Population dynamics of a recombinant culture in a chemostat under prolonged cultivation

The dynamics of a chemostat culture of Escherichia coli K12 harboring plasmid pBR322 under prolonged cultivation with a nonselective complex medium were studied. The ability of the culture to form colonies on plates supplemented with different ampicillin concentrations was monitored. It was observed that almost all cells sampled were able to grow on a high concentration of ampicillin at the beginning of the experiment. However, a subpopulation which formed colonies on intermediate-concentration (500-1000 mg/L) plates, but not on a high-concentration (2000 mg/L) plate, was detected just before the appearance of the plasmid-free cells. As time progressed, the percentage of this subpopulation increased, reached a maximum, then decreased toward the end of experiment. At this time the culture was dominated by a subpopulation which could not form colonies on the 100 mg/L ampicillin plates. These results indicate that three major processes may occur in the chemostat: a gradual shift of the higher plasmid copy number population toward a relatively lower copy number population; the complete shedding of the plasmid due to faulty segregation of plasmids during cell division; and growth competition among the subpopulations. A previously derived model is extended to account for all subpopulations. The model agrees qualitatively with the experimental results.     

The impact of population dynamics on Y-chromosome microsatellite polymorphism. Mathematical modeling

In this article, we use mathematical modeling to study the impact of population dynamics on Y-chromosome STR-polymorphism accumulation in two independently evolving populations, namely, on the changes in genetic distance between the populations. Comparative analysis using two definitions of genetic distance—(δμ)² and ASD—shows that, in contrast to (δμ)², ASD is almost linearly dependent on time (except for sparse stationary populations, where deviations are observed). When the population numbers undergo oscillations, ASD proves to be smaller than that for stationary populations.     

Mathematical modeling of the population dynamics of a distinct interactions type system with local dispersal

Distinct biotic interactions in multi-species communities are a ubiquitous force in the natural ecosystem, and this force is an essential determinant of community stability and species coexistence outcomes. We conduct numerical simulations and bifurcation analysis of partial differential equations to gain better understanding and ecological insights into how predation (a), predator handling time (h), and local dispersal affect multi-species community dynamics. This system consists of resource-mutualist-exploiter-competitor interactions and local dispersal. From the inspection of our numerical simulations and co-dimension one bifurcation analysis findings, we discover several critical values that correspond to transcritical bifurcation, subcritical and supercritical Hopf bifurcations. This occurs as we vary the bifurcation parameters a and h in this complex ecological system under symmetric and asymmetric dispersal scenarios. Furthermore, the interplay between these local bifurcation points results in an exciting co-dimension two bifurcations, i.e., Bogdanov-Takens and cusp bifurcation points, respectively, which act as the synchronization points in this complex ecological system. From an ecological viewpoint, we find that (i) the effect of the no-dispersal scenario supports the maintenance of species biodiversity when the predation strength is moderate; (ii) symmetric dispersal induces both subcritical and supercritical Hopf bifurcation and support species diversity for moderate predation strength; and (iii) asymmetric dispersal promotes species diversity as it simplifies the bifurcation changes in dynamics by eliminating the subcritical bifurcations that trigger uncertainty, and this dispersal mechanism mediates species coexistence outcomes. Fundamentally, stable limit cycles have been reported as predator handling time varies in some ecological models; however, we observed in our bifurcation analysis the emergence of the unstable limit cycle as predator handling time changes. We discover that intense predator handling time destabilizes this complex ecological community. In general, our results demonstrate the influential roles of predation, predator handling time, and local dispersal in determining this system’s coexistence dynamics. This knowledge provides a better understanding of species conservation and biological control management.     

The impact of population dynamics on Y-chromosome microsatellite Polymorphism. Mathematical modeling

In this article, we use mathematical modeling to study the impact of population dynamics on Y-chromosome STR-polymorphism accumulation in two independently evolving populations, namely, on the changes in genetic distance among the populations. Using two definitions of the genetic distance: (deltamu)2 and ASD, we carry out comparative research on the genetic distance changes and show that in contrast to (deltamu)2, ASD is characterized by a near-linear dependence on time. As the populations undergo oscillations, ASD is shown to be smaller than that in stationary populations. The linear dependence of ASD on time is shown to break down in relatively scanty stationary populations.     

Circadian rhythmicity during prolonged chemostat cultivation of Neurospora crassa

Following exposure to light and attainment of steady-state in the chemostat, Neurospora was grown in constant conditions of darkness at 25 degrees C for 6 days. Biomass samples were taken every 4h for the extraction of RNA and protein, and the state of the circadian clock was assessed by assaying the levels of three rhythmically expressed mRNAs; frequency (frq), antisense frq (qrf) and clock-controlled gene-14 (ccg-14), and by monitoring the clock-controlled rhythm of sporulation. Our results indicate that the Neurospora clock continued to run in the chemostat. This is the longest reported time that Neurospora has been grown in a chemostat in filamentous form and opens up the possibility of studying the response of Neurospora to a range of stimuli in the absence of confounding effects due to; alterations in growth rate, aging, and changing conditions of the growth medium.     

Stability and expression of a plasmid-containing killer toxin cDNA in batch and chemostat cultures of saccharomyces cerevisiae

A chimeric plasmid (pYT760-ADH1) containing the yeast killer toxin-immunity cDNA was transformed into a leucine-histidine mutant (AH22) and into four industrial toxin-sensitive yeasts. The chimeric plasmid was very stable and expressed toxin production (89.5 +/- 4.8% killer cells) in two of the transformed yeasts that contained the 2mu plasmid, but was lost within 10 generations from two other transformed pickle yeasts that did not contain the 2mu plasmid. It suggested that plasmid stability was dependent on the presence of the 2mu plasmid which is naturally present in some yeasts. The plasmid was extremely stable (100% killer cells) and expressed more toxin in the mutant strain AH22. The effects of dilution rate, D(h(-1)) on plasmid stability and toxin expression were studied in transformed AH22 (AH22/T3) and Montrachet 522 (522/T1) wine yeast grown in glucose-limited chemostat cultures. The results show that killer toxin production by AH22/T3 cells increased as a function of D(h(-1)) and that plasmid stability reached 100% at D >/= 0.09 +/- 0.01 h(-1). However, with Montrachet 522/T1 transformed cells, 100% plasmid stability was seen at D >/= 0.18 +/- 0.02. h(-1). We also challenged the AH22/T3 in chemostat culture (D = 0.25 h(-1)) with an equal number of untransformed cells (AH22). Transformed cells dominated the population (100%) within 8-10 h of growth, a time equivalent to two mean residence time.     

Persistence of bacteria and phages in a chemostat

The model of bacteriophage predation on bacteria in a chemostat formulated by Levin et al. (Am Nat 111:3–24, 1977) is generalized to include a distributed latent period, distributed viral progeny release from infected bacteria, unproductive adsorption of phages to infected cells, and possible nutrient uptake by infected cells. Indeed, two formulations of the model are given: a system of delay differential equations with infinite delay, and a more general infection-age model that leads to a system of integro-differential equations. It is shown that the bacteria persist, and sharp conditions for persistence and extinction of phages are determined by the reproductive ratio for phage relative to the phage-free equilibrium. A novel feature of our analysis is the use of the Laplace transform.     

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.     

Mathematical modeling of viral infection dynamics in spherical organs

A general mathematical model of viral infections inside a spherical organ is presented. Transported quantities are used to represent external cells or viral particles that penetrate the organ surface to either promote or combat the infection. A diffusion mechanism is considered for the migration of transported quantities to the organ inner tissue. Cases that include the effect of penetration, diffusion and proliferation of immune system cells, the generation of latently infected cells and the delivery of antiviral treatment are analyzed. Different antiviral mechanisms are modeled in the context of spatial variation. Equilibrium conditions are also calculated to determine the radial profile after the infection progresses and antiviral therapy is delivered for a long period of time. The dynamic and equilibrium solutions obtained in this paper provide insight into the temporal and spatial evolution of viral infections.     

Generalized modeling of ecological population dynamics

Over the past 7 years, several authors have used the approach of generalized modeling to study the dynamics of food chains and food webs. Generalized models come close to the efficiency of random matrix models, while being as directly interpretable as conventional differential-equation-based models. Here, we present a pedagogical introduction to the approach of generalized modeling. This introduction places more emphasis on the underlying concepts of generalized modeling than previous publications. Moreover, we propose a shortcut that can significantly accelerate the formulation of generalized models and introduce an iterative procedure that can be used to refine existing generalized models by integrating new biological insights.     

Experimental and mathematical modeling of population dynamics of rhizospheric bacteria under conditions of cadmium stress

The method of membrane filters was used to study the population dynamics of bacteria belonging to the genera Arthrobacter, Flavobacterium, and Klebsiella in barley (Hordeum vulgare) rhizosphere under conditions of cadmium stress (5-15 mg Cd/g soil). Mathematical modeling allowed us to demonstrate that the phytoprotective effect is implemented via the following succession of events: the bacteria synthesize phytohormones (IAA and ethylene)-->root excretory activity increases-->the number of the bacteria in the rhizoplane grows-->the flux of bacteria migrating from the rhizoplane to the rhizosphere increases-->the number of bacteria binding cadmium ions in the rhizosphere grows-->the amount of free ions entering the plant decreases. Among the bacteria studied, K. mobilis 880 displayed the highest migration and immobilization activity and the best survival rate under conditions of cadmium stress. Consequently, K. mobilis 880 is recommended for use in biopreparations for stimulating plant growth under conditions of heavy metal pollution.     

A study of long-term effects on plasmid-containing Escherichia coli in carbon-limited chemostat using 2D-fluorescence spectrofluorimetry

Strain stability of plasmid-containing recombinant organisms is clearly important for industrial applications. Stability is normally assessed by methods such as selective colony forming units or by simply measuring the recombinant product. These methods are typically performed off-line, are time-consuming, and do not give detailed information on the changes in the metabolism. In the current work, long-term stability of a plasmid-containing strain of Escherichia coli (W3110.shik1) capable of shikimic acid overproduction was studied by means of a 2D-fluorescence sensor (BioView) able to emit and detect light in ranges of 260-560 nm and 300-600 nm, respectively. Long-term carbon-limited chemostat experiments were made under both selective (tetracycline-containing medium) and nonselective conditions. It is shown that the fluorescence spectra provide information about metabolic changes at an earlier stage, thereby giving a noninvasive method for monitoring of strain stability. Further, the fluorescence measurements showed that (i) the metabolic changes in the strain W3110.shik1 with time were qualitatively different in selective and nonselective environment, (ii) plasmid recombination resulted primarily in increased biomass yield, and (iii) a change in metabolism probably involving FAD/FMN and pyridoxal-5-P occurred in all experiments. It was concluded that the strain was not stable in any growth condition for more than about 25 growth generations and even less if plasmid recombination took place.     

Acidogenic fermentation of pectin by a mixed population of bacteria in continuous culture

Summary Pectin, dissolved in a mineral salts solution, was degraded anaerobically by a mixed population of bacteria in chemostat cultures (pH=6, T=30°C). At a dilution rate of 0.3 h^–1, the specific volume activity was 45.7 (g substrate). (l reactor)^–1.d^–1.     

Mathematical modeling and analysis of meningococcal meningitis transmission dynamics

Meningococcal meningitis(MCM)is one of the serious public health threats in the tropical and sub-tropical regions.In this paper,we propose an epidemic model to study the transmission dynamics of MCM with high-and low-risk susceptible populations.The model considers two different groups of susceptible individuals depending on the availability of medical resources(MR,including hospitals,health workers,etc.),which varies the infection risk.We find that the model exhibits the phenomenon of backward bifurcation(BB),which increases the difficulty of MCM control since the dynamics are not merely relying on the basic reproduction number,TZo.This study explores the effects of MR on the MCM epidemics by mathematical analysis and shows the existence of BB on MCM disease.Our findings suggest that providing adequate MR in a community is crucial in mitigating MCM incidences and deaths,especially,in the MCM endemic regions.