Determination of the inherent kinetics of immobilized glucose oxidase using a diffusion cell

The enzyme glucose oxidase (GO) was covalently immobilized onto a poly(vinyl alcohol) hydrogel, cross-linked with glutardialdehyde and a polyazonium salt. To compare the kinetic parameters of immobilized GO with the known kinetic parameters of soluble GO, the diffusion cell method was used.Between two compartments, containing solutions with different glucose concentrations, a GO-containing hydrogel membrane was placed. Simultaneous diffusion through and enzymatic reaction in the membrane occurred. In this way diffusional effects of the membrane could be eliminated from the effective kinetic parameters to yield the inherent kinetic parameters.It appeared that the enzymatic reaction is independent of the oxygen concentration at oxygen concentrations 0.22 mol m^–3 (Michaelis constant for oxygen < 0.22 mol m^–3). Further, the Michaelis constant for glucose does not change dramatically after immobilizing the enzyme. The maximal reaction rate is depending on the enzyme concentration. As the enzyme concentration in the membrane is not exactly known (mainly due to leakage of enzyme out of the membrane during membrane preparation), only an estimation of the turnover number can be made.The diffusion cell method is easy to carry out. Still, some recommendations can be made on the performance.List of Symbols _g , _0x partition coefficient of glucose and oxygen, respectively - thickness of the wetted membrane (m) - A _m surface area of membrane (m^–2) - C constant (mol² m^–3) - c _g , c _0x concentration of glucose and oxygen, respectively (mol m^–3) - c _g,0 c _g, glucose concentration at the filter-paper/membrane interface next to compartment A and B, respectively (mol m^–3) - c _{g, A} c _{g, B} glucose concentration in compartment A and B, respectively (mol m^–3) - c _GO glucose oxidase concentration (mol m^–3) - D _eff effective diffusion coefficient (m² s^–1) - D _m , D _sl diffusion coefficient in, respectively, the membrane and the solution layer (m² s^–1) - d _dl , d _df , d _sl thickness of, respectively, the diffusion layer, the filter-paper and the solution layer (m) - h _B initial slope of concentration versus time curve of compartment B (mol m^–3 s^–1) - J flux (mol m^–2 s^–1) - J ₀ flux in the membrane at membrane/filter-paper interface next to compartment A and B, respectively (mol m^–2 s^–1) - J _A , J _B flux leaving compartment A and entering compartment B, respectively (mol m^–2 s^–1) - J _m flux through the membrane (mol m^–2 s^–1) - k total mass transfer coefficient (m s^–1) - k ₁ , k ₂ rate constant of a particular reaction step (m³ mol^–1 s^–1) - k_–1, k_–2 rate constant of a particular reaction step (s^–1) - k _cat (intrinsic) catalytic constant of turnover number (s^–1) - k _cat ^* inherent catalytic constant, determined by inserting D _m (s^–1) - k _cat ^** inherent catalytic constant, determined by inserting D _eff (s^–1) - k _m (g) (intrinsic) Michaelis constant for glucose (mol m^–3) - k _m (o) (intrinsic) Michaelis constant for oxygen (mol m^–3) - k _m ^* (g) inherent Michaelis constant for glucose (mol m^–3) - k _m ^* (o) inherent Michaelis constant for oxygen (mol m^–3) - m _GO number of moles of GO present (mol) - P _m permeability of glucose in the mebrane (m s^–1) - P _eff effective permeability (m s^–1) - V volume (m³) - v ₀ initial reaction velocity (mol m^–3 s^–1) - V _max ^** inherent maximal reaction velocity, determined by inserting D_eff (mol m^–3 s^–1) - x distance (m)     

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)     

Hybridomas in a bioreactor cascade: modeling and determination of growth and death kinetics

Hybridomas were cultured under steady-state conditions in a series of two continuous stirred-tank reactors (CSTRs), using a serum-free medium. The substrate not completely converted in the first CSTR, was transported with the cells to the second one and very low growth rates, high death rates, and lysis of viable cells were observed in this second CSTR. These conditions are hardly accessible in a single vessel, because such experiments would be extremely time-consuming and unstable due to a low viability. In contrast to what is often observed in literature, kinetic parameters could thus be derived without the neccessity for extrapolation to lower growth rates. Good agreement with literature averages for other hybridomas was found. Furthermore, showing that the reactor series is a valuable research tool for kinetic studies under extreme conditions, the possibility to observe cell death under stable and defined steady-state conditions offers interesting opportunities to investigate apoptosis and necrosis. Additionally, a model was developed that describes hybridoma growth and monoclonal antibody production in the bioreactor cascade on the basis of glutamine metabolism. Good agreement between the model and the experiments was found.Abbreviation MAb Monoclonal antibody Nomenclature C _AConcentration of any (mol m^-3) component A D Dilution rate (s^-1) K _dDeath-rate constant (mol m^-3) K _lLysis-rate constant (mol m^-3) K _sMonod constant (mol m^-3) m Maintenance coefficient (mol cell^-1 s^-1) q Specific consumption (mol cell^-1 s^-1) or production rate t Time (s) X Cell concentration (cell m^-3) Y Yield coefficient (cell mol^-1) Greek symbols _d Specific death rate (s^-1) _l Specific lysis rate (s^-1) of viable cells _net Net specific growth (s^-1) rate _true True specific growth (s^-1) rate     

Viscous media in tower bioreactors: Hydrodynamic characteristics and mass transfer properties

Studies in tower reactors with viscous liquids on flow regime, effective shear rate, liquid mixing, gas holdup and gas/ liquid mass transfer (k _La) are reviewed. Additional new data are reported for solutions of glycerol, CMC, PAA, and xanthan in bubble columns with diameters of 0.06, 0.14 and 0.30 m diameter. The wide variation of the flow behaviour index (1 to 0.18) allows to evaluate the effective shear rate due to the gas flow. New dimensionless correlations are developed based on the own and literature data, applied to predict k _La in fermentation broths, and compared to other reactor types.List of Symbols a(a) m^–1 specific interfacial area referred to reactor (liquid) volume - Bo Bond number (g D _c ² _L/) - c _L(c _L ^* ) kmol m^–3 (equilibrium) liquid phase oxygen concentration - C coefficient characterising the velocity profile in liquid slugs - C _s m^–1 coefficient in Eq. (2) - d _B(d_vs) m bubble diameter (Sauter mean of d _B) - d ₀ m diameter of the openings in the gas distributor plate - D _c m column diameter - D _L m²s^–1 diffusivity - E _L(E_W) m² s^–1 dispersion coefficient (in water) - E ² square relative error - Fr Froude number (u _G/(g D_c)^0.5) - g m s^–2 gravity acceleration - Ga Gallilei number (g D _c ³ _L ² / _eff ² ) - h m height above the gas distributor the gas holdup is characteristic for - k Pasⁿ fluid consistency index (Eq. 1) - k _L m s^–1 liquid side mass transfer coefficient - k _La(k_La) s^–1 volumetric mass transfer coefficient referred to reactor (liquid) volume - L m dispersion height - n flow behaviour index (Eq. 1) - P W power input - Re liquid slug Reynolds number ( _L(u _G +u _L) D _c/_eff) - Sc Schmidt number ( _eff/( _L D _L )) - Sh Sherwood number (k _La D _c ² /D_L) - t s time - u _B(u_sw) m s^–1 bubble (swarm) rise velocity - u _G(u_L) m s^–1 superficial gas (liquid) velocity - V(V_L) m³ reactor (liquid) volume Greec Symbols W m^–2 K^–1 heat transfer coefficient - y(y _eff) s^–1 (effective) shear rate - _G relative gas holdup - s relaxation time of viscoelastic liquid - _L(_eff) Pa s (effective) liquid viscosity (Eq. 1) - _L kg m^–3 liquid density - N/m surface tension     

Turbulent breakage of protein precipitates in mechanically stirred bioreactors

Experimental data relating to the breakage of isoelectric Soya protein precipitates in a mechanically agitated bioreactor are provided and examined in the light of a proposed mechanistic model which relates the size of the maximum attainable aggregate diameter to the energy dissipation rate in the vessel. The analysis suggests that protein precipitation results in the formation of scale-invariant fractal aggregates with a dimensionality of 2.2. Comparing the fractal dimensionality of the protein precipitates with reported values based on computer simulation studies suggests that the aggregates undergo considerable restructuring during agitation.List of Symbols A Hamaker constant (J) - D impeller diameter (m) - d _p primary particle diameter (m) - d _f maximum aggregate diameter (m) - G shear rate (s^–1) - H ₀ separation distance between two primary particles (m) - k constant in Eq. (5) - K constant in Eq. (6) - N impeller speed (rpm or rps) - r radial position in an aggregate, measured from the centre (m) - t time of exposure to shear (mins) - T _e eddy period (s^–1) - v _f aggregate volume (m³) Greek Symbols aggregate dimensionality constant - energy dissipation rate (W/kg) - dynamic viscosity of particle-free liquid (kg/ms) - kinematic viscosity of particle-free liquid (m²/s) - collision probability (–) - _p aggregate density (kg/m³) - _p continuous phase density (kg/m³) - aggregate mechanical strength (N/m²) - shear stress (N/m²) - particle concentration in an aggregate (m³/m³) - (r) porosity at radial position, r     

Comparison of three granular support materials for anaerobic fluidized bed systems

Summary Three different materials, kaolin, pozzolana and biolite (a material used in a commercial anaerobic fluidized bed treatment process) when tested as supports for an anaerobic fluidized bed system had similar physical and fluidization properties but behaved differently towards the biomass hold-up. However, all three systems attained similar removal efficiency rates.Nomenclature U Fluidization velocity (m/s) - U₁ Terminal fluidization velocity (m/s) - g Local acceleration due to gravity (m/s²) - _s Solid density (kg/m³) - _f Fluid density (kg/m³) - P Pressure drop (Pa) - HRT Hydraulic retention time (days) - H_mf Height of bed at minimum fluidization (m) - H Height of bed (m) - C_d Drag coefficient (dimensionless) - W Mass of solids in bed (kg) - dp Particle diameter (m) - A Cross-sectional area of column (m²) - h column height (m) - Rc_t Terminal Reynolds no. - Voidagc (fractional free volume, dimensionless) - _mf Voidage (fractional free volume) at minimum of fluidization (dimensionless)     

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.     

Development of reactor model for glucose isomerization catalyzed by whole-cell immobilized glucose isomerase

Based on the kinetic constants determined and the mathematical model of the reactor system developed, the performance of axial flow packed bed continuous enzyme reactor system was studied experimentally and also simulated with the aid of a computer for ultimate objective of optimization of the glucose isomerase reactor system.A reactor model was established analogous to heterogeneous catalytic reactor model taking into account the effect of fluid mass transfer and reversible kinetics. The investigated catalyst system consists of immobilized Streptomyces bambergiensis cells containing the enzyme glucose isomerase, which catalyzes the isomerization of glucose to fructose.List of Symbols A ₀, A ₁, A ₂ parameters in axial dispersion reactor model - c _go, c_g, c_gemol m^–3 glucose concentration at time t=0, at any time and at equilibrium conditions - c _gsmol m^–3 glucose concentration at particle surface - C dimensionless glucose concentration - d _pm particle diameter - d _rm diameter of reactor tube - Da Damkohler number - D _eff m² s^–1 effective glucose diffusion coefficient in Ca-alginate gel beads - k _fm s^–1 film transfer coefficient - K _e equilibrium constant - K _mg, K_mfmol m^–3 Michaelis-Menten constant for glucose and fructose, respectively - K _mmol m^–3 modified Michaelis-Menten constant - K dimensionless parameter - K ^* dimensionless parameter - L m length of reactor tube - Pe Peclet number - Pe _p particle Peclet number - Q m³ s^–1 volumetric flow rate - (-r _g) mol m^–3 s^–1 reaction rate - Re _p Reynolds particle number - Sc Schmidt number - Sh Sherwood number - t s time - v ₀ m s^–1 linear superficial fluid velocity - V _mg, V_mfmol g^–1 s^–1 maximal reaction rate for glucose and fructose, respectively - V _mmol m^–3 s^–1 modified maximal reaction rate for glucose - V _mg ^x mol m^–2 s^–1 maximal reaction rate for glucose - X _g, X_ge glucose conversion and glucose conversion at equilibrium conditions - X normalized conversion - Y dimensionless glucose concentration - void fraction of fixed bed - effectiveness factor of biocatalyst - Pa s kinematic viscosity of substrate - ₁ s first absolute weighted moment - ₂ s² second central weighted moment - _gkg m^–3 substrate density - _pkg m^–3 particle density - ² dimensionless variance of RTD curve - s residence time     

Residence time distribution of liquid phase in an external-loop airlift bioreactor

The residence time distribution analysis was used to investigated the flow behaviour in an external-loop airlift bioreactor regarded as a single unit and discriminating its different sections. The experimental results were fitted according to plug flow with superimposed axial dispersion and tank-in-series models, which have proved that it is reasonable to assume plug flow with axial dispersion in the overall reactor, in riser and downcomer sections, as well, while the gas separator should be considered as a perfectly mixed zone. Also, the whole reactor could be replaced with 105-30 zones with perfect mixing in series, while its separate zones, that is the riser with 104-27, the downcomer with 115-35 and the gas separator with 25-5 perfectly mixed zones in series, respectively, depending on gas superficial velocity, A_D/A_R ratio and the liquid feed rate.List of Symbols A _D cross sectional area of downcomer (m²) - A _R cross sectional area of riser (m²) - A ₁ A ₂ length of connecting pipes (m) - Bo Bodenstein number (Bo=vL·L/D _ax (-) - C concentration (kg m^–3) - C residence time distribution function - C ₀ coefficientEquation (12) - C _r dimensionless concentration - D _D diameter of downcomer (m) - D _R diameter of riser column (m) - D _ax axial dispersion coefficient (m²s^–1) - H _d height of gas-liquid dispersion (m) - H _L height of clear liquid (m) - i number of complete circulations - L length of path (m) - m order of moments - N _eq number of perfectly mixed zones in series - n _c circulating number - Q _c recirculating liquid flow rate (m³ s^–1) - q _F liquid feed flow rate (m³s^–1) - Q _G gas flow rate (m³s^–1) - Q _T total liquid flow rate (m³s^–1) - r recycle factor - s exponent inEquation (12) regarded as logarithmic decrement of the oscillating part of RTD curve - t time (s) - t _C circulation time (s) - t _s mean residence time (s) - t ₉₉ time necessary to remove 99% of the tracer concentration (s) - V _A volume of connecting pipes (m³) - V _D volume of downcomer (m³) - V _L liquid volume in reactor (m³) - V _R volume of riser (m³) - V _LD linear liquid velocity in downcomer (m s^–1) - V _LR linear liquid velocity in riser (m s^–1) - V _SLD superficial liquid velocity in downcomer (m s^–1) - V _SLR superficial liquid velocity in riser (m s^–1) - x independent variable inEquation (1) - ¯x mean value of x - z axial coordinate - _GR gas holdup in riser - _m(x) central moment of m order - ² variance - dimensionless time     

Gas holdup and mass transfer characteristics of carboxymethyl cellulose solutions in a bubble column with a radial gas sparger

The gas phase holdup and mass transfer characteristics of carboxymethyl cellulose (CMC) solutions in a bubble column having a radial gas sparger have been determined and a new flow regime map has been proposed. The gas holdup increases with gas velocity in the bubbly flow regime, decreases in the churn-turbulent flow regime, and increases again in the slug flow regime. The volumetric mass transfer coefficient (k _La) significantly decreases with increasing liquid viscosity. The gas holdup and k _La values in the present bubble column of CMC solutions are found to be much higher than those in bubble columns or external-loop airlift columns with a plate-type sparger. The obtained gas phase holdup ( _g) and k _La data have been correlated with pertinent dimensionless groups in both the bubbly and the churn-turbulent flow regimes.List of Symbols a m^–1 specific gas-liquid interfacial area per total volume - A _d m² cross-sectional area of downcomer - A _r m² cross-sectional area of riser - d _b m individual bubble diameter - d _vs m Sauter mean bubble diameter - D _c m column diameter - D _L m²/s oxygen diffusivity in the liquid - Fr Froude number, U _g/(g D_c)^1/2 - g m/s² gravitational acceleration - G _a Galileo number, gD _c ^{3 2}/² _app - H _a m aerated liquid height - H _c m unaerated liquid height - K Pa · sⁿ fluid consistency index - k _L a s^–1 volumetric mass transfer coefficient - n flow behavior index - N _i number of bubbles having diameter d _bi - Sc Schmidt number, _app/( D _L) - Sh Sherwood number, k _L a D _c ² /D_L - U _sg m/s superficial gas velocity - U _gr m/s superficial riser gas velocity - V _a m³ aerated liquid volume - V _c m³ unaerated liquid volume - N/m surface tension of the liquid phase - _g gas holdup - _app Pa · s effective viscosity of non-Newtonian liquid - kg/m³ liquid density - ý s^–1 shear rate - Pa shear stress     

Cytochromec oxidase fromParacoccus denitrificans in Triton X-100: Aggregation state and kinetics

Cytochromec oxidase fromParacoccus denitrificans was homogenously dispersed in Triton X-100. Using gel exclusion chromatography and sucrose gradient centrifugation analysis a molecular weight of the detergent-protein complex of 155,000 was determined. After subtraction of the bound detergent (111 mol/mol hemeaa ₃) a molecular weight of 85,000 resulted, which agreed well with the model of a monomer containing two subunits. This monomer showed high cytochromec oxidase activity when measured spectrophotometrically in the presence of Triton X-100 (V _max=85 s^–1). The molecular activity, plotted according to Eadie-Hofstee, was monophasic as a function of the cytochromec concentration. AK _m of 3.6×10^–6 M was evaluated, similar to theK _m observed in the presence of dodecyl maltoside [Naeczet al. (1985).Biochim. Biophys. Acta 808, 259–272].     

Estimation of oxygen penetration depth in immobilized cells

Summary A simple method is proposed for calculating oxygen pentration depth in immobilized cells by assuming zero order kinetics in the presence of several external oxygen transport resistances. Calculations indicate that typical penetration depths of oxygen for immobilized microbial cells are in the range of 50–200 and those for immobilized or encapsulated animal and plant tissue culture are about 500–1000 . Based on calculations, oxygen transport in microencapsulation and microcarriers for tissue cultures are not transport-limited, but a slight limitation is expected for those in a hollow fiber reactor.Nomenclature a_s specific area of a support (cm) - Bi Biot number - dimensionless - C_b oxygen concentration in the bulk liquid (mM) - C _b C _b ^* -C_cr (mM) - C _b ^* bulk oxygen concentration in equilibrium with air (mM) - C_cr critical oxygen concentration (mM) - C_s oxygen concentration in the solid phase (mM) - d_p diameter or thickness of a support (cm) - D_eff effective diffusivity of oxygen in the solid phase (cm²/s) - k_m membrane permeability of oxygen (cm/s) - k _m ^* D_eff/_m - k_La_L liquid phase mass transfer rate coefficient (1/s) - k_sa_s solid phase mass transfer rate coefficient (1/s) - (OUR)_v volumetric oxygen uptake rate (mmol O₂/l) - p geometry parameter, p=0 for slab, p=1 for cylinder, p=2 for sphere - P_d oxygen penetration depth (cm) - P _d oxygen penetration depth in the absence of external diffusion limitation (cm) - Q volumetric oxygen uptake rate, (mmol O₂/l·h) - specific oxygen uptake rate (mmol O₂gm biomass (dry)·h) - r length coordinate (cm) - r_c oxygen penetration depth for sphere (cm) - r _c r_c in the absence of external diffusion limitation (cm) - r _c ^* oxygen penetration depth for cylinder (cm) - r _c ^* r _c ^* in the absence of external diffusion limitation (cm) - r_com combined mass transfer rate resistance (s) - r_d location where C_s becomes zero or C_cr (cm) - r_i radius of cylinder or sphere, half thickness of slab (cm) - U_sg superficial gas velocity (cm/s) - X cell concentration (g/l) Greek letters Thiele modulus, dimensionless - _L, _s liquid and solid phase volume fraction, respectively, dimensionless - effectiveness factor On sabbatical leave from KAIST, Seoul, Korea     

Enhancement of protein precipitate strength and density by low-frequency conditioning

The use of a continuous, low-frequency conditioning process to alter the structure of protein precipitate aggregates is examined. An increase in the density of aggregates is correlated with the levels of fluid acceleration and hence hydrodynamic stress to which the aggregates are exposed during conditioning. A combination of low-frequency conditioning followed by shear break-up (as in the feed zone to a high-speed disk-stack centrifuge) is shown to result in a precipitate suspension of increased particle size at the fine end of the distribution, and having a greater sedimentation velocity. The resistance of large aggregates to shear disruption is increased by low-frequency conditioning.List of Symbols CR conditioning ratio - CRS conditioning ratio after shearing - d m amplitude of displacement - D m particle size - D _c m critical size for centrifuge recovery - f s^–1 frequency of vibration - G s^–1 mean velocity gradient - Q m³/s volumetric throughput - SR shear ratio - t s ageing time Greek Symbols s^–1 mass-average shear rate - K sedimentation shape factor - _a kg/m³ aggregate density - _f kg/m³ fluid density - _s kg/m³ solids density - kg/m³ aggregate-suspension density difference - Ns/m² kinematic viscosity - amplitude of pulse ratio (ref. 23, 9) - s mean residence time - _s solids volume fraction     

Analysis of gas exchange in seedlings of Acer saccharum: integration of field and laboratory studies

In the field, photosynthesis of Acer saccharum seedlings was rarely light saturated, even though light saturation occurs at about 100 mol quanta m^-2 s^-1 photosynthetic photon flux density (PPFD). PPFD during more than 75% of the daylight period was 50 mol m^-2 s^-1 or less. At these low PPFD's there is a marked interaction of PPFD with the initial slope (CE) of the CO₂ response. At PPFD-saturation CE was 0.018 mol m^-2 s^-1/(l/l). The apparent quantum efficiency (incident PPFD) at saturating CO₂ was 0.05–0.08 mol/mol. and PPFD-saturated CO₂ exchange was 6–8 mol m^-2 s^-1. The ratio of internal CO₂ concentration to external (C _i /C _a ) was 0.7 to 0.8 except during sunflecks when it decreased to 0.5. The decrease in C _i /C _a during sunflecks was the result of the slow response of stomates to increased PPFD compared to the response of net photosynthesis. An empirical model, which included the above parameters was used to simulate the measured CO₂ exchange rate for portions of two days. Parameter values for the model were determined in experiments separate from the daily time courses being sumulated. Analysis of the field data, partly through the use of simulations, indicate that the elimination of sunflecks would reduce net carbon gain by 5–10%.List of symbols A measured photosynthetic rate under any set of conditions (mol m^-2 s^-1) - A _m (atm) measured photosynthetic rate at saturating PPFD, 350 l/l CO₂ and 21% (v/v) O₂ (mol m^-2 s^-1) - C constant in equation of Smith (1937, 1938) - C _a CO₂ concentration in the air (l/l) - C _i CO₂ concentration in the intercellular air space (l/l) - C _i ^/* C _i corrected for CO₂ compensation point, i.e., C _i -I ^*, (l/l) - CE initial slope of the CO₂ response of photosynthesis (mol m^-2 s^-1/(l/l)) - CEM CE at PPFD saturation - E transpiration rate (mmol m^-2 s^-1) - F predicted photosynthetic rate (mol m^-2 s^-1) - G leaf conductance to H₂O (mol m^-2 s^-1) - I photosynthetic photon flux density (mol m^-2 s^-1) - N number of data points - P _m predicted photosynthetic rate at saturating CO₂ and given PPFD (mol m^-2 s^-1) - P _ml predicted photosynthetic rate at saturating CO₂ and PPFD (mol m^-2 s^-1) - R _d residual respiratory rate (mol m^-2 s^-1) - T _a air temperature (°C) - T _l leaf temperature (°C) - V reaction velocity in equation of Smith (1937, 1938) - V _max saturated reaction velocity in equation of Smith (1937, 1938) - VPA vapor pressure of water in the air (mbar/bar) - VPD vapor pressure difference between leaf and air (mbar/bar) - X substrate concentration in equation of Smith (1937, 1938) - initial slope of the PPFD response of photosynthesis at saturating CO₂ (mol CO₂/mol quanta) - (atm) initial slope of the PPFD response of photosynthesis at 340 l/l CO₂ and 21% (v/v) O₂ (mol CO₂/mol quanta) - I ^* CO₂ compensation point after correction for residual respiration (l/l) - PPFD compensation point (mol m^-2 s^-1)     

High-light damage in air-dry thalli of the old forest lichen Lobaria pulmonaria-interactions of irradiance, exposure duration and high temperature

High-light damage in air-dry thalli of Lobaria pulmonaria were measured in the laboratory as reductions in maximal PSII efficiency (Fv/Fm) after a 48 h recovery in a hydrated state at low light to account for permanent damage. Thalli treated with the lowest light dose (90 mol photons m^-2) recovered normal Fv/Fm-values with increasing irradiances (400-700 nm) up to 1000 mol photons m^-2 s^-1. Doubling this dose lowered the threshold level for damage from 1000 to 320 mol photons m^-2 s^-1, and reduced Fv/Fm at 1000 mol photons m^-2 s^-1 by more than 50%. A second doubling of the dose to 360 mol photons m^-2 caused damage at 200 mol photons m^-2 s^-1, and a nearly complete cessation of PSII efficiency occurred at 1000 mol photons m^-2 s^-1. No reciprocity of irradiance and duration of illumination for PSII function was found. The measured time-dependent decrease in Fv/Fm was remarkably similar for the naturally coupled, but artificially separated, light and temperature factors. Therefore, the damage of high light on desiccated L. pulmonaria seemed to be an additive effect of high irradiance and high temperatures. Air-dry thalli were highly heat susceptible, being affected already at temperatures around 40C. Logging operations in forests are likely to raise the solar radiation at remaining lichen sites to destructive levels.Keywords: Lichens, high-light damage, heat stress, poikilohydric organisms, reciprocity.      

Gas exchange characteristics and nitrogen relations of two Mediterranean root hemiparasites:Bartsia trixago andParentucellia viscosa

Plant height, light-saturated rates of photosynthesis (A _max) and foliar nitrogen concentration (N ₁) were measured forBartsia trixago under field conditions in Mallorca. All three variables were postively correlated, and were also positively related to the abundance of nitrogen-fixing legumes in the associated vegetation (putative host species).A _max forB. trixago ranged from 7.7 to 18.8 mol m^-2 s^-1; similar rates were measured for a second hemiparasiteParentucellia viscosa, and both species were within the range of rates measured for six putative hosts (10.6–19.2 mol m^-2 s^-1). Fertilization of unattachedB. trixago plants with inorganic nitrogen (ammonium nitrate) elicited neither the growth nor the photosynthetic responses observed in plants considered to be parasitic on legumes and in receipt of an enriched organic nitrogen supply. Both hemiparasites had high diurnal leaf conductances (g _s) (469–2291 mmol m^-2 s^-1) and were at the upper end of the range of those measured in putative hosts (409–879 mmol m^-2 s^-1). In contrast with the latter, high nocturnal rates ofg _s were also recorded for the two hemiparasites (517–1862 mmol m^-2 s^-1). There was no clear relationship between eitherA _max orN ₁ and eitherg _s, transpiration (E) or water use efficiency (A _max/E) inB. trixago plants. The economics of water loss appear to be independent of both the supply of nitrogen from the host and autotrophic carbon fixation.     

Theoretical analysis of the baker's yeast production: An experimental verification at a laboratory scale

The scale-down procedure seems an adequate tool in the design, optimization and scale-up fermentation processes. The first step in this procedure is a theoretical analysis, called process analysis, which is based on characteristic times of the mechanisms which may influence the performance of the bioreactor. This analysis must give information about the behaviour of large and small scale fermentation processes. At a small scale a verification of the results of such an analysis of the fed-batch baker's yeast production is carried out.In this paper a comparison of calculated and measured characteristic times of liquid mixing and mass transfer is presented. It was concluded that the literature correlations give a rough estimation of the characteristic times and can be used in the process analysis. Depending on the kind of sparger, the medium and the scale of the reactor, more knowledge is needed about bubble coalescence in fermentation media.The volumetric oxygen transfer coefficient increased when the biomass concentration increased. Probably this is caused by the interaction between biomass and the anti-foaming agent used.List of Symbols C kg/m³ concentration - D m diameter - m²/s effective dispersion coefficient - d m holes of the sparger - g m/s² gravitational acceleration - H m height - k _L a s^–1 volumetric mass transfer coefficient based on the liquid volume - L m length - m kg/kg gas liquid distribution coefficient - OTR kg/(m³ · s) oxygen transfer rate - OUR kg/(m³ · s) oxygen uptake rate - t s time - ^s m/s superficial gas flow rate - m length - s time constant - _g m³/s gas flow rate Indices 0 value at t=0 - cal calculated - e value at t=t (end) - g gas phase - in flow going to the fermentor - l liquid phase - m mixing - mt mass transfer - O ₂ oxygen - out flow coming out the fermentor     

Reactor design for the enzymatic isomerization of glucose to fructose

A comprehensive methodology is presented for the design of reactors using immobilized enzymes as catalysts. The design is based on material balances and rate equations for enzyme action and decay and considers the effect of mass transfer limitations on the expression of enzyme activity. The enzymatic isomerization of glucose into fructose with a commercial immobilized glucose isomerase was selected as a case study. Results obtained are consistent with data obtained from existing high-fructose syrup plants. The methodology may be extended to other cases, provided sound expressions for enzyme action and decay are available and a simple flow pattern within the reactor might be assumed.List of Symbols C kat/kg specific activity of the catalyst - D m²/s substrate diffusivity within the catalyst particle - Dr m reactor diameter - d d operating time of each reactor - E kat initial enzyme activity - E _i kat initial enzyme activity in each reactor - F m³/s process flowrate - F _i m³/s reactor feed flowrate at a given time - F ₀ m³/s initial feed flowrate to each reactor - H number of enzyme half-lives used in the reactors - K mole/m³ equilibrium constant - K _S mole/m³ Michaelis constant for substrate - K _P mole/m³ Michaelis constant for product - K _m mole/m³ apparent Michaelis constant f(K, K _s, K_p, s₀) - k mole/s · kat reaction rate constant - k _d d^–1 first-order thermal inactivation rate constant - L m reactor height - L _r m height of catalyst bed - N _R number of reactors - P _i kg catalyst weight in each reactor - p mole/m³ product concentration - R m particle radius - R _P ratio of minimum to maximum process flowrate - r m distance to the center of the spherical particle - s mole/m³ substrate concentration - s _0i mole/m³ substrate concentration at reactor inlet - s ₀ mole/m³ bulk substrate concentration - s mole/m³ apparent substrate concentration - T K temperature - t d time - t _i d operating time for reactor i - t _s d time elapsed between two successive charges of each reactor - V m³ reactor volumen - V _m mole/m³ s maximum apparent reaction rate - V _p mole/m³ s maximum reaction rate for product - V _R m³ actual volume of catalyst bed - V _r m³ calculated volume of catalyst bed - V _S mol/m³ s maximum reaction rate for substrate - v mol/m³ s initial reaction rate - v _i m/s linear velocity - v _m mol/m³ s apparent initial reaction rate f(K_m, s,V_m) - X substrate conversion - X _eq substrate conversion at equilibrium - =s/K dimensionless substrate concentration - ₀=s₀/K bulk dimensionless substrate concentration - _eq=s_eq/K dimensionless substrate concentration at equilibrium - local effectiveness factor - mean integrated effectiveness factor - Thiéle modulus - =r/R dimensionless radius - _s kg/m³ hydrated support density - substrate protection factor - s residence time     

Relationship Between Photosystem 2 Electron Transport and Photosynthetic CO2 Assimilation Responses to Irradiance in Young Apple Tree Leaves

The responses to irradiance of photosynthetic CO₂ assimilation and photosystem 2 (PS2) electron transport were simultaneously studied by gas exchange and chlorophyll (Chl) fluorescence measurement in two-year-old apple tree leaves (Malus pumila Mill. cv. Tengmu No.1/Malus hupehensis Rehd). Net photosynthetic rate (P _N) was saturated at photosynthetic photon flux density (PPFD) 600-1 100 (mol m^-2 s^-1, while the PS2 non-cyclic electron transport (P-rate) showed a maximum at PPFD 800 mol m^-2 s^-1. With PPFD increasing, either leaf potential photosynthetic CO₂ assimilation activity (F_d/F_s) and PS2 maximal photochemical activity (F_v/F_m) decreased or the ratio of the inactive PS2 reaction centres (RC) [(F_i – F_o)/(F_m – F_o)] and the slow relaxing non-photochemical Chl fluorescence quenching (q_s) increased from PPFD 1 200 mol m^-2 s^-1, but cyclic electron transport around photosystem 1 (RFp), irradiance induced PS2 RC closure [(F_s – F_o)/F_m – F_o)], and the fast and medium relaxing non-photochemical Chl fluorescence quenching (q_f and q_m) increased remarkably from PPFD 900 (mol m^-2 s^-1. Hence leaf photosynthesis of young apple leaves saturated at PPFD 800 mol m^-2 s^-1 and photoinhibition occurred above PPFD 900 mol m^-2 s^-1. During the photoinhibition at different irradiances, young apple tree leaves could dissipate excess photons mainly by energy quenching and state transition mechanisms at PPFD 900-1 100 mol m^-2 s^-1, but photosynthetic apparatus damage was unavoidable from PPFD 1 200 mol m^-2 s^-1. We propose that Chl fluorescence parameter P-rate is superior to the gas exchange parameter P _N and the Chl fluorescence parameter F_v/F_m as a definition of saturation irradiance and photoinhibition of plant leaves.     

Analysing the responses of photosynthetic CO2 assimilation to long-term elevation of atmospheric CO2 concentration

Understanding how photosynthetic capacity acclimatises when plants are grown in an atmosphere of rising CO₂ concentrations will be vital to the development of mechanistic models of the response of plant productivity to global environmental change. A limitation to the study of acclimatisation is the small amount of material that may be destructively harvested from long-term studies of the effects of elevation of CO₂ concentration. Technological developments in the measurement of gas exchange, fluorescence and absorption spectroscopy, coupled with theoretical developments in the interpretation of measured values now allow detailed analyses of limitations to photosynthesisin vivo. The use of leaf chambers with Ulbricht integrating spheres allows separation of change in the maximum efficiency of energy transduction in the assimilation of CO₂ from changes in tissue absorptance. Analysis of the response of CO₂ assimilation to intercellular CO₂ concentration allows quantitative determination of the limitation imposed by stomata, carboxylation efficiency, and the rate of regeneration of ribulose 1:5 bisphosphate. Chlorophyll fluorescence provides a rapid method for detecting photoinhibition in heterogeneously illuminated leaves within canopies in the field. Modulated fluorescence and absorption spectroscopy allow parallel measurements of the efficiency of light utilisation in electron transport through photosystems I and IIin situ.Abbreviations A net rate of CO₂ uptke per unit leaf area (µmol m^–2 s^–1) - A_sat light-saturated A - A₈₂₀ change in absorptance of PSI on removal of illumination (OD) - c CO₂ concentration in air (µmol mol^–1) - c_a c in the bulk air; c_i, c in the intercellular spaces - ce carboxylation efficiency (mol m^–2 s^–1) - E transpiration per unit leaf area (mol m^–2 s^–1) - F fluorescence emission of PSII (relative units) - F_m maximal level of F - F_o minimal level of F upon illumination when PSII is maximally oxidised - F_s the steady-state F following the m peak - F_v the difference between F_m and F_o - F'_m maximal F' generated after the m peak by addition of a saturating light pulse - F'_o the minimal level of F' after the m peak determined by re-oxidising PSII by far-red light - g₁ leaf conductance to CO₂ diffusion in the gas phase (mol m^–2 s^–1) - g'₁ leaf conductance to water vapour diffusion in the gas phase (mol m^–2 s^–1) - k_c and k_o the Michaelis constants for CO₂ and O₂, respectively, (µmol mol^–1); - J_max the maximum rate of regeneration of rubP (µmol m^–2 s^–1) - l stomatal limitation to CO₂ uptake (dimensionless, 0–1) - LCP light compensation point of photosynthesis (µmol m^–2 s^–1) - o_i the intercellular O₂ concentration (mmol mol^–1) - Pi cytosol inorganic phosphate concentration - PSI photosystem I - PSII photosystem II - Q photon flux (µmol m^–2 s^–1) - Q_abs Q absorbed by the leaf - rubisCO ribulose 1:5 bisphosphate carboxylase/oxygenase; rubP, ribulose 1:5 bisphosphate; s, projected surface area of a leaf (m²) - V_c,max is the maximum rate of carboxylation (µmol m^–2 s^–1) - W_c the rubisCO limited rate of carboxylation (µmol m^–2 s¹) - W_j the electron transport limited rate of regeneration of rubP (µmol m^–2 s^–1) - W_p the inorganic phosphate limited rate of regeneration of rubP (µmol m^–2 s^–1) - absorptance of light (dimensionless, 0–1) - _a of standard black absorber ₁, of leaf - _s of integrating sphere walls - , CO₂ compensation point of photosynthesis (µmol mol^–1) - the specificity factor for rubisCO carboxylation (dimensionless) - , convexity of the response of A to Q (dimensionless 0–1) - the quantum yield of photosynthesis on an absorbed light basis (A/Q_abs; dimensionless) - the quantum yield of photosynthesis on an incident light basis (A/Q; dimensionless) - _app the maximum - _m the maximum - _m,app the photochemical efficiency of PSII (dimensionless, 0–1) - _PSII,m the maximum