Bacteriophage and Bacteria in a Flow Reactor

The Levin-Stewart model of bacteriophage predation of bacteria in a chemostat is modified for a flow reactor in which bacteria are motile, phage diffuse, and advection brings fresh nutrient and removes medium, cells and phage. A fixed latent period for phage results in a system of delayed reaction-diffusion equations with non-local nonlinearities. Basic reproductive numbers are obtained for bacteria and for phage which predict survival of each in the bio-reactor. These are expressed in terms of physical and biological parameters. Persistence and extinction results are obtained for both bacteria and phage. Numerical simulations are in general agreement with those for the chemostat model.     

A theoretical and empirical investigation of delayed growth response in the continuous culture of bacteria

When the growth of bacteria in a chemostat is controlled by limiting the supply of a single essential nutrient, the growth rate is affected both by the concentration of this nutrient in the culture medium and by the amount of time that it takes for the chemical and physiological processes that result in the production of new biomass. Thus, although the uptake of nutrient by cells is an essentially instantaneous process, the addition of new biomass is delayed by the amount of time that it takes to metabolize the nutrient. Mathematical models that incorporate this "delayed growth response" (DGR) phenomenon have been developed and analysed. However, because they are formulated in terms of parameters that are difficult to measure directly, these models are of limited value to experimentalists. In this paper, we introduce a DGR model that is formulated in terms of measurable parameters. In addition, we provide for this model a complete set of criteria for determining persistence versus extinction of the bacterial culture in the chemostat. Specifically, we show that DGR plays a role in determining persistence versus extinction only under certain ranges of chemostat operating parameters. It is also shown, however, that DGR plays a role in determining the steady-state nutrient and bacteria concentrations in all instances of persistence. The steady state and transient behavior of solutions of our model is found to be in agreement with data that we obtained in growing Escherichia coli 23716 in a chemostat with glucose as a limiting nutrient. One of the theoretical predictions of our model that does not occur in other DGR models is that under certain conditions a large delay in growth response might actually have a positive effect on the bacteria's ability to persist.     

CHARACTERISTICS OF A STAPHYLOCOCCAL PHAGE CAPABLE OF TRANSDUCTION.

Morse, M. L. (University of Colorado Medical Center, Denver) and J. W. LaBelle. Characteristics of a staphylococcal phage capable of transduction. J. Bacteriol. 83:775-780. 1962-The growth of staphylococcal phage 53, a temperate phage, has been studied. The latent periods in nutrient broth are: infected sensitive cells, 45 min; ultraviolet-induced lysogenic cells, 83 min. The burst size, as indicated by one-step growth studies and single-burst experiments, is 25 to 30 particles per lysing cell. Phage particles transducing streptomycin resistance and novobiocin resistance are produced at the same time as nontransducing particles. Some observations have been made on the host, Staphylococcus aureus NCTC 8511.     

Population Dynamics of a Salmonella Lytic Phage and Its Host: Implications of the Host Bacterial Growth Rate in Modelling

The prevalence and impact of bacteriophages in the ecology of bacterial communities coupled with their ability to control pathogens turn essential to understand and predict the dynamics between phage and bacteria populations. To achieve this knowledge it is essential to develop mathematical models able to explain and simulate the population dynamics of phage and bacteria. We have developed an unstructured mathematical model using delay-differential equations to predict the interactions between a broad-host-range Salmonella phage and its pathogenic host. The model takes into consideration the main biological parameters that rule phage-bacteria interactions likewise the adsorption rate, latent period, burst size, bacterial growth rate, and substrate uptake rate, among others. The experimental validation of the model was performed with data from phage-interaction studies in a 5 L bioreactor. The key and innovative aspect of the model was the introduction of variations in the latent period and adsorption rate values that are considered as constants in previous developed models. By modelling the latent period as a normal distribution of values and the adsorption rate as a function of the bacterial growth rate it was possible to accurately predict the behaviour of the phage-bacteria population. The model was shown to predict simulated data with a good agreement with the experimental observations and explains how a lytic phage and its host bacteria are able to coexist.     

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.     

Dynamical types of bacteria and bacteriophages interaction: shielding by debris

The dynamics of the bacteria and bacteriophages interaction process was explored in depth, and laid on a firm basis through simulation and analysis. A modified Campbell model of phage-bacteria interaction was used to simulate three interacting species: bacteria, phages and bacterial debris, and their time behavior in terms of three parameters, in selected range values: the phages burst size (β), the dissolution rate of the bacterial debris (q), and the lysing time delay (τ). Six types of dynamical behavior were identified, occupying various zones in the two-dimensional (2D) plane (q, β) for several values of τ, allowing the determination of the region where shielding by bacterial debris is in effect. The problem of the occurrence of stability transitions between stable and unstable dynamical regimes was also addressed analytically, and compared with simulation results.     

Bacteriophages of methanotrophs isolated from fish.

Bacteriophages of methanotrophic bacteria were isolated from 67 fish. Only two phages isolated from two fish species specifically lysed Methylocystis sp. and Flavobacterium gasotypicum. The phages lysing these species were designated 63-F and CMF-1-F, respectively. The isolated phages differed greatly in the fine structure of the virion, plaque morphology, spectrum of lytic action, serological properties, and UV sensitivity. At the same time, they had identical one-step growth characteristics: their latent period equalled 5 h, lysis time was 3 to 4 h, and burst size was about 240 virions. The phages had guanine- and cytosine-rich double-stranded DNAs consisting of common nitrogen bases. The molecular masses of the DNAs as determined by the sums of restriction endonuclease cleavage fragments were 28 X 10(6) daltons for phage 63-F and 31 X 10(6) daltons for phage CMF-1-F.     

Bacteriophages of methanotrophs isolated from fish

Bacteriophages of methanotrophic bacteria were isolated from 67 fish. Only two phages isolated from two fish species specifically lysed Methylocystis sp. and Flavobacterium gasotypicum. The phages lysing these species were designated 63-F and CMF-1-F, respectively. The isolated phages differed greatly in the fine structure of the virion, plaque morphology, spectrum of lytic action, serological properties, and UV sensitivity. At the same time, they had identical one-step growth characteristics: their latent period equalled 5 h, lysis time was 3 to 4 h, and burst size was about 240 virions. The phages had guanine- and cytosine-rich double-stranded DNAs consisting of common nitrogen bases. The molecular masses of the DNAs as determined by the sums of restriction endonuclease cleavage fragments were 28 X 10(6) daltons for phage 63-F and 31 X 10(6) daltons for phage CMF-1-F.     

Experimental Examination of Bacteriophage Latent-Period Evolution as a Response to Bacterial Availability

For obligately lytic bacteriophage (phage) a trade-off exists between fecundity (burst size) and latent period (a component of generation time). This trade-off occurs because release of phage progeny from infected bacteria coincides with destruction of the machinery necessary to produce more phage progeny. Here we employ phage mutants to explore issues of phage latent-period evolution as a function of the density of phage-susceptible bacteria. Theory suggests that higher bacterial densities should select for shorter phage latent periods. Consistently, we have found that higher host densities (≥~10⁷ bacteria/ml) can enrich stocks of phage RB69 for variants that display shorter latent periods than the wild type. One such variant, dubbed sta5, displays a latent period that is ~70 to 80% of that of the wild type—which is nearly as short as the RB69 eclipse period—and which has a corresponding burst size that is ~30% of that of the wild type. We show that at higher host densities (≥~10⁷ bacteria/ml) the sta5 phage can outcompete the RB69 wild type, though only under conditions of direct (same-culture) competition. We interpret this advantage as corresponding to slightly faster sta5 population growth, resulting in multifold increases in mutant frequency during same-culture growth. The sta5 advantage is lost, however, given indirect (different-culture) competition between the wild type and mutant or given same-culture competition but at lower densities of phage-susceptible bacteria (≤~10⁶ bacteria/ml). From these observations we suggest that phage displaying very short latent periods may be viewed as specialists for propagation when bacteria within cultures are highly prevalent and transmission between cultures is easily accomplished.     

Dynamics of a Producer–Grazer Model Incorporating the Effects of Excess Food Nutrient Content on Grazer’s Growth

Modeling under the framework of ecological stoichiometric allows the investigation of the effects of food quality on food web population dynamics. Recent discoveries in ecological stoichiometry suggest that grazer dynamics are affected by insufficient food nutrient content (low phosphorus (P)/carbon (C) ratio) as well as excess food nutrient content (high P:C). This phenomenon is known as the “stoichiometric knife edge.” While previous models have captured this phenomenon, they do not explicitly track P in the producer or in the media that supports the producer, which brings questions to the validity of their predictions. Here, we extend a Lotka–Volterra-type stoichiometric model by mechanistically deriving and tracking P in the producer and free P in the environment in order to investigate the growth response of Daphnia to algae of varying P:C ratios. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, lead to quantitative different predictions than previous models that neglect to track free nutrients. The full model shows that the fate of the grazer population can be very sensitive to excess nutrient concentrations. Dynamical free nutrient pool seems to induce extreme grazer population density changes when total nutrient is in an intermediate range.     

裂解或溶源-细菌遭遇噬菌体后的命运抉择

噬菌体是地球上数量最丰富的有机体,其在自然生态系统的塑造和细菌进化驱动中发挥着至关重要的作用。在与宿主的相互斗争中,噬菌体可以选择以下2种方式决定其与宿主的命运:(1)裂解:通过裂解宿主细胞最终大量释放噬菌体颗粒;(2)溶源:将其染色体整合到宿主细胞基因组中,与宿主建立一种潜在的互存关系。对于一些温和的噬菌体,这种倾向进一步受到感染多样性的调节,其中单一感染主要是裂解性的,而多重感染则多是溶源性的。溶源性的噬菌体不仅可以根据外界环境的理化因子,还可以通过细菌自身的群体感应系统来启动裂解-溶源开关,进而决定其宿主菌的命运。与此同时,宿主细菌在与噬菌体长时间的斗争中也进化出了针对噬菌体的手段。总而言之,噬菌体深刻影响着细菌的群落动态、基因组进化和生态系统等,而这一切都取决于噬菌体与宿主间的斗争模式(裂解/溶源性感染)。本文探讨了导致温和噬菌体对宿主菌进行裂解-溶源命运抉择的影响因素并系统性总结了细菌在面对噬菌体侵染时的应对策略的最新研究进展,以期能为噬菌体与宿主的研究提供建议和帮助。     

Effects of multiple timescales of resource supply on the maintenance of species and functional diversity

It is well known that variable resource supply can allow competitors to coexist on a single limiting resource, and this is one mechanism that may explain the maintenance of diversity in paradoxically speciose communities. Ecosystems experience fluctuations in resource supply on a range of timescales, but we have a poor understanding of how multiple frequencies of resource supply affect the maintenance of diversity and community structure. Here we explore this question using a model of phytoplankton competition for a limiting nutrient, parameterized using empirical tradeoffs between rapid growth, nutrient storage capacity and nutrient uptake affinity. Compared to a single frequency of nutrient supply, we find that multiple frequencies of nutrient supply increase functional diversity, by permitting the coexistence of strategies adapted to different frequencies of supply. Species richness is also promoted by multiple modes of nutrient supply, but not as consistently as functional diversity. Although this model is parameterized for phytoplankton, the fundamental dynamics and tradeoffs likely occur in a variety of ecosystems. Our results suggest that the spectrum of temporal variation driving communities should be further investigated in the context of the maintenance of diversity and the functional composition of communities under different environmental regimes.     

The intracellular growth of bacteriophages. I. Liberation of intracellular bacteriophage T4 by premature lysis with another phage or with cyanide

A method is described for liberating and estimating intracellular bacteriophage at any stage during the latent period by arresting phage growth and inducing premature lysis of the infected cells. This is brought about by placing the infected bacteria into the growth medium supplemented with 0.01 M cyanide and with a high titer T6 lysate. It was found in some of the later experiments that the T6 lysate is essential only during the first half of the latent period. Cyanide alone will induce lysis during the latter part of the latent period. Using this method on T4-infected bacteria it is found that during the first half of the latent period no phage particles, not even those originally infecting the bacteria, are recovered. This result is in agreement with the gradually emerging concept that a profound alteration of the infecting phage particle takes place before reproduction ensues. During the second half of the latent period mature phage is found to accumulate within the bacteria at a rate which is parallel to the approximately linear increase of intracellular DNA in this system. However, the phage production lags several minutes behind DNA production. When 5-methyltryptophan replaced cyanide as the metabolic inhibitor, similar results were obtained. The curves were, however, displaced several minutes to the left on the time axis. The results are compared with Latarjet's (16) data on x-radiation of infected bacteria and with Foster's data (18) concerning the effect of proflavine on infected bacteria. Essential agreement with both is apparent.     

Bacteriophage latent-period evolution as a response to resource availability

Bacteriophages (phages) modify microbial communities by lysing hosts, transferring genetic material, and effecting lysogenic conversion. To understand how natural communities are affected it is important to develop predictive models. Here we consider how variation between models--in eclipse period, latent period, adsorption constant, burst size, the handling of differences in host quantity and host quality, and in modeling strategy--can affect predictions. First we compare two published models of phage growth, which differ primarily in terms of how they model the kinetics of phage adsorption; one is a computer simulation and the other is an explicit calculation. At higher host quantities (approximately 10(8) cells/ml), both models closely predict experimentally determined phage population growth rates. At lower host quantities (10(7) cells/ml), the computer simulation continues to closely predict phage growth rates, but the explicit model does not. Next we concentrate on predictions of latent-period optima. A latent-period optimum is the latent period that maximizes the population growth of a specific phage growing in the presence of a specific quantity and quality of host cells. Both models predict similar latent-period optima at higher host densities (e.g., 17 min at 10(8) cells/ml). At lower host densities, however, the computer simulation predicts latent-period optima that are much shorter than those suggested by explicit calculations (e.g., 90 versus 1,250 min at 10(5) cells/ml). Finally, we consider the impact of host quality on phage latent-period evolution. By taking care to differentiate latent-period phenotypic plasticity from latent-period evolution, we argue that the impact of host quality on phage latent-period evolution may be relatively small.     

Emergence of adaptability to time delay in bipedal locomotion

Based on neurophysiological evidence, theoretical studies have shown that locomotion is generated by mutual entrainment between the oscillatory activities of central pattern generators (CPGs) and body motion. However, it has also been shown that the time delay in the sensorimotor loop can destabilize mutual entrainment and result in the failure to walk. In this study, a new mechanism called flexible-phase locking is proposed to overcome the time delay. It is realized by employing the Bonhoeffer–Van der Pol formalism – well known as a physiologically faithful neuronal model – for neurons in the CPG. The formalism states that neurons modulate their phase according to the delay so that mutual entrainment is stabilized. Flexible-phase locking derives from the phase dynamics related to an asymptotically stable limit cycle of the neuron. The effectiveness of the mechanism is verified by computer simulations of a bipedal locomotion model.     

Optimizing bacteriophage plaque fecundity

Bacteriophages (phages), the viruses of bacteria, form visible lesions within bacterial lawns (called plaques), which are employed ubiquitously in phage isolation and characterization. Plaques also can serve as models for phage population growth within environments that display significant spatial structure, e.g. soils, sediments, animal mucosal tissue, etc. Furthermore, phages growing within plaques, in experimental evolution studies, may become adapted to novel conditions, may be selected for faster expansion, or may evolve toward producing more virions per plaque. Here, we examine the evolution of the latter, greater plaque fecundity, considering especially tradeoffs between phage latent period and phage burst size. This evolution is interesting because genetically lengthening latent periods, as seen with phage lysis-timing mutants, should increase phage burst sizes, as more time is available for phage-progeny maturation during infection. Genetically shortening latent periods, however, is a means toward producing larger phage plaques since phage virions then can spend more time diffusing rather than infecting. With these larger plaques more bacteria become phage infected, resulting in more phage bursts. Given this conflict between latent period's impact on per-plaque burst number versus per-infection burst size, and based on analysis of existing models of plaque expansion, we provide two assertions. First, latent periods that optimize plaque fecundity are longer (e.g. at least two-fold longer) than latent periods that optimize plaque size (or that optimize phage population growth within broth). Second, if increases in burst size can contribute to plaque size (i.e. larger plaques with larger bursts), then latent-period optima that maximize plaque fecundity should be longer still. As a part of our analysis, we provide a means for predicting latent-period optima-for maximizing either plaque size or plaque fecundity-which is based on knowledge of only phage eclipse period and the relative contribution of phage burst size versus latent period toward plaque size.     

Integer-ratio entrainment in mutually-coupled non-linear oscillators

In recent years entrainment conditions for mutually-coupled, non-linear oscillators have been studied for a number of biomedical applications and using different analytical methods. The emphasis has been on entrainment between oscillators of similar frequencies. In this paper entrainment conditions are considered for oscillators having intrinsic frequency ratio of about 3:1 and which exhibit integer-ratio synchronization. This condition has application in the study of blood pressure regulation particularly in relation to respiratory effects. Coupling has been observed between respiration and the vasomotor activity associated with the baroreceptor reflex, which has an intrinsic 0·1 Hz component. At normal breathing frequencies the frequency ratio of the respiratory and vasomotor components is in the region of 3:1 hence integer-ratio entrainment is feasible. Using a coupled van der Pol model the entrainment zones for different parameters are described. The parameters considered allow for varying amounts of output, output rate and delay in the intercoupling structure. In particular, it is shown that the entrainment regions are strongly affected by the nature of the coupling. Within these zones the harmonic balance method is developed to provide an analytical solution to frequency, amplitudes and phase conditions. The assumed solution is valid only for certain regions of the stability zones and the reason for this is demonstrated and the means whereby this can be overcome are indicated.     

Dynamics of Baltic Sea phages driven by environmental changes

Phage predation constitutes a major mortality factor for bacteria in aquatic ecosystems, and thus, directly impacts nutrient cycling and microbial community dynamics. Yet, the population dynamics of specific phages across time scales from days to months remain largely unexplored, which limits our understanding of their influence on microbial succession. To investigate temporal changes in diversity and abundance of phages infecting particular host strains, we isolated 121 phage strains that infected three bacterial hosts during a Baltic Sea mesocosm experiment. Genome analysis revealed a novel Flavobacterium phage genus harboring gene sets putatively coding for synthesis of modified nucleotides and glycosylation of bacterial cell surface components. Another novel phage genus revealed a microdiversity of phage species that was largely maintained during the experiment and across mesocosms amended with different nutrients. In contrast to the newly described Flavobacterium phages, phages isolated from a Rheinheimera strain were highly similar to previously isolated genotypes, pointing to genomic consistency in this population. In the mesocosm experiment, the investigated phages were mainly detected after a phytoplankton bloom peak. This concurred with recurrent detection of the phages in the Baltic Proper during summer months, suggesting an influence on the succession of heterotrophic bacteria associated with phytoplankton blooms.