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     

Redistribution of hepatocyte chloride during l-alanine uptake

We used ion-sensitive, double-barrel microelectrodes to measure changes in hepatocyte transmembrane potential (V _m), intracellular K⁺, Cl^-, and Na⁺ activities (a ⁱ _k, a _Cl ⁱ and a _Na ⁱ ), and water volume during l-alanine uptake. Mouse liver slices were superfused with control and experimental Krebs physiological salt solutions. The experimental solution contained 20 m l-alanine, and the control solution was adjusted to the same osmolality (305 mOsm) with added sucrose. Hepatocytes also were loaded with 50 mm tetramethylammonium ion (TMA⁺) for 10 min. Changes in cell water volume during l-alanine uptake were determined by changes in intracellular, steady-state TMA⁺ activity measured with the K⁺ electrode. Hepatocyte control V _m was -33±1 mV. l-alanine uptake first depolarized V _m by 2±0.2 mV and then hyperpolarized V _m by 5 mV to-38±1 mV (n = 16) over 6 to 13 min. During this hyperpolarization, a _Na ⁱ increased by 30% from 19±2 to 25±3 mm (P < 0.01), and a _K ⁱ did not change significantly from 83±3 mm. However, with added ouabain (1 mm) l-alanine caused only a 2-mV increase in V _m, but now a _K ⁱ decreased from 61±3 to 54±5 mm (P < 0.05). Hyperpolarization of V _m by l-alanine uptake also resulted in a 38% decrease of a _Cl ⁱ from 20±2 to 12±3 mm (P < 0.001). Changes in V _m and V _Cl — V _m voltage traces were parallel during the time of l-alanine hyperpolarization, which is consistent with passive distribution of intracellular Cl^– with the V _m in hepatocytes. Added Ba²⁺ abolished the l-alanineinduced hyperpolarization, and a _Cl ⁱ remained unchanged. Hepatocyte water volume during l-alanine uptake increased by 12±3%. This swelling did not account for any changes in ion activities following l-alanine uptake. We conclude that hepatocyte a _K ⁱ is regulated by increased Na⁺-K⁺ pump activity during l-alanine uptake in spite of cell swelling and increased V _m due to increased K⁺ conductance. The hyperpolarization of V _m during l-alanine uptake provides electromotive force to decrease a _Cl ⁱ . The latter may contribute to hepatocyte volume regulation during organic solute transport.This work was supported by grant AA-08867 from the Alcohol, Drug Abuse, and Mental Health Association.     

Rat osseous plate alkaline phosphatase: mechanism of action of manganese ions

Polidocanol-solubilized osseous plate alkaline phosphatase was modulated by manganese ions in a similar way as by zinc ions. For concentrations up to 1.0 nm, the enzyme was stimulated by manganese ions, showing site-site interactions (n = 2.2). However, larger concentrations (> 0.1 m) were inhibitory. Manganese ions could play the role of zinc ions stimulating the enzyme synergistically in the presence of magnesium ions (K _d = 7.2 m; V = 1005.5 U mg^–1). Manganese ions could also play the role of magnesium ions, stimulating the enzyme synergistically in the presence of zinc ions (K _d = 2.2 m; V = 1036.7 U mg^–1). However, manganese ions could not substitute for zinc and magnesium at the same time since ion assymetry is necessary for full activity of the enzyme. A steady-state kinetic model for the modulation of enzyme activity by manganese ions is proposed.     

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)     

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)     

Induction of ELF transmembrane potentials in relation to power-frequency electric field bioeffects in a plant root model system

Summary Seminal roots ofCucumis sativus andCucurbita maxima were exposed to 60 Hz electric fields of 100–500 Vm^–1 in a conducting aqueous inorganic growth medium. Root growth rates were measured to produce a dose-response relationship for each species. The species were selected for study because of their familial relationship, reported sensitivity to 60 Hz, 360 Vm^–1 electric fields, and differing average root cell sizes. The latter characteristic influences the magnitude of ELF membrane potentials induced by constant-strength applied electric fields, but does not affect the magnitude of the electric field strength tangent to the cell surface. The difference in average root cell size betweenC. sativus (smaller cells) andC. maxima (larger cells) was used to evaluate two alternate hypotheses that the observed effect on root growth is stimulated by [1] the electric field tangent to the cell surface, or (2) a field-induced perturbation in the normal transmembrane potential of the cells.The results of the dose-response relationship studies are qualitatively consistent with the hypothesis that the effect is elicited by induced transmembrane potentials. The smaller-celled roots showed a substantially higher response threshold [C. sativus; E ₀ ^TH 330 Vm^–1] than did the larger-celled species [C. maxima; E ₀ ^TH 200 Vm^–1]. At field strengths above the response thresholds in both species, the growth rate ofC. sativus roots was less affected than that ofC. maxima roots exposed to the same field strength.     

High-conductance K+ channel in pancreatic islet cells can be activated and inactivated by internal calcium

Summary The Ca²⁺-activated K⁺ channel in rat pancreatic islet cells has been studied using patch-clamp single-channel current recording in excised inside-out and outside-out membrane patches. In membrane patches exposed to quasi-physiological cation gradients (Na⁺ outside, K⁺ inside) large outward current steps were observed when the membrane was depolarized. The single-channel current voltage (I/V) relationship showed outward rectification and the null potential was more negative than –40 mV. In symmetrical K⁺-rich solutions the single-channelI/V relationship was linear, the null potential was 0 mV and the singlechannel conductance was about 250 pS. Membrane depolarization evoked channel opening also when the inside of the membrane was exposed to a Ca²⁺-free solution containing 2mm EGTA, but large positive membrane potentials (70 to 80 mV) were required in order to obtain open-state probabilities (P) above 0.1. Raising the free Ca²⁺ concentration in contact with the membrane inside ([Ca²⁺]_i) to 1.5×10^–7 m had little effect on the relationship between membrane potential andP. When [Ca²⁺]_i was increased to 3×10^–7 m and 6×10^–7 m smaller potential changes were required to open the channels. Increasing [Ca²⁺]_i further to 8×10^–7 m again activated the channels, but the relationship between membrane potential andP was complex. Changing the membrane potential from –50 mV to +20 mV increasedP from near 0 to 0.6 but further polarization to +50 mV decreasedP to about 0.2. The pattern of voltage activation and inactivation was even more pronounced at [Ca²⁺]_i=1 and 2 m. In this situation a membrane potential change from –70 to +20 mV increasedP from near 0 to about 0.7 but further polarization to +80 mV reducedP to less than 0.1. The high-conductance K⁺ channel in rat pancreatic islet cells is remarkably sensitive to changes in [Ca²⁺]_i within the range 0.1 to 1 m which suggests a physiological role for this channel in regulating the membrane potential and Ca²⁺ influx through voltage-activated Ca²⁺ channels.     

Differential regulation of membrane potential and conductance via intra-and extracellular pH in fused proximal tubular cells of frog kidney

Intracellular pH (pH _i ), membrane potential (V _m ) and membrane conductance (G _m ) in fused proximal tubular cells of the frog kidney, were determined at three extracellular pH (pH _o ) values, 7.5, 8.5 and 6.5. Imposed changes of pH _o by ±1 pH unit induced parallel but smaller shifts of pH _i . The alkaline milieu hyperpolarized the cells and increased G _m , whereas the acid milieu depolarized and lowered G _m . We subsequently introduced a weak acid and its conjugate base (acetic acid/acetate), or a weak base and its conjugate acid (NH₃/NH ₄ ⁺ ), at pH _o 7.5, 8.5 and 6.5 to shift pH _i -without altering pH _o , or to shift pH _i against imposed changes of pH _o . From these experiments, we observed that under some circumstances V _m varied with pH _o but without G _m or pH _i changes, whereas under other circumstances changes of G _m occurred during alterations of pH _i while pH _o and V _m remained unaltered. At pH _i 6.5 associated with V _m –10 mV, G _m dramatically increased to quasi-infinite values. This increase was not an artifact since G _m returned to its control value following recovery to the control solution or in the presence of hyperosmotic solution. In conclusion, we demonstrate a differential regulation whereby V _m and G _m are controlled by pH _o and pH _i : pH _o modulates mainly V _m , and pH _i modulates chiefly G _m . Furthermore, at pH _i 6.5 and V _m –10 mV, our data reveal a large G _m that tends towards infinite values in a reversible fashion.     

The effect of micro- and macromixing on enzyme reaction in a real CSTR

The effect of micromixing and macromixing on enzyme reaction of Michaelis-Menten type in a real continuously stirred tank reactor (CSTR) is considered. The effect of bypassing of a fraction of feed stream, dead space, initial enzyme concentration and Michaelis-Menten constant on substrate conversion is evaluated. Bypass reduces the substrate conversion significantly compared with other parameters in the case of micro and macromixing. Micromixing predicts higher substrate conversions compared with macromixing. The effect of micro and macromixing on substrate conversion is negligible at low and high conversions.List of Symbols C kmol/m³ concentration of reactant - ¯C kmol/m³ average concentration of reactant - C_A kmol/m³ exit concentration of reactant A - C_Aa kmol/m³ exit concentration of reactant A from active zone - C_AO kmol/m³ initial concentration of reactant A - C_EO kmol/m³ initial enzyme concentration - C_O kmol/m³ initial concentration of reactant - E(t) 1/s exit age distribution function - k 1/s reaction rate constant - M kmol/m³ Michaelis-Menten constant - r kmol/(m³s) rate of reaction - –r_A kmol/(m³s) rate of reaction with respect to A - t s time - v m³/s volumetric feed rate - v_a m³/s volumetric feed rate entering the active zone - v_b m³/s volumetric feed rate entering the bypass stream - V m³ total volume of the vessel - V_a m³ active volume of the vessel - V_d m³ volume of dead space - X_A conversion of A Greek Letters fraction of feed stream bypassing the vessel (v_b/v) - fraction of the total volume as dead space (V_d/V) - (t) 1/s Dirac delta function, an ideal pulse occurring at time t = 0 - s life expectancy of a molecule - 1/s intensity function or escape probability function - s space time or mean residence time     

Electrical membrane potential and resistance in photoautotrophic suspension cells of Chenopodium rubrum L.

On photoautotrophically grown, suspension-cultured cells of Chenopodium rubrum L. the electrical potential difference V _mand the electrical resistance across plasmalemma and tonoplast have been measured using one or two intracellular micro-electrodes. In a mineral test-medium of 5.8 mM ionic strength V _mvalues between 100 and 250 mV, 40% thereof between 170 and 200 mV, and a mean value (±S.E.M.) of 180.6±3.4 mV have been recorded. The average membrane input resistance R _mwas 269±36 M, corresponding to an average membrane resistivity r _mof 3.0 m². V _mand r _mare sensitive to light, temperature, and addition of cyanide, suggesting the presence of an electrogenic hyperpolarizing ion pump, and are ascribed essentially to the plasmalemma. A hexose-specific saturable electrogenic membrane channel is identified through a decrease of V _mand r _mupon addition of hexoses. The hexoseconcentration-dependent depolarization V _msaturates at 92 mV and returns half-saturating concentrations (apparent k _mvalues) of 0.16 mM galactose, 0.28 mM glucose, and 0.48 mM fructose. The magnitude of V _mand r _mwell agrees with pertinent data from mesophyll cells in situ (where only V _mdata are available) and from photoautotrophic lower plant cells. However, V _mis markedly higher than reported for heterotrophically grown suspension cells of different higher plants (with which r _mdata have not been reported so far). It is concluded from the present study and a companion paper on water transport (Büchner et al., Planta, in press) that photoautotrophically grown Chenopodium suspension cells closely resemble mesophyll cells as to cell membrane transport properties.Abbreviations V _m membrane potential(mV) - R _o input resistance () - R _m membrane input resistance () - r _m specific resistance (resistivity) of the membrane (m²)     

The problem of nonstationary ion fluxes in excitable membranes

Time-dependent electrodiffusion through a membrane is analysed within a simple model treating the boundary-layers in a consistent manner. It is shown that time-independent reversal potentials for the ion fluxes exist only under steady-state conditions. We argue that this result holds very generally. Therefore nonstationary effects like ion storage and depletion inside the membrane should not contribute to the phenomena of excitability.Glossary of Symbols A _mv [V] functional cf. Equation (3) - C membrane capacitance - d one half the thickness of the membrane - F[V] functional cf. Equation (1) - g _i electrochemical potential inside membrane - g _i electrochemical potentials outside membrane at x ±d, respectively - i (index) refers to i-th ionic species - J electric current across membrane - j = j ^} = j ^< current density measured by external electrodes - j _i (x) current density inside membrane in x-direction - j _i ^inst(x) instantaneous current density - J _i ^stat steady-state current density - k Boltzmann constant - m (index) is used in Sec. 2 to denote the independent diffusion currents - n ^< ionic strength of electrolyte at x = - - n _i density of ions inside membrane - n _i density of ions outside membrane at x = ±, respectively - Q charge per unit area of boundary layers at x ± d, respectively - Q ₀ fixed charge per unit area of membrane - q elementary charge - q _i ionic charges - T temperature - it time - V membrane potential (= (-)-()) - V _i Nernst potential - V potential drops inside boundary layers (can be neglected, see Appendix II) - V ^± potential steps at x = ± d, cf. Equation (29) - V ₀ = V ^–-V ⁺ - w _i activation energy inside membrane - x spatial coordinate perpendicular to membrane - y, z spatial coordinates parallel to membrane - dielecric constant - ₀ dielectric constant of electrolyte solution ( 80) - _m dielectric constant of membrane ( 5) - (x) electrostatic potential - charge density of boundary layers - ⁰ fixed charge density inside membrane - spatial average, cf. Equation (12)     

Amplification of small signals by voltage-gated sodium channels in drone photoreceptors

Summary Photoreceptor cells of the drone,Apismellifera , have a voltage-gated Na⁺ membrane conductance that can be blocked by tetrodotoxin (TTX) and generates an action potential on abrupt depolarization: an action potential is triggered by the rising phase of a receptor potential evoked by an intense light flash (Autrum and von Zwehl 1964; Baumann 1968). We measured the intracellular voltage response to a small (9%), brief (30 ms) decrease in light intensity from a background, and found that its amplitude was decreased by 1M TTX. The response amplitude was maximal when the background intensity depolarized the cell to –38 mV. With intensities depolarizing the cell membrane to –45 to –33 mV the average response amplitude was decreased by TTX from 1.2mV to 0.5mV. TTX is also known to decrease the voltage noise during steady illumination (Ferraro et al. 1983) but, despite this, the ratio of peak-to-peak signal to noise was, on average, decreased by TTX. The results suggest that drone photoreceptors use voltage-gated Na⁺ channels for graded amplification of responses to small, rapid changes in light intensity.Abbreviations TTX tetrodotoxin - V _i intracellular potential with respect to the bath - V _o extracellular potential - V _m,V _i-V _o approximate transmembrane potential - S amplitude of the voltage response to an 8.9% decrease in light intensity - N voltage noise, usually measured as root mean square voltage deviation as described in Methods     

Properties of the phosphate and phosphite transport systems of Phytophthora palmivora

Germlings of Phytophthora palmivora possess at least two systems for the uptake of inorganic phosphate (P_i). The first is synthesized on germination in medium containing 50 M P_i and has a K_m of approx. 30 M (V_max=7–9 nmol P_i/h·10⁶ cells). The second is synthesized under conditions of P_i-deprivation and has a higher affinity for P_i (K_m=1–2 M), but a lower V_max (0.5–2 nmol P_i/h·10⁶ cells). The fungicide phosphite likewise enters the germlings via two different transport systems, the synthesis of which also depends on the concentration of P_i in the medium. The K_m of the lower affinity system is 3 mM (V_max=20 nmol phosphite/h·10⁶ cells) and that of the higher affinity system is 0.6 mM (V_max=12 nmol/h·10⁶ cells). P_i and phosphite are competitive inhibitors for each other's transport in both systems. However, whereas mM concentrations of phosphite are necessary to inhibit P_i transport, only M concentrations of P_i are required to inhibit phosphite transport. A third system of uptake for P_i also exists, since when phosphate-deprived cells are presented with mM concentrations of P_i, they transport the anion at a very high rate (around 100 nmol/h·10⁶ cells). High rates of transport of phosphite are also observed when these cells are presented with mM concentrations of this anion.     

Large plasma-membrane depolarization precedes rapid blue-light-induced growth inhibition in cucumber

Blue-light (BL)-induced suppression of elongation of etiolated Cucumis sativus L. hypocotyls began after a 30-s lag time, which was halved by increasing the fluence rate from 10 to 100 mol·m^-2·s^-1. Prior to the growth suppression, the plasma-membrane of the irradiated cells depolarized by as much as 100 mV, then returned within 2–3 min to near its initial value. The potential difference measured with surface electrodes changed with an identical time course but opposite polarity. The lag time for the change in surface potential showed an inverse dependence on fluence rate, similar to the lag for the growth inhibition. Green light and red light caused neither the electrical response nor the rapid inhibition of growth. The depolarization by BL did not propagate to nonirradiated regions and exhibited a refractory period of about 10 min following a BL pulse. Fluenceresponse relationships for the electrical and growth responses provide correlational evidence that the plasma-membrane depolarization reflects an event in the transduction chain of this light-growth response.Abbreviations and symbols BL blue light - V _m membrane potential - V ₈ surface 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     

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.     

Optimization and control of a continuous stirred tank fermenter using learning system

A variable structure learning automaton is used as an optimization and control of a continuous stirred tank fermenter. The algorithm requires no modelling of the process. The use of appropriate learning rules enables to locate the optimum dilution rate in order to maximize an objective cost function. It is shown that a hierarchical structure of automata can adapt to environmental changes and can also modify efficiently the domain of variation of the control variable in order to encompass the optimum value.List of Symbols f Random number - F Dimensionless flow rate (F/V ₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective 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 equation (3) (k _s/s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - L Number of levels of the hierarchical system of automata - N Number of possible control actions - p Probability - S Dimensionless substrate concentration (s/s ₀) - s kg/m³ Substrate concentration - T Dimensionless sampling period - t h Time - v Dimensionless volume (V/V ₀) - V m³ Liquid volume in fermenter - W Input to the stochastic automaton - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ^*) - ^* h^–1 Maximum specific growth rate - h^–1 Specific growth rate - Dimensionless time ( t)     

Enhancement of product selectivity via enzyme immobilization in sequential degradation reactions of polymeric substrates

The balance equations pertaining to the modelling of a slap-shaped bead containing immobilized enzyme uniformly distributed which catalyzes the sequential reactions of degradation of a polymeric substrate were written and analytically solved in dimensionless form. The effect of the Thiele modulus on the selectivity of consumption of each multimeric product was studied for a simple case. Whereas plain diffusional regime leads to lower selectivities than plain kinetic regime, improvements in selectivity of species A _i relative to species A_i+1 may be obtained at the expense of higher Thiele moduli within a limited range when the diffusivity of A _i is larger than that of A _i +1, or when the pseudo first order kinetic constant describing the rate of consumption of A _i is lower than that of A_i+1.List of Symbols A _i polymeric substrate containing i monomeric subunits - C _i mol·m^–3 normalized counterpart of C _i - C _i mol·m^–3 concentration of substrate A _i - C _i,0 mol·m^–3 initial concentration of substrate A _i - C _i,0 normalized counterpart of C _i,0 - D _ap,i m²·s^–1 apparent diffusivity of substrate A _i - k _i s^–1 pseudo-first order rate constant - K _m,i mol·m^–3 Michaelis-Menten constant associated with substrate A _i - L m half-thickness of the catalyst slab - N number of monomeric subunits of the largest substrate molecule - Th Thiele modulus - V _i mol·m^–3·s^–1 rate of rection of substrate A _i - V_max,i mol·m^–3·s^–1 maximum rate of reaction under saturating conditions of substrate A _i - x m longitudinal coordinate - S _i,i+1 selectivity of enzyme with respect to substrates with consecutive numbers of monomeric subunits Greek Symbols _i ratio of maximum rates of reaction - _i ratio of apparent diffusivities     

Effect of adherence,cell morphology,and lipopolysaccharide on potassium conductance and passive membrane properties of murine macrophage J774.1 cells

Summary The effects of adherence, cell morphology, and lipopolysaccharide on electrical membrane properties and on the expression of the inwardly rectifying K conductance in J774.1 cells were investigated. Whole-cell inwardly rectifying K currents (K _i), membrane capacitance (C _m), and membrane potential (V _m) were measured using the patch-clamp technique. SpecificK _i conductance (G _K i, whole-cell Ki conductance corrected for leak and normalized to membrane capacitance) was measured as a function of time after adherence, and was found to increase almost twofold one day after plating. Membrane potential (V _m) also increased from –42±4 mV (n=32) to –58±2 mV (n=47) over the same time period.G _K i andV _m were correlated with each other;G _L (leak conductance normalized to membrane capacitance) andV _m were not. The magnitudes ofG _K i andV _m 15 min to 2 hr after adherence were unaffected by the presence of 100 m cycloheximide, but the increase inG _K iandV _m that normally occurred between 2 and 8 hr after adherence was abolished by cycloheximide treatment. Membrane properties were analyzed as a function of cell morphology, by dividing cells into three categories ranging from small round cells to large, extremely spread cells. The capacitance of spread cells increased more than twofold within one day after adherence, which indicates that spread cells inserted new membrane. Spread cells had more negative resting membrane potentials than round cells, butG _K i andG _L were not significantly different. Lipopolysaccharide-(LPS; 1 or 10 g/ml) treated cells showed increasedC _m compared to control cells plated for comparable times. In contrast to the effect of adherence, LPS-treated cells exhibited a significantly lowerG _K i than control cells, indicating that the additional membrane did not have as high a density of functionalG _K i channels. We conclude that both adherence and LPS treatment increase the total surface membrane area of J774 cells and change the density of Ki channels. In addition, this study demonstrates that membrane area and density of Ki channels can vary independently of one another.