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.     

Growth of yeast on n-alkanes. I. Stochastic model

In a system where yeast cells grow on n-alkanes dissolved in oil drops suspended in water, the dispersed oil phase will, in most cases, be fully segregated. This means that each drop has its own history that depends on its degree of saturation with yeast cells. This degree of saturation with yeast cells is determined by a stochastic process depending on adsorption, desorption, and cell production. Although many authors mention segregation as a phenomenon likely to occur, so far this segregation has hardly been taken into account. In this paper the interaction of the population of completely segregated oil drops with the population of yeast cells, which results in growth, is described. The consequences of the model are elucidated by the discussion of some extreme cases. The batch fermentation of hydrocarbons by yeast cell is simulated by means of a Monte Carlo procedure. Adsorption, desorption, and production of yeast cells are considered as chance processes. The history of all individual drops is recorder. The influence of the chance of desorption appears to be much larger than that of the chance of adsorption (at the investigated range). Also the size of the inoculum at the start of the process appears to have a strong influence on the course of fermentation.     

A dynamic mathematical model for microbial removal of pyritic sulfur from coal

A dynamic mathematical model has been developed to describe microbial desulfurization of coal by Thiobacillus ferrooxidans. The model considers adsorption and desorption of cells on coal particles and microbial oxidation of pyritic sulfur on particle surfaces. The influence of certain parameters, such as microbial growth rate constants, adsorption-descrption constants, pulp density, coal particle size, initial cell and solid phase substrate concentration on the maximum rate of pyritic sulfur removal, have been elucidated. The maximum rate of pyritic sulfur removal was strongly dependent upon the number of attached cells per coal particle. At sufficiently high initial cell concentrations, the surfaces of coal particles are nearly saturated by the cells and the maximum leaching rate is limited either by total external surface area of coal particles or by the concentration of pyritic sulfur in the coal phase. The maximum volumetric rate of pyritic sulfur removal (mg S/h cm(3) mixture) increases with the pulp density of coal and reaches a saturation level at high pulp densities (e.g. 45%). The maximum rate also increases with decreasing particle diameter in a hyperbolic form. Increases in adsorption coefficient or decreases in the desorption coefficient also result in considerable improvements in this rate. The model can be applied to other systems consisting of suspended solid substrate particles in liquid medium with microbial oxidation occurring on the particle surfaces (e.g., bacterial ore leaching). The results obtained from this model are in good agreement with published experimental data on microbial desulfurization of coal and bacterial ore leaching.     

Growth kinetics of microalgae in microfluidic static droplet arrays

We investigated growth kinetics of microalgae, Chlorella vulgaris, in immobilized arrays of nanoliter‐scale microfluidic drops. These static drop arrays enabled simultaneous monitoring of growth of single as well as multiple cells encapsulated in individual droplets. To monitor the growth, individual drop volumes were kept nearly intact for more than a month by controlling the permeation of water in and out of the microfluidic device. The kinetic growth parameters were quantified by counting the increase in the number of cells in each drop over time. In addition to determining the kinetic parameters, the cell‐size distribution of the microalgae was correlated with different stages of the growth. The single‐cell growth kinetics of C. vulgaris showed significant heterogeneity. The specific growth rate ranged from 0.55 to 1.52 day^?1 for different single cells grown in the same microfluidic device. In comparison, the specific growth rate in bulk‐scale experiment was 1.12 day^?1. It was found that the average cell size changes significantly at different stages of the cell growth. The mean cell‐size increased from 5.99 ± 1.08 to 7.33 ± 1.3 µm from exponential to stationary growth phase. In particular, when multiple cells are grown in individual drops, we find that in the stationary growth phase, the cell size increases with the age of cell suggesting enhanced accumulation of fatty acids in older cells. Biotechnol. Bioeng. 2012; 109: 2987–2996. © 2012 Wiley Periodicals, Inc.     

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.     

Growth of yeast on n-alkanes. II. Batch experiments

In this paper the results of the Monte Carlo simulations as described in an earlier paper are compared with those of batch experiments. A number of batch experiments were carried out at a low inoculation rate so that only a fraction of the oil drops were inoculated. Under these conditions the effect of the segregation of the oil phase is more clearly demonstrated. Special attention is paid to the preparation of actively growing yeast cells with which the cultures is inoculated. Also a method is developed to estimate the amount of actively growing cells with which the culture is inoculated. The other parameters necessary for the Monte Carlo simulation are measured in separate experiments: the maximum growth rate of the cells, oil drop size, and the drop parameters. Finally the growth curves (measured in the batch experiments) are compared with those calculated with the Monte Carlo procedure. A good agreement is found.     

Exchange of monooleoylphosphatidylcholine with single egg phosphatidylcholine vesicle membranes.

In a previous paper we described the experiments and the framework of a model for the exchange of monooleoylphosphatidylcholine with a single egg phosphatidylcholine membrane. In the present paper a model is presented that relates the experimentally measured apparent characteristics of the overall kinetics of lysolipid exchange to the true rates of lysolipid exchange and interbilayer transfer. It is shown that the adsorption of the lysolipid follows two pathways: one through the adsorption of lipid monomers and other through the fusion of micelles. The desorption of lysolipid follows a single pathway, namely, the desorption of monomers. The overall rate of fast desorption under convective flow conditions gives the true rate of monomer desorption from the outer membrane monolayer. The overall rate of both slow lysolipid uptake and slow desorption gives the rate of interbilayer transfer. Because of the uneven distribution of lysolipid between the two monolayers during its uptake, one of the membrane monolayers is apparently extended relative to the other. This relative extension of one of the monolayers induces a monolayer tension. The induced monolayer tension can increase up to 7 mN.m-1, when most of the intercalated lysolipid only partitions into the monolayer facing the lysolipid solution. This value is similar to the measured value for the critical monolayer tension of membrane failure, which is on the order of 5 mN.m-1. The similarity of the magnitudes of the induced monolayer tension during monooleoylphosphatidylcholine exchange and the monolayer tension of membrane failure suggests that the interbilayer lipid transfer may be affected by the formation of short living membrane defects. Furthermore, the pH-induced interbilayer exchange of phosphatidylglycerol is considered. In this case, it is shown that the rate of interbilayer transfer is a function of the phosphatidylglycerol concentration in the membrane.     

大孔吸附树脂纯化唐古特白刺红色素的研究

通过静态吸附解析实验,确定了利用大孔吸附树脂初步纯化唐古特白刺红色素的条件,并根据所得条件做了扩大实验。结果表明．X-5树脂的吸附能力最好,吸附率为76．85％,pH在1—3范围内对吸附效果无影响;较高的乙醇浓度和pH值有利于色素的解析,解析液以80％酸化乙醇（含1％HCI）效果最佳,解析时间为40min;扩大实验得到紫红色色素粉末,得率为1．24％,水溶性好,不含糖类、蛋白质等水溶性杂质;树脂通过回收再生可重复利用。本实验为色素产品的开发及白刺果实的综合利用提供了理论依据。     

A stochastic killing system for biological containment of Escherichia coli.

Bacteria with a stochastic conditional lethal containment system have been constructed. The invertible switch promoter located upstream of the fimA gene from Escherichia coli was inserted as expression cassette in front of the lethal gef gene deleted of its own natural promoter. The resulting fusion was placed on a plasmid and transformed to E. coli. The phenotype connected with the presence of such a plasmid was to reduce the population growth rate with increasing significance as the cell growth rate was reduced. In very fast growing cells, there was no measurable effect on growth rate. When a culture of E. coli harboring the plasmid comprising the containment system is left as stationary cells in suspension without nutrients, viability drops exponentially over a period of several days, in contrast to the control cells, which maintain viability nearly unaffected during the same period of time. Similar results were obtained with a strain in which the killing cassette was inserted in the chromosome. In competition with noncontained cells during growth, the contained cells are always outcompeted. Stochastic killing obtained by the fim-gef fusion is at present relevant only as a containment approach for E. coli, but the model may be mimicked in other organisms by using species-specific stochastic expression systems.     

Generality of the growth kinetics of the average individual cell in different bacterial populations.

The kinetics of growth of all the cells in a population is reflected in the shape of the size distribution of the population. To ascertain whether the kinetics of growth of the average individual cell is similar for different strains or growth conditions, we compared the shape of normalized size distributions obtained from steady-state populations. Significant differences in the size distributions were found, but these could be ascribed either to the precision achieved at division or to a constriction period which is long relative to the total cell cycle time. The remaining difference is quite small. Thus, without establishing the pattern itself, it is concluded that the basic course of growth is very similar for the various Escherichia coli strains examined and probably also for other rod-shaped bacteria. The effects of differences in culture technique (batch or chemostat culture), growth rate, and differences among strains were not found to influence the shape of the size distributions and hence the growth kinetics in a direct manner; small differences were found, but only when the precision at division or the fraction of constricted cells (long constriction period) were different as well.     

Predicted steady-state cell size distributions for various growth models

The question of how an individual bacterial cell grows during its life cycle remains controversial. In 1962 Collins and Richmond derived a very general expression relating the size distributions of newborn, dividing and extant cells in steady-state growth and their growth rate; it represents the most powerful framework currently available for the analysis of bacterial growth kinetics. The Collins-Richmond equation is in effect a statement of the conservation of cell numbers for populations in steady-state exponential growth. It has usually been used to calculate the growth rate from a measured cell size distribution under various assumptions regarding the dividing and newborn cell distributions, but can also be applied in reverse--to compute the theoretical cell size distribution from a specified growth law. This has the advantage that it is not limited to models in which growth rate is a deterministic function of cell size, such as in simple exponential or linear growth, but permits evaluation of far more sophisticated hypotheses. Here we employed this reverse approach to obtain theoretical cell size distributions for two exponential and six linear growth models. The former differ as to whether there exists in each cell a minimal size that does not contribute to growth, the latter as to when the presumptive doubling of the growth rate takes place: in the linear age models, it is taken to occur at a particular cell age, at a fixed time prior to division, or at division itself; in the linear size models, the growth rate is considered to double with a constant probability from cell birth, with a constant probability but only after the cell has reached a minimal size, or after the minimal size has been attained but with a probability that increases linearly with cell size. Each model contains a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. In the present article, the various growth laws are described and rigorous mathematical expressions developed to predict the size distribution of extant cells in steady-state exponential growth; in the following paper, these predictions are tested against high-quality experimental data.     

Electrostatic and hydrophobic effects in affinity chromatography

A semi–quantitative theory is developed to explain the nonspecific binding of proteins to substituted affinity chromatography supports due to electrostatic and hydrophobic interactions. The equilibrium constant for the absorption of an enzyme to a solid support, and the rate of desorption of the enzyme are studied as functions of ionic strength. Experimental measurements were taken of the adsorption equilibrium constant and rate of desorption of E. coli β–galactosidase on Sepharose 4B substituted with 3, 3,-diaminodipropylamine in batch systems. It was found that the enzyme adsorption exhibits a hysteresis effect as the ionic strength is increased and then decreased. Furthermore, the adsorption of theenzyme becomes more reversible at the lower ionic strengths, while at the higher ionic strengths it is essentially irreversible. Using the measured equilibrium constants, and knowing the region of ionic strength where the adsorption becomes reversible, we were able to predict the desorption of enzyme in a continuous stirred tank as a function of time when a decreasing linear gradient of ionic strength was introduced into a slurry. It was found that the presence of another protein, hemoglobin, does not affect these results, and therefore can be separated from the enzyme.     

Quantitative study of sensitive and lysogenic bacteria surviving infection of aStaphylococcus by a temperate bacteriophage

Infection of a culture ofStaphylococcus aureus by a phage left more surviving colony-forming, sensitive bacteria than might be expected from the calculation of P_o according to the Poisson distribution. The discrepancy could at least partly be explained by the heterogeneity in surface area of the colony-forming units before infection. The ratio lysogens/lysed cells shows a tendency to decrease when multiplicity is increased from 6 to 130.The experiments stress the influence of the bacterial density on the adsorption rate constant of the bacteriophage.Single step growth curve experiments gave low burst size values. The latent period was about 30 min. The stationary period began 45 to 50 min after infection.     

A model of drop size distribution for a system with evaporation

Abstract. The size and shape of drops on leaf surfaces strongly affect their persistence. The relationship between volume and exposed surface area of drops on wheat leaves and the log-normal drop size distribution in a wheat canopy after rain are used to derive equations to describe how the total volume and drop number change with evaporation. Firstly, the behaviour of a single drop as it evaporates is considered and then equations describing the change in a population of drops with an initial log-normal distribution are derived. The time taken for all the drops to reach complete dryness is about thirty times that for the same volume of water spread uniformly over the surface with the same potential evaporation rate.     

The biophysics of DNA hybridization with immobilized oligonucleotide probes.

A mathematical model based on receptor-ligand interactions at a cell surface has been modified and further developed to represent heterogeneous DNA-DNA hybridization on a solid surface. The immobilized DNA molecules with known sequences are called probes, and the DNA molecules in solution with unknown sequences are called targets in this model. Capture of the perfectly complementary target is modeled as a combined reaction-diffusion limited irreversible reaction. In the model, there are two different mechanisms by which targets can hybridize with the complementary probes: direct hybridization from the solution and hybridization by molecules that adsorb nonspecifically and then surface diffuse to the probe. The results indicate that nonspecific adsorption of single-stranded DNA on the surface and subsequent two-dimensional diffusion can significantly enhance the overall reaction rate. Heterogeneous hybridization depends strongly on the rate constants for DNA adsorption/desorption in the non-probe-covered regions of the surface, the two-dimensional (2D) diffusion coefficient, and the size of probes and targets. The model shows that the overall kinetics of DNA hybridization to DNA on a solid support may be an extremely efficient process for physically realistic 2D diffusion coefficients, target concentrations, and surface probe densities. The implication for design and operation of a DNA hybridization surface is that there is an optimal surface probe density when 2D diffusion occurs; values above that optimum do not increase the capture rate. Our model predicts capture rates in agreement with those from recent experimental literature. The results of our analysis predict that several things can be done to improve heterogeneous hybridization: 1) the solution phase target molecules should be about 100 bases or less in size to speed solution-phase and surface diffusion; 2) conditions should be created such that reversible adsorption and two-dimensional diffusion occur in the surface regions between DNA probe molecules; 3) provided that 2) is satisfied, one can achieve results with a sparse probe coverage that are equal to or better than those obtained with a surface totally covered with DNA probes.     

Longitudinal study of adipose cell size in the dorsoscapular and perirenal depots of the growing rabbit

The changes in fat cell size during normal growth of New Zealand rabbits were investigated longitudinally with serial dorsoscapular and perirenal fat biopsies. A remarkably complex pattern of changes appeared when individual evolutions were considered. About 50% of the rabbits were characterized by "significant drops" of mean diameter during fat tissue growth with shifting of distributions toward the smaller cells. These "drops" could not be attributed to regional variation observed within each depot or to growth or food intake disorders. Differences in behavior of perirenal and dorsoscapular depots were noted. The "drops" occurred earlier in perirenal than in dorsoscapular depots. The meaning of these "drops" remains unclear, but the results suggest that they may be due to a discontinuous recruitment of new observable cells. These results are discussed in relation to the hypothesis of a "critical size" of adipocytes.     

An explicit representation of the Luria–Delbrück distribution

The probability distribution of the number of mutant cells in a growing single-cell population is presented in explicit form. We use a discrete model for mutation and population growth which in the limit of large cell numbers and small mutation rates reduces to certain classical models of the Luria-Delbrück distribution. Our results hold for arbitrarily large values of the mutation rate and for cell populations of arbitrary size. We discuss the influence of cell death on fluctuation experiments and investigate a version of our model that accounts for the possibility that both daughter cells of a non-mutant cell might be mutants. An algorithm is presented for the quick calculation of the distribution. Then, we focus on the derivation of two essentially different limit laws, the first of which applies if the population size tends to infinity while the mutation rate tends to zero such that the product of mutation rate times population size converges. The second limit law emerges after a suitable rescaling of the distribution of non-mutant cells in the population and applies if the product of mutation rate times population size tends to infinity. We discuss the distribution of mutation events for arbitrary values of the mutation rate and cell populations of arbitrary size, and, finally, consider limit laws for this distribution with respect to the behavior of the product of mutation rate times population size. Thus, the present paper substantially extends results due to Lea and Coulson (1949), Bartlett (1955), Stewart et al. (1990), and others.     

Reaction rate enhancement by surface diffusion of adsorbates.

Ligands can be captured by a surface target through either direct bulk diffusion or surface diffusion following reversible adsorption to the surface. We have solved a steady state boundary value problem for a perfect sink disk target in the surface, taking into account bulk and surface diffusion coefficients D and Ds and adsorption/desorption kinetic rate constants ka and kd at non-target regions. Solutions have been successfully found by numerical computation. The results show that the rate of capture from the surface depends non-linearly on Ds, D, ka, kd and geometrical dimensions. In particular, we demonstrate that not only is the non-target region equilibrium constant Keq (= ka/kd) important in determining the rate of capture from the surface, but so are the kinetic rate constants ka and kd separately. In all cases, the surface adsorption/diffusion combination enhances the total rate of capture. The results should be useful for predicting reaction rates of biological membrane bound receptor clusters and substrate-immobilized enzymes.     

光皮桦群落邻体干扰指数的研究

影响植物个体生长的因素很多 ,这其中不仅有其自身的遗传特性在起作用 ,而且与其所处的生境立地质量以及它对环境资源的利用状况也有着密切地内在联系。生境在影响植物生长的同时 ,植物的生命活动及生长过程也在不断地影响和改变着环境条件 ,使其朝着有利于或不利于邻体生长的方向发展。生物与环境之间这种相互作用、相互影响 ,就是生态学领域里的邻体干扰。本文通过对福建卫闽光皮桦 (Ｂｅｔｕｌａｌｕｍｉｎｉｆｅｒａ)群落邻体干扰指数的研究 ,分析了邻体干扰指数与光皮桦生长速度间的相互联系 ,揭示了光皮桦个体大小与邻体干扰指数和生…     

Glycoprotein gIII of pseudorabies virus is multifunctional.

One of the major glycoproteins of pseudorabies virus, gIII, is nonessential for growth in cell culture. Mutants defective in gIII, however, consistently yield lower titers of infectious virus (3- to 20-fold) than does wild-type virus. The interactions of gIII- mutants with their host cells were compared with those of wild-type virus in an attempt to uncover the functions of gIII. We show that gIII plays a major role in the stable adsorption of the virus to its host cell; in the absence of gIII, the rate of adsorption is reduced and adsorption is easily reversed by washing. Thus, adsorption of pseudorabies virus can be said to occur in at least the following two ways: (i) a gIII-mediated rapid adsorption or (ii) a slower and more labile adsorption that is independent of gIII. After virions have been complexed with monoclonal antibodies against gIII (but not some monoclonal antibodies against other glycoproteins), both modes of adsorption were inhibited. Glycoprotein gIII affects virus stability and virus release, as well as adsorption. The effect on virus release is marked when the virus is defective in additional functions. Thus, although we found no obvious difference in the release of virus from gIII- or wild-type virus-infected rabbit kidney cells, release of a gIII-/gI- double mutant from the cells occurred less readily than did release of a gI- mutant. The gIII-/gI- and gIII- mutants, however, adsorbed to cells at a similar rate, indicating that the effects of gIII on adsorption and virus release constitute separate functions. The Bartha vaccine strain of pseudorabies virus has a defective gIII gene and is released poorly from rabbit kidney cells. After the resident Bartha gIII gene was replaced by the gIII gene of wild-type virus, virus release was enhanced considerably. Since inactivation of gIII in wild-type pseudorabies virus did not significantly affect virus release, the Bartha strain must be defective in another function which, in conjunction with gIII, significantly affects virus release. These results indicate again that gIII affects virus release in conjunction with other functions. Also, although the Bartha strain was functionally defective in virus release, it adsorbed to cells as well as wild-type virus did, showing that the effects of gIII on virus adsorption and release constitute separate functions. We conclude that gIII is a multifunctional glycoprotein.