New solution method for equations of reaction and mass transfer in biocatalyst particles

Summary For numerical solution of the reaction-mass transfer equations for immobilised biocatalysts it may be better to start integration at the particle surface and proceed inwards: calculations are targetted on the region to which practically interesting changes are often confined (because concentrations are effectively zero in the interior); and during iterative solution wrong initial estimates may be rejected after detecting anomalies early in the integration.Symbols C_b substrate concentration in bulk (mol m^–3) - c dimensionless substrate concentration (C/C_b) (-) - D_e effective diffusion coefficient (m²s^–1) - Da Damkohler number (V.r_o ²/D_e.K_s) (-) - K_s substrate concentration kinetic coefficient (mol m^–3) - k_e external mass transfer coefficient (ms^–1) - r_o bead radius (m) - Sh Sherwood number (k_e.r_o/D_e) (-) - V maximum rate per unit volume in beads (mol m^–3s^–1) - x dimensionless distance from bead centre (r/r_o) (-) - dimensionless kinetic coefficient (K_s/C_b) (-) - _o effectiveness factor (-)     

Study of the Solute Flows of Multicomponent and Heterogeneous Non-Ionic Solutions in Double-Membrane System

The solute flows were studied in a double-membrane osmotic-diffusive cell, in which two membranes mounted in horizontal planes separate three compartments (l,m,r) containing the non-homogeneous, non-electrolytic binary and ternary solutions. The volume of inter-membrane compartment (m), which is the infinitesimally layer of solution, and volume of external compartments (l and r) fulfill the conditions V _m 0 and V _l =V _r , respectively. In an initial moment, the solution concentrations satisfy the condition (C ^o _s ) _l < (C ^o _s ) _m >(C ^o _s ) _r. The double-membrane osmotic-diffusive cell is composed of two complexes: boundary layer/membrane/boundary layer, mounted in horizontal planes. In the cell, solute flux was measured as a function of concentration and gravitational configuration. The linear dependencies of the solute flux on concentration difference in binary solutions and nonlinear – in ternary solutions were obtained. It was shown that the double-membrane osmotic-diffusive cell has rectifying and amplifying properties of solute flows.     

Enzyme inactivation and stabilization studies in an ultrafiltration reactor

Summary An ultrafiltration membrane enzymatic reactor is used in connection with different reacting systems.The experimental conditions are such that the enzyme, which operates at fairly high concentration levels because of the concentration polarization phenomena taking place in the reactor, is still in soluble form.The analysis of the system unsteady-state response enables the identification of the mechanism of enzyme deactivation and the extraction of the kinetic parameters of both the deactivation and the main reaction.The stabilizing effect observed in connection with enzyme entrapment within an inert gel deposited onto the U.F. membrane active surface is also discussed.List of Symbols A U.F. membrane cross sectional area cm² - C_E Enzyme concentration mg/ml - C_EI Enzyme concentration at the active membrane surface mg/ml - C_E Mean enzyme concentration mg/ml - c _s ^o Substrate concentration in the feed m moles/ml - c _s ^u Substrate concentration in the outlet m moles/ml - D_E Enzyme diffusivity cm²/s - Km michaelis constant mM - k₂ Kinetic constant of the enzymatic reaction m moles/mg s - k_d Kinetic constant of the enzyme deactivation reaction s^–1 - N^o Initial amount of active enzyme mg - N(t) Active enzyme amount at reaction time t mg - Q Flow rate ml/s - r Rate of the main reaction m moles/ml s - t Reaction time s - t^* Reaction time at which product concentration in the outlet is within ± 2% of the steady-state value s - v Fluid velocity cm/s - V Cell volume ml - V_B Volume within which 99% of the enzyme fed is contained at the steady-state ml - V_S Volume within which 99% of the total substrate concentration drop occurs at the steady-state ml - x Distance upstream the membrane measured from the membrane surface cm     

Quinoprotein glucose dehydrogenase and its application in an amperometric glucose sensor

Glucose dehydrogenase (GDH), one of the recently discovered NAD(P)⁺-independent ‘quinoprotein’ class of oxidoreductase enzymes, was purified from Acinetobacter calcoaceticus LMD 79.41 and immobilised on a 1,1'-dimethylferrocene-modified graphite foil electrode.The second-order rate constant (k_s) for the transfer of electrons between GDH and ferrocenemonocarboxylic acid (FMCA) in a homogeneous system, determined using direct current (DC) cyclic voltammetry, was found to be 9.4 × 10⁶ litres mol⁻¹ s⁻¹. This value of k_s for GDH was more than 40 times greater than that for the flavoprotein glucose oxidase (GOD) under identical conditions. Such high catalytic activities were also observed when GDH was immobilised in the presence of an insoluble ferrocene derivative; a biosensor based on GDH was found to produce more than twice the current density of similar GOD-based electrodes. The steady-state current produced by the GDH-based electrode was limited by the enzymic reaction since methods which increased the enzyme loadings elevated the upper limit of glucose detection from 5 mM to 15 mM.The temperature, pH, stability and response characteristics of the GDH-based glucose sensor illustrate its potential usefulness for a variety of practical applications. In particular, the high catalytic activity and oxygen insensitivity of this biosensor make it suitable for in vivo blood glucose monitoring in the management of diabetes.     

A comparison of five distance‐based methods for spatial pattern analysis

Abstract. The behaviour of five statistics (extensions of Pielou's, Clark and Evansapos;, Pollard's, Johnson & Zimmer's, and Eberhardt's statistics, which are denoted as P_i, C_e, P_o, J_z and E_b respectively) that involve the distance from a random point to its jth nearest neighbour were examined against several alternative patterns (lattice‐based regular, inhomogeneous random, and Poisson cluster patterns) through Monte Carlo simulation to test their powers to detect patterns. The powers of all the five statistics increase as distance order j increases against inhomogeneous random pattern. They decrease for P_i and C_e and increase for P_o, J_z, and E_b against regular and Poisson cluster patterns. P_o, J_z, and E_b can reach high powers with the third or higher order distances in most cases. However, P_o is recommended because no extra information is needed, it can reach a high power with the second or third distance even though the sample size is not large in most cases, and the test can be performed with an approximate χ² distribution associated with it. When a regular pattern is expected, J_z is recommended because it is more sensitive to lattice‐based regular pattern than P_o and E_b, especially for the first distance. However, simulation tests should be used because the speed of convergence of J_z to normal distribution is very slow.     

Protein production from whey usingPenicillium cyclopium; growth parameters and cellular composition

Summary The growth parameters ofPenicillium cyclopium have been evaluated in a continuous culture system for the production of fungal protein from whey. Dilution rates varied from 0.05 to 0.20 h^–1 under constant conditions of temperature (28°C) and pH (3.5). The saturation coefficients in the Monod equation were 0.74 g l^–1 for lactose and 0.14 mg l^–1 for oxygen, respectively. For a wide range of dilution rates, the yield was 0.68 g g^–1 biomass per lactose and the maintenance coefficient 0.005 g g^–1 h^–1 lactose per biomass, respectively. The maximum biomass productivity achieved was 2 g l^–1 h^–1 biomass at dilution rates of 0.16–0.17 h^–1 with a lactose concentration of 20 g l^–1 in the feed. The crude protein and total nucleic acid contents increased with a dilution rate, crude protein content varied from 43% to 54% and total nucleic acids from 6 to 9% in the range of dilution rates from 0.05 to 0.2 h^–1, while the Lowry protein content was almost constant at approximately 37.5% of dry matter.Nomenclature (mg l^–1) C_o initial concentration of dissolved oxygen - (h^–1) D dilution rate - (mg l^–1) K₀₂ saturation coefficient for oxygen - (g l^–1) K_s saturation coefficient for substrate - (g g^–1 h^–1) lactose per biomass) m maintenance energy coefficient - (mM g^–1 h^–1O₂ per biomass) Q₀₂ specific oxygen uptake rate - (g l^–1) S residual substrate concentration at steady state - (g l^–1) S_o initial substrate concentration in feed - (min) t_1/2 time when C_o is equal to C_o/2 - (g l^–1) X biomass concentration - (g l^–1) X biomass concentration at steady state - (g g^–1 biomass per lactose) Y_G yield coefficient for cell growth - (g g^–1 biomass per lactose) Y_x/s overall yield coefficient - (h^–1) specific growth rate     

Reproduction rate,feeding process,and liebig limitations in cell populations—II

A biological system consisting of a population of cells suspended in a liquid substrate is considered. The general problem addressed in the paper is the derivation of the kinetic pattern of population growth as a statistical effect of a very large number of elementary interactions between a single cell and the molecules of nutrient in substrate. Solution of the problem is obtained in the form of equation expressing the population growth ratec as a function of substrate concentration,C _s. The analytical expression derived is applied to a real bacterial population (Escherichi coli) and kinetic patterns are theoretically computed. The major findings, expressed roughly, without nuances, are: (i) the concentration of nutrient at the cell membrane,C _c, can only be equal to either 0 (for theC _s below some threshold valueC ^*) orC _s (forC _s>C ^*); (ii) the Michaelis-Menten-Monod kinetics observed in experiments is an artifact: the pure (not contaminated by foreign factors) dependence ofc onC _s is actually such that the functionc=c(C _s) has practically linear increase whenC _s<C ^*, and is constant,c=c(C ^*)=const, whenC _s>C ^*; (iii) the Liebig principle is strictly fulfilled: up to a feasible accuracy of observation, under no circumstances can population growth be limited (controlled) by more than one substrate component—replacement of a limiting component for another one is an instant event rather than a gradual process.     

A critical appraisal of a combined stomatal-photosynthesis model for C3 plants

Gas-exchange measurements on Eucalyptus grandis leaves and data extracted from the literature were used to test a semi-empirical model of stomatal conductance for CO₂ g_Sc=g_o+a₁A/(c_s-I) (1+D_s/D_o)] where A is the assimilation rate; D_s and c_s are the humidity deficit and the CO₂ concentration at the leaf surface, respectively; g₀ is the conductance as A → 0 when leaf irradiance → 0; and D₀ and a₁ are empirical coefficients. This model is a modified version of g_sc=a₁A h_s/c_s first proposed by Ball, Woodrow & Berry (1987, in Progress in Photosynthesis Research, Martinus Mijhoff, Publ., pp. 221–224), in which h_s is relative humidity. Inclusion of the CO₂ compensation point, τ, improved the behaviour of the model at low values of c_s, while a hyperbolic function of D_s for humidity response correctly accounted for the observed hyperbolic and linear variation of g_sc and c_i/c_s as a function of D_s, where C_i is the intercellular CO₂ concentration. In contrast, use of relative humidity as the humidity variable led to predictions of a linear decrease in g_sc and a hyperbolic variation in c_i/c_s as a function of D_s, contrary to data from E. grandis leaves. The revised model also successfully described the response of stomata to variations in A, D_s and c_s for published responses of the leaves of several other species. Coupling of the revised stomatal model with a biochemical model for photosynthesis of C₃ plants synthesizes many of the observed responses of leaves to light, humidity deficit, leaf temperature and CO₂ concentration. Best results are obtained for well-watered plants.     

Continuous penicillin G hydrolysis in an electro-membrane reactor with immobilized penicillin G acylase

Penicillin G (2%, w/v in phosphate buffer, pH 8) was hydrolysed in a flow-through, miniature electro-membrane reactor with the penicillin G acylase immobilized in 5% (w/v) polyacrylamide (diam. 10 mm, thickness 2.6 mm, enzyme activity 24 U ml^–1). The conversion of penicillin G increased from 0.15 to almost 0.5 when the electric current applied to the reactor was changed from –600 to +600 A/m² with a substrate residency of 1 h. Symbols and abbreviations c _j ^p & concentration of component j in product stream (M) c _j ^s & concentration of component j in substrate stream (M) c _s ^o & substrate concentration at reactor inlet (M) C _j ^p=c _j ^p/c _S ⁰ & scaled concentration of component j in product stream C _j ^s=c _j ^s/c _S ⁰ & scaled concentration of component j in substrate stream i & electric current density (A/m²) j & reaction component, j P, Q or S P & main reaction product (6-aminopenicillanic acid) PGA & penicillin G acylase Q & side reaction product (phenylacetic acid) S & substrate (penicillin G) Y _s=C _P ^s+C _P ^p & substrate conversion & mean residence time of substrate and product streams in reactor (h) =C _Q ^s+C _Q ^p+C _S ^s+C _S ^s & check-sum of scaled concentrations =C _P ^p/(C _P ^s+C _P ^p) & separation factor of 6-aminopenicillanic acid (0 1)     

Research on benzene,toluene and dimethylbenzene detection based on a cataluminescence sensor

We present a sensitive and quick way to determine benzene, toluene and dimethylbenzene (BTEX) in air, applying a cataluminescence (CTL) sensor based on a nano‐sized composite material, γ‐Al₂O₃/PtO₂. The factors that affect the sensor's performance were studied, including the sensing material, temperature, rate of air carrier and wavelength. It was shown that when Pt accounted for 0.2% of the sensing material, the rate of the air carrier that carries target gas was 450 mL/min, the determination wavelength was 400 nm and temperature was 236°C, this sensor showed the best CTL intensity to BTEX. In addition, the CTL intensity had a high linear relation with the concentration of BTEX, with a linear range from 0.5 to 100 mL/m³, and a detection limit 0.22 mL/m³. This nano‐sized material had a quick response within 1.5 s, short recovery time within 1 min and a long lifetime, showing good potential for a variety of applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Biphasic nature in the autoxidation reaction of human oxyhemoglobin

In comparison with myoglobin molecule as a reference, we have studied the autoxidation rate of human oxyhemoglobin (HbO₂) as a function of its concentration in 0.1 M buffer at 35°C and in the presence of 1 mM EDTA. At pH 6.5, HbA showed a biphasic autoxidation reaction that can be described completely by a first-order rate equation containing two rate constants — k_f, for fast autoxidation of the α-chain, and k_s, for slow autoxidation of the β-chain, respectively. When tetrameric HbO₂ was dissociated into αβ-dimers by dilution, the value of k_f increased markedly to an extent comparable with the autoxidation rate of horse heart oxymyoglobin (MbO₂). The rate constant k_s, on the other hand, was found to remain at an almost constant value over the whole concentration range from 1.0 × 10⁻³ M to 3.2 × 10⁻⁶ M in heme. At pH 8.5 and pH 10.0, however, the autoxidation of HbO₂ was monophasic, and no enhancement in the rate was observed by diluting hemoglobin solutions. Taking into consideration the effects of 2,3-diphosphoglyceric acid and chloride anion on the autoxidation rate of HbO₂, we have characterized the differential susceptibility of the α- and β-chains to the autoxidation reaction in aqueous solution.     

Modeling of enzyme-potentiometric sensors involving acid- or base-forming reactions

Enzyme-potentiometric sensors in which the chemical conversion of the analyte leads to the formation of an acid and/or a base can often display complex response characteristics. In these sensors, the, electrochemically monitored species is usually the H(+) ion (pH-based sensors). However, in some cases the conjugate-ion of the H(+) (or OH(-)) ion of the acid (or base) produced-can also be monitored-a specific example being the urease-NH(4) (+) sensor. The response of both types of sensors is strongly affected by: (1) the degree of dissociation of the products and their transport properties in the enzymic film, (2) the amounts of pH-buffers present in the test solution, (3) the test solution's pH, and (4) the diffusion coefficients of the various species. In this article, a previously developed theoretical model for pH-based sensors-in which the differences in diffusivities of the various species were ignored-is generalized to accommodate for such differences, and extended to the latter of the above two types of sensors. It is shown that when the sensor operates under analyte diffusion-controlled conditions, the response of either type of sensor can be predicted by a simple algebraic equation which is independent of the actual kinetics of the enzymic reaction.     

Thermal denaturation of Na- and Li-DNA in salt-free solutions

Thermal denaturation of Na- and Li-DNA from chicken erythrocytes was studied by means of scanning microcalorimetry in salt-free solutions at DNA concentrations (C_p) from 4.5 · 10^?2 to 1 · 10^?3 moles of nucleotides/liter (M). Linear dependencies of DNA melting temperature (T_m) vs lgC_p were obtained: ((1)) ((2)) for Na- and Li-DNA, respectively. Microcalorimetry data were compared with the results of spectrophotometric studies at 260 nm of DNA thermal denaturation in Me-DNA + MeCl solutions at C_p ? (6–8) · 10^?5 M and C_s = 0–40 mM (Me is Na or Li, C_s is salt concentration). It was found that Eqs. (1) and (2) are valid in DNA salt-free solutions over the C_p range 6 · 10^?5?4.5 · 10^?2M. Protonation of DNA bases due to the absorption of CO₂ from air in Na-DNA + NaCl solutions affects DNA melting parameters at C_s < 4 mM. Linear dependence of T_m on lga₊ is found in Na-DNA + NaCl at C_s > 0.4 mMin the absence of contact of solutions with CO₂ from air (a₊ is cation activity). A dependence of [dT_m/dlga₊] on Li⁺ activity was observed in Li-DNA + LiCl solutions at C_s < 10 mM: [dT_m/dlga₊] increases from 17°–18° at C_s > 10 mM to 28°–30° at C_s ? 0.2–0.4 mM. Spectrophotometric measurements at 282 nm show that this effect was caused by protonation of bases in fragments of denatured DNA in neutral solutions. The Poisson–Boltzmann (PB) equation was solved for salt-free DNA at the melting point. The linear dependence of T_m vs lgC_p was interpreted in terms of Manning's condensation theory. PB and Manning's theories fit the experimental data if charge density parameter (ξ) of denatured DNA is in the range 1.8–2.1 (assuming for native DNA ξ = 4.2). Specificity of Li ions in interactions with DNA is discussed. © 1994 John Wiley & Sons, Inc.     

The concentration jump method

Lipophilic cationic fluorescent dyes (D) specifically stain the mitochondria of living cells. A perfusion chamber for cell cultures is described, which can be used to determine the kinetics of vital staining of the mitochondria of single selected cells in situ. In these experiments styrylpyridinium dyes and cultures of HeLa cells were used. The dyes differ strongly in their lipophilic properties; R _m values and the partition coefficients P _o/w between n-octanol (o) and water (w) were determined in order to characterize their lipophilicity. In the thermostat-regulated chamber the concentration of the dye C _D can be increased from C _D=0 to C _D>0 within a few seconds (concentration jump). Thus, the time t=0 for the beginning of the vital staining and the dye concentration in the cell medium during the staining experiment, C _D=const., are unambiguously defined. The concentration of the dye, C _b, which is bound to the mitochondria (b), is proportional to the intensity of the fluorescence I _b. On the other hand, the free dye molecules (f) in the aqueous medium exhibit practically no fluorescence, I _fI _b. The intensity of the fluorescence I=I _b was measured as a function of time t; the measured values were corrected for photobleaching. The fluorescence intensity I(t) at first increases linearly with t and reaches a saturation value for t . In the linear range of I(t) the flow J _o=(dI/dt)_o of the dye into the cell depends strongly on the dye concentration and increases linearly with C _D. The concentration range C _D=10^–9–10^–5 M at 37° C was investigated. From the linear correlation between J _o and C _D it follows that the kinetics of the vital staining of mitochondria is controlled by diffusion. At t=0 the flow of the xenobiotic agent through the cell membrane determines the rate of staining. The slope dJ _o/dC _D of the plot J _o vs C _D describes the efficiency of dye accumulation at the mitochondria and strongly increases with increasing lipophilicity of the dye molecules. Thus lipophilic dyes pass through the cell membrane more easily than less lipophilic molecules.     

River and lake sediments as sources of infective Frankia (Alnus)

Exudation of carboxylic anions and protons by plant roots plays an important role in mobilizing soil P under P-deficiency conditions. The objective of this work was to quantify short-term (6 h) carboxylate and H⁺ exudation by tomato roots in response to P concentration (0, 0.1, 0.5 and 1.0 mt M P) in nutrient solution (C_p). The exudation rate of tri- and dicarboxylates decreased exponentially with increasing C_p, from 0.3 to 0.03 mol plant^–1 6h^–1. At low C_p the predominant exudates were fumarate, citrate and succinate, while at C_p=0.5 and 1.0 mt M the prevalent anions were succinate and citrate. The solution pH declined sharply as C_p was lowered from 0.1 (pH=4.2) to 0 mt M P (pH=3.7).     

Verification studies of a simplified model for the removal of dichloromethane from waste gases using a biological trickling filter

The removal of dichloromethane from waste gases in a biological trickling filter was studied experimentally as well as theoretically within the concentration range of 0–10,000 ppm. A stable dichloromethane elimination performance was achieved during two years of operation, while the start-up of the system only amounted to several weeks at constant inlet concentrations. The trickling filter system was operated co-currently as well as counter-currently.However, experimental and theoretical results revealed that the relative flow direction of the mobile phases did not significantly affect the elimination performance. Moreover, it was found that the gas-liquid mass-transfer resistance in the trickling filter bed applied was negligible, which leaves the biological process inside the biofilm to be the rate limiting step.A simplified model was developed, the Uniform-Concentration-Model, which showed to predict the filter performance close to the numerical solutions of the model equations. This model gives an analytical expression for the degree of conversion and can thus be easily applied in practice.The dichloromethane eliminating performance of the trickling filter described in this paper, is reflected by a maximum dichloromethane elimination capacity EC _max=157 g/(m³ · h) and a critical liquid concentration C _lcr=45 g/m³ at a superficial liquid velocity of 3.6 m/h, inpendent of the gas velocity and temperature.List of Symbols a _s m²/m³ specific area - a _w m²/m³ specific wetted area - A m² cross-sectional area - C _g g/m³ gas phase concentration - C _go g/m³ inlet gas phase concentration - C _gocr g/m³ critical gas phase concentration - C _g ^* C_g/C_go dimensionless gas concentration - C _l g/m³ liquid concentration - C _lcr g/m³ critical liquid concentration - C _lcr ^* mC_lcr/C_go dimensionless critical concentration - c _li g/m³ substrate concentration at liquid-biofilm interface - C _l ^* mC_l/C_go dimensionless liquid concentration - C _o g/m³ oxygen concentration inside the biofilm - C _oi g/m³ oxygen concentration at liquid-biofilm interface - C_s g/m³ substrate concentration inside the biofilm - C _si g/m³ substrate concentration at liquid-biofilm interface - D _eff m²/h effective diffusion coefficient in the biofilm - D _o m²/h effective diffusion coefficient for oxygen in the biolayer - E mu_g/u_l extraction factor - E _act kJ/mol activation energy for the biological reaction - EC g/(m³· h) K _o a _w : elimination capacity, or the amount of substrate degraded per unit of reactor volume and time - EC _max g/(m³ · h) K _o a_w: maximum elimination capacity - f degree of conversion - h m coordinate in height - H m height of the packed bed - K ₀ g/(m³ · h) _maxX_b/Y zeroth order reaction defined per unit of biofilm volume - k _og m/h overall gas phase mass transfer coefficient - K ^* dimensionless constant given by Eq. (A.5) - K _l ^* dimensionless constant given by Eq. (A.6) - K ₂ ^* dimensionless constant given by Eq. (A.6) - m C _g /C_l gas liquid distribution coefficient - N g/(m² · h) liquid-biofilm interfacial flux of substrate - N _og k_oga_wH/u_g number of gas phase transfer units - N _r k_o a_w H/u_g C_go number of reaction units - OL g/(m³· h) u _g C _go /H organic load - r _s g/(m³ ·h) zeroth order substrate degradation rate given by Eq. (1) - R _s g/(g TSS ·h) specific activity - T K absolute temperature - u _g m/h superficial gas velocity - u _t m/h superficial liquid velocity - X _b g TSS/m₃ biomass concentration inside biofilm - X _s g TSS/m₃ liquid suspended biomass concentration - x m coordinate inside the biofilm - Y g TSS/(g_DCM) yield coefficient Greek Symbols dimensionless parameter given by Eq. (2) - m averaged biofilm thickness - biofilm effectiveness factor given by Eqs. (7a)–(7c) - m penetration depth of substrate into the biofilm - _max d^–1 microbiological maximum growth rate - v _o stoichiometric utilization coefficient for oxygen - v _s stoichiometric utilization coefficient for substrate - dimensionless height in the filter bed - h H/u _g superficial gas phase contact time - _o (K ₀ /DC _ii )^1/2 - _o C _o /C _oi dimensionless oxygen concentration inside the biofilm - _s C _s /C _si dimensionless substrate concentration inside the biofilm Experimental results, verifying the model presented will be discussed Part II (to be published in Vol. 6, No. 4)     

THE OXIDATION-REDUCTION POTENTIAL OF THE LUCIFERIN-OXYLUCIFERIN SYSTEM

The oxidation-reduction potential of the Cypridina luciferin-oxyluciferin system determined by a method of "bracketing" lies somewhere between that of anthraquinone 2-6-di Na sulfonate (E_o ^'' at pH of 7.7 = –.22) which reduces luciferin, and quinhydrone (E_o ^'' at pH of 7.7 = +.24), which oxidizes luciferin. Systems having an E_o ^'' value between –.22 and +.24 volt neither reduce oxyluciferin nor oxidize luciferin. If the luciferin-oxyluciferin system were truly reversible considerable reduction and oxidation should occur between –.22 and +.24. The system appears to be an irreversible one, with both "apparent oxidation" and "apparent reduction potentials" in Conant''s sense. Hydrosulfites, sulfides, CrCl₂, TiCl₃, and nascent hydrogen reduce oxyluciferin readily in absence of oxygen but without luminescence. Luminescence only appears in water solution if luciferin is oxidized by dissolved oxygen in presence of luciferase. Rapid oxidation of luciferin by oxygen without luciferase or oxidation by K₃Fe(CN)₆ in presence of luciferase but without oxygen never gives luminescence.     

Further Study on the Statistical Test to Detect Spatial Pattern

In the study of spatial patterns, the statistic I' = (n — 1)s²/x was commonly used. In this paper, we found that x — s² has an approximated normal distribution with zero mean if the x_i's (i = 1 to n) are independent identically distributed Poisson variables. Based on this conclusion, the hypothesis that a point pattern is completely random can be tested directly. And a method for the test of spatial patterns was proposed which can be sued as an alternative to the Chi-square based dispersion index test.     

Mathematical modeling and analysis of the flocculation process in chambers in series

In this study, the flocculation process in continuous systems with chambers in series was analyzed using the classical kinetic model of aggregation and break-up proposed by Argaman and Kaufman, which incorporates two main parameters: K _a and K _b. Typical values for these parameters were used, i. e., K _a = 3.68 × 10^?5–1.83 × 10^?4 and K _b = 1.83 × 10^?7–2.30 × 10^?7 s^?1. The analysis consisted of performing simulations of system behavior under different operating conditions, including variations in the number of chambers used and the utilization of fixed or scaled velocity gradients in the units. The response variable analyzed in all simulations was the total retention time necessary to achieve a given flocculation efficiency, which was determined by means of conventional solution methods of nonlinear algebraic equations, corresponding to the material balances on the system. Values for the number of chambers ranging from 1 to 5, velocity gradients of 20–60 s^?1 and flocculation efficiencies of 50–90 % were adopted.     

A widely applicable rate equation for the determination of enzyme activity at advanced stages of reaction

Summary An empirical equation for representing the course of the reaction has been developed for amylase ofAspergillus oryzae by using the method of time value estimation as a measure of enzyme activity. A convenient form of the equation for calculating and plotting results is t/x=bt+a/(E), where t=reaction time, x=amount of reaction products formed, (E)=enzyme concentration, a/(E)=reciprocal of initial velocity. The parameter b makes the equation of a rather universal applicability over large portions of the reaction curves. If b=0, the reaction is of zero order; if b=1/(S)_o, the reaction is of second order; a first order reaction can be represented over a range from 0 to 55% if b≏1/2(S)_o. In the case of aMichaelis-Menten mechanism, b=K_s/2(S)_o[(S)_o+K_s] afterBrant andAlberty (1961, personal communication), and then the ratio of (S)_o/K_s limits the range of validity of the empirical equation. As a tool for determining enzyme activity over a wide range of reaction, the equation is most useful in cases where the rate of reaction decreases rapidly,e.g. if (S)_o/K_s is small, or if inactivation and/or inhibition of the enzyme during the reaction is involved. For the assay of enzymes the main advantages of the empirical equation over the integratedMichaelis-Menten equation, and other more complicated variations thereof, are ease of handling and applicability to a large number of enzymes.