The effective diffusion coefficient and the distribution constant for small molecules in calcium-alginate gel beads

The effective diffusion coefficient, D(e), and the distribution constant, K(i), for selected mono- and disaccharides and organic acids were determined in homogeneous calcium-alginate gel with and without entrapped bacteria. Results were obtained from transient concentration changes in well-stirred solutions of limited volume, in which the gel beads were suspended. The effective diffusioncoefficients and the distribution constants were estimated by fitting mathematical model predictions to the experimental data using a nonlinear model fitting program (MODFIT). Both single solute diffusion and multiple solute diffusion were performed. A small positive effect was obtained onthe values of D(e) for the system of multiple solute diffusion; however, the values of K(i) were not significantly influenced. For the nine solutes tested, D(e) for 2% Ca-alginate gel beads was found to be approximately 85% of the diffusivity measured in water. The effects on D(e) and K(i), for lactose and lactic acid were determined for variations of alginate concentration, pH, temperature, and biomass content in the beads. D(e) decreased linearly for both lactose and lactic acid with increasing cell concentration in the Ca-alginate gel. K(i), was constant for both lactose and lactic acid with increasing cell concentration. D(e) was significantly lower at pH 4.5 than at pH 5.5 and 6.5 for both lactose and lactic acid. Furthermore, D(e) seemed to decrease with increased alginate concentration in the range of 1% to 4%. The diffusion rate increased with increasing temperature, and the activation energy for the diffusion process for both lactose and lactic acid was constant in the temperature range tested. (c) 1995 John Wiley & Sons Inc.     

Evaluation of effective diffusion coefficient and intrinsic kinetic parameters on azo dye biodegradation using PVA-immobilized cell beads

An immobilized mixed culture (Aeromonas hydrophila, Comamonas testosteroni, and Acinetobacter baumannii) was prepared by entrapment into phosphorylated polyvinyl alcohol (PVA) gel beads. The unsteady-state diffusion mechanism in a gel bead was applied to estimate the effective diffusion coefficients (D(e)) and the partition coefficients (K(p)) of azo dye. In addition, a simple method was developed to determine the intrinsic kinetic parameters of immobilized cells from observed reaction rates and the intrinsic kinetic parameters were then verified by fitting the experimental data into the reaction-diffusion model in a batch reactor running at a well-stirred state. The calculated effectiveness factor (eta(cal)) approached unity at Thiele modulus (Phi) < 0.3 (i.e., d(p) < 0.475 mm). The experimental effectiveness factor (eta(exp)) was in the range of 0.71-0.45 for a corresponding sphere diameter (d(p)) of 1.91 +/- 0.16 to 4.43 +/- 0.07 mm at an initial dye concentration of 200 mg/L. The results show that intraparticle diffusion resistance has a significant effect on the azo dye biodegradation rate.     

Kinetic and equilibrium models for biosorption of Cr(VI) on chemically modified seaweed,Cystoseira indica

The biosorption data of hexavalent chromium by marine brown algae Cystoseira indica, which was chemically modified by crosslinking with epichlorohydrin (CB1, CB2), or oxidized by potassium permanganate (CB3), or only washed with distilled water (RB), has been used for kinetic studies based on fractional power, Elovich, pseudo-first order and pseudo-second order rate expressions. Five three parameter biosorption isotherm models, viz. Redlich–Peterson, Sips, Khan, Radke–Prausnitz and Toth are tested for their applicability apart from 6 two-parameter models. Non-linear curve fitting procedure was adopted for fitting the kinetic as well as equilibrium data in the kinetic and isotherm models and for the determination of parameters. The time-dependent Cr(VI) biosorption data were well-described by pseudo-second-order kinetic model. The intraparticle diffusion study revealed that film diffusion might be involved in Cr(VI) biosorption in the present case. Among the two-parameter models, the Langmuir model produces the best fit, while, among the three-parameter models, the best fit is produced by the Khan model, for the biosorption of Cr(VI) on all the four biosorbents studied.     

Transient response method for evaluating the rate constants of reactions over immobilized enzymes

The transient response method was utilized to evaluate the rate constants of reaction over immobilized enzyme. Glucose oxidation catalyzed by the immobilized glucose oxidase in a fixed-bed reactor was selected as an example. A theoretical model including the effects of axial dispersion, film diffusion, and intraparticle diffusion was established for the reactor. The individual rate constant of each elementary step of this enzymatic reaction was determined through direct fitting of the experimental response data to the model.     

Kinetics of the processes of desorption from fatty acid monolayers

The surface area, A, of contracting fatty acid monolayers was measured as a function of time, t, at constant surface pressure. In the initial temporal phase, ln A was linear with radical t. In a subsequent steady-state phase, ln A was linear with t. The initial desorption coefficient for sodium palmitate, K(i), and the steady-state desorption coefficient, K(s), varied directly with surface pressure and subphase pH, and these desorption coefficients also varied with the composition of the subphase buffer. However, the K(s)/K(i) ratio was independent of these variables. The diffusion coefficient, D(25), for sodium palmitate calculated from desorption coefficient ratios was 4.8 +/- 0.6 x 10(-6) cm(2)/sec. This value was in reasonable agreement with D(25) for sodium palmitate measured by time-lag diffusion, 3.7 +/- 0.6 x 10(-6) cm(2)/sec. D(25) values obtained for a series of fatty acids suggested that higher members of the series diffused as small aggregates averaging two to four molecules in size. Kinetic and diffusion data both supported a model for the desorption process described by Ter Minassian-Saraga.     

Analysis of substrate protection of an immobilized glucose isomerase reactor

The effect of substrate protection on enzyme deactivation was studied in a differential bed and a packed bed reactor using a commercial immobilized glucose isomerase (Swetase, Nagase Co.). Experimental data obtained from differential bed reactor were analyzed based on Briggs-Haldane kinetics in which enzyme deactivation accompanying the protection of substrate was considered. The deactivation constant of the enzyme-substrate complex was found to be about half of that of the free enzyme. The mathematical analysis describing the performance of a packed bed reactor under the considerations of the effects of substrate protection, diffusion resistance, and enzyme deactivation was studied. The system equations for the packed bed reactor were solved using an orthogonal collocation method. The presence of substrate protection and the diffusion effect within the enzyme particles resulted in an axial variation of effectiveness factor, eta(D), along the length of the packed bed. The axial distribution profile of eta(D) was found to be dependent on the operation temperature, Based on the effect of substrate protection, a better substrate feed policy could be theoretically found for promoting productivity in long-term operation. (c) 1993 John Wiley & Sons, Inc.     

Two-photon excitation and photolysis by pulsed laser illumination modelled by spatially non-uniform reactions with simultaneous diffusion

Two-photon absorption in the focus of a pulsed laser has the potential for localized photolysis of caged compounds, generating high concentrations of neurotransmitters, hormones and messengers. The concentrations of cage, intermediates and products in the femtolitre focal volume depend on reaction rates and diffusional exchange with the external volume. This problem of reaction with diffusion was analysed with analytical and numerical methods to determine simple relations between parameters useful in the design and interpretation of experiments. The diffraction-limited laser spot is approximated well by a sphere, radius A, in diffusional exchange with either an infinite uniform medium, representing extracellular photolysis, or within a non-permeable sphere, a "cell" of radius B, representing intracellular photolysis. Photolysis is modelled as sequential irreversible reactions, with either the excitation step alone, rate constant k(e), or with a subsequent "dark" reaction, rate constant k(p). For extracellular photolysis, steady-state depletion of a cage averaged in a spherical spot increases hyperbolically with k(e) with half-maximum depletion at k(e) = K0.5 = 2.5 D/A2, where D is the diffusion coefficient. With measured parameters for spot size A = 0.3 microm and diffusion D = 800 microm2/s, K0.5 = 22,200 s(-1). The optimal exposure for localized photolysis is the characteristic diffusion time tau = A2/D, 113 micros in this example, and is the time taken to reach 57% of steady state in the diffusion-limited case. In the two-step model, with excitation and "dark" reaction steps, rate constants both exceeding K0.5 are necessary to generate 50% of maximal product concentration in the illuminated volume. High concentrations of photolysis products depend particularly on a high excitation rate constant (k(e) > K0.5), and localization of the products requires fast dark reactions (k(p) > K0.5). If products diffuse faster than the cage, their steady-state concentrations are decreased, and concentration transients may occur. For localized intracellular photolysis, the duration of exposure that generates product concentration at the cell boundary, B, less than 10% of the spot concentration should be shorter than 0.043(B/A)3tau, and is determined by diffusion.     

Operational stability of immobilized d-glucose isomerase in a continuous feed stirred tank reactor

d-Glucose isomerization has been studied using immobilized cells of Streptomyces phaeochromogenes in a continuous feed stirred tank reactor (CSTR) where the external film diffusion resistance was negligible. Experiments conducted with various sizes of enzyme particles indicated that a strong internal diffusion resistance improved the apparent stability of these particles. The performance equations of the CSTR were constructed by associating the material balances for the inside porous support matrix with the bulk liquid phase, and enzyme deactivation was also taken into consideration. An iterative method together with the orthogonal collocation method is proposed for the evaluation of effectiveness factor and the substrate concentration profile within the enzyme particles. The numerical results offer an alternative analytical proof for the observation that under strong internal diffusion control the apparent operational stability of immobilized enzyme is improved.     

Modeling biofilm kinetics for a low-loaded expanded-bed anaerobic reactor

The effect of surface coverage of biomass on biofilm kinetics in an expanded-bed, granular activated carbon an aerobic reactor was evaluated. Acetate was used as the sole organic carbon source. An assumption of 10% surface coverage of biofilm was examined and compared to 100% coverage. Best estimated values of k(a) and K(sa) did not differ significantly from one case to the other. The confidence region analysis also showed that the biofilm was fully penetrated in the expanded-bed reactor for the case of 10% coverage, as well as when 100% coverage was assumed. Because the biofilm was fully penetrated, a model having no internal diffusion resistance and using the best estimates of k(a) and K(sa) obtained from the 10 and 100% coverage assumptions was capable of giving good predictions of effluent acetate concentrations for an in dependent experiment having a reduced liquid detention time. Consideration of biofilm surface-loading criteria demonstrated how the results can be applied to other reactors for the purpose of predicting when the extent of surface coverage and internal diffusion resistance are not significant factors in biofilm modeling.     

Lateral diffusion in substrate-supported lipid monolayers as a function of ambient relative humidity

We analyzed the influence of water activity on the lateral self-diffusion of supported phospholipid monolayers. Lipid monolayer membranes were supported by polysaccharide cushions (chitosan and agarose), or glass. A simple diffusion model was derived, based on activated diffusion with an activation energy, E(a), which depends on the hydration state of the lipid headgroup. A crucial assumption of the derived model is that E(a) can be calculated assuming an exponential decay of the humidity-dependent disjoining pressure in the monolayer/substrate interface with respect to the equilibrium separation distance. A plot of ln(D) against ln(p(0)/p), where D is the measured diffusion coefficient and p(0) and p are the partial water pressures at saturation and at a particular relative humidity, respectively, was observed to be linear in all cases (i.e., for differing lipids, lateral monolayer pressures, temperatures, and substrates), in accordance with the above-mentioned diffusion model. No indications for humidity-induced first-order phase transitions in the supported phospholipid monolayers were found. Many biological processes such as vesicle fusion and recognition processes involve dehydration/hydration cycles, and it can be expected that the water activity significantly affects the kinetics of these processes in a manner similar to that examined in the present work.     

Determination of the intracellular dissociation constant, K(D), of the fluo-3. Ca(2+) complex in mouse sperm for use in estimating intracellular Ca(2+) concentrations.

In order to calculate the actual, rather than the relative, intracellular Ca(2+) concentration (Ca(2+))(i) in mammalian sperm cells, using fluorescent probes whose fluorescence emission differs between the probe. Ca(2+) complex and free probe, the value of the dissociation constant for the probe. Ca(2+) complex, K(D), is required. Interaction of the probe with cellular components may change the intracellular value of K(D) from that determined in buffered solution. We had previously shown that fluo-3, whose Ca(2+) complex is highly fluorescent whereas free fluo-3 is not, could be used to monitor changes of (Ca(2+))(i) in mouse sperm. In this report, we describe a method for determining K(D) for the fluo-3. Ca(2+) complex in mouse sperm suspended in medium MJB, a medium in which the sperm remain viable, but which contains high Ca(2+). The method involved treating the sperm with ionomycin to provide a plasma membrane Ca(2+) carrier, with nigericin to eliminate pH gradient, and with gramicidin D to eliminate membrane potential, such that (Ca(2+))(i) equilibrates with medium Ca(2+) concentration (Ca(2+))(e), then titrating (Ca(2+))(e) with EGTA in added aliquots to near nil concentration. At EGTA concentrations in excess of total medium Ca(2+), an approximation algorithm was used to calculate (Ca(2+))(e), based on the known K(D) for the EGTA. Ca(2+) complex. The fluorescence of the intracellular fluo-3. Ca(2+) complex, F, decreased with increasing additions of EGTA; (Ca(2+))(i) = (Ca(2+))(e) was plotted as a linear function of F/[F(max) - F]; the slope gives K(D). At 37 degrees C, intracellular K(D) was calculated to be 0.636 +/- 0.018 microM (+/-SEM, n = 8). At 37 degrees C and 20 degrees C, K(D) values in MJB were calculated to be 0.502 +/- 0.022 and 0.578 +/- 0.029 (+/-SEM, n =8 and n = 6), respectively. The higher intracellular K(D) value implies probe interaction with cytosol components, primarily those in the head, as this compartment is the major contributor to sperm fluorescence. Changes in (Ca(2+))(i), monitored with fluo-3 fluorescence, that occur on interaction of capacitated mouse sperm with the zona pellucida and may now be quantified, using 0.636 microM for K(D) of the intracellular fluo-3. Ca(2+) complex.     

Diffusion of bacteriophages through artificial biofilm models

The simple two-chamber diffusion method was improved to study the diffusion properties of bacteriophage (phage) T4 through a model biofilm agarose gel membrane (AGM) embedded with dead host Escherichia coli K12 cells. The apparent diffusion coefficient (D(app) ) of phage T4 was calculated to be 2.4 × 10(-12) m(2) /s in 0.5% AGM, which was lower than the coefficient of 4.2 × 10(-12) m(2) /s in 0.5% AGM without host cells. The phage adsorption process by dead host cells slowed the apparent phage diffusion. The Langmuir adsorption equation was used to simulate phage adsorption under different multiplicity of infections (MOIs); the maximum adsorbed phage MOI was calculated to be 417 PFU/CFU, and the Langmuir adsorption constant K(L) was 6.9 × 10(-4) CFU/PFU. To evaluate the effects of phage proliferation on diffusion, a simple syringe-based biofilm model was developed. The phage was added into this homogenous biofilm model when the host cells were in an exponential growth phase, and the apparent diffusion coefficient was greatly enhanced. We concluded that D(app) of phages through biofilms could be distinctly affected by phage adsorption and proliferation, and that the idea of D(app) and these methods can be used to study diffusion properties through real biofilms.     

Effect of immobilized enzyme deactivation in fixed- and fluid-bed reactors

A two-parameter theoretical model is developed to evaluate the effect of immobilized enzyme deactivation on substrate conversion in fixed- and fluid-bed reactors under diffusion-free conditions. The method describes a simple reaction in which three different immobilized enzyme deactivation forms are considered, and an expression is developed to evaluate the effect of immobilized enzyme deactivation on yield in a consecutive reaction. Comparison of reactor performances for the two reactor types reduces to a comparison of the appropriate dimensionless parameters. The practical implications of the development are illustrated through an example.     

A novel method for determination of the affinity of protein: protein interactions in homogeneous assays

Nonradioactive homogeneous assays are widely used to screen for inhibitors of biomolecular interactions. To ensure optimal sensitivity for the detection of competitive inhibitors, reagent concentrations should be fixed at or below the K(D) of the protein-protein interaction. Accurate measurement of K(D) during assay development is therefore critical. Although conventional methods work well with heterogeneous assays, they are generally unsatisfactory with homogeneous systems. Here the authors describe an alternative method to determine the K(D) of protein-protein interactions in homogeneous assays. The method uses a rearrangement of the Cheng-Prusoff equation: IC(50)= (([K(i)]/K(D)) x [L]) + K(i). A competitive inhibitor is titrated into the ligand-receptor binding assay at a range of ligand concentrations and IC(50) values are calculated. Plotting measured IC(50) versus concentration of ligand gives a linear plot with y-intercept (K(i)) and gradient (K(i)/K(D)). K(D) is the affinity constant for the ligand-receptor interaction. Here the authors use homogeneous time-resolved fluorescence (HTRF((R))) in 2 model systems (TRAIL/TRAIL receptor 4 and OX40 ligand/OX40 receptor) and demonstrate that measured K(D) values calculated using the linearized Cheng-Prusoff plot compare favorably with those from independent experiments. The advantages and limitations of the method are discussed.     

Site-directed mutagenesis studies of selected motif and charged residues and of cysteines of the multifunctional tetracycline efflux protein Tet(L)

All of the transmembrane glutamates of Tet(L) are essential for tetracycline (TET) resistance, and E397 has been shown to be essential for all catalytic modes, i.e., TET-Me(2+) and Na(+) efflux and K(+) uptake. Loop residues D74 and G70 are essential for TET flux but not for Na(+) or K(+) flux. A cysteineless Tet(L) protein exhibits all activities.     

Probing the peripheral anionic site of acetylcholinesterase with quantitative structure activity relationships for inhibition by biphenyl-4-acyoxylate-4'-N-Butylcarbamates

Biphenyl-4-acyoxylate-4'-N-butylcarbamates 1-8 are synthesized from 4,4'-biphenol and are characterized as the pseudosubstrate inhibitors of acetylcholinesterase. In other words, the inhibitors bind to the enzyme and react with the enzyme to form the tetrahedral intermediates for the K(i) steps, and then the tetrahedral intermediates exclude the leaving groups to form a common N-butycarbamyl enzyme intermediate for the k(c) steps. Due to a linear character of the 4,4'-biphenyl moiety, the 4'-N-butylcarbamate moieties of the inhibitors react with the Ser200 residue of the enzyme while the 4-acyoxylate moieties of the inhibitors, on the other hand, should fit in the peripheral anionic site of the enzyme, which is located at the mouth of the deep active site gorge. Thus, carbamates with varied acyl substituents at the 4-position of the biphenyl ring are good candidates for probing the quantitative structure activity relationships for the peripheral anionic site of the enzyme. The fact that the pK(i), log k(c), and log K(i) values are correlated with neither the Taft substituent constant (sigma*) nor the Taft steric constant (E(s)) indicates that the 4-acyoxylate moieties of the inhibitors are too far away from the reaction center. However, the pK(i), log k(c), and log K(i) values are linearly correlated with the Hansch hydrophobicity constant, pi. The intensity constants (psi) for these correlations are 0.16, -0.035, and 0.13, respectively. These results indicate that interactions between the 4-acyoxylate groups of the inhibitors and the peripheral anionic site of the enzyme are mainly hydrophobic ones. The correlation results are slightly improved by using the two-parameter correlations with the Taft substituent steric constant, E(s), and pi. For pK(i), log k(c), and log K(i)-E(s)-pi correlations, the psi values are 0.21, -0.021, and 0.19, respectively; the intensity constants for steric effect (delta) are 0.08, 0.022, and 0.10, respectively. Besides hydrophobic interactions, the two-parameter correlations also suggest that little steric hindrance occurs for the bulkier inhibitors to pass by the peripheral anionic site of the enzyme.     

Diffusion of water in cat ventricular myocardium

The rates of diffusion of tritiated water (THO) and [14C]sucrose across cat right ventricular myocardium were studied at 23 degrees C in an Ussing-type diffusion cell, recording the time-course of increase in concentration of tracer in one chamber over 4--6 h after adding tracers to the other. Sucrose data were fitted with a model for a homogeneous sheet of uneven thickness in which the tissue is considered to be an array of parallel independent pathways (parallel pathway model) of varying length. The volume of the sucrose diffusion space, presumably a wholly extracellular pathway, was 23% of the tissue or 27.4 +/-1.7% (mean +/- SEM; n=11) of the tissue water. The effective intramyocardial sucrose diffusion coefficient, D8, was 1.51 +/- 0.19 X 10(-6)cm2.s-1 (n=11). Combining these data with earlier data, D8 was 22.6 +/- 1.1% (n=95) of the free diffusion coefficient in aqueous solution D degrees 8. The parallel pathway model and a dead-end pore model, which might have accounted for intracellular sequestration of water, gave estimates of DW/D degrees W (observed/free) of 15%. Because hindrance to water diffusion must be less than for sucrose (where D8/D degrees 8=22.6%), this showed the inadequacy of these models to account simultaneously for the diffusional resistance and the tissue water content. The third or cell-matrix model, a heterogeneous system of permeable cells arrayed in the extracellular matrix, allowed logical and geometrically reasonable interpretations of the steady-state data and implied estimates of DW in the cellular and extracellular fluid of approximately 25% of the aqueous diffusion coefficient.     

菜蚜茧蜂对甲胺磷和灭多威的抗性机制

采用试管药膜法测定了菜蚜茧蜂 Diaeretiella rapae 对甲胺磷和灭多威的抗性及增效剂的增效作用,并测定了菜蚜茧蜂和菜缢管蚜 Lipaphis erysimi 乙酰胆碱酯酶动力学参数、解毒酶活性及增效剂对菜蚜茧蜂酶活性的体内抑制作用。福州地区菜蚜茧蜂已对甲胺磷和灭多威产生5.6和9.1倍的抗性,胡椒基丁醚、磷酸三苯酯和马来酸二乙酯对两种杀虫剂的抗性品系均有显著增效作用,胡椒基丁醚的作用最为显著。胡椒基丁醚对抗性菜蚜茧蜂杀虫剂敏感性的增效作用远高于对敏感菜蚜茧蜂的影响。3种增效剂对菜蚜茧蜂乙酰胆碱酯酶均无抑制作用;磷酸三苯酯和胡椒基丁醚对羧酸酯酶,马来酸二乙酯对谷胱甘肽S转移酶有显著抑制作用。抗性和敏感菜蚜茧蜂乙酰胆碱酯酶的米氏常数K_m）、最大反应速度（V_max）、羧酸酯酶及谷胱甘肽S转移酶活性值相近,但敏感菜蚜茧蜂乙酰胆碱酯酶的双分子速度常数（K_I）值远高于抗性的。此外,对菜蚜茧蜂和菜缢管蚜乙酰胆碱酯酶、羧酸酯酶和谷胱甘肽S转移酶进行了比较研究。结果表明菜蚜茧蜂对甲胺磷和灭多威的低水平抗性与乙酰胆碱酯酶的不敏感性及解毒酶的解毒代谢有关。