Generalization of monod kinetics for analysis of growth data with substrate inhibition

The inhibitory effect of butanol on yeast growth has been studied for the strain Candida utilis ATCC 8205 growing aerobically on butanol under batch conditions. A mathematical expression was then proposed to fit the kinetic pattern of butanol inhibition on the specific growth rate: \documentclass{article}\pagestyle{empty}\begin{document}$$ \mu = \frac{{\mu _m S}}{{K_s + S}}\left[{1 - \frac{S}{{S_m }}} \right];n $$\end{document}The maximum allowable butanol concentration above which cells do not grow was predicted to be 9.16g/L. The proposed model appears to accurately represent the experimental data obtained in this study and the literature data developed for a variety of batch culture systems at widely ranging substrate concentrations.     

Kinetics of ethanol inhibition in alcohol fermentation

The inhibitory effect of ethanol on yeast growth and fermentation has been studied for the strain Saccharomyces cerevisiae ATCC No. 4126 under anaerobic batch conditions. The results obtained reveal that there is no striking difference between the response of growth and ethanol fermentation. Two kinetic models are also proposed to describe the kinetic pattern of ethanol inhibition on the specific rates of growth and ethanol fermentation: \documentclass{article}\pagestyle{empty}\begin{document}$$\begin{array}{*{20}c} {\frac{{\mu _i }}{{\mu _0 }} = 1{\rm } - {\rm }\left( {\frac{P}{{P_m }}} \right);\alpha } \hfill & {\left( {{\rm for}\ {\rm growth}} \right)} \hfill \\ {\frac{{\nu _i }}{{\nu _0 }} = 1{\rm } - {\rm }\left( {\frac{P}{{P'_m }}} \right);\beta } \hfill & {\left( {{\rm for}\ {\rm ethanol}\ {\rm production}} \right)} \hfill \\ \end{array}$$\end{document} The maximum allowable ethanol concentration above which cells do not grow was predicted to be 112 g/L. The ethanol-producing capability of the cells was completely inhibited at 115 g/L ethanol. The proposed models appear to accurately represent the experimental data obtained in this study and the literature data.     

Transient method for proposing the mechanisms of reactions over immobilized enzymes

The transient response method is introduced to elucidate the mechanism of reaction over immobilized enzyme. Glucose oxidation over the glucose oxidase that was immobilized on ion-exchange resin using glutaraldehyde as a linking agent is selected as an example here. The transient responses of a fixed-bed reactor to step increases and decreases in glucose, oxygen, and gluconolactone feed concentrations have been monitored and interpreted. From some responses, we have found that gluconolactone is formed in the reaction of glucose with adsorbed oxygen, while hydrogen peroxide is formed in the reaction of oxygen with adsorbed glucose. Combining all information from interpreting the responses with the literature, a mechanistic picture can be obtained as follows: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {E_{{\rm ox}} + G \to E_{{\rm red}} GL} \\ {E_{{\rm red}} GL \to E_{{\rm red}} + GL} \\ {E_{{\rm red}} + {\rm O}_2 \to E_{{\rm ox}} {\rm H}_2 {\rm O}_2 } \\ {E_{{\rm ox}} {\rm H}_2 {\rm O}_2 \to E_{{\rm ox}} + {\rm H}_2 {\rm O}_2 } \\ \end{array} $$\end{document}.     

An electrochemical method of measuring the oxidation rate of ferrous to ferric iron with oxygen in the presence of Thiobacillus ferrooxidans

The oxidation of Fe(2+) with oxygen in sulfate solutions was studied in the presence of T. ferrooxidans. To measure the chemical activity of bacteria, and the oxidation rate of iron, the redox potentials of solutions were continuously monitored during the experiments. The redox potentials were simultaneously monitored on the platinum and pyrite indicator electrodes. The redox potential versus time curves were further used to calculate the basic kinetic parameters, such as the reaction orders, the activation energy, and the frequency factor. It was found that under atmospheric conditions, and at Fe(2+) < 0.001M, T < 25 degrees C, and at pH above 2.2, the oxidation of iron is governed by the following rate expression: \documentclass{article}\pagestyle{empty}\begin{document}$$ - \frac{{d[{\rm Fe};{2 + }]}}{{dt}} = 1.62 \times 10;{11} C_{{\rm bact}} [{\rm H}; + ][{\rm Fe};{2 + }]p{\rm O}_2 e;{ - (58.77/RT)} $$\end{document} Below pH = 2.2, the oxidation rate is independent of H(+) Concentration.     

The density of protein precipitates and its effect on centrifugal sedimentation

Isoelectric soya-protein precipitate densities were measured for mean particle sizes ranging from 3.4-65 mum by gradient centrifugation, centrifugation in water-immiscible solvents, tracerdilution, gravity sedimentation of isolated particles. Coulter counter volume determination, and a comparison of Coulter counter and centrifugal sedimentation size distributions. The immiscible system and tracer dilution methods were both found to be unreliable due to experimental uncertainties. The Coulter counter volume measurement indicated the existence of a density-size relationship with the aggregate density decreasing as the size increased. Comparison with sedimentation measurements showed that the Coulter counter measures 80% of the total aggregate volume for 6-mum particles. The relation between aggregate density (rho(a), kg m (-3)) and size (d, mum) was measured for isoelectric soya protein and casein precipitated by ammonium sulfate, using a comparison of the Coulter counter size distribution and centrifugal sedimentation. The functions were described for soya by \documentclass{article}\pagestyle{empty}\begin{document}$$ \rho _a - 1004 = 246d;{ - 0.408} $$\end{document} and for casein by \documentclass{article}\pagestyle{empty}\begin{document}$$ \rho _a - 1136 = 31d;{ - 0.441} $$\end{document} The gradient centrifugation method measured the buoyant density of hydrated protein precipitate which was independent of size, and is consistent with an aggregate structure consisting of primary particles. However, the aggregate structure was not described for all sizes by the theoretical cubic packing of hard-sphere primary particles, nor by the successive random addition of primary particles. The density-size functions indicated up to a fivefold difference in Stokes settling velocities compared to those calculated assuming a constant density difference.     

Inhibierungserscheinungen bei der alkoholischen Gärung,I. Einfluß der Ethanolkonzentration auf die spezifische Ethanolbildungsgeschwindigkeit von Saccharomyces cerevisiae

Differential values of the specific ethanol production rate \documentclass{article}\pagestyle{empty}\begin{document}$$ v_{(t)} = \frac{1}{{x_{(t)} }} \cdot \frac{{dP}}{{dt}} $$ \end{document} can be calculated exactly from experimental batch fermentation process data by use of a nonlinear regression programme. The method used is based on the fact, that the function P = f(t) can be approximated by an exponential equation. The specific ethanol production rate is calculated then from the first differential derivation of this equation using the appropriated values of actual biomass concentration. For two strains of Saccharomyces cerevisiae a linear and nonlinear kinetic pattern, respectively, was found for product formation. This result can be explained by a simple mathematical relation according to ν=ν₀ ? a . P^b,in which the exponent becomes 1 in the case of linear kinetic pattern.     

Prognose des Stoffhaushaltes von Staugewässern mit Hilfe kontinuierlicher und semikontinuierlicher biologischer Modelle. II. Prüfung der Prognosegenauigkeit. Prediction of the Balance of Matter in Storage Reservoirs by Means of Continuous or Semicontinuous Biological Models. II. Reliability of the Prediction Method

The phosphate removal in small, completely mixed storage reservoirs (preimpoundment basins) mainly is a function of the production of biomass by the phytoplankton. The knowledge of the critical detention time of the water is the most important premise to the prediction. The critical detention time t̄ is computed from the equation: \documentclass{article}\pagestyle{empty}\begin{document}$ \overline t _c = \frac{1}{{\mu ^* - 0,1}} $\end{document} and the growth rate μ* at a given combination of the light intensity J, temperature T and phosphate concentration P is computed from: \documentclass{article}\pagestyle{empty}\begin{document}$ \mu ^* = \frac{{\mu T \cdot \mu J \cdot \mu P}}{{\mu \max ^2 }}\mu \max \cdot \frac{P}{{K_p + P}}\frac{J}{{K_j + J}}\frac{T}{{T_{opt} }}, $\end{document} (μmax = maximum possible growth rate of the dominant species; K_p, K_j and T_opt are constants computed from batch cultures). The quotient \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\bar t_{act.} }}{{\bar t_c }}(\bar t_{act.} = {\rm actual detention time in the water body)} $\end{document} enables prediction of the phosphate removal. A comparison of the predicted results from semicontinuous cultures and from the preimpoundment basin of the Weida reservoir revealed a satisfactory degree of conformity.     

Kinetics of aflatoxin biosynthesis by Aspergillus parasiticus in the presence of N(alpha)-palmitoyl-L-lysyl-L-lysine-ethyl ester dihydrochloride or dichlorvos

N(alpha)-Palmitoyl-L-lysyl-L-lysine-ethyl ester dihydrochloride (PLL) has antimicrobial properties and may be useful as a food preservative. This study was conducted to see if PLL can inhibit growth and synthesis of aflatoxin by Aspergillus parasiticus. Growth of mold and accumulation of aflatoxins were monitored for up to 15 days. To compare these data with those of a known inhibitor of aflatoxin synthesis, dichlorvos was added to media, and mold growth and aflatoxin accumulation were monitored. The kinetic model of Brown and Vass that correlates growth and formation of secondary metabolites was applied to results of this study, and values for maturation time (t(m)) and aflatoxin accumulation rate constant (alpha) were calculated. Values of t(m) decreased when cultures contained PLL, whereas presence of dichlorvos resulted in a considerable increase. The lag phase of mold growth increased in the presence of PLL. The values of alpha increased with an increasing amount (up to 300 ppm) of PLL in media. Higher concentrations of PLL decreased the value of alpha. All levels of dichlorvos tested decreased the value of alpha. The aflatoxin accumulation rate constant (alpha) as a function of concentration of additive (C) followed the general equation: \documentclass{article}\pagestyle{empty}\begin{document}$$\alpha = \frac{{\alpha _m C\exp (- {C \mathord{\left/ {\vphantom {C {K_i }}} \right. \kern-\nulldelimiterspace} {K_i }})}}{{C + K_a }}$$\end{document} where alpha(m), K(a), and K(i) are constants.     

Kinetics of anaerobic purification of industrial wastewater

As a part of the development of an integral mathematical model describing the up-flow anaerobic sludge blanket (UASB) reactor, the kinetics of the conversion of organic wastes has to be known. We compared the Monod model with the model proposed by Andrews et al. Together with the assumption that the substrate for the anaerobic bacteria is formed by nonionized, volatile fatty acids, the Andrews model is able to describe substrate inhibition and reactor failure due to pH changes.From four batch experiments, with different concentrations of microorganisms, it could be concluded with a reliability of over 95% that the monod model was inadequate and Andrews' model was adequate to describe the measurements. Standard statistical techniques like the X2- and the F-test were used for this purpose.From a parameter sensitivity analysis for the Andrews model it followed that the maximum specific growth rate mu(A) (max) of the bacteria and the inhibition constant K(1) are the parameters which influence the system most. Thus, these parameter were determined experimentally and most accurately. The results are: \documentclass{article}\pagestyle{empty}\begin{document}$$\mu;{A}_{\max} = 16*10;{-4}{\rm h};{-1}\pm 2\%\quad {\rm and}\quad K_l = 0.0158\,{\rm g}\,{\rm HAc/L}\pm 2.5\%$$\end{document} The other parameters were taken from literature. From calculation of the Thiele modulus for the particles it follows that transport limitation of the substrate in the flocus is not significant. The efficiency eta is 0.85 in the worst case.     

Catabolite repression of amylase synthesis in yeast

Amylase synthesis by the yeasts Saccharomycopsis fibuligera and Schwanniomyces castellii and alluvius is repressed by glucose. Steady state continuous culture data for amylase activity, E, biomass concentration, X, and reducing sugar concentration, S, were fitted to the three-parameter catabolite repression model \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{E}{X} = \frac{{[1 + a(S/X)]}}{{[1 + b(S/X)]}}, $\end{document} and biomass productivity, DX, and amylase productivity, DE, were determined for S. castellii and S. alluvius.     

Alcoholic fermentation: modelling based on sole substrate and product measurement

Optimal automatic bioreactor control requires a mathematical model adapted to the potency of reliable sensors. A new relationship describing the kinetic behavior of alcoholic fermentation is discussed. By analogy with chemical kinetics, the biological rate of substrate consumption is related to substrate and product concentration by the following equation: \documentclass{article}\pagestyle{empty}\begin{document}$$r_s = kS;\alpha P;\beta$$\end{document} Using the well known yield relation between product and substrate, it is possible to describe in both batch and continuous cultures the ethanol and sugar concentrations versus time. This pattern has been successfully tested on several fermentations performed by yeasts (S. cerevisiae, S. bayanus, and S. cerevisiae sake) and a bacterium (Z. mobilis). This simple relationship is proposed as a tool for process control alcoholic fermentation.     

Regional Assessment of N Saturation using Foliar and Root \varvec {\delta}^{\bf 15}{\bf N}

N saturation induced by atmospheric N deposition can have serious consequences for forest health in many regions. In order to evaluate whether foliar may be a robust, regional-scale measure of the onset of N saturation in forest ecosystems, we assembled a large dataset on atmospheric N deposition, foliar and root and N concentration, soil C:N, mineralization and nitrification. The dataset included sites in northeastern North America, Colorado, Alaska, southern Chile and Europe. Local drivers of N cycling (net nitrification and mineralization, and forest floor and soil C:N) were more closely coupled with foliar than the regional driver of N deposition. Foliar increased non-linearly with nitrification:mineralization ratio and decreased with forest floor C:N. Foliar was more strongly related to nitrification rates than was foliar N concentration, but concentration was more strongly correlated with N deposition. Root was more tightly coupled to forest floor properties than was foliar . We observed a pattern of decreasing foliar values across the following species: American beech>yellow birch>sugar maple. Other factors that affected foliar included species composition and climate. Relationships between foliar and soil variables were stronger when analyzed on a species by species basis than when many species were lumped. European sites showed distinct patterns of lower foliar , due to the importance of ammonium deposition in this region. Our results suggest that examining values of foliage may improve understanding of how forests respond to the cascading effects of N deposition.     

Extracellular microbial polysaccharides: Generalized power law for biopolysaccharide solutions

A generalized power low model, \documentclass{article}\pagestyle{empty}\begin{document}$ \eta \, = \,\eta _0 [1\, + \,(\dot \gamma /\gamma _0 )];{N - 1} $\end{document}, is shown to described satisfactorily the shear viscosity data for xanthan gum solutions from 0.18 g/L to nearly 4 g/L and low to intermediate shear rates. Since mixing, mass and heat transfer, residence time distributions, and power input for agitation and aeration all depend on shear viscosity, this equation provides a simple prediction of this important quantity over the shear rate ranges characteristic of fermentations.     

External-circulation-loop airlift bioreactors: study of the liquid circulating velocity in highly viscous non-Newtonian liquids

In order to obtain further information on the behavior and optimal design of external-circulation-loop airlift (ECL-AL) bioreactors, the liquid circulating velocity, gas holdup and average bubble diameter in the downcomer were studied using highly viscous pseudoplastic solutions of various types of CMC. A few comparative measurements also were made using a viscous Newtonian aqueous sucrose solution. For the liquid velocity measurements, an ultrasonic flow meter (Doppler frequency shift principle) was applied for the first time to the gas/non-Newtonian liquid dispersion in downward flow and satisfactory results were obtained. For viscous liquids, the circulating liquid velocity in the riser section of an ECL-AL (u(LR)) is shown to be dependent mainly on the downcomer-to-riser cross-sectional area ratio (A(d)/A(r)), the effective viscosity (eta(eff)) and the gas superficial velocity (u(GR)) as described by the following equation \documentclass{article}\pagestyle{empty}\begin{document}$$ u_{LR} = 0.23u_{GR};{0.32} (A_d /A_r);{0.97} \eta _{eff};{ - 0.39} $$\end{document} The circulating liquid velocity exerts opposing effects on the mass transfer and liquid-phase mixing performances of ECL-AL fermentors. Therefore, it is proposed that the optimum operating conditions for a given fermentation may be best achieved by means of independently regulating the circulating liquid velocity.     

Regional Assessment of N Saturation using Foliar and Root $\varvec {\delta}^{\bf 15}{\bf N}$\varvec {\delta}^{\bf 15}{\bf N}

N saturation induced by atmospheric N deposition can have serious consequences for forest health in many regions. In order to evaluate whether foliar may be a robust, regional-scale measure of the onset of N saturation in forest ecosystems, we assembled a large dataset on atmospheric N deposition, foliar and root and N concentration, soil C:N, mineralization and nitrification. The dataset included sites in northeastern North America, Colorado, Alaska, southern Chile and Europe. Local drivers of N cycling (net nitrification and mineralization, and forest floor and soil C:N) were more closely coupled with foliar than the regional driver of N deposition. Foliar increased non-linearly with nitrification:mineralization ratio and decreased with forest floor C:N. Foliar was more strongly related to nitrification rates than was foliar N concentration, but concentration was more strongly correlated with N deposition. Root was more tightly coupled to forest floor properties than was foliar . We observed a pattern of decreasing foliar values across the following species: American beech>yellow birch>sugar maple. Other factors that affected foliar included species composition and climate. Relationships between foliar and soil variables were stronger when analyzed on a species by species basis than when many species were lumped. European sites showed distinct patterns of lower foliar , due to the importance of ammonium deposition in this region. Our results suggest that examining values of foliage may improve understanding of how forests respond to the cascading effects of N deposition.     

Phosphorus uptake and growth of blue-green alga, Microcystis aeruginosa

The specific uptake rate Q(p) of orthophosphate (expressed throughout as phosphorus) and the specific growth rate mu of Microcystis aeruginosa were measured using batch-precultured cells, whose growth phase, and intracellular and extracellular phosphorus concentrations f(p) and P, respectively, had been changed. When the cells from phosphorus-rich precultures were used, smaller values of Q(p) (0.1-0.3 mug P mg dry wt. (-1) h (-1)) were observed. However, if phosphorusstarved cells were used, the initial value of Q(p) was enhanced to more than ten times those smaller values referred to above, but declined rapidly with time after the transfer. Q(p) leveled off at around t = 4 h, when f(p) approached the maximum value, even if phosphorus was still available in the medium. A new correlation was presented here with respect to Q(p) as a function of P and f(p) as follows: \documentclass{article}\pagestyle{empty}\begin{document}$$ Q_p = Q_{p,\max } \frac{P}{{K_p + P}}\frac{{(f_{p,\max } - f_p )}}{{(f_{p,\max } - f_p )}} $$\end{document} Although numerical values of parameters involved in the equation depend on physiological state (or preculture history) of the cells, the above equation could account not only for phosphorus uptake, during which changes in phosphorus content in the cells were observed, but also for initial rates of uptake presented previously by other workers. mu Values were confirmed to be a hyperbolic function of f(p) as has been suggested by previous workers.     

Polarized fluorescence in an electric field. A model calculation with application to the geometry of the 2-hydroxy-4,4′-diamidinostilbene–DNA complex

Theoretical expressions are derived for the change in the polarized components of the fluorescence, resulting from the orientation of a rigid molecule bearing a chromophore with arbitrary angles for the absorption and transition moments \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _a $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _e $\end{document} with respect to the molecular axis. The break in the symmetry relation H_V = V_H is related to the tilt angle between \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _a $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _e $\end{document}. The theory is applied to a sonicated DNA–2-hydroxy-4,4′-diamidinostilbene complex, in the blue and red emission bands of this peculiar dye. Simultaneous measurements of linear dichroism and fluorescence lead to the determination of an angle of 47° between a fluorescent bound dye and the DNA axis, with no difference for the blue- and red-emitting species, but confirm the presence of nonfluorescent bound dye in a more perpendicular arrangement.     

Optical anisotropy of polypeptide chains

Optical anisotropies γ² of N-t-butylacetamide (tBA), N-Methylacetamide (MA), and N, N-dimethylacetamide (DMA) have been determined from the Rayleigh ratios for depolarzed scattering by dilute solutions of the amides in p-dioxane. Traceless optical polarizability tensors \documentclass{article}\pagestyle{empty}\begin{document}$ \widehat{\rm \alpha } $\end{document} for the amides are derived from these results in conjunction with the Kerr constant for tBA determined by LeGèvre and co-workers. It is shown that the tensor \documentclass{article}\pagestyle{empty}\begin{document}$ \widehat{\rm \alpha } $\end{document}_i for the glycyle unit in a polypeptide chain may be identified with \documentclass{article}\pagestyle{empty}\begin{document}$ \widehat{\rm \alpha } $\end{document}MA . Methods for deriving corresponding tensors for other peptide units are indicated and the traceless polarizability tensor \documentclass{article}\pagestyle{empty}\begin{document}$ \widehat{\rm \alpha } $\end{document} for a polypeptide chain in any specified configuration is formulated.     

Rheological properties of mammalian cell culture suspensions: Hybridoma and HeLa cell lines

Data on viscous (eta') and elastic (eta') components of the complex viscosity versus oscillatory angular frequency (0.01 to 4.0 rad/s) with increasing strains were obtained for hybridoma cell (62'D3) and HeLa cell (S3) suspensions in PBS at 0.9 (mL/mL) cell volume fraction using a Weissenberg rheogoniometer equipped with two parallel plate geometry at ambient temperature. Both cell suspensions exhibited shear thinning behavior. From the measured viscoelastic properties, the yield stress was calculated. Hybridoma cell suspension (15 mum as the mean diameter of cells) showed the yield stress at 550 dyne/cm(2) that was 1.8 times higher than the value of HeLa cell suspension (22 mum mean diameter) as measured at the oscillatory angular frequency, 4.0 rad/s. The apparent viscosities of HeLa cell suspension at four concentrations and varying steady shear rate were also determined using the Brookfield rotational viscometer. The yield stress to steady shear test was about 130 dyne/cm(2) for HeLa cell suspension at 0.9 (mL/mL) cell volume fraction. The apparent viscosity was in the range about 1 approximately 1000 Poise depending on the cell concentration and shear rate applied. A modified semiempirical Mooney equation, \documentclass{article}\pagestyle{empty}\begin{document}$ \eta = \eta _0 \exp [K\dot \gamma ;{ - \beta } \phi /(1 - K'\sigma \phi _c /D)] $\end{document} was derived based on the cell concentration, the cell morphology, and the steady shear rate. The beta, shear rate index, was estimated as 0.159 in the range of shear rate, 0.16 to 22.1 s(-1), for the cell volume fractions from 0.6 to 0.9 (mL/mL). In this study, the methods of determining the shear sensitivity and the viscous and the elastic components of mammalian cell suspensions are described under the steady shear field. (c) 1993 John Wiley & Sons, Inc.