Concentrationo-dependence of nonelectrolyte permeability of toad bladder

Summary A theoretical formulation was derived for the dependence of bulk solute permeability,P, defined as net flux :- concentration gradient, c, across any membrane in which solute concentration is controlling for net flux, . According to this formulation, is stimulated by increments in trans concentration,c ₂, in the rangec ₂/c ₁=0.0–0.1. Net flux of urea across toad bladder down concentration gradients was shown to be stimulated threefold by small increments in trans urea concentration. The theory also predicts that, in the absence of concentration gradients, tracer permeability,P ^*, defined as tracer flux :- tracer concentration, will be independent ofc provided thatP=P ^*, but will diminish with increasingc ifP/P ^*<1.P/P ^* was not significantly different from unity for urea, and bothP andP ^* were independent ofc in the absence of concentration gradients. However,P/P ^* was significantly less than unity (0.90 and 0.85) for thiourea and mannitol, respectively. In conformity with theory,P ^* (and alsoP) of these two solutes, measured asc was increased by 3–4 orders of magnitude, diminished progressively. These effects are more consistent with this formulation than with transport via a saturable carrier.     

Improvement of the culture stability of non-anchorage-dependent animal cells grown in serum-free media through immobilization

A murine hybridoma cell line producing a monoclonal antibody against penicillin-G-amidase and a murine transfectoma cell line secreting a monovalent chimeric human/mouse Fab-antibody fragment were cultivated in three different media (serum-containing, low protein serum-free, and iron-rich protein-free) in flask cultures, stirred reactors and a fixed bed reactor. In static batch cultures in flasks both cell lines showed similar good growth in all three media.In suspension in a stirred reactor, the hybridoma cell line could be cultivated satisfactory only in serum-containing medium. In low protein serum-free medium, Pluronic F68 had to be added to protect the hybridoma cells against shear stress. But even with this supplement only batch, not chemostat mode was possible. In iron-rich protein-free medium the hybridoma cells grew also in continuous chemostat mode, but the stability of the culture was low. The transfectoma cell line did not grow in stirred reactors in any of the three media.Good results with both cell lines were obtained in fixed bed experiments, where the cells were immobilized in macroporous Siran^®-carriers. The media, which were optimized in flask cultures, could be used without any further adaptation in the fixed bed reactor. Immobilization improved the stability and reliability of cultures of non-adherent animal cells in serum-free media tremendously compared to suspension cultures in stirred reactors. The volume-specific glucose uptake rate, an, indicator of the activity of the immobilized cells, was similar in all three media. Deviations in the metabolism of immobilized and suspended cells seem to be mainly due to low oxygen concentrations within the macroporous carriers, where the cells are supplied with oxygen only by diffusion.List of symbols c substrate or product concentration mmol l^–1 - c₀ substrate or product concentration in the feed mmol l^–1 - c_Glc glucose concentration mmol l^–1 - c_Gln glutamine concentration mmol l^–1 - c_Amm ammonia concentration mmol l^–1 - c_Lac lactate concentration mmol l^–1 - c_FAB concentration of Fab# 10 antibody fragment g l^–1 - c_MAb monoclonal antibody concentration mg l^–1 - D dilution rate d^–1 - q cell-specific substrate uptake or metabolite production rate mmol cell^–1 h^–1 - q_Glc cell-specific glucose uptake rate mmol cell^–1 h^–1 - q_Gln cell-specific glutamine uptake rate mmol cell^–1 h^–1 - q_MAb cell-specific MAb production rate mg cell^–1 h^–1 - q^* volume-specific substrate uptake or metabolite production rate mmol l^–1 h^–1 - q^*FB volume-specific substrate uptake or metabolite production rate related to the fixed bed volume mmol l_FB ^–1 h^–1 - q^*FB,Glc volume-specific glucose uptake rate related to the fixed bed volume mmol l_FB ^–1 h^–1 - q^*FB,Gln volume-specific glutamine uptake rate related to the fixed volume mmol l_FB ^–1 h^–1 - q^*FB,MAb volume-specific MAb production rate related to the fixed volume mg l_FB ^–1 h^–1 - q^*FB,02 volume-specific oxygen uptake rate related to the fixed bed volume mmol l_FB ^–1 h^–1 - t time h - U superficial flow velocity mm s^–1 - V medium volume in the conditioning vessel of the fixed bed reactor l - V_FB volume of the fixed bed l - x_v viable cell concentration cells ml^–1 - y_Amm,Gln yield of Ammonia from glutamine - y_Lac,Glc yield of lactate from glucose - specific growth rate h^–1 - _d specific death rate h^–1     

Excitation-revealed changes in cytoplasmic Cl− concentration in “Cl−-starved”Chara cells

Summary The changes in the cytoplasmic Cl^– concentration, [Cl^–] _c , are monitored at the time of withdrawal (starvation) and subsequent replacement of Cl^– in the outside medium. The measurement technique exploits the involvement of Cl^– inChara excitation. The transient clamp current due to Cl^–,I _Cl, is separated from other excitation transients through Hodgkin-Huxley (HH) equations, which have been adjusted toChara. TheI _Cl amplitude depends on HH parameters, [Cl^–] _c and the maximum membrane conductance to Cl^–, . The results are discussed in terms of these quantities.I _Cl and were found to fall after 6–10 hr of Cl^– starvation, thus supporting the hypothesis that [Cl^– _c decreases in Cl^–-free medium. The best HH fit to starved data was obtained with [Cl^– _c =3.5mm. The time-course forI _Cl decline is considerably slower than the time-course of the rise of the starvation-stimulated influx. As cells starved for periods longer than 24 hr are re-exposed to Cl^–, it is revealed that while [Cl^–] _c remains low during long starvation, increases to values greater than those of the normal cells. Such differences among cells starved for various lengths of time have not been detected previously.     

Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations

In this paper we use a dynamical systems approach to prove the existence of a unique critical value c ^* of the speed c for which the degenerate density-dependent diffusion equation u _ct = [D(u)u _x ] _x + g(u) has: 1. no travelling wave solutions for 0 < c < c ^*, 2. a travelling wave solution u(x, t) = (x - c ^* t) of sharp type satisfying (– ) = 1, () = 0 ^*; '(^*–) = – c ^*/D'(0), '(^*+) = 0 and 3. a continuum of travelling wave solutions of monotone decreasing front type for each c > c ^*. These fronts satisfy the boundary conditions (– ) = 1, '(– ) = (+ ) = '(+ ) = 0. We illustrate our analytical results with some numerical solutions.     

Averaging methods in the delayed-logistic equation

The delayed logistic equation is analyzed using the averaging method. Using the transformation of coordinates v=ln N/K it is shown that the first order term in perturbation theory yields N=K exp(r ^* cos t/2) when the delay time T exceeds some critical value T _c. The amplitude r^* is equal to (40/3 – 2)^1/2 and is an expansion parameter that is proportional to (T – T_c). Comparison of the exponential solution of N and numerical results for the ratio N _maximum/N _minimum provides a good fit for values of larger than the results using the N coordinate as the perturbed coordinate.     

Determination of the effective diffusion coefficient of oxygen in gel materials in relation to gel concentration

Summary The effective diffusion coefficient of oxygen, ID_e, was determined in different gel support materials (calcium alginate, -carrageenan, gellan gum, agar and agarose) which are generally used for immobilization of cells. The method used was based upon fitting Crank's model on the experimental data. The model describes the solute diffusion from a well-stirred solution into gel beads which are initially free of solute. The effect of the gel concentration on ID_e of oxygen in the gel was investigated. The results showed a decreasing ID_e for both agar and agarose at increasing gel concentration. In case of calcium alginate and gellan gum, a maximum in ID_e at the intermediate gel concentration was observed. It is hypothesized that this phenomenon is due to a changing gelpore structure at increasing gel concentrations. The ID_e of oxygen in calcium alginate, -carrageenan and gellan gum varied from 1.5^*10^–9 to 2.1^*10^–9 m²s^–1 in the gel concentration range of 0.5 to 5% (w/v).     

Intestinal HCO 3 − secretion inAmphiuma: Stimulation by mucosal Cl− and serosal Na+

Summary The requirement for Na⁺ and Cl^– in the bathing media to obtain a maximal HCO ₃ ^– secretory flux ( ) across isolated short-circuitedAmphiuma duodenum was investigated using titration techniques and ion substitution. Upon substitution of media Na⁺ with choline, HCO ₃ ^– secretion was markedly reduced. Replacement of media Cl^– produced a smaller reduction of . The presence of Cl^– enhanced HCO ₃ ^– secretion only if Na⁺ was also in the media. Elevation of media Na⁺ or Cl^– in the presence of the other ion produced a saturable increase of . In the presence of Na⁺, Cl^– stimulated when added to the mucosal but not the serosal medium. In the presence of Cl^–, Na⁺ elevated when added to the serosal but not the mucosal medium. The ability of mucosal Cl^– to stimulate was not apparently dependent on mucosal Na⁺. Simultaneous addition of 10mm Cl^– to the Na⁺-free mucosal medium and 10mm Na⁺ to the Cl^–-free serosal medium stimulated above levels produced by serosal Na⁺ alone. In conclusion, intestinal HCO ₃ ^– secretion required mucosal Cl^– and serosal Na⁺ and did not involve mucosal NaCl cotransport. The results are consistent with a mucosal Cl^– absorptive mechanism in series with parallel basolateral Na⁺–H⁺ and Cl^––HCO ₃ ^– exchange mechanisms.     

Optimum temperature policy for batch reactors performing biochemical reactions in the presence of enzyme deactivation

A necessary condition is found for the optimum temperature policy which leads to the minimum reaction time for a given final conversion of substrate in a well stirred, enzymatic batch reactor performing an enzyme-catalyzed reaction following Michaelis-Menten kinetics in the presence of first order enzyme decay. The reasoning, which is based on Euler's classical approach to variational calculus, is relevant for the predesign steps because it indicates in a simple fashion which temperature program should be followed in order to obtain the maximum advantage of existing enzyme using the type of reactor usually elected by technologists in the fine biochemistry field. In order to highlight the relevance and applicability of the work reported here, the case of optimality under isothermal operating conditions is considered and a practical example is worked out.List of Symbols C _E mol.m^–3 concentration of active enzyme - C _E ^* dimensionless counterpart of C_E - C _E,0 mol.m^–3 initial concentration of active enzyme - C _E,b mol.m^–3 final concentration of active enzyme - C _E,opt ^* optimal dimensionless counterpart of C_E - C _smol.m^–3 concentration of substrate - C _S ^Emphasis>/* dimensionless counterpart of C_S - C _S,0mol.m^–3 initial concentration of substrate - C _S,bmol.m^–3 final concentration of substrate - E enzyme in active form - E ₃ ^* dimensionless counterpart of E_a,3 - E _a,1J.mol^–1 activation energy associated with k₁ - E _a,3J.mol^–1 activation energy associated with k₃ - E _d enzyme in deactivated form - ES enzyme/substrate complex - k ₁ s^–1 kinetic constant associated with the enzyme-catalyzed transformation of substrate - k _1,0 s^–1 preexponential factor associated with k₁ - k ₂ mol^–1.m³s^–1 kinetic constant associated with the binding of substrate to the enzyme - k _–2 s^–1 kinetic constant associated with the dissociation of the enzyme/substrate complex - K _2,0 mol.m^–3 constant value of K₂ - K _2,0 ^* dimensionless counterpart of K_2,0 - k ₃ s^–1 kinetic constant associated with the deactivation of enzyme - k _3,0 s^–1 preexponential factor associated with k₃ - k _3,0 ^* dimensionless counterpart of k_3,0 - P product - R J.K^–1.mol^–1 ideal gas constant - S substrate - t s time since start-up of reaction - T K absolute temperature - T ^* dimensionless absolute temperature - T _i,opt ^* optimal dimensionless isothermal temperature of operation - T _opt ^* optimal dimensionless temperature of operation - t _b s time of a batch - t _b ^* dimensionless counterpart of t_b - t _b,min ^* minimum value of the dimensionless counterpart of t_b Greek Symbols dimensionless counterpart of C_E,0 - dimensionless counterpart of C_E,b - dummmy variable of integration - dummy variable of integration - auxiliary dimensionless variable - ^* dimensionless variation of k₁ with temperature - _i ^* dimensionless value of k₁ under isothermal conditions - _opt ^* optimal dimensionless variation of k₁ with temperature     

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)     

Dialysis cultures with immobilized hybridoma cells for effective production of monoclonal antibodies

An industrial scale reactor concept for continuous cultivation of immobilized animal cells (e.g. hybridoma cells) in a radial-flow fixed bed is presented, where low molecular weight metabolites are removed via dialysis membrane and high molecular products (e.g. monoclonal antibodies) are enriched. In a new nutrient-split feeding strategy concentrated medium is fed directly to the fixed bed unit, whereas a buffer solution is used as dialysis fluid. This feeding strategy was investigated in a laboratory scale reactor with hybridoma cells for production of monoclonal antibodies. A steady state monoclonal antibody concentration of 478 mg l^-1 was reached, appr. 15 times more compared to the concentration reached in chemostat cultures with suspended cells. Glucose and glutamine were used up to 98%. The experiments were described successfully with a kinetic model for immobilized growing cells. Conclusions were drawn for scale-up and design of the large scale system.Abbreviations: c_Glc – glucose concentration, mmol l^-1; c_Gln – glutamine concentration, mmol l^-1; c_Amm – ammonia concentration, mmol l^-1; c_Lac – lactate concentration, mmol l^-1; c_MAb – MAb concentration, mg l^-1; D – dilution rate, d^-1; D_i – dilution rate in the inner chamber of the membrane dialysis reactor, d^-1; D₀ – dilution rate in the outer chamber of the membrane dialysis reactor, d^-1; q*_FB,Glc – volume specific glucose uptake rate related to the fixed bed volume, mmol l_FB ^-1 h^-1; q*_FB,Gln – volume specific glutamine uptake rate related to the fixed bed volume, mmol l_FB ^-1 h^-1.     

High density fed-batch cultures for hybridoma cells performed with the aid of a kinetic model

Hybridoma fed-batch cultures with either standard medium as feed or concentrated medium as feed and removal of toxic metabolites through dialysis were performed by using model calculations for a priori determination of process parameters. In a first step a kinetic model for specific growth and death rate, respectively as well as for substrate uptake and metabolite production rates was formulated. In a bed-batch culture with standard medium as feed the appropriate time for start of the feeding pump and the increase of feed rate were determined a priori. The glutamine concentration was controlled at 0.04 mmoll^–1. A priori calculation and course of the culture coincided rather well. A cell concentration of 3.2×10⁶ cells ml^–1, a MAb-concentration of 54 mg _MAb l^–1 and a MAb-time-space-yield of 0.53 mg _MAb l^–1h^–1 were obtained.For further increase of the efficiency a high density fed-batch process was developed, where concentrated medium is fed to the cells and the accumulating toxic low molecular weight metabolites are removed through a dialysis membrane into a dialyizng fluid. In a membrane dialysis reactor consisting of a culture chamber and a dialyzing chamber, which are separated by a cylindrical dialysis membrane, again model calculations were used to determine feed rate and exchange rate of dialyzing fluid. A viable cell density of 1.2×10⁷ cells ml^–1 and a MAb concentration of 425 mg l^–1 were reached in a culture with stepwise feeding of 10 x concentrated medium and exchange of dialyzing fluid for removal of low molecular metabolites. The course of the culture could be predicted a priori rather well. The MAb-time-space-yield was 2.47 mg _MAb l^–1h^–1, appr. 5 times higher compared to fed-batch cultures with standard medium as feed.List of Symbols A membrane area m² - c _i substrate or product concentration in culture chamber mmoll^–1 - c _a substrate or product concentration in dialyzing chamber mmoll^–1 - c _0i substrate or product concentration in the feed of culture chamber mmoll^–1 - c _0a substrate or product concentration in the feed of dialyzing chamber mmoll^–1 - c _Gln glutamine concentration mmoll^–1 - c _Amm ammonia concentration mmoll^–1 - c _MAb MAb concentration mmoll^–1 - D _a dilution rate in dialyzing chamber d^–1 - F _i feed rate during fed-batch to the culture chamber mlh^–1 - V _a volume of dialyzing chamber l - V _i volume of culture chamber l - P membrane permeability coefficient cm min^–1 - q specific substrate uptake or metabolite production rate mmol cell^–1 h^–1 - q _Gln spec. glutamine uptake rate mmol cell^–1 h^–1 - q _MAb spec. MAb production rate mmol cell^–1 h^–1 - t time h - X _v viable cell concentration cells ml^–1 - _MAb MAb-time-space-yield mgl^–1 h^–1 - specific growth rate h^–1 - _d specific death rate h^–1 Financial support from the Volkswagen-Stiftung, Germany, grand nr. I/69 359 is gratefully acknowledged.The concentrated medium was kindly provided by SERVA, Heidelberg, Germany. The hybridoma cell line was donated by Prof. fil. dr. Volker Kasche, Technische Universität Hamburg-Harburg, Germany.We express our special thanks to Andreas Schütt, Ralf Gassner, Katja Herbers and Thomas Schäfer for their help in this project.     

The electrical response ofAvena coleoptile cortex to auxins

Solute mobilities of 28 compounds in isolated cuticular membranes (CM) from Capsicum annuum L. fruit, Citrus aurantium L. and Pyrus communis L. leaves were studied using unilateral desorption from the outer surface. First-order rate constants of desorption (k^*), which are directly proportional to the diffusion coefficient in the waxy outer limiting skins of cuticles were measured. When log k^* was plotted vs. molar volumes of test compounds linear graphs were obtained. The y-intercepts of these graphs (k^*) represent the mobility of a hypothetical molecule having zero molar volume and the slopes of the graphs () represent the size selectivity of the barrier and are related to the free volume available for diffusion. Thus, solute mobilities in cuticles are composed of two independent terms which are subtractive. If k^* and are known, k^* can be estimated for any solute from its molar volume (V_x) using the equation log k^*=log k^* –V_x. These parameters were used to analyse the effects of plant species, extraction of cuticular waxes and molecular structure of solutes on solute mobilities in plant cuticles. For aliphatic solutes, k^* was a factor of 10 smaller than for cyclic compounds, while was 0.011 and 0.012, respectively. The k^*-values for CM of the three species were very similar, but was higher for bitter-orange CM (0.012) than for those of pepper fruits and pear leaves (0.009). This has the consequence that differences in solute mobilities (k^*) among cuticles from different plan species increase with increasing molar volumes of solutes. Our data and our analysis provide evidence that constituents of cuticular waxes are mobile, at least in the solid amorphous wax fraction, but mobility decreases rapidly with increasing molar volume. For instance, if amounts to 0.01, mobilities of wax monomers decrease by a factor of 10 for every increase in molar volume of 100 cm³ · mol^–1. Thus, hexadecanoic acid is quite mobile in the amorphous wax fraction of Citrus (k^*=1.5×10^–6·s^–1), but for dotriacontane having twice the molar volume, k^* was only 2.5×10^–9·s^–1, which is almost three orders of magnitude smaller. Wax esters have even higher molar volumes and their mobilities will be even smaller (about 4×10^–12·s^–1 for a C₄₈-ester). Since low chain mobilities are a prerequisite for low mobilities and permeabilities, the selective advantage of high-molecular-weight wax monomers in plant cuticular waxes becomes obvious. Extracting cuticular waxes from pear leaf CM increased solute mobilities by a factor of 182, but it had no effect on size selectivity. We interpret this result as evidence to the effect that cuticular waxes reduce mobility by increasing tortuosity of the diffusion path, rather than by decreasing the mean free path of diffusional jumps and jump frequencies of diffusants.Abbreviations CM cuticular membrane(s) - 2,4-D 2,4-dichloro-phenoxyacetic acid - LAB lactic acid buffer - MX polymer matrix membranes - UDOS unilateral desorption from the outer surface     

Optimization of cell density and dilution rate in <Emphasis Type="Italic">Pichia pastoris</Emphasis> continuous fermentations for production of recombinant proteins

This paper provides an approach for optimizing the cell density (X_c) and dilution rate (D) in a chemostat for a Pichia pastoris continuous fermentation for the extracellular production of a recombinant protein, interferon (INF-). The objective was to maximize the volumetric productivity (Q, mg INF- l^–1 h^–1), which was accomplished using response surface methodology (RSM) to model the response of Q as a function of X_c and D within the ranges 150 X_c 450 g cells (wet weight) l^–1 and 0.1 _mD0.9 _m (_m=0.0678 h^–1, the maximum specific growth rate obtained from a fed-batch phase controlled with a methanol sensor). The methanol and medium feed rates that resulted in the desired X_c and D were determined based on the mass balance. From the RSM model, the optimal X_c and D were 328.9 g l^–1 and 0.0333 h^–1 for a maximum Q of 2.73 mg l^–1 h^–1. The model of specific production rate (, mg INF- g^–1 cells h^–1) was also established and showed the optimal X_c=287.7 g l^–1 and D=0.0361 h^–1 for the maximum (predicted to be 8.92×10^–3 mg^–1 g^–1 h^–1). The methanol specific consumption rate (, g methanol g^–1 cells h^–1) was calculated and shown to be independent of the cell density. The relationship between and (specific growth rate) was the same as that discovered from fed-batch fermentations of the same strain. The approach developed in this study is expected to be applicable to the optimization of continuous fermentations by other microorganisms.     

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      

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     

Modeling of the pyruvate production with<Emphasis Type="Italic"> Escherichia coli</Emphasis> in a fed-batch bioreactor

A family of 10 competing, unstructured models has been developed to model cell growth, substrate consumption, and product formation of the pyruvate producing strain Escherichia coli YYC202 ldhA::Kan strain used in fed-batch processes. The strain is completely blocked in its ability to convert pyruvate into acetyl-CoA or acetate (using glucose as the carbon source) resulting in an acetate auxotrophy during growth in glucose minimal medium. Parameter estimation was carried out using data from fed-batch fermentation performed at constant glucose feed rates of q_VG=10 mL h^–1. Acetate was fed according to the previously developed feeding strategy. While the model identification was realized by least-square fit, the model discrimination was based on the model selection criterion (MSC). The validation of model parameters was performed applying data from two different fed-batch experiments with glucose feed rate q_VG=20 and 30 mL h^–1, respectively. Consequently, the most suitable model was identified that reflected the pyruvate and biomass curves adequately by considering a pyruvate inhibited growth (Jerusalimsky approach) and pyruvate inhibited product formation (described by modified Luedeking–Piret/Levenspiel term).List of symbols c_A acetate concentration (g L^–1) - c_A,0 acetate concentration in the feed (g L^–1) - c_G glucose concentration (g L^–1) - c_G,0 glucose concentration in the feed (g L^–1) - c_P pyruvate concentration (g L^–1) - c_P,max critical pyruvate concentration above which reaction cannot proceed (g L^–1) - c_X biomass concentration (g L^–1) - K_I inhibition constant for pyruvate production (g L^–1) - K_I^A inhibition constant for biomass growth on acetate (g L^–1) - K_P saturation constant for pyruvate production (g L^–1) - K_P inhibition constant of Jerusalimsky (g L^–1) - K_S^A Monod growth constant for acetate (g L^–1) - K_S^G Monod growth constant for glucose (g L^–1) - m_A maintenance coefficient for growth on acetate (g g^–1 h^–1) - m_G maintenance coefficient for growth on glucose (g g^–1 h^–1) - n constant of extended Monod kinetics (Levenspiel) (–) - q_V volumetric flow rate (L h^–1) - q_VA volumetric flow rate of acetate (L h^–1) - q_VG volumetric flow rate of glucose (L h^–1) - r_A specific rate of acetate consumption (g g^–1 h^–1) - r_G specific rate of glucose consumption (g g^–1 h^–1) - r_P specific rate of pyruvate production (g g^–1 h^–1) - r_P,max maximum specific rate of pyruvate production (g g^–1 h^–1) - t time (h) - V reaction (broth) volume (L) - Y_P/G yield coefficient pyruvate from glucose (g g^–1) - Y_X/A yield coefficient biomass from acetate (g g^–1) - Y_X/A,max maximum yield coefficient biomass from acetate (g g^–1) - Y_X/G yield coefficient biomass from glucose (g g^–1) - Y_X/G,max maximum yield coefficient biomass from glucose (g g^–1) - growth associated product formation coefficient (g g^–1) - non-growth associated product formation coefficient (g g^–1 h^–1) - specific growth rate (h^–1) - _max maximum specific growth rate (h^–1)     

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     

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     

Growth simulation ofHansenula polymorpha

Summary Using the model presented in part I, the measured time and spacial variations of process variables were simulated with satisfactory accuracy. Especially the experimentally found minima of the longitudinal dissolved oxygen concentration profiles in the substrate limiting growth range, which are caused by the transition from oxygen transfer limited to substrate limited growth along the tower, can be simulated with great accuracy.Symbols L length - M mass - T time - K temperature - M_M mole mass - a Specific gas/liquid interfacial area with regard to the liquid volume in the tower (L^–1) - DS_R Substrate feed rate (ML^–3T^–1) - K_O Saturation constant of Monod kinetics with regard to oxygen (ML^–3) - K_S Saturation constant of Monod kinetics with regard to the substrate (ML^–3) - K_ST Constant - K_L Mass transfer coefficient (LT^–1) - k_La Volumetric mass transfer coefficient (T^–1) - k_La^E Volumetric mass transfer coefficient at the entrance (T^–1) - k_La Volumetric mass transfer coefficient at large distances from the entrance (T^–1) - k_La ₀ Volumetric mass transfer coefficient in the absence of substrate (ethanol) (T^–1) - L_R Gas-liquid layer height in the tower (L) - L_R Height of the loop (L) - - O_B Dissolved oxygen concentration in the loop liquid (ML^–3) - O_F Dissolved oxygen concentration in the tower liquid (ML^–3) - O _F ^* Saturation value of O_F (ML^–3) - OTR Oxygen transfer rate (ML^–3T^–1) - P Pressure - Oxygen transfer rate (ML^–3T) - S_B Substrate concentration in the loop liquid (ML^–3) - S_D Substrate concentration at which k_La=2 k_La ₀ (ML^–3) - S_F Substrate concentration in the tower liquid (ML^–3) - T Absolute temperature - t Time (T) - u_Go Superficial gas velocity in the tower - V_R Reactor volume (L³) - V_G Volumetric gas flow rate in the tower (L³T^–1) - V_B Volumetric liquid flow rate in the loop (L³T^–1) - V_F Volumetric liquid flow rate in the tower (L³T^–3) - V_u Liquid recycling rate (L³T^–1) - X_B Biomass concentration in the loop liquid (ML^–3) - X_F Biomass concentration in the tower liquid (ML^–3) - x Longitudinal coordinate in the tower (L) - x^* Longitudinal coordinate in the loop (L) - x_OG O₂ mole fraction in the gas phase - Y_X/O Yield coefficient of biomass with regard to oxygen - Y_X/S Yield coefficient of biomass with regard to substrate - z=x/L_R Dimensionless longitudinal coordinate in the tower - z^*=x^*/L_B Dimensionless longitudinal coordinate in the loop - Constant (L_R is the distance from the aerator on which k_L a is space dependent) - Liquid recirculation ratio - _G Mean relative gas holdup in the tower - _exp Experimentally determined (T^–1) - _max Maximum specific growth rate (T^–1) - _F Liquid density (ML^–3) - A At the exit - E At the inlet     

Kinetics and thermodynamic transitions of N-acetyl-β-D-glucosaminidase A and B in free and bound forms: Role of cellulose ion-exchangers

Summary The kinetic and thermodynamic properties of N-acetyl--D-glucosaminidase A (Hex A) and N-acetyl--D-D-glucosaminidase (Hex B) from goat testes were investigated in free and bound (after binding them on ion-exchangers such as DEAE- or CM-cellulose respectively) forms. The optimum pH of free Hex A and Hex B was at 4.2 and 5.4, whereas the bound forms showed the optimum pH at 4.0 and 5.2 respectively. While apparent K_m of free and bound Hex A (0.8 and 1.0 mM respectively) did not differ, the K_m of Hex B increased when bound on CM-cellulose (K_m of free Hex B = 0.96 mM versus bound Hex B = 1.6 mM). Though the free Hex A was more thermo-labile than the free Hex B, both isozymes, on insoluble matrices decayed at faster rates on heating. Activation analysis revealed that the energy of activation (E _infa ^supo ) for transition state of free Hex B (81 Kcal deg^–1 mole^–1) did not differ from E _infa ^supo of bound Hex B. On the other hand, E _infa ^supo of free Hex A declined from 77.2 to 71.1 Kcal deg^–1 mole^–1 when heat transitions were carried out in free and bound state respectively. Thermodynamic analysis suggested a change in entropy of activation (S^*) of free Hex A and Hex B as 200 and 211 eu respectively. While S^* of Hex B did not change after heat transitions, S^* of Hex A was 182.5 eu.