Growth models of cultures with two liquid phases. II. Pure substrate in dispersed phase

Mathematical models which can be used to describe batch frowth in fermentations with two liquid phases are developed for systems in which the growth limiting substrate is the dispersed liquid phase. Three special cases are considered assuming pure substrate in the dispersed phase and a decreasing interfacial area due to substrate consumption. In the first, it is assumed that all growth occurs at the surface of the dispersed phase. In the second and third growth occurs at the interface and in the continuous phase. The second case assumes substrate equilibrium between the two phases while the third assumes substrate consumption in the continuous phase is limited by rate of substrate transport to that phase. Since the amount of growth at the interface and substrate transport to the continuous phase depend on the interfacial area, two limiting cases for the decrease of interfacial area with substrate consumption are also considered in this investigation. The first and third models are compared with available experimental data.     

Growth models of cultures with two liquid phases. III. Continuous cultures

Some mathematical models, which have been used to describe batch growth in fermentations with two liquid phases present, are used to predict the behavior of continuous fermentations in a chemostat. Two types of dispersed systems are considered in this investigation. In the first, type, it is assumed that the composition of the dispersed phase is such that, increased substrate utilization results in a decreased substrate concentration with no change in the interfacial area. In the second type of system, the dispersed phase is assumed to be pure substrate; therefore, the substrate concentration in the dispersed phase remains constant but the interfacial area is affected by changes in dilution rate. Three special cases are examined for each type of system in order to examine the effect of the interfacial area, the phase equilibrium constant, and the mass transfer coefficient on system performance. Comparison of two of the models with available experimental data shows fair agreement, between model and data.     

Growth models of cultures with two liquid phases. IV. Cell adsorption, drop size distribution, and batch growth

In this work, a mathematical model which can be used to describe butch growth in fermentations with two liquid phases present is developed for systems in which the growth limiting substrate is dissolved in the dispersed phase. The model takes into account the drop size distribution, the rate of adsorption of cells on the drop surface, the rate of desorption of cells from the drop surface, substrate transport between phases, phase equilibrium, and growth kinetics. The model also considers the effect, of coalescence and redispersion of oil drops in the system. It is assumed that the composition of the dispersed phase is such that substrate utilization from it causes little or no change in the interfacial area. A discrete uniform distribution and a discrete normal distribution which is obtained from an experimental distribution curve are used as drop size distributions. Simulation results are obtained for a wide range of parameter values using the IBM S/360 Continuous System Modeling Program.     

The kinetics of yeast growth on pure hydrocarbons

The kinetics of C. tropicalis growth were investigated with pure n-hexadecane as dispersed phase substrate. Two distinct growth phases were found: In the first phase, exponential growth was independent of stirrer speed. The onset of the second phase, one of linear growth, was determined by stirrer speed. By the use of two different fermenter types, it was shown that the drop size of the dispersed phase was not primarily responsible for the observed kinetics. It was considered that the formation of biological flocs determined the observed growth pattern. This was substantiated by the results of continuous cultures in the different fermenter types, with various substrate concentrations.     

Activation and inhibition of the calcium-release channel of isolated skeletal muscle heavy sarcoplasmic reticulum. Models of the calcium-release channel.

Calcium-independent calcium efflux from heavy sarcoplasmic reticulum (HSR) of skeletal muscle was found to be biphasic, with half-times of 2-6 s and 200-400 s for the first and second phase, respectively. Calcium-, AMP- and caffeine-induced calcium efflux was triphasic, with half-times of 0.05-0.2 s, 1-5 s and 100-400 s for the first, second and third phases, respectively. This very fast first phase is certainly due to calcium efflux via the calcium-release channel of HSR vesicles. Both ruthenium red and neomycin inhibited the first phase of the calcium-independent calcium efflux and the first phase of the calcium-, AMP- or caffeine-induced calcium efflux completely, whilst the second phase was fully inhibited by ruthenium red only and partially inhibited by neomycin at high concentrations, indicating that the second phase of calcium release also occurs via the calcium-release channel. Various models for calcium efflux through the release channel have been tested by simulation. Activation and inhibition of the channel-mediated calcium efflux from HSR cannot be explained by two states of the calcium-release channel (open or closed), but requires the existence of at least three states. A channel with one open state and two closed states, resulting in a rapid inactivation, is the most simple model compatible with the experimental data. According to this model, activation is assumed to reduce inactivation of the channel, whilst inhibition assumes an acceleration of channel inactivation. This mechanism most likely applies to neomycin. An additional open-blocked state has to be assumed for inhibition by ruthenium red.     

Optimal sex ratios in structured populations

In this paper, we develop a general method to determine evolutionary equilibrium sex ratios and to check evolutionary stability, continuous stability and invadability in exact genetic models with or without dominance. This method is then applied to three kinds of models for structured populations: the first one concerns Hamilton's LMC model, except that only a fraction beta of female offspring mate with male offspring born in the same colonies, while a fraction 1-beta mate with male offspring chosen at random within the whole population; in the second model, it is assumed that partial dispersal of inseminated females occurs after mating; in the third model, partial dispersal of male and female offspring occurs before mating. In the first model, the effect of population regulation is studied while, in the other models, two kinds of dispersal are considered: proportional and uniform.     

Design and physical characteristics of a multistage,continuous tower fermentor

A multistage tower laboratory fermentor has been constructed consisting of eight compartments separated by sieve plates. Flow of substrate and air is concurrent from the bottom to the top of the column. It, was hoped that this system could be used to reproduce, simultaneously on a continuous basis, eight distinct phases of a batch growth curve. It was believed that the extent of batch curve simulation would depend upon the character of hydraulic mean residence time of broth in the column and in the individual compartments. The expected relationship did not occur. Rather it was found that growth in the column involved residence time characteristics not only for the fluid but also for the microorganisms, and for the growth limiting substrate. Depending upon the column operation, these could be distinct and different. The purpose of this investigation was to study the residence time distribution (RTD) of the continous (fluid) and dispersed (microorganisms) phases for model systems as well as for a yeast fermentation. Various degrees of flow nonideality, i.e., fluid blackflow and dispersed phase sedimentation, were noticed. The former seems to be due to interaction of the concurrent gas and liquid flow; it is particularly dependent upon void area of the sieve plate holes. Sedimentation is probably a function of plate design as well as cell size and density. It wa concluded that for a particular plate design the gas hold-up wass controlled by superficial air velocity and was the main parameter governing the differences between dispersed and continous phase(Rt1). This conclusion was supported by a computeraided styudy utilizing a mathematical model of fluid flow to fit the growth kinetics and cell distribution observed experimentally throughout the fermentor. Some advantages of foam control in the tower fermentor by surface active compounds are mentioned. Also, suggestions are made for carrying out fermentations that have two liquid phases, such as a hydrocarbon fermentation. The possibility of closely approximating plug-flow conditions in the multistage tower fermentor, a necessary condition for batch growth simulation, is discussed from a practical point of view.     

RETRODISPLACEMENT OF THE ORAL AND ANAL OPENINGS IN DENDRASTERID SAND DOLLARS

In regular echinoids, the mouth opening (or peristome) and the anal opening (or periproct) are located centrally. In irregular echinoids, the peristome tends to shift toward the anterior end of the test, whereas the periproct typically shifts toward the posterior end. This produces an anatomically polarized morphology, which is consistent with functional expectations. In the dendrasterid sand dollars, however, the peristome and periproct have been displaced in the “wrong” directions; the peristome has shifted posteriorly, whereas the periproct has shifted anteriorly. These movements, which run counter to functional expectations, may be termed “retrodisplacements.” This study presents a new model for the development of the oral surface in dendrasterids. The model assumes that the “Dendraster pattern” of development (which occurs in dendrasterids) was derived from the older “Echinarachnius pattern” (which occurs in other northern Pacific sand dollars). The Echinarachnius pattern includes two successive phases of asymmetric growth: the first phase favors anterior growth, whereas the second phase favors posterior growth. These two phases are normally balanced, and at maturity, the test appears to be symmetrical. But if the second phase of unequal growth were suppressed through a heterochronic change in development, the effects on test development would be profound. On the aboral surface, the predicted effects include posterior displacement of the apical system. On the oral surface, the predicted effects include retrodisplacement of the peristome and periproct, as well as conspicuous changes in ambulacral and interambulacral development. In fact, all of the predicted effects are characteristic features of dendrasterids. The model assumes that the oral and aboral surfaces could be simultaneously affected by the same developmental processes. This assumption is supported by empirical evidence: in dendrasterids, there is a strong correlation between the displacement of the apical system (on the aboral surface) and the displacement of the peristome (on the oral surface). The displacement of the apical system (known as “apical eccentricity”) is regarded as a valuable adaptation, because it facilitates suspension feeding. But if oral and aboral development are linked, then selective pressure for apical eccentricity would simultaneously produce new oral characters as well. Thus, the retrodisplacement of the peristome and periproct in dendrasterids may be related to developmental constraints. These unusual characters may have little or no functional significance.     

Production models for nonlinear stochastic age-structured fisheries

The overriding feature of stock-recruitment data for most fisheries is the amount of variability involved. Previous production models have assumed either an underlying linear stock-recruitment relationship [11] or an equilibrium condition [23]. Here a production model is derived for an age-structured fishery exhibiting nonlinear stochastic recruitment under nonequilibrium conditions. In the first section deterministic age-structured production models are reviewed, and in the next section corresponding random variable models are presented. Equations for the first and second order moments for each age class, for the stock, and for the yield are then derived using two approaches. The first approach assumes that third and order higher moments associated with the noise can be neglected (thus extending the “small noise” approach in [23]). The second approach assumes that the distributions associated with the random variables can be characterized by a particular two parameter distribution. This latter approximation can be applied to systems with “large noise,” and precision will not be lost for situations where the exact form of the distribution, associated with the stock-recruitment data, is unknown. Equations are derived for the solution under equilibrium recruitment and constant harvesting conditions. Detailed expressions are also obtained for the case where the random variables are assumed to satisfy a gamma distribution.     

A simple structured model describing the growth of Streptomyces lividans

The growth of Streptomyces lividans in defined media was modeled using a simple structured growth model. Conventional unstructured models like Monod kinetics, substrate inhibition kinetics, and the logistic equation were also used in an attempt to fit the data, but the results were all unsatisfactory. The main reason for failure in applying simple unstructured models is that they cannot describe the long lag phases sometimes observed during growth of S. lividans. The simple structured growth model was derived along similar principles to cybernetic growth models. This model quite accurately describes the growth of S. lividans. It assumes that the rate of assimilation of a substrate depends on the concentration of a specific key enzyme. This key enzyme is only produced in the presence of the substrate, and it is broken down at a steady rate. An enzyme synthesis allocation variable, w, similar to the cybernetic variable, u, described in cybernetic growth models, is proposed to control enzyme synthesis. Until the key enzyme concentration approaches its maximum level, very little substrate is consumed. And consequently, the lag phase is sustained.     

The adsorption of Thiobacillus ferrooxidans on coal surfaces

The adsorption of Thiobacillus ferrooxidans to coal surfaces has been studied. Adsorption experiments were conducted on coal samples from eight different Eastern coal fields. In all cases the adsorption process was at least 90% complete within the first two minutes following inoculation. The results of these experiments were used to test the validity of two proposed adsorption models. The first model assumes that bacterial adsorption follows second-order irreversible kinetics of the second kind with respect to the concentration of bacteria and substratum surface area in the system. The second model allows for the contribution of reversible adsorption detected in desorption experiments. It was found that the combined reversible-irreversible model more accurately describes the initial stages of adsorption. Rate constants in both models were calculated for each coal sample. The relation of each of these constants to the pyrite concentration in coal is presented and the significance of these relations is discussed.Scanning electron micrographs of inoculated coal samples sho that Thiobacillus ferrooxidans selectively adsorb to exposed pyrite phases dispersed throughout the organic coal matrix. Preferential attachment was also observed along topographical faults in the caol surface. Mercury contact angle measurements on coal indicate that the selective adsorption of Thiobacillus ferrooxidans may be attributable to the lower surface free energy of pyrite relative to the organic coal matrix.     

Effect of the development phase and growth rate of a Shigella sonnei population on the reproduction of homologous bacteriophage

This study showed that the minimum latent period (20 minutes) of the intracellular multiplication of dysentery bacteriophage S-9 in the population of S. sonnei substrate strain under the conditions of static heterogeneous surface batch cultivation was observed at the end of the lag phase and at the growth acceleration phase, in the first and second thirds of the exponential curve, while the maximum latent period (35-40 minutes) was observed at the stationary phase. The maximum yield of phage S-9 from one infected bacterial cell (628.3 +/- 116.8) was registered during the first third of the phase of the exponential growth of the bacterial population and the minimum yield (18.66 +/- 6.6), at the beginning of the lag phase. The significant direct correlation between the specific growth rate of the bacterial population and the yield of the phage from one infected bacterial cell at the end of the lag phase, at the growth acceleration and deceleration phases, as well as the significant inverse correlation between the yield of the phage and the time of the generation of the bacterial population at the growth acceleration phase were established.     

Periodic phenomena in Proteus mirabilis swarm colony development.

Proteus mirabilis colonies exhibit striking geometric regularity. Basic microbiological methods and imaging techniques were used to measure periodic macroscopic events in swarm colony morphogenesis. We distinguished three initial phases (lag phase, first swarming phase, and first consolidation phase) followed by repeating cycles of subsequent swarming plus consolidation phases. Each Proteus swarm colony terrace corresponds to one swarming-plus-consolidation cycle. The duration of the lag phase was dependent upon inoculation density in a way that indicated the operation of both cooperative and inhibitory multicellular effects. On our standard medium, the second and subsequent swarm phases displayed structure in the form of internal waves visible with reflected and dark-field illumination. These internal waves resulted from organization of the migrating bacteria into successively thicker cohorts of swarmer cells. Bacterial growth and motility were independently modified by altering the composition of the growth medium. By varying the glucose concentration in the substrate, it was possible to alter biomass production without greatly affecting the kinetics of colony surface area expansion. By varying the agar concentration in the substrate, initial bacterial biomass production was unaffected but colony expansion dynamics were significantly altered. Higher agar concentrations led to slower, shorter swarm phases and longer consolidation phases. Thus, colony growth was restricted by higher agar concentrations but the overall timing of the swarming-plus-consolidation cycles remained constant. None of a variety of factors which had significant effects on colony expansion altered terracing frequencies at 32 degrees C, but the length of the swarming-plus-consolidation cycle was affected by temperature and medium enrichment. Some clinical isolates displayed significant differences in terracing frequencies at 32 degrees C. Our results defined a number of readily quantifiable parameters in swarm colony development. The data showed no connection between nutrient (glucose) depletion and the onset of different phases in swarm colony morphogenesis. Several observations point to the operation of density-dependent thresholds in controlling the transitions between distinct phases.     

Growth of Leishmania infantum in continuous culture

It has been studied the continuous growth of a Leishmania infantum canine strain from Marseille. The authors used a modified liquid medium with Panmed : foetal calf serum and calf serum. They used a bench to chemistat at 24 degrees C. With an optimum concentration inoculum they obtained a diphasic growth curve with a first exponential phase from the third to the fifth day, in which the average time of generation is 15 hours and 20 minutes, and a second growth phase from the ninth to the eleventh day. It is a--diauxie growth--(according to the J. Monod Theory). If some medium is added on the third day this first exponential growth phase continues up to the eleventh day.     

A kinetic model for microbial growth on liquid hydrocarbons

A kinetic model is presented to explain microbial growth using liquid n-alkanes as substrate. The model is based on the assumption that growth occurs on the soluble alkane and that the metabolite produced by the growing cells helps the dissolution of liquid alkanes in the aqueous medium. Growth curves based on that model fit well with growth data for batch and continuous culture reported by various authors. The model also explains the differences between the relative length of exponential and linear phases of growth reported earlier.     

Mathematical models for estimating fluxes at the sediment-water interface in benthic chamber experiments

Experimental data collected by means of benthic chambers have been used to develop simple mathematical models in order to predict heavy metal and non-metal fluxes at the sediment-water interface. In particular, two mathematical models have been applied to Ba, Co, Fe, Pb, Mn and Cu.Both models estimate benthic fluxes by means of Fick's law but they differ in the modelling of partition between liquid and solid phases. The first model, which is appropriate for Ba and Co, assumes that sorption is the most important process in determining partition. The second model, which gives discrete results for Fe and Pb, assumes that precipitation is the most important process determining the time variation of concentrations. Neither model is suitable to explain experimental data for Mn and Cu.This paper demonstrates the benefit of the use of mathematical models in the interpretation of benthic chambers experiments and in the identification of the relevant processes occurring at the sediment-water interface.     

Metabolic flux model for an anchorage-dependent MDCK cell line: characteristic growth phases and minimum substrate consumption flux distribution

Up to now cell-culture based vaccine production processes only reach low productivities. The reasons are: (i) slow cell growth and (ii) low cell concentrations. To address these shortcomings, a quantitative analysis of the process conditions, especially the cell growth and the metabolic capabilities of the host cell line is required. For this purpose a MDCK cell based influenza vaccine production process was investigated. With a segregated growth model four distinct cell growth phases are distinguished in the batch process. In the first phase the cells attach to the surface of the microcarriers and show low metabolic activity. The second phase is characterized by exponential cell growth. In the third phase, preceded by a change in oxygen consumption, contact inhibition leads to a decrease in cell growth. Finally, the last phase before infection shows no further increase in cell numbers. To gain insight into the metabolic activity during these phases, a detailed metabolic model of MDCK cell was developed based on genome information and experimental analysis. The MDCK model was also used to calculate a theoretical flux distribution representing an optimized cell that only consumes a minimum of carbon sources. Comparing this minimum substrate consumption flux distribution to the fluxes estimated from experiments unveiled high overflow metabolism under the applied process conditions.     

Growth models of cultures with two liquid phases. VI. Parameter estimation and statistical analysis

Parameter estimation studies have been conducted employing mathematical models developed previously by the investigators and experimental data collected by the last author. A batch fermentation process in which Candida lipolytica were cultured on n-hexadecane dissolved in dewaxed gas oil was employed to obtain the experimental data. The kinetic data from a number of batch experiments conducted at different initial substrate concentrations and different dispersed phase volume fractions were analyzed assuming that, the basic model parameters (maximum specific growth rate, saturation constant, substrate phase equilibrium constant, adsorption constant, desorption constant, etc.) did not change from experiment to experiment. The Gauss-Newton method with modification by Greenstadt, Eisenpress, Bard, and Carroll was used to minimize the conventional sum of squares criterion on the IBM 300/50 computer. The individual confidence intervals were obtained for each individual parameter. Tin- models were compared employing the F-test for equality of variances and an analysis of residuals. For the two best models, the estimated parameter values were compared with available experimental information. The results showed good agreement between the experimental data and the values predicted by the mathematical models. The results presented in this work did suggest that growth on small segregated drops may be more important than continuous phase growth on dissolved substrate.     

Oviposition behaviour of the soil mite Pergamasus brevicornis (Acari: Parasitidae)

We observed the oviposition behaviour of the soil mite Pergamasus brevicornis Berlese (Acari: Parasitidae) using continuous video-monitoring. Oviposition consisted of six sequential phases. The first phase (I) involved inspection of the substrate. In the second phase (II) there were rhythmic movements of the first pair of legs and slight reciprocating movements of the body. The third (III) was a resting phase. In the fourth phase (IV) the gnathosoma was lowered and the body was raised. In the next phase (V) there were two sub-phases. During the first (Va), the female held the egg below the gnathosoma. In the second sub-phase (Vb), the gnathosoma moved up holding the egg, which was then placed on the substrate. The last phase (VI) involved intense ‘cleaning’ movements of the chelicerae and palps. During Va a protective external eggshell structure is gradually formed, involving a phase where the egg shell is sticky. After moving the egg to the substrate, the female freed her palps and chelicerae from the sticky egg shell and cleaned her gnathosomal appendages. Phases II–V took on average 207 ± 69 s.     

A whole-plant analysis of the dynamics of expansion of individual leaves of two sunflower hybrids

Common features in the time-course of expansion of leaves which considerably differed in final area, due to phytomer position, growing conditions and genotype, were identified. Leaf development consisted of two phases of exponential growth, followed by a third phase of continuous decrease of the relative expansion rate. The rate and the duration of the first exponential phase were common to all phytomers, growing conditions and genotypes. Leaves differed in the rate and the duration of the second exponential phase. The decrease of the relative expansion rate during the third phase depended on neither genotype nor growing conditions. It was phytomer-dependent and was deduced from the rate of the second phase via a parameter common to all cases studied. Differences in final leaf area among growing conditions were linked to different expansion rates during the second exponential phase. The duration of the phases at any given phytomer position was the same for the two hybrids in different growing conditions. The dates of developmental events (initiation, end of the two exponential phases, full expansion), and the rate of the second exponential phase, were related to phytomer position, defining a strict pattern of leaf development at the whole plant level. Using this framework simplified the analysis of the response of leaf expansion to genotype and environment.