Protozoan feeding and bacterial wall growth.

Monod's model is often assumed to describe the kinetics of feeding of a protozoan population on a bacterial population in a chemostat. An earlier study (J. L. Jost et al., J. Bacteriol., 113, 84 (1973)) of the feeding of Tetrahymena pyriformis on either Escherichia coli or Azotobacter vinelandii found that this model correctly predicted the occurrence of sustained oscillations of population densities but made predictions of minimum bacterial population densities that were much smaller than those observed. The earlier study removed the discrepancy between the model and data by replacing Monod's model with a different model. It is shown in the present study that the discrepancy can be explained equally as well if Monod's model for the feed relation is retained and if, in addition, growth of bacteria on the chemostat walls is allowed for in the model equations.     

A simulation program based on a structured population model for biotechnological yeast processes

Summary A segregated population model for budding yeasts and a simulation program based on it are presented. They enable the study of bioprocesses utilizing yeasts in steady and perturbed conditions and in particular the comparison between the model predictions and the experimental results obtained by flow cytometry, which allows the measurement of segregated parameters of cell populations.Nomenclature a genealogical age - A parameter of the budding law - CV coefficient of variation - F _in(t) volumetric input flow - F _out(t) volumetric output flow - h parameter of the division law - K _s parameter of the Monod's law - m cell mass - M _i discretized cell mass - m _b (a,s) critical mass level for budding - m _p cell mass at the time of budding - n(t) cell number per unit volume - n _p number of sub-populations - n _c number of channels - p (a, i, j, k) discrete density function - Q parameter of the budding law - s(t) substrate concentration - S _in(t) substrate concentration in the input flow - t time - T _m minimal length of the budded phase - V(t) culture volume - x(t) biomass concentration - Y yield coefficient - channel width - (s) specific growth rate - _max parameter of the Monod's law     

Modeling the growth curve for Spirulina (Arthrospira) maxima, a versatile microalga for producing uniformly labelled compounds with stable isotopes

The paper presents a five-phase model to describe batch culture of Spirulina maxima under limitations of light and nutrients nitrogen andsulfur. The general equation for the exponential, linear, decelerating andstationary phases of the growth curve took into account that (i) the specificgrowth rate was proportional to the local light intensity in thephotobioreactor; (ii) light attenuation was due to cell's absorption andreflection and observed the Lambert-Beer's law with a total absorptioncoefficient (_T) that was the sum of absorption coefficient(_a) and reflection coefficient (_r); (iii) thecomposition of the alga and its absorption _a changed withtime and (iv) the specific growth rate was influenced by nutrients ofnitrogen and sulfur in the culture medium according to a Monod's law.Two successive equations describing the death phase were proposed basedon the hypothesis that the death rate accelerated with the %PSC until itreached its maximum. From that point the %PSC decreased and the deathrate reduced. Our model fitted very well the cultures grown in the photobioreactor developed in our laboratory.     

Enrichment of diazotrophic bacteria from rice soil in continuous culture

Summary A chemostat was used as a model system to study competitive interactions of diazotrophic microorganisms. Enrichment experiments were carried out under microaerobic conditions (8.7 mol O₂/l) with malate as the sole carbon source. The starting material was a Korean rice soil including intact root pieces. The enrichment process was governed by the dilution rate. High dilution rates resulted in the enrichment ofAzospirillum lipoferum, whereas low dilution rates led to the predominance of an unidentified organism, named Isolate R. Dilution rates were set in the range from D=0.005 to D=0.1 h^–1. The growth kinetics of both organisms followed Monod's model in the enrichment culture. From the experiments, the maximum specific growth rate ofA. lipoferum and Isolate R were 0.069 h^–1 and 0.025 h^–1, respectively. The corresponding K_s-values were 8.4 and 0.9 (mg. 1^–1). The point of theoretical coexistence of both organisms was calculated to occur at a substrate concentration of s=3.0 (mg.l^–1) with a growth of rate =0.018 h^–1. Hence the preset nutritional niches occupied by at least two organisms.Azospirillum lipoferum seems to represent the copiotroph microflora and Isolate R is of the oligotroph type. In addition to its high substrate affinity Isolate R liberatedca. 75% of the fixed nitrogen into the medium, which indicates its potential role for mutualistic interactions in the rhizosphere.     

Comparative study of the growth of two strains ofNitrobacter in batch and continuous culture

Growth kinetics of 2Nitrobacter strains (N.w. and L) coexisting in the same soil are studied in batch and continuous culture. Monod's parameters are estimated numerically from experimental data in the case of the batch experiment, and from steady-state equations in the case of the chemostat. In both cases, the 2 strains show different values for their growth parameters. N.w. may be characterized by its high _max-K_s values, relative to strain L. But for each strain, _max is significantly lowered between batch and continuous culture. In this latter case, at N-NO₂ ^– concentrations less than 1.5g·ml^–1, the 2 strains exhibit similar growth rates showing that for concentrations of the limiting substrate prevailing in the soil, they may compete for this substrate.     

Use of the Golden Section search method to estimate the parameters of the Monod model employing spread-sheets

An alternative procedure to obtain the parameters of Monod's growth model in batch culture is presented. It is based on the integral kinetic analysis methodology, employs a one-dimensional Golden Section search optimization method and is implemented on a spread-sheet programme. The procedure is discussed in detail and is illustrated by analysis of batch substrate consumption data by an aerobic bacterial consortium.     

Model of steady-state-biofilm kinetics

A steady-state biofilm is defined as one that has neither net growth nor decay over time. The model, developed for steady-state-biofilm kinetics with a single substrate, couples the flux of substrate into a biofilm to the mass (or thickness) of biofilm that would exist at steady-state for a given bulk substrate concentration. Based on kinetic and energetic constraints, this model predicts for a single substrate that a steady-state bulk concentration, S_min, exists below which a steady-state biofilm cannot exist. Thus, in the absence of adsorption of bacteria from the bulk water and for substrate concentration below S_min, substrate flux and biofilm thickness are zero. Equations are provided for calculating the steady-state substrate flux and biofilm thickness for S greater than S_min. An example is provided to demonstrate the use of the steadystate model.     

Chaotic dynamics of a food web in a chemostat

We analyze a mathematical model of a simple food web consisting of one predator and two prey populations in a chemostat. Monod's model is employed for the dependence of the specific growth rates of the two prey populations on the concentration of the rate-limiting substrate and a generalization of Monod's model for the dependence of the specific growth rate of the predator on the concentrations of the prey populations. We use numerical bifurcation techniques to determine the effect of the operating conditions of the chemostat on the dynamics of the system and construct its operating diagram. Chaotic behavior resulting from successive period doublings is observed. Multistability phenomena of coexistence of steady and periodic states at the same operating conditions are also found.     

Dependence of the specific growth rate of methanogenic mutualistic cocultures on the methanogen

Methanogenesis from ethanol was studied in batch cocultures of a proton-reducing acetogenic Desulfovibrio sp. together with one of eight methanogenic bacteria representing five genera. A mathematical model of mutualistic cocultures predicts an equalisation in the specific growth rates of the two species which defines a specific growth rate for the coculture. At non-limiting ethanol concentrations the model predicts that the specific growth rate of the coculture is dependent upon the K _s (H₂) of the methanogen and its maximum specific growth rate in axenic culture when utilising H₂ as the energy source. We demonstrate experimentally that with methanogens known to have similar K _s (H₂) values, the specific growth rates of methanogenic mutualistic cocultures are dependent upon the maximum specific growth rates of the methanogens.     

Feasibility study of exponential feeding strategy in fed-batch cultures for phenol degradation using Cupriavidus taiwanensis

An indigenous phenol-degrading bacterial isolate Cupriavidus taiwanensis R186 was used to degrade phenol from an aqueous solution under fed-batch operation. An exponential feeding strategy combined with dissolved oxygen control was applied based on kinetic characteristics of cell growth and phenol degradation to meet sufficient metabolic needs for cellular growth and achieve the best phenol removal efficiency. Without the stress of phenol inhibition, the optimal set point of specific growth rate of exponential feeding for fed-batch phenol degradation was found to be 0.50–0.55μ_max (μ_max denotes the maximum specific growth rate from Monod model). Meanwhile, the sufficient set point of dissolved oxygen for maximal phenol degradation efficiency was approximately at 10–55% air saturation. With the optimal operation conditions, the best phenol degradation rate was 0.213 g phenol h⁻¹, while a shortest treatment time of 15 h was achieved for complete degradation of 11.35 mM (ca. 3.20 g) of phenol.     

Strategies to enhance cell growth and achieve high‐level oil production of a Chlorella vulgaris isolate

The autotrophic growth of an oil‐rich indigenous microalgal isolate, identified as Chlorella vulgaris C? C, was promoted by using engineering strategies to obtain the microalgal oil for biodiesel synthesis. Illumination with a light/dark cycle of 14/10 (i.e., 14 h light‐on and 10 h light‐off) resulted in a high overall oil production rate (v_oil) of 9.78 mg/L/day and a high electricity conversion efficiency (E_c) of 23.7 mg cell/kw h. When using a NaHCO₃ concentration of 1,500 mg/L as carbon source, the v_oil and E_c were maximal at 100 mg/L/day and 128 mg/kw h, respectively. A Monod type model was used to describe the microalgal growth kinetics with an estimated maximum specific growth rate (μ_max) of 0.605 day^?1 and a half saturation coefficient (K_s) of 124.9 mg/L. An optimal nitrogen source (KNO₃) concentration of 625 mg/L could further enhance the microalgal biomass and oil production, leading to a nearly 6.19 fold increase in v_oil value. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Growth yield and energy generation in anaerobically-grown Campylobacter spec.

An anaerobic continuous culture study was made with Campylobacter spec. to determine growth yields under various growth conditions. The growth media contained 0.1% (w/v) yeast extract as carbon source. When grown in an aspartate-limited culture Y _asp ^max was 4.6. Inclusion of formate in the culture medium hardly affected the true growth yield. The number of ATP equivalents generated in the fumaratereductase system was 0.66 and the Y _ATP ^max was 7.0. In the nitrate reduction with formate 1.7 ATP equivalents were generated, and a YNO _3- ^max of 12.2 was observed. The true growth yield obtained with a mixture of lactate and aspartate was lower than that found with aspartate alone.     

Mortality as a mathematical function of organic growth and diameter structure

ABSTRACT

An indirect method to determine the exponential mortality coefficient (λ) as well as the annual mortality (m) is proposed. In this method, both parameters are deduced mathematically from a model of organic growth (von Bertalanffy) and from a model of uneven-aged population structure (De Liocourt and Meyer) used with forest trees, which relates the frequency of individuals by size classes. The resultant equations allow the determination of either the instantaneous or mean value for λ or m between any two ages t ₁ and t ₂. Both concepts of mortality were used to determine the half-life (t _0.5) as a function of λ and m . The method is applied to determine the curves of mortality and the half-life of Otoba gracilipes (Myristicaceae), a tropical tree that grows in the forested wetlands of the Colombian Pacific coast.     

Approximation of continuous fermentation by semicontinuous cultures

Semicontinuous fermentations, in which a fraction of a culture is replaced with fresh media at regular intervals, have been previously used as a means of approximating continuous growth. In most cases deviations from continuous operation were erroneously estimated using Fencl's model, which is only valid when the specific growth rate is independent of the substrate concentration. An approach to modeling Semicontinuous growth that incorporates the same kinetics followed in batch and continuous growth was developed and tested for Monod's expression for the specific growth rate. A dimensionless form of the model was used to simulate Semicontinuous fermentations for comparison to continuous growth. Differences between Semicontinuous and continuous growth were found to depend on three dimensionless variables: feed concentration, replacement rate, and time between replacements. For given values of the dimensionless feed concentration and time between replacements, a range of dimensionless replacement rates can be determined over which semi-continuous cultures are approximately continuous.     

Energetics of Saccharomyces cerevisiae CBS 426: Comparison of anaerobic and aerobic glucose limitation

Saccharomyces cerevisiae CBS 426 was grown aerobically and anaerobically in a glucose-limited chemostat. The flows of biomass, glucose, ethanol, carbon dioxide, oxygen, glycerol, and the elemental composition of the biomass were measured. Models for anaerobic and aerobic growth are constructed. Values for Y_ATP and P/O are obtained from continuous culture data for aerobic growth; this Y_ATP value is compared with that obtained from the anaerobic growth results. The ratio between the heat produced and the oxygen consumed increases if more glucose in fermented to ethanol and carbon dioxide. An equation for ?_H/?_O as a function of the respiratory quotient is given.     

Changes in the levels of jasmonates and free polyamines induced by Na<Subscript>2</Subscript>SO<Subscript>4</Subscript> and NaCl in roots and leaves of the halophyte <Emphasis Type="Italic">Prosopis strombulifera</Emphasis>

Prosopis strombulifera, a common legume in high-salinity soils of Argentina, is a useful model for elucidation of salt tolerance mechanisms and specific biochemical pathways in halophytes, since its NaCl tolerance exceeds the limit described for most halophytic plants. We analyzed the effects of the increasing concentration of two main soil salts, Na₂SO₄ and NaCl, on growth parameters of P. strombulifera, chlorophyll levels, and content of jasmonates (JAs) and polyamines (PAs), which are key molecules involved in stress responses. P. strombulifera showed a halophytic response (growth promotion) to NaCl, but strong growth inhibition by iso-osmotic solutions of Na₂SO₄. Chlorophyll levels, number of leaves and leaf area were also differentially affected. An important finding was the partial alleviation of SO₄²⁻ toxicity by treatment with two-salt mixture. JAs are not directly involved in salt tolerance in this species since its levels decrease under all salt treatments. Beneficial effects of Putrescine (Put) accumulation in NaCl treated plants maybe inferred probably associated with the antioxidative defense system. Another novel finding is the accumulation of the uncommon PA cadaverine in roots under high Na₂SO₄, which may be related to SO₄²⁻ toxicity.     

Two Bayesian methods for estimating parameters of the von Bertalanffy growth equation

The von Bertalanffy growth equation (VBGE) is commonly used in ecology and fisheries management to model individual growth of an organism. Generally, a nonlinear regression is used with length-at-age data to recover key life history parameters: L _∞ (asymptotic size), k (the growth coefficient), and t ₀ (a time used to calculate size at age 0). However, age data are often unavailable for many species of interest, which makes the regression impossible. To confront this problem, we have developed a Bayesian model to find L _∞ using only length data. We use length-at-age data for female blue shark, Prionace glauca, to test our hypothesis. Preliminary comparisons of the model output and the results of a nonlinear regression using the VBGE show similar estimates of L _∞ . We also developed a full Bayesian model that fits the VBGE to the same data used in the classical regression and the length-based Bayesian model. Classical regression methods are highly sensitive to missing data points, and our analysis shows that fitting the VBGE in a Bayesian framework is more robust. We investigate the assumptions made with the traditional curve fitting methods, and argue that either the full Bayesian or the length-based Bayesian models are preferable to classical nonlinear regressions. These methods clarify and address assumptions␣made in classical regressions using von Bertalanffy growth and facilitate more detailed stock assessments of species for which data are sparse.     

Hydrocarbon fermentation: Kinetics of microbial cell growth

Modeling of microbial growth using nonmiscible substrate is studied when kinetics of substrate dissolution is rate limiting. When the substrate concentration is low, the growth rate is described by an analytical relation that can be identified as a Contois relationship. If the substrate concentration is greater than a critical value S_crit, the potentially useful hydrocarbon S* concentration is described by S* = S_crit/(1 + S_crit/S). A relationship was found between S_crit and the biomass concentration X. When X increased, S_crit decreased. The cell growth rate is related to a relation μ = μ_m[A(X/S_crit)(1 + S_crit/S) + 1]^?1. This model describes the evolution of the growth rate when exponential or linear growth occurs, which is related to physico-chemical properties and hydrodynamic fermentation conditions. Experimental data to support the model are presented.     

Temperature and prey quality effects on growth of juvenile walleye pollock Theragra chalcogramma (Pallas): a spatially explicit bioenergetics approach

A bioenergetics model for juvenile age‐0 year walleye pollock Theragra chalcogramma was applied to a spatially distinct grid of samples in the western Gulf of Alaska to investigate the influence of temperature and prey quality on size‐specific growth. Daily growth estimates for 50, 70 and 90 mm standard length (L_S) walleye pollock during September 2000 were generated using the bioenergetics model with a fixed ration size. Similarities in independent estimates of prey consumption generated from the bioenergetics model and a gastric evacuation model corroborated the performance of the bioenergetics model, concordance correlation (r_c) = 0·945, lower 95% CL (transformed) (L₁) = 0·834, upper 95% CL (transformed) (L₂) = 0·982, P < 0·001. A mean squared error analysis (M_SE) was also used to partition the sources of error between both model estimates of consumption into a mean component (M_C), slope component (S_C), and random component (R_C). Differences between estimates of daily consumption were largely due to differences in the means of estimates (M_C= 0·45) and random sources (R_C= 0·49) of error, and not differences in slopes (S_C= 0·06). Similarly, daily growth estimates of 0·031–0·167 g day^?1 generated from the bioenergetics model was within the range of growth estimates of 0·026–0·190 g day^?1 obtained from otolith analysis of juvenile walleye pollock. Temperature and prey quality alone accounted for 66% of the observed variation between bioenergetics and otolith growth estimates across all sizes of juvenile walleye pollock. These results suggest that the bioenergetics model for juvenile walleye pollock is a useful tool for evaluating the influence of spatially variable habitat conditions on the growth potential of juvenile walleye pollock.     

A novel polyculture growth model of native microalgal communities to estimate biomass productivity for biofuel production

Native polyculture microalgae is a promising scheme to produce microalgal biomass as biofuel feedstock in an open raceway pond. However, predicting biomass productivity of native polycultures microalgae is incredibly complicated. Therefore, developing polyculture growth model to forecast biomass yield is indispensable for commercial-scale production. This research aims to develop a polyculture growth model for native microalgal communities in the Minamisoma algae plant and to estimate biomass and biocrude oil productivity in a semicontinuous open raceway pond. The model was built based on monoculture growth of polyculture species and it is later formulated using species growth, polyculture factor (k_value), initial concentration, light intensity, and temperature. In order to calculate species growth, a simplified Monod model was applied. In the simulation, 115 samples of the 2014–2015 field dataset were used for model training, and 70 samples of the 2017 field dataset were used for model validation. The model simulation on biomass concentration showed that the polyculture growth model with k_value had a root-mean-square error of 0.12, whereas model validation provided a better result with a root-mean-square error of 0.08. Biomass productivity forecast showed maximum productivity of 18.87 g/m²/d in June with an annual average of 13.59 g/m²/d. Biocrude oil yield forecast indicated that hydrothermal liquefaction process was more suitable with a maximum productivity of 0.59 g/m²/d compared with solvent extraction which was only 0.19 g/m²/d. With satisfactory root-mean-square errors less than 0.3, this polyculture growth model can be applied to forecast the productivity of native microalgae.