One-dimensional model of the acid hydrolysis of cellulosic substrates in a solid-liquid cyclone reactor

The use of rotating flow in an annulus is investigated as a means of enhancing the yield of glucose and xylose in the acid hydrolysis of cellulosic slurries. A one-dimensional model of such a cyclone reactor is developed for flow cases, co-current and counter-current flow. For the case of 250°C, 1% w/w acid, the one-dimensional model indicates an increase in the maximum glucose yield from 48.1% in a plug flow reactor to 69.3% in a co-current cyclone reactor, and up to 81.0% in a countercurrent cyclone reactor. The corresponding xylose yields are 91.6% for co-current operation and 97.7% for countercurrent operation. In the co-current case the maximum glucose and xylose yields do not occur at the same location in the reactor; however, in the countercurrent case they do. Although product yields are dramatically improved over those obtained in a plug flow reactor, the product concentrations are lower than would typically be obtained in a plug flow reactor.List of Symbols A cm² cross sectional area perpendicular to radial flow - A _c cm² cross sectional area of slurry inlet - A _c cm² cross sectional area of steam inlet - A _w cm² cross sectional area of water inlet - C _c concentration of cellulose as potential glucose (grams of potential glucose/cm³ of total stream) - C _c ^* grams cellulose/cm³ of solids concentration of cellulose as potential glucose - C _ginitial ^* grams glulose/cm³ of solids concentration of cellulose entering reactor - C _g grams glucose/cm³ of total stream concentration of glucose - C _g ^* grams glucose/cm³ of liquid stream concentration of glucose - C _cinitial ^* grams cellulose/cm³ of liquid concentration of glucose entering reactor - C _xn concentration of xylan as potential xylose (grams of potential xylose/cm³ of total stream) - C _xs grams xyclose/cm³ of total stream concentration of nylose - d _f dilution factor - dr cm radial increment - g cm/s² gravitational acceleration - g ^* centrifugal acceleration proportionality constant - h cm height of cyclone reactor - j cm/s flux - K constant in general equation for vortex flow, Eq. (4.9) - k ₁ 1/s kinetic rate constant of cellulose hydrolysis - k _a 1/s kinetic rate constant of xylan hydrolysis - k ₂ 1/s kinetic rate constant of glucose decomposition - k _2a 1/s kinetic rate constant of xylose decomposition - m vortex exponent - M _steam g/s mass rate of steam addition at outer radius - M _water g/s mass rate of cold water addition at outer radius - n cm³/s empirically determined settling parameter - Q cm³/s net volumetric flow in outward radial direction - Q _tot cm³/s total volumetric flow through reactor - q _c cm³/s volumetric flow of slurry feed - q _s cm³/s volumetric flow of stream feed - q _water cm³/s volumetric flow of cold water feed - r cm radial position - r _c 1/s rate of cellulose hydrolysis - r _g 1/s rate of glucose decomposition - r _i cm inner radius - r _o cm outer radius - r _xn 1/s rate of xylan hydrolysis - r _xs 1/s rate of xylose decomposition - s _mom cm g/s² inlet steam momentum - T _bulk s bulk residence time in reactor - T °C reactor temperature - v _c cm³/g specific volume of slurry feed - v _s cm³/g specific volume of steam - v _w cm³/g specific volume of water - V _f cm/s velocity of liquid as a function of radius - V _i cm/s inlet velocity - V _s cm/s velocity of solids as a function of radius - V _steam cm/s inlet steam velocity to cyclone - V cm/s terminal settling velocity - V _q cm/s tangential velocity - w _mom cm g/s² water inlet momentum - Y grams product out/grams reactant in yield of product - solids volumetric fraction - _f solids volumetric fraction in slurry feed - _i initial solids volumetric fraction of slurry - Pi     

Flow dynamics of immobilized enzyme reactors

Summary Enzymic conversion of glucose to fructose was carried out in a packed bed and in a fluidized bed reactor. The flow dynamics of these two flow systems, loaded with two different types of immobilized loaded with two different types of immobilized glucose isomerase particles, were studied. The theoretical RTD curve calculated from the axial dispersed plug flow model equation was matched to the experimental RTD curve by an optimization technique. The effect of fluid velocity on the extent of liquid dispersion was established. Theoretical predictions on the conversion of glucose to fructose were calculated using three mathematical models, namely, a plug flow model, a continuous stirred tank reactor (CSTR) model and an axial dispersed plug flow model. The experimental results showed that the axial dispersed plug flow model was superior in predicting the performance of both the packed bed and fluidized bed reactor.Abbreviations C Dimensionless concentration - D Dispersion coefficient [cm²/sec] - d _p Mean particle diameter [cm] - E Enzyme concentration [mol/gm] - F Fructose concentration [mol/cm³] - F _e Equilibrium fructose concentration [mol/cm³] - G Glucose concentration [mol/cm³] - G _e Equílibrium glucose concentration [mol/cm³] - G _o Initial glucose concentration [mol/cm³] - Reduced glucose concentration [mol/cm³] - K Equilibrium constant - K _mf Forward reaction rate constant [mol/cm³] - K _mr Reserve reaction rate constant [mol/cm³] - K _m Rate constant [mol/cm³] - L Total length of the reactor bed [cm] - l Length [cm] - Q Flow rate [cm³/s] - r Rate of reaction based on volume of substrate - u Superficial liquid velocity [cm/s] - v Interstitial liquid velocity [cm/s] - V Reactor bed volume [cm³] - V _mf Forward reaction rate constant [mol/s·g enzyme] - V _mr Reserve reaction rate constant [mol/s·g enzyme] - z Dimensionless distance along the reactor - Density [g/cm²]     

Continuous lipolysis in a reversed micellar membrane bioreactor

The enzymatic hydrolysis of olive oil using Chromobacterium viscosum lipase B encapsulated in reversed micelles of AOT in isooctane was carried out in a continous reversed micellar membrane bioreactor. A tubular ceramic membrane installed in an ultrafiltration module was used to retain the lipase and separate the products from the reaction media. Water filled micelles were supplemented to the reactor together with the substrate/solvent solution to compensate for the permeation of reversed micelles. The influence of substrate concentration, residence time and water content in the productivity and conversion of the system were investigated. A linear relationship between productivity and conversion degree was found for each substrate concentration tested. Operational stability of the bioreactor was tested in a long term operation confirming the high stability of this catalytic system.List of Symbols a(S ₀ ), b(S ₀ ) parameters of Eq. (3) - [AOT] mM AOT concentration - C _c mM concentration in the concentrate - C _p mM concentration in the permeate - E _t mg total amount of lipase - [lipase] mg/cm³ overall lipase concentration - [OIL] mM olive oil concentration - [OLEIC] mM oleic acid concentration in the permeate - P mol/(min · mg) oleic acid productivity - Q _in cm³/min inlet flow rate - Q _out cm³/min outlet flow rate (equal to permeate flow rate) - Q _r cm³/min recirculation flow rate - W _o ratio of water to AOT molar concentrations - X steady state conversion degree in the permeate stream - T °C temperature - rejection coefficient     

Packed-bed immobilized enzyme reactors for complex processes

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

Simulation of a multicolumn recirculated packed bed reactor (MRPBR) for penicillin acylase

Enzyme reactors for the industrial hydrolysis of penicillin are analyzed in terms of biocatalyst stability to pH. A multicolumn system with packed beds placed in parallel and operating under recirculating conditions is proposed as an adequate reactor for this process. The system is studied both experimentally and with the aid of a simulation program.List of Symbols A transversal area (cm²) - C _A ammonia concentration in the reaction mixture (M) - C ₁ concentration of KH₂PO₄ in buffer (M) - C ₂ concentration of K₂HPO₄ in buffer (M) - d _p biocatalyst diameter (cm) - E enzyme or biocatalyst concentration (gcat l^–1) - K _APA APA non competitive inhibition constant (M) - K _IS excess substrate inhibition constant (M) - Km constant Michaelis-Menten (M) - K _PAA PAA competitive inhibition constant (M) - Q recirculation flow rate (cm³ min^–1) - Q _T recirculation flow rate per column (cm³ min^–1) - Re Reynolds number - S _E substrate concentration entering the neutralization tank (M) - S ₀ initial substrate concentration (M) - S _T substrate concentration in neutralization tank (M) - t time (min) - v _i initial reactor rate (mol min^–1 gcat^–1) - V _s superficial velocity (cm seg^–1) - V _T volume of neutralization tank (cm³) - X _E substrate conversion entering tank - X _T substrate conversion in neutralization tank - X conversion - Z reactor length (cm) - z axial position in reactor (cm) - z ^* non-dimensional axial position in reactor - biocatalyst's density (gcat cm^–3) - p pressure drop in the packed-bed reactor     

Characterization of the physical properties of yeast flocs

Summary Physical characteristics, namely floc density function, floc size distribution, and relative floc strength, of a number of flocculent yeast types were measured. A straight-line relationship was found to exist between log values of size and density for the yeasts examined. Each yeast type had coefficients from this relationship which could be used to interpret settling behaviour. Indices of relative floc strength were also obtained and together with the floc density function allowed fuller interpretation of yeast settling than with simpler theories.Symbols a constant (g·cm^-3) - B ₂/B ₁ floc binding strength of floc₂ relative to floc₁ - d _f floc diameter (cm) - d _i image diameter on print (cm) - d _max maximum floc diameter (cm) - f _d Ploc effective density (g·cm^-3) - g gravitational constant (981 cm·s^-1) - K _p constant (-) - R _l rate of enlargement on film - R ₂ rate of enlargement on print - S _s density of suspending liquid phase (g·cm^-3) - S _f density of solid (floc) phase (g·cm^-3) - U _t terminal settling velocity (cm·s^-1) - u liquid viscosity (g·cm^-3·^-1)     

Magnesium influx in dialyzed squid axons

Summary The influx of magnesium from seawater into squid giant axons has been measured under conditions where internal solute control in the axon was maintained by dialysis. Mg influx is smallest (1 pmol/cm² sec) when both Na and ATP have been removed from the axoplasm by dialysis. The addition of 3mm ATP to the dialysis fluid gives a Mg influx of 2.5 pmol/cm² sec while the addition of [Na] _i and [ATP] _i gives 3 pmol/cm² sec as a value for Mg influx; this corresponds well with fluxes measured in intact squid giant axons.The Mg content of squid axons is 6 mmol/kg axoplasm; this is unaffected by soaking axons in Li or Na seawater for periods of up to 100 min.     

Volume flows across gallbladder epithelium induced by small hydrostatic and osmotic gradients

Summary The hydraulic conductivity of rabbit gallbladder epithelium has been studied using a continuous volumetric method based on capacitance measurements. The time resolution for measuring osmotic flows is in the range of seconds. Volume flows have been induced by osmotic gradients between 0 and 100 mosmol. In this range the flow-force relation is linear and theP _f value is 9.3×10^–3 cm/sec. After correction for solute polarization effects, theP _f value amounts to 0.05 cm/sec. The observed flow is constant between 5 sec up to 20 min after a sudden increase in the osmolarity of the mucosal solution. The wet weight of the gallbladder tissue decreases by 22% and increases by 30% during osmotic flows from serosa to mucosa and from mucosa to serosa, respectively. Volume flows induced by hydrostatic pressure gradients on the mucosal surface are linearly related to the driving forces between 0 and 40 mbar. TheP _f value is 0.15 cm/sec. The volume flows are constant between 2 sec and 15 min after pressure application. The flow-force relation for pressure gradients on the serosal surface is markedly nonlinear for gradients greater than 5 mbar. Below 5 mbar theP _f value is 4.5 cm/sec. From electrical measurements, e.g., resistance and streaming potentials, and from flux studies with inulin and polyethylene glycol 4000, it is concluded that hydrostatic and osmotic gradients are not comparable when they are applied to gallbladder epithelium. They induce volume flows across different pathways, e.g., osmosis predominantly across the cellular route and pressure filtration predominantly across paracellular routes.     

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

The scale-down procedure can be used to optimize and scale up fermentation processes. The first step in this procedure, a theoretical analysis of the process at a large scale, must give information about the regime, or bottle necks, ruling the process. In order to verify the theoretical results the process analysis has been applied to the fed-batch baker's yeast production at a laboratory scale. The results of this analysis are compared with results from fed-batch experiments. It was concluded that if only one mechanism is ruling the process, for instance mass transfer, the results of the analysis are quite clear. If more than one mechanism is important, for example mass transfer and liquid mixing, additional knowledge is needed to predict the behaviour of the process.Concerning the baker's yeast production, it was concluded that if oxygen limitation occurs, liquid mixing is of little importance.List of Symbols C kg/m³ concentration - C ^* kg/m³ saturation concentration - D m diameter - D _E m²/s effective dispersion coefficient - d m holes of the sparger - F _sm³/s substrate flow to the fermentor - g m/s² gravitational acceleration - H m height - k _La s^–1 volumetric mass transfer coefficient based on the liquid volume - L m length - m _skg/(kg·s) maintenance coefficient - OTR kg/(m³·s) oxygen transfer rate - OUR kg/(m³·s) oxygen uptake rate - r kg/(m³·s) reaction rate - t s time - V m³ volume - v m/s velocity - v _sm/s superficial gas flow rate - y _ijkg/kg yield of componentj oni - s^–1 specific growth rate - s time constant - _gm³/s gas flow rate Indices 0 value att=0 - cir liquid circulation - e ethanol - f feed concentration - g gas phase - in flow going to the fermentor - l liquid phase - m mixing - mt mass transfer - o, O₂ oxygen - oc oxygen consumption - out flow coming out the fermentor - s substrate - sa substrate addition - sc substrate consumption - x biomass     

A mechanism for isotonic fluid flow through the tight junctions of Necturus gallbladder epithelium

During isotonic fluid flow, Necturus gallbladder epithelium mediates net fluxes of paracellular probes by a convective process. We show here that the paracellular system is modeled by permeation through three populations of channels: (i) convective parallel-sided ones of width 7.7 nm (ii) small diffusive ones of radius 0.6 nm, and (ii) large diffusive ones of radius exceeding 50 nm. The reflexion coefficient of the convective channels is very low and the calculated osmotic flow rate is close to zero when compared with the observed fluid absorptive rate of 2 x 10^–6 cm/sec. Analysis reveals that the convective channels behave as though closed to back-diffusion of probes; if this is due to solvent drag then very high fluid velocities are required, acting through minute areas. There are no transjunctional gradients that could drive the flow, and so the fluid must be propelled through the channel by components of the junction.We propose a mechanism based upon an active junctional peristalsis which allows discrimination on the basis of molecular size, in which the channels are always occluded at some point and so back-diffusion cannot occur. There is no local gradient of salt distal to the junctions and therefore the osmotic permeability of the membranes is irrelevant. High fluid velocities are not required, and the flow can occur over a substantial fraction of the junction. The mechanism must involve motile and contractile elements associated with the junction for which there is already considerable evidence.Symbols A _i filtration area of channel i;i=b (big), s (small) and c (convectional) - B constant for streamline flow - C _i concentration of probe at i - D diffusion coefficient - D ^o diffusion coefficient in free solution - d width of junction - F _i diffusive drag factor in channel i - g ionic conductivity - G _i convective drag factor in channel i - J _ij probe flux from i to j - J _net net probe flux - J _v volume flow per cm² of epithelium - l linear extent of junction per cm² epithelial plane - L length of junctional channel - L _p hydraulic conductivity - N Avogadro's number - q available filtration area fraction of channel - r _s probe molecular radius - r _c channel radius or half-width - S _i steric factor in channel i - V _w,s partial molar volume of water or salt - v _i fluid velocity in channel i - _w dynamic viscosity of water - specific conductivity - ratio of solute radius to channel radius or half-width - diffusive/pressure-driven flow ratio - reflexion coefficient     

Ion exchange properties of plant root cell walls

Acid-base properties and the swelling capacity of wheat, lupin and pea root cell walls were investigated. Roots of seedlings and green plants of different age were analysed by the potentiometric method. The ion exchange capacity (S _i) and the swelling coefficient (K ^cw) of root cell walls were estimated at various pH values (from 2 to 12) and at different ionic strength (between 0.3 and 1000 mM). To analyse the polysigmoid titration curves pH_i = f (S _i), the Gregor's equation was employed. It was shown that the Gregor's model fits well the experimental data. The total number of the cation exchange (S _t ^cat) and the anion exchange (S _t ^an) groups were determined in the root cell walls. The number of the functional group of each type (S ^j) was estimated, and the corresponding values of pK _a ^j were calculated. It was shown that for all types of cation exchangeable groups arranged in the cell wall structure the acid properties are enhanced by the increasing concentration of electrolyte. For each ionogenic group the coefficients of Helfferich's equation [pK _a ^j = f (C ^K+)] were determined. It was found that the swelling of root cell walls changes with pH, C ^K+ and strongly depends on plant species. Within the experimental pH and C ^K+ range the swelling coefficient changes as follows: lupin > pea > wheat. The obtained results show that for the plant species under investigation the differences in the swelling coefficients originate from (a) the differences in the cross-linking degrees of polymeric chains arranged in the cell wall structure, (b) the differences in the number of carboxyl groups and (c) the differences in the total number of functional groups. Based on the estimated swelling coefficients in water it could be inferred that for wheat the cross-linking degree of the polymeric chains in the root cell walls is higher than those for lupin or pea. It has been emphasized that the calculated parameters (S ^j, pK _a ^j, K ^cw), the equation {pK _a ^j = f (C^K+)} and the dependencies {K ^cw = f (C^K+, pH)} allow to estimate quantitatively the changes in the ion exchange capacity of the root cell walls in response to the changes in an ionic composition of an outer solution. The results of these estimations allow to suggest that (a) the root apoplast is a compartment where the accumulation of cations takes place during the first stage of cation uptake from an outer medium, and (b) the accumulation degree is defined by pH and ionic composition of an outer solution. On the basis of the literature review and the results of the present experimental study it was proposed that the changes in the cell wall swelling in response to variances of environmental or experimental conditions could lead to a change of the water flow through a root apoplast. It has been supported that there is direct relationship between the swelling of root cell walls and the water flow within the plant root apoplast.     

Determination of the Pressure Drop Across an Arterial Stenosis Utilizing Angiocinedensitometry

A method is presented for an evaluation of the hemodynamic significance of a stenotic lesion in the arterial tree.Twenty-three patients were examined with arteriosclerosis obliterans and intermittent claudication of the same severity. Flow velocity data obtained by angiodensitometry and viscosity values calculated from the hematocrit were inserted into the Poiseuille''s flow formula to obtain the pressure drop across a stenotic lesion in the left external iliac artery. By the same way, the pressure gradient was calculated in 33 “normal” subjects.The normal pressure gradient along the external iliac artery varied between 23 to 110 dynes/cm² (52 ± 24 dynes/cm² for mean and S.d), and the normal resistance to flow was 6.08 ± 4.1 dyne sec/cm⁵).Stenotic lesions of similar dimensions gave widely varying pressure drops (114-4,736 dynes/cm²) (mean and S.d 1,309 ± 1,224 dynes/cm²) indicating a difference in the hemodynamic significance of the various lesions. These values were significantly different (p(t) < 0.001) from the normal values. The resistance across these stenotic lesions ranged between 21 to 768 dyne sec/cm⁵ (196 ± 192 dyne sec/cm⁵) for the mean and S.d and this was significantly different from the normal group; p(t) < 0.001.Direct measurement of blood viscosity coupled with angiocinedensitometry at rest and after forced vasodilatation should provide an accurate means of determining the relative significance of a stenotic lesion and distal vessel disease in a given patient on blood flow to the leg.     

Transient state analysis of biochemical reactor using coimmobilized system

The transient state analysis of the consecutive sequence of reactions S P ₁ P ₂ taking place inside a porous spherical coimmobilized biocatalyst is discussed for the case in which each step follows Michaelis Menten type kinetics. The theoretical analysis includes intraparticle diffusional limitations. The model equations are solved by the explicit finite difference method. The effect of various parameters of importance on the batch reactor performance is discussed. Comparison of the model with experimental results has been shown.List of Symbols c _p Dimensionless substrate concentration inside the particle, (s _p/ss _o) - c _{pi, j} Dimensionless substrate concentration inside the particle at i, j - c _s Dimensionless substrate concentration at the surface of the particle, (s _s/s ₀) - d _p cm particle diameter - D _s, D _p cm²/s Diffusion coefficient of the substrate S and intermediate P ₁ inside the particle respectively - h Space step size inside the particle - i Grid point inside the particle - j Grid point along the time coordinate - k Time step size - K _m1, K _m2 g/l Michaelis constants for the first and second reaction respectively - K _I1,K _I2 g/l Substrate inhibition parameters for first and second reaction respectively - P _m g/l Product inhibition parameter for the second reaction - P _1p , P _1s g/l Concentration of the intermediate inside the particle and at the surface of the particle respectively - P _2p , P _2s g/l Concentration of the product P ₂ inside the particle and at the surface of the particle respectively - p _1p Dimensionless intermediate concentration inside the particle, (p _1p/s₀) - p _1s Dimensionless intermediate concentration at the surface of the particle, (p _1s /S ₀) - P _2p Dimensionless product concentration inside the particle, (p _2p /S₀) - p _2s Dimensionless product concentration at the surface of the particle, (p _2s/S₀) - p _{1pi, j} Dimensionless intermediate concentration inside the particle at i, j - P _{2pi, j} Dimensionless product concentration inside the particle at i, j - q Ratio of diffusion coefficients, D _p/D _s - r cm Radial position inside the particle - R cm Radius of the pellet - S ₀ g/l Initial substrate concentration in the bulk liquid - S _p g/l Substrate concentration inside the particle - S _s g/l Substrate concentration at the surface of the particle - t s Time, - V _max1 g/(ls) Maximum reaction velocity for the first reaction - V _max2 g/(ls) Maximum reaction velocity for the second reaction - y Dimensionless radial distance, (r/R) - y _{1, j} Dimensionless radial distance at i, j Greek Letters ₁ Parameter, S ₀/K _m1 - ₂ Parameter, S ₀/K _m2 - _I1 Parameter, S ₀/K _I1 - _I2 Parameter, S ₀/K _I2 - _I3 Parameter, S ₀/P _m - Dimensionless time defined as (D _s t/R ²) - ₁ ² V _max1R ²/K_m1D_s - ₂ ² V _max2R ²/K_m2D_s     

Aldosterone regulates paracellular pathway resistance in rabbit distal colon

Summary Regulation of the paracellular pathway in rabbit distal colon by the hormone aldosterone was investigated in vitro in Ussing chambers by means of transepithelial and microelectrode techniques. To evaluate the cellular and paracellular resistances an equivalent circuit analysis was used. For the analysis the apical membrane resistance was altered using the antibiotic nystatin. Under control conditions two groups of epithelia were found, each clearly dependent on the light: dark regime. Low-transporting epithelia (LT) were observed in the morning and high-transporting epithelia (HT) in the afternoon. Na⁺ transport was about 3-fold higher in HT than in LT epithelia. Incubating epithelia of both groups with 0.1 mol·1^-1 aldosterone on the serosal side nearly doubled in LT epithelia the short circuit current and transepithelial voltage but the transepithelial resistance was not influenced. Maximal values were reached after 4–5 h of aldosterone treatment. In HT epithelia due to the effect of aldosterone all three transepithelial parameters remained constant over time. Evaluation of the paracellular resistance revealed a significant increase after aldosterone stimulation in both epithelial groups. This increase suggests that tight junctions might have been regulated by aldosterone. The hormonal effect on electrolyte transport was also dependent on the physiological state of the rabbit colon. Since net Na⁺ absorption in distal colon is, in addition to transcellular absorption capacity, also dependent on the permeability of the paracellular pathway, the regulation of tight junctions by aldosterone may be a potent mechanism for improving Na⁺ absorption during hormone-stimulated ion transport.Abbreviations V _t transepithelial potential difference (mV) - R _t transepithelial resistance (·cm²) - G _t transepithelial conductance (mS·cm^-2) - I_sc calculated short circuit current (A·cm^-2) - V _a apical membrane potential difference (mV) - V _bl basolateral membrane potential difference (mV) - voltage divider ratio - R _a apical membrane resistance (·cm²) - R _bl basolateral membrane resistance (·cm²) - R _c cellular resistance ( of apical and basolateral resistance) (·cm²) - R _p resistance of the paracellular pathway (·cm²) - G _a apical membrane conductance (mS·cm^-2) - G _bl basolateral membrane conductance (mS·cm^-2) - G _p paracellular conductance (mS·cm^-2) - G _t transepithelial conductance (mS·cm^-2) - HT _contr high transporting control epithelia - LT _contr low transporting control epithelia - HT _aldo aldosterone incubated high transporting epithelia - LT _aldo aldosterone incubated low transporting epithelia     

Analysis of dark-relaxation kinetics of variable fluorescence in intact leaves

The dark-relaxation kinetics of variable fluorescence, F_v, in intact green leaves of Pisum stativum L. and Dolichos lablab L. were analyzed using modulated fluorometers. Fast (t_1/2 = 1 s) and slow (t_1/2 = 7–8 s) phases in f_v dark-decay kinetics were observed; the rate and the relative contribution of each phase in total relaxation depended upon the fluence rate of the actinic light and the point in the induction curve at which the actinic light was switched off. The rate of the slow phase was accelerated markedly by illumination with far-red light; the slow phase was abolished by methyl viologen. The halftime of the fast phase of F_v dark decay decreased from 250 ms in dark-adapted leaves to 12–15 ms upon adaptation to red light which is absorbed by PSII. The analysis of the effect of far-red light, which is absorbed mainly by PSI, on F_v dark decay indicates that the slow phase develops when a fraction of Q_A ^– (the primary stable electron acceptor of PSII) cannot transfer electrons to PSI because of limitation on the availability of P700⁺ (the primary electron donor of PSI). After prolonged illumination of dark-adapted leaves in red (PSII-absorbed) light, a transient. F_v rise appears which is prevented by far-red (PSI-absorbed) light. This transient f_v rise reflects the accumulation of Q_A ^– in the dark. The observation of this transient F_v rise even in the presence of the uncoupler carbonylcyanide m-chlorophenyl hydrazone (CCCP) indicates that a mechanism other than ATP-driven back-transfer of electrons to QA may be responsible for the phenomenon. It is suggested that the fast phase in F_v dark-decay kinetics represents the reoxidation of Q_A ^– by the electron-transport chain to PSI, whereas the slow phase is likely to be related to the interaction of Q_A ^– with the donor side of PSII.Abbreviations CCCP carbonylcyanide m-chlorophenylhydrazone - F_O initial fluorescence level - F_v variable fluorescence - P700 primary electron donor of PSI - PSI, II photosystem I, II - Q_A (Q_A ^–) Q_B (Q_B ^–) primary and secondary stable electron acceptor of PSII in oxidized (reduced) state Supported by grant B6.1/88 DST, Govt. of India.     

Pre-steady-state analysis of the turn-on and turn-off of water permeability in the kidney collecting tubule

Summary Water transport across the mammalian collecting tubule is regulated by vasopressin-dependent water channel insertion into and retrieval from the cell apical membrane. The time course of osmotic water permeability (P _f ) following addition and removal of vasopressin (VP) and 8-Br-cAMP was measured continuously by quantitative fluorescence microscopy using an impermeant fluorophore perfused in the lumen. Cortical collecting tubules were subjected to a 120 mOsm bath-to-lumen osmotic gradient at 37°C with 10–15 nl/min lumen perfusion and 10–20 ml/min bath exchange rate. With addition of VP (250 U/ml), there was a 23±3 sec (sem,n=16) lag in whichP _f did not change, followed by a rise inP _f (initial rate 1.4±0.2×10^–4 cm/sec²) to a maximum of 265±10×10^–4 cm/sec. With addition of 8-Br-cAMP (0.01–1mm) there was an 11±2 sec lag. For [8-Br-cAMP]=0.01, 0.1 and 1mm, the initial rate ofP _f increase following the lag was (units 10^–4 cm/sec²): 1.1±0.1, 1.2±0.1 and 1.7±0.3. MaximumP _f was (units 10^–4 cm/sec): 64±4, 199±9 and 285±11. With removal of VP,P _f decreased to baseline (12×10^–4 cm/sec) with aT _1/2 of 18 min; removal of 0.1 and 1mm 8-Br-cAMP gaveT _1/2 of 4 and 8.5 min. These results demonstrate (i) a brief lag in theP _f response, longer for stimulation by VP than by 8-Br-cAMP, representing the transient build-up of biochemical intermediates proximal to the water channel insertion step, (ii) similar initialdP _f /dt (water channel insertion) over a wide range of [8-Br-cAMP] and steady-stateP _f values, and (iii) more rapidP _f decrease with removal of 8-Br-cAMP than with VP. These pre-steady-state results define the detailed kinetics of the turn-on and turn-off of tubuleP _f and provide kinetic evidence that the rate-limiting step for turn-on ofP _f is not the step at which VP regulates steady-stateP _f . If water channel insertion is assumed to be the rate-limiting step in the turn-on ofP _f , these results raise the possibility that water channels must be activated following insertion into the apical membrane.     

Comparison of models for subtractive and shunting lateral-inhibition in receptor-neuron fields

Summary Two types of neuronal lateral inhibition in one-dimensional fields of receptors and neurons are considered. The first type, which has been demonstrated in the eye of Limulus, is called subtractive inhibition (SI): it assumes that neuronal activity depends on the difference between the total excitation and inhibition. The second type is called shunting inhibition (SHI): it assumes that inhibitory influences cause a shunting of a portion of the excitation-produced depolarizing current. Consideration of the shunting model is dictated by its considerable physiological plausibility. The actions of SI and SHI, examined for a variety of coupling conditions and time-stationary positive inputs, are shown to be markedly different. The results indicate that SI is most suited for obtaining (1) a linearity between input and output, (2) a contrasting effect that does not depend on the presence of input discontinuities, and (3) contrasting whose degree is independent of input amplitude. SI is especially useful if coupling coefficients can be varied to accommodate the various input form functions or if, for fixed coupling coefficients, the class of input form functions is limited. On the other hand SHI appears most suited for obtaining (1) a nonlinear input-output relation, (2) a relative contrasting only of discontinuities, and (3) a dependence of the contrasting upon input amplitude.List of Main Symbols a coupling coefficient for neighboring units, also called coupling amplitude - V _j output of receptor number j - i _j generator current of neuron number j - g inhibitory function for subtractive inhibition - h inhibitory function for shunting inhibition - v ₂/v ₁ [applies to two-unit case] - N _k neuron number k - I _k total source current produced by excitatory influences on N _k - G _k conductance for source current not shunted (with shunting inhibition) - i portion of source current shunted as a result of inhibition - m number of inhibitory influences [in Eq. (1)] - G _kj conductance of inhibitory shunt path j for neuron N _k - q number of receptors - n number of neurons - R _j receptor number j - x distance - y(x) input stimulus to receptors - y _j =y(x _j ) input stimulus to receptor R _j - v _j v_j for v _j 0, zero otherwise - a _kj G _kj /v _j , inhibitory coupling coefficient for forward shunting inhibition [refer to Eq. (2)] - b _kj excitatory coupling coefficient for contribution to source current of neuron N _k by receptor R _j [refer to Eq. (3)] - i _j i _j for i _j 0, zero otherwise - c _kj G _kj /i _j , inhibitory coupling coefficient for backward shunting inhibition [refer to Eq. (4)] - â _kj inhibitory coupling coefficient for forward subtractive inhibition [refer to Eq. (5)] - _kj inhibitory coupling coefficient for backward subtractive inhibition [refer to Eq. (6)] - y(x _j )=Af(x _j ) sensory input function - A input amplitude - f(x _j ) sensory input form function, also called a sensory image - i(x _j ) generator current output of neuron Nj which is located at x=x _j - y (y ₁, y ₂, ..., y _n), a column vector - i (i ₁, i ₂, ..., i _n), a column vector, also called generator current configuration - a an n by n matrix having a _kj as the term in the k-th row, j-th column - U the unit matrix - d ¦k-j¦, separation between neurons N _k and N _j - a a _kj for d=1, called coupling amplitude - SI subtractive inhibition - SHI shunting inhibition - FSI forward subtractive inhibition - BSI backward subtractive inhibition - FSHI forward shunting inhibition - BSHI backward shunting inhibition - s i/i ₅₁ = (s ₁, s ₂, ..., s _n), normalized generator current vector, also called normalized generator current configuration - s _j i _j/i ₅₁, normalized generator current of neuron N _j - f(x) continuous input form function of which f(x _j ) is a sampled version - ^p f(x)/x ^p p-th order derivative of f(x)     

Growth of E. coli in a stirred tank and in an air lift tower reactor with an outer loop

E. coli ATCC 11105 was cultivated in a 10-1 stirred tank reactor and in a 60-1 tower loop reactor in batch and continuous operation. By on-line measurements of O₂ and CO₂ concentrations in the outlet gas, pH, temperature, cell mass concentration X as well as dissolved O₂ concentration along the tower in the broth, gas holdup, broth recirculation rate through the loop and by offline measurements of substrate concentration DOC and cell mass concentration along the tower, the maximum specific growth rate _m , yield coefficients Y _X/S. Y _X/DOC and were evaluated in stirred tank and tower loop in batch and continuous cultures with and without motionless mixers in the tower and at different broth circulation rates through the loop. To control the accuracy of the measurements the C balance was calculated and 95% of the C content was covered.The biological parameters determined depend on the mode of operation as well as on the reactor used. Furthermore, they depend on the recirculation rate of the broth and built-ins in the tower. The unstructured cell and reactor models are unable to explain these differences. Obviously, structured cell and reactor models are needed. The cell mass concentration can be determined on line by NADH fluorescence in balanced growth, if the model parameters are determined under the same operational conditions in the same reactor.List of Symbols a, b empirical parameters in Eq. (1) - CPR kg/(m³ h) CO₂ production rate - C kg/m³ concentration - D l/h dilution rate - DOC kg/m³ dissolved organic carbon - I net. fluorescence intensity - K _S kg/m³ Monod constant - k _L a l/h volumetric mass transfer coefficient - OTR kg/(m³ h) oxygen transfer rate - OUR kg/(m³ h) oxygen utilization rate - RQ = CPR/OUR respiratory quotient - S kg/m³ substrate concentration - t h,min, s time - t _u min recirculation time - t _M min mixing time - v m³/h volumetric flow rate through the loop - X kg/m³ (dry) cell mass concentration - Y _X/S yield coefficient of cell mass with regard to the consumed substrate - Y _X/DOC yield coefficient of the cell mass with regard to the consumed DOC - Y _X/O yield coefficient of the cell mass with regard to the consumed oxygen - Z relative distance in the tower from the aerator with regard to the height of the aerated broth - l/h specific growth rate - _m l/h maximum specific growth rate Indices f feed - e outlet     

Light saturation response of inactive photosystem II reaction centers in spinach

Oxygen evolving photosystem II particles were exposed to 100 and 250 W m^–2 white light at 20°C under aerobic, anaerobic and strongly reducing (presence of dithionite) conditions. Three types of photoinactivation processes with different kinetics could be distinguished: (1) The fast process which occurs under strongly reducing (t _1/21–3 min) and anaerobic conditions (t _1/24–12 min). (2) The slow process (t _1/215–40 min) and (3) the very slow process (t _1/2>100 min), both of which occur under all three sets of conditions.The fast process results in a parallel decline of variable fluorescence (F _v) and of Hill reaction rate, accompanied by an antiparallel increase of constant fluorescence (F _o). We assume that trapping of Q_A in a negatively charged stable state, (Q_A ^–)_stab, is responsible for the effects observed.The slow process is characterized by a decline of maximal fluorescence (F _m). In presence of oxygen this decline is due to the well known disappearance of F _v which proceeds in parallel with the inhibition of the Hill reaction; F _o remains essentially constant. Under anaerobic and reducing conditions the decline of F _m represents the disappearance of the increment in F _o generated by the fast process. We assume that the slow process consists in neutralization of the negative charge in the domain of Q_A in a manner that renders Q_A non-functional. The charge separation in the RC is still possible, but energy of excitation becomes thermally dissipated.The very slow photoinactivation process is linked to loss of charge separation ability of the PS II RC and will be analyzed in a forthcoming paper.Abbreviations F chlorophyll a fluorescence - F _o, F _v, F _m constant, variable, maximum fluorescence - F _o, F _v, F _m the same, measured in presence of dithionite (F _v suppression method) - PS II photosystem II - RC reaction centre (P680. Pheo) - P680 primary electron donor - Pheo pheophytin, intermediary electron acceptor - Q_A, Q_B the primary and secondary electron acceptor - Z, D electron donors to P680 - (Q_A)_stab, (Q_A H)_stab hypothetical modifications of Q_A resulting from photoinactivation - O-, A- and R-conditions aerobic, anaerobic and strongly reducing (presence of dithionite) conditions - MES 2-(N-morpholine) ethanesulphonic acid - DCPIP 2,6-dichlorphenolindophenol - GGOC mixture of glucose, glucose oxidase and catalase - DT-20 oxygen-evolving PS II particles     

A model of the plant-to-plant movement of aphids I. Description of the model

The plant-to-plant movement of insects in one of the factors determining the distribution of individuals in insect populations. In this report the movement of barley aphids was analyzed by a statistical model. The model is represented as the convolution of three probability functions:

1. The probability that s individuals are found on a plant at time t₀:Q(s);
2. The probability that i individuals leave the plant and remain on the ground from time t₀ to t₁:_sC_ipⁱq^s−i and p+q=1, where p and q are the proportions of individuals which do not leave a plant and which leave it once or more, respectively;
3. The probability that j individuals climb a plant between time t₀ to t₁ and stay there at time t₁:e^−λλ^j/λ^!, where λ is the mean of the individuals.

The probability that l individuals are located on a plant at time t₁ is represented by the following equation It was shown by simple experiments that the experimental populations were well fitted to the model.