coefficient, related to A - D(N) drag - F _w(N) body weight - F _wp weight of paper fragment lost at flight start - f wingbeat frequency (s^-1) - g(=9.81 m·s^-2) gravitational acceleration - I(Ns)=R(t) dt total impulse of a flight - L(N) lift vertical sustaining force component - P _m(J·s^-1=W) metabolic power - P_{m ret} (W·g^-1) metabolic power, related to body mass - R(N) resultant aerodynamic force - Re v·bl·v ^-1 (dimensionless) Reynolds number, related to body length - s(m) v(t) dt virtual flight distance of a flight - s(km) total virtual flight distance - T (N) thrust horizontal force component of horizontal flight - T _a (°C) ambient temperature - t(s) time - t _tot (s or min) total flight time - v(m·s^-1) flight velocity - v(l) volume of feeding solution - W (J) energy and energy content of V - ( °) body angle of attack between body longitudinal axis and flow direction - ( °) tilting angle ( 90°) between R and the horizont in horizontal flight v(=1.53·10^-5m²·s^-1 for air at 25°) kinematic viscosity - (=1.2 kg·m^-3 at 25°C) air density     

Decreased ribulose-1,5-bisphosphate carboxylase-oxygenase in transgenic tobacco transformed with “antisense” rbcS

Tobacco (Nicotiana tabacum L.) plants transformed with antisense rbcS to decrease the expression of ribulose-1,5-bisphosphate carboxylase-oxygenase (Rubisco) have been used to investigate the contribution of Rubisco to the control of photosynthesis in plants growing at different irradiances. Tobacco plants were grown in controlled-climate chambers under ambient CO₂ at 20°C at 100, 300 and 750 mol·m^–2·s^–1 irradiance, and at 28°C at 100, 300 and 1000 mol·m^–2·s^–1 irradiance. (i) Measurement of photosynthesis under ambient conditions showed that the flux control coefficient of Rubisco (C _infRubisco ^supA ) was very low (0.01–0.03) at low growth irradiance, and still fairly low (0.24–0.27) at higher irradiance. (ii) Short-term changes in the irradiance used to measure photosynthesis showed that C _infRubisco ^supA increases as incident irradiance rises, (iii) When low-light (100 mol·m^–2·s^–1)-grown plants are exposed to high (750–1000 mol·m^–2·s^–1) irradiance, Rubisco is almost totally limiting for photosynthesis in wild types. However, when high-light-grown leaves (750–1000 mol·m^–2·s^–1) are suddenly exposed to high and saturating irradiance (1500–2000 mol·m^–2·s^–1), C _infRubisco ^supA remained relatively low (0.23–0.33), showing that in saturating light Rubisco only exerts partial control over the light-saturated rate of photosynthesis in sun leaves; apparently additional factors are co-limiting photosynthetic performance, (iv) Growth of plants at high irradiance led to a small decrease in the percentage of total protein found in the insoluble (thylakoid fraction), and a decrease of chlorophyll, relative to protein or structural leaf dry weight. As a consequence of this change, high-irradiance-grown leaves illuminated at growth irradiance avoided an inbalance between the light reactions and Rubisco; this was shown by the low value of C _infRubisco ^supA (see above) and by measurements showing that non-photochemical quenching was low, photochemical quenching high, and NADP-malate dehydrogenase activation was low at the growth irradiance. In contrast, when a leaf adapted to low irradiance was illuminated at a higher irradiance, Rubisco exerted more control, non-photochemical quenching was higher, photochemical quenching was lower, and NADP-malate dehydrogenase activation was higher than in a leaf which had grown at that irradiance. We conclude that changes in leaf composition allow the leaf to avoid a one-sided limitation by Rubisco and, hence, overexcitation and overreduction of the thylakoids in high-irradiance growth conditions, (v) Antisense plants with less Rubisco contained a higher content of insoluble (thylakoid) protein and chlorophyll, compared to total protein or structural leaf dry weight. They also showed a higher rate of photosynthesis than the wild type, when measured at an irradiance below that at which the plant had grown. We propose that N-allocation in low light is not optimal in tobacco and that genetic manipulation to decrease Rubisco may, in some circumstances, increase photosynthetic performance in low light.Abbreviations A rate of photosynthesis - C _infRubisco ^supA flux control coefficient of Rubisco for photosynthesis - c_i internal CO₂ concentration - qE energy-dependent quenching of chlorophyll fluorescense - qQ photochemical quenching of chlorophyll fluorescence - NADP-MDH NADP-dependent malate dehydrogenase - Rubisco ribulose-1,5-bisphosphate carboxylase-oxygenase - RuBP ribulose-1,5-bisphosphate This work was supported by the Deutsche Forschungsgemeinschaft (SFB 137).     

Development of a new method for testing strength of cells against fluid shear stress

A new method for testing the strength of cells against fluid shear stress by using a long capillary column was proposed. The trajectories of cells in the column were simulated by introducing the Brownian motion model. The Brownian motion was performed by the generation of random numbers. The mean exposure time to shear stress and the mean shear stress acting on the surface of cells were discussed by the result of computer simulation. The mean shear stress acting on the surface of cells flowing in the capillary column was estimated as 4/3-fold of the shear stress at the column wall provided that the ratio of the cell radius to the column radius does not exceed 0.08. The effectiveness of this new method for testing the strength of cells against fluid shear stress was shown.List of Symbols a m radius of cell - c constant - E distribution function - L m length of capillary column - M number of division - N number of division - p probability - Q m³/s flow rate - R m radius of capillary column - r m radial position - t s time - T s exposure time - T _m s mean exposure time - T ₀ s mean residence time - m/s axial velocity - u _m m/s cross-sectional flow velocity - z m axial position - s^–1 shear rate - _w s^–1 shear rate at wall - Pa s viscosity - spherical coordinate - spherical coordinate - Pa shear stress - _m Pa mean shear stress - _w Pa shear stress at wall     

A new technique for continuous measurement of the heat of fermentation

Summary A special temperature control system has been developed and applied to continuous measuring of the heat evolved during a fermentation process. In this system, the fermentation broth was overcooled by a given constant cooling water flow. The excess heat removed from the fermentor was then made up by an immersion electrical heater. The action of the temperature controller was precisely monitored as it varied in response to the amount of heat produced by the microbial activities.The technique was used for determining the heat evolution byEscherichia coli grown on glucose. The ratio between quantities of total heat release and total oxygen consumption has been determined to be 0.556 MJ/mol O₂.The newly developed technique can be employed as an online sensor to monitor the microbial activities of either aerobic or anaerobic fermentation systems.Symbols C_c Heat capacity of cooling water (MJ/kg · °C) - C_p Heat capacity (MJ/kg · °C) - I Current of immersion heater (A) - K Constant in Equation (2) (h) - K Constant in Equation (13) (m³ · h · °C/MJ) - Q_c Flow rate of cooling water (m³/h) - Heat of agitation (MJ/m³ · h) - Heat dissipated by the bubbling gas (MJ/m³ · h) - Heat removal by the action of controller (MJ/m³ · h) - Heat of fermentation (MJ/m³ · h) - Heat loss to the surroundings (MJ/m³ · h) - Q_pass Constant average power dissipated by the immersion heater (MJ/m³ · h) - Fluctuating power dissipated by the immersion heater (MJ/m³ · h) - Power dissipated by the immersion heater (MJ/m³ · h) - T Temperature of fermentation broth (°C) - Constant average temperature of fermentation broth (°C) - Fluctuating temperature of fermentation broth (°C) - T_a Temperature of the ambient air (°C) - T_c Inlet temperature of cooling water (°C) - U₁A₁ Specific heat transfer coefficient for determination of heat loss to the surroundings (MJ/m³ · h · °C) - U₂A₂ Specific heat transfer coefficient for cooling surfaces (MJ/m³ · h · °C) - U₃A₃ Constant in Equation (16) (MJ/m³ · h · °C) - V Voltage of immersion heater (V) - V_L Liquid volume (m³) - OUR Oxygen uptake rate (mol O₂/m³ · h) Greek Letters H_fo The ratio between the total heat release and the total oxygen uptake (MJ/mol O₂) - _c Density of cooling water (kg/m³) - Time constant defined in Equation (6) (h) - _iM_iC_pi Heat capacity of system components (fermentation broth + fermentor jar + stainless steel) (MJ/m³ · °C)     

Photoinhibition of photosynthesis under natural conditions in ivy (Hedera helix L.) growing in an understory of deciduous trees

We investigated to what extent south-exposed leaves (E-leaves) of the evergreen ivy (Hedera helix L.) growing in the shadow of two deciduous trees suffered from photoinhibition of photosynthesis when leaf-shedding started in autumn. Since air temperatures drop concomitantly with increase in light levels, changes in photosynthetic parameters (apparent quantum yield, _i and maximal photosynthetic capacity of O₂ evolution, P_max; chlorophyll-a fluorescence at room temperature) as well as pigment composition were compared with those in north-exposed leaves of the same clone (N-leaves; photosynthetic photon flux density PPFD< 100 mol · m^–2 · s^–2) and phenotypic sun leaves (S-leaves; PPFD up to 2000 mol · m^–2 · s^–1).In leaves exposed to drastic light changes during winter (E-leaves) strong photoinhibition of photosynthesis could be observed as soon as the incident PPFD increased in autumn. In contrast, in N-leaves the ratio of variable fluorescence to maximum fluorescence (F_V/F_Mm) and _i did not decline appreciably prior to severe frosts (up to -12° C) in January. At this time, _i was reduced to a similar extent in all leaves, from about 0.073 mol O₂ · mol^–1 photons before stress to about 0.020. Changes in _i were linearly correlated with changes in f_v/f_m (r = 0.955). The strong reduction in F_V/F_M on exposure to stress was caused by quenching in F_M. The initial fluorescence (F₀), however, was also quenched in all leaves. The diminished fluorescence yield was accompanied by an increase in zeaxanthin content. These effects indicate that winter stress in ivy primarily induces an increase in non-radiative energy-dissipation followed by photoinhibitory damage of PSII. Although a pronounced photooxidative bleaching of chloroplast pigments occurred in January (especially in E-leaves), photosynthetic parameters recovered completely in spring. Thus, the reduction in potential photosynthetic yield in winter may be up to three times greater in leaves subjected to increasing light levels than in leaves not exposed to a changing light environment.Abbreviations and Symbols F₀, F_M initial and maximal fluorescence yield when all PSII centres are open and closed - F_V variable fluorescence (F_M-F₀) - P_max maximal photosynthetic capacity at 1000 umol · m^–2 · s^–1 PPFD and CO₂ saturation - PPFD photosynthetic photon flux density - _i apparent quantum yield of photosynthetic O₂ evolution - E-leaves, N-leaves shade leaves exposed, not exposed to drastic light changes during winter - S-leaves sun leaves from an open ivy stand Dedicated to Professor Otto Härtel on the occasion of his 80th birthdayThis work was supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung.     

A simple dynamic method for on-line and off-line determination of kLa during cultivation of animal cells

Summary A new, fast method is described to determine k_La either off-line, or on-line during animal-cell cultivation. Since it does not need the equilibrium concentration of oxygen in the liquid phase (C*), it is not required to await a new steady state. Furthermore, the results do not depend on the calibration value of the dissolved-oxygen probe. The method yielded accurate values for k_La, both for an oxygen-consuming and a non-consuming system.Nomenclature C _L Dissolved-oxygen concentration [mol·m^-3] - C ^* C _L in equilibrium with the oxygen concentration in the gas phase [mol·m^-3] - C _L, Equilibrium oxygen concentration at stationary conditions [mol·m^-3] - k_La Volumetric oxygen transfer coefficient [s^-1] - r Specific oxygen consumption of biomass [mol·cell^-1·s^-1] - X Cell concentration [cells·m^-3] - t Time [s] - Noise of dissolved-oxygen probe [mol·m^-3] - Absolute error of k_La-measurement [s^-1]     

Biotransformation of cephalosporin C to 7-aminocephalosporanic acid with coimmobilized biocatalyst in a batch bioreactor

The permeabilized cells of Trigonopsis variabilis CCY 15-1-3 having D-amino acid oxidase (DAAO) activity were used to convert cephalosporin C (CPS-C) into 7-(-ketoadipyl amido) cephalosporanic acid (CO-GL-7-ACA) in a batch bioreactor with good aeration and stirring during the process. The deacylation of 7--(4-carboxybutanamido)-cephalosporanic acid (GL-7-ACA) to 7-cephalosporanic acid (7-ACA) by permeabilized cells of Pseudomonas species 3635 having 4--(4-carboxybutamido)-cephalosporanic acid acylase (GL-7-ACA acylase) activity was performed in a batch bioreactor. A spectrophotometric method for the determination of CO-GL-7-ACA and 7-ACA was proposed. Experimental data were fitted by non-linear regression with parameters optimization. The sorption method (without reaction) was applied for the determination of cephalosporin effective diffusion coefficients in Ca-pectate gel beads. These beads were prepared by dropping a potassium pectate gel suspension of inactive permeabilized cells of Trigonopsis variabilis and Pseudomonas species, crosslinked with glutaraldehyde, into a stirred 0.2 M calcium chloride solution. Concentrations of appropriate cephem components were measured by the refractive method. Values of effective diffusion coefficients were calculated by the Fibbonacci optimization method.List of Symbols c _L mol/dm³ concentration on the surface of a bead - c _L0 mol/dm³ initial cephalosporin concentration - c _L mol/dm³ equilibrium cephalosporin concentration in the solution - c _s1 mol/dm³ concentration of CPS-C - c _s2 mol/dm³ concentration of GL-7-ACA - D _ei m²/s effective diffusion coefficient of the components - K _i mol/dm³ inhibition parameter in Eq. (2) - K _{m i} mol/dm³ Michaelis constant in Eq. (1) - K _{m 2} mol/dm³ Michaelis constant in Eq. (2) - n number of beads - q _n nonzero positive roots in Eq. (7) - r ₁ mol/(dm³·s) rate of the conversion of CPS-S to CO-GL-7-ACA - r ₂ mol/(dm³·s) rate of the conversion of GL-7-ACA to 7-ACA - R m radius of the bead - S( ) symbol for total residual sum of squares in Eq. (1) - t s time - V _{m 1} mol/(dm³·s) max. reaction rate in Eq. (1) - V _{m 2} mol/(dm³·s) max. reaction rate in Eq. (2) - V _L dm³ volume of the solution excluding the space occupied by beads - V _s dm³ volume of beads - y _i mol/(dm³ · s) symbol for experimental data in Eq. (1) - _i mol/(dm³· s) symbol for calculated data in Eq. (1) - _P porosity, defined by Eq. (5) - dimensionless parameter, defined by Eq. (6) The authors wish to thank Dr. P. Gemeiner of Slovak Academy of Sciences for rendering of pectate gel. This work is supported by Ministry of Education (Grant No. 1/990 935/93)     

Transport of phenylalanine into vacuoles isolated from barley mesophyll protoplasts

The energy-dependent transport of phenylalanine into isolated vacuoles of barley (Hordeum vulgare L.) mesophyll protoplasts has been studied by silicone-layer floatation filtering. The uptake of this aromatic amino acid into the vacuolar compartment is markedly increased by MgATP, showing saturation kinetics; the K _m values were 0.5 mM for MgATP and 1.2 mM for phenylalanine. V _max for phenylalanine transport was estimated to 140 nmol phenylalanine·(mg·Chl)^-1·h^-1. The transport shows a distinct pH optimum at 7.3 and is markedly inhibited by 40 mM nitrate. Azide (1 mM) and vanadate (400 M) had no or little effect on rates of transport while p-fluorophenylalanine seemed to be an effective inhibitor, indicating a possible competition at an amino-acid carrier. Ionophores such as valinomycin, nigericin or gramicidin were strong inhibitors of phenylalanine transport, indicating that this process is coupled to both the transmembrane pH gradient (pH) and the transmembrane potential ().Abbreviations and symbols BSA bovine serum albumin - Chl chlorophyll - Hepes 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid - pH transmembrane pH gradient - transmembrane potential     

Mixing-models applied to industrial batch bioreactors

Mixing models for bioreactors on the basis of the tanks-in-series concept are presented and a suitable parameter-estimation method is introduced. The Monte-Carlo-optimization procedure with the inhomogeneity-curve included in the objective function is used. Results of the parameter optimization procedure are given for stirred-tank-bioreactors equipped with one and three Rushton turbines under aerated conditions. The model designed for the stirredtank with three Rushton turbines is capable to describe the mixing properties, while in case of the stirred-tank with one Rushton turbine the simulated radial circulation time does not correlate with the measured one.List of Symbols a ₀₀...a _XY coefficients in Eq. (9) - d _i m stirrer diameter - D m tank diameter - E relative error - F _AX m³/s axial liquid flow rate - F _G m³/s aeration flow rate - F _RAD m³/s radial liquid flow rate - g m/s² acceleration of gravity - h _l m height of fluid in the tank - i _s(t) simulated inhomogeneity-curve - i _m(t) measured inhomogeneity-curve - k number of sensors - n 1/s stirrer revolutions - N number of tanks in the tanks-of-series-cascade - p number of measured time intervalls - t s time - t _c.AX s axial circulation time - t _c,RAD s radial circulation time - T _i °C temperature of sensors - T °C temperature at the end of the experiment - T ₀ °C temperature before pulse injection - V _tot m³ total liquid volume - V _C m³ liquid volume of circulation cascade, additional index specifications describe the cascade elements (Figs.1 and 2) - V _M m³ liquid volume of well mixed stirrer compartment - w ₀ m/s superficial gas velocity - X, Y exponents in eq. (9) - kg/m³ density - Pas dynamic viscosity - m²/s kinematic viscosity - s time constant (time for 63,2% of T ) of the signal Dimensionless Numbers stirrer Froude number - aeration Froude number