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.     

Seed dispersal in a patchy environment with global age dependence

A model of seed population dynamics proposed by S. A. Levin, A. Hastings, and D. Cohen is presented and analyzed. With the environment considered as a mosaic of patches, patch age is used along with time as an independent variable. Local dynamics depend not only on the local state, but also on the global environment via dispersal modelled by an integral over all patch ages. Basic technical properties of the time varying solutions are examined; necessary and sufficient conditions for nontrivial steady states are given; and general sufficient conditions for global asymptotic stability of these steady states are established. Primary tools of analysis include a hybrid Picard iteration, fixed point methods, monotonicity of solution structure, and upper and lower solutions for differential equations.This work was supported in part by National Science Foundation Grants MCS-7903497 and MCS-790349701     

Pause point spectra in DNA constant-force unzipping

Under constant applied force, the separation of double-stranded DNA into two single strands is known to proceed through a series of pauses and jumps. Given experimental traces of constant-force unzipping, we present a method whereby the locations of pause points can be extracted in the form of a pause point spectrum. A simple theoretical model of DNA constant-force unzipping is presented, which generates theoretical pause point spectra through Monte Carlo simulation of the unzipping process. The locations of peaks in the experimental and theoretical pause point spectra are found to be nearly coincident below 6000 basepairs for unzipping the bacteriophage lambda-genome. The model only requires the sequence, temperature, and a set of empirical basepair binding and stacking energy parameters, and the good agreement with experiment suggests that pause point locations are primarily determined by the DNA sequence. The model is also used to predict pause point spectra for the bacteriophage phi X174 genome. The algorithm for extracting the pause point spectrum might also be useful for studying related systems which exhibit pausing behavior such as molecular motors.     

Risk-sensitive fertility: The variance compensation hypothesis

Two conditions are sufficient to indicate the need for risk-sensitive, adaptive analysis: (i) the outcomes of a behavior must be unpredictable to some degree and (ii) the relationship between outcomes and their value (in terms of fitness or utility) must be nonlinear. We argue that these conditions are common, and develop a general model for the analysis of risk-sensitive fertility behavior when long-term reproductive outcomes are unpredictable. We show that unpredictability is likely to have a patterned effect on fertility behavior, beyond adjustment for expected or average mortality, and we analyze the conditions under which that effect will be to promote or dampen fertility (positive or negative variance compensation, respectively). We then describe the implications of this variance compensation hypothesis (VCH) for the analysis of demographic transitions, agricultural intensification, fertility differences in natural-fertility populations, and clutch size. We conclude by lamenting that data are lacking to test the VCH, probably because it has not been appreciated that there can be patterned and effective behavioral adjustments to stochastic features of the environment.     

Sufficient and necessary conditions for Lyapunov stability of genetic networks with SUM regulatory logic

In this paper, a nonlinear model for genetic regulator networks (GRNs) with SUM regulatory logic is presented. Four sufficient and necessary conditions of global asymptotical stability and global exponential stability for the equilibrium point of the GRNs are proposed, respectively. Specifically, three weak sufficient conditions and corresponding corollaries are derived by using comparing theorem and Dini derivative method. Then, a famous GRN model is used as the example to illustrate the effectiveness of our theoretical results. Comparing to the results in the previous literature, some novel ideas, study methods and interesting results are explored.     

Spiteful soldiers and sex ratio conflict in polyembryonic parasitoid wasps

The existence of spiteful behaviors remains controversial. Spiteful behaviors are those that are harmful to both the actor and the recipient, and they represent one of the four fundamental types of social behavior (alongside selfishness, altruism, and mutual benefit). It has generally been assumed that the conditions required for spite to evolve are too restrictive, and so spite is unlikely to be important. This idea has been challenged in recent years, with the realization that localized competition can relax the conditions required for spite to evolve. Here we develop a theoretical model for a prime candidate for a spiteful behavior, the production of the sterile soldier caste in polyembryonic wasps. Our results show that (a) the biology of these soldiers is consistent with their main role being to mediate conflict over the sex ratio and not to defend against competitors and (b) greater conflict will occur in more outbred populations. We also show that the production of the sterile soldier caste can be classed as a spiteful behavior but that, to an extent, this is merely a semantic choice, and other interpretations such as altruism or indirect altruism are valid. However, the spite interpretation is useful in that it can lead to a more natural interpretation of relatedness and facilitate the classification of behaviors in a way that emphasizes biologically interesting differences that can be empirically tested.     

The population biology of bacterial viruses: why be temperate

A model of the interactions between populations of temperate and virulent bacteriophage with sensitive, lysogenic, and resistant bacteria is presented. In the analysis of the properties of this model, particular consideration is given to the conditions under which temperate bacteriophage can become established and will be maintained in bacterial populations. The effects of the presence of resistant bacteria and virulent phage on these "existence" conditions for temperate viruses are considered. It is demonstrated that under broad conditions temperate phage will be maintained in bacterial populations and will coexist with virulent phage. Extrapolating from this formal consideration of the population biology of temperate bacteriophage, a number of hypotheses for the conditions under which temperate, rather than virulent, modes of phage reproduction are to be anticipated and the nature of the selective pressures leading to the evolution and persistence of this "benign" type of bacterial virus are reviewed and critically evaluated. Two hypotheses for the "advantages of temperance" are championed: (1) As a consequence of the allelopathic effects of diffusing phage, in physically structured habitats, lysogenic colonies are able to sequester resources and, in that way, have an advantage when competing with sensitive nonlysogens. (2) Lysogeny is an adaptation for phage to maintain their populations in "hard times," when the host bacterial density oscillates below that necessary for phage to be maintained by lytic infection alone.     

A unified theory of nucleation-rate-limited DNA renaturation kinetics

DNA renaturations under nucleation-rate-limiting conditions on simple DNA such as bacterial and bacteriophage DNA show significant deviation from ideal second-order kinetics when followed by optical density measurements at 260 nm. Ideal second-order kinetics yield linear plots when the data is plotted in the standard reciprocal second-order (RSO) manner. The observed deviations from ideal second-order behavior take the form of steadily downward-curving RSO plots. In this paper, experiments are presented for E. coli and T2 DNA documenting this non-ideal behavior. Since experiments using T4, T5 and B, subtilis DNA yield identical non-ideal behavior, this behavior appears to be a property of DNA renaturation followed by optical density, not a peculiarity of a particular DNA. Identical non-ideal behavior is also seen in kinetics followed by S1 nuclease assay. A theory is developed to explain this deviation from ideal second-order kinetics. The theory also explains why kinetics followed by hydroxyapatite chromatography show nearly ideal second-order kinetics. In contrast to the approach taken by others in developing equations that describe S1 nuclease monitored reactions, our view is that nonideal second-order kinetics are fundamentally due to the reacton of free single strands to yield partially helical duplex species. Later reactions of these species tend to reduce the deviations from non-ideal second-order kinetics.     

Chlorination of indicator bacteria and viruses in primary sewage effluent

Wastewater disinfection is used in many countries for reducing fecal coliform levels in effluents. Disinfection is therefore frequently used to improve recreational bathing waters which do not comply with microbiological standards. It is unknown whether human enteric viruses (which are responsible for waterborne disease) are simultaneously inactivated alongside fecal coliforms. This laboratory study focused on the chlorination of primary treated effluent with three doses (8, 16, and 30 mg/liter) of free chlorine as sodium hypochlorite. Seeding experiments showed that inactivation (>5 log(10) units) of Escherichia coli and Enterococcus faecalis was rapid and complete but that there was poor inactivation (0.2 to 1.0 log(10) unit) of F(+)-specific RNA (FRNA) bacteriophage (MS2) (a potential virus indicator) at all three doses. However, seeded poliovirus was significantly more susceptible (2.8 log(10) units) to inactivation by chlorine than was the FRNA bacteriophage. To ensure that these results were not artifacts of the seeding process, comparisons were made between inactivation rates of laboratory-seeded organisms in sterilized sewage and inactivation rates of organisms occurring naturally in sewage. Multifactorial analysis of variance showed that there was no significant difference (P > 0.05) between the inactivation rates for seeded and naturally occurring FRNA bacteriophage. However, laboratory-grown poliovirus was inactivated much more rapidly than were naturally occurring, indigenous enteroviruses (P < 0.001). This may reflect differences in the way indigenous virus is presented to the disinfectant. Inactivation rates for indigenous enteroviruses were quite similar to those seen for FRNA bacteriophage at lower doses of chlorine. These results have significance for the effectiveness of chlorination as a sewage treatment process, particularly where virus contamination is of concern, and suggest that FRNA bacteriophage would be an appropriate indicator of such viral inactivation under field conditions.     

Bifurcation analysis of nonlinear reaction-diffusion equations—II. Steady state solutions and comparison with numerical simulations

The steady state spatial patterns arising in nonlinear reaction-diffusion systems beyond an instability point of the thermodynamic branch are studied on a simple model network. A detailed comparison between the analytical solutions of the kinetic equations, obtained by bifurcation theory, and the results of computer simulations is presented for different boundary conditions. The characteristics of the dissipative structures are discussed and it is shown that the observed behavior depends strongly on both the boundary and initial conditions. The theoretical expressions are limited to the neighborhood of the marginal stability point. Computer simulations allow not only the verification of their predictions but also the investigation of the behavior of the system for larger deviations from the instability point. It is shown that new features such as multiplicity of solutions and secondary bifurcations can appear in this region.     

Mechanisms for stabilisation and destabilisation of systems of reaction-diffusion equations

Potential mechanisms for stabilising and destabilising the spatially uniform steady states of systems of reaction-diffusion equations are examined. In the first instance the effect of introducing small periodic perturbations of the diffusion coefficients in a general system of reaction-diffusion equations is studied. Analytical results are proved for the case where the uniform steady state is marginally stable and demonstrate that the effect on the original system of such perturbations is one of stabilisation. Numerical simulations carried out on an ecological model of Levin and Segel (1976) confirm the analysis as well as extending it to the case where the perturbations are no longer small. Spatio-temporal delay is then introduced into the model. Analytical and numerical results are presented which show that the effect of the delay is to destabilise the original system.     

Isolation and characteristics of the bacteriophage from the vaccine strain Tohama phase I

Some properties of bacteriophage phi T isolated from the vaccine strain Bordetella pertussis Tohama phase I and propagated in Bordetella parapertussis 504 cells are presented. Phage phi T belongs to the IV group in accordance with Tikhonenko classification. The diameter of head and length of noncontractile tail sheath are 49.5 +/- 0.5 and 145 +/- 7 nm, respectively. Diameter of the tail sheath is 3.2 +/- 0.6 nm. Molecular mass of the phage DNA is 37 +/- 3 kb. Population of phi T phage is polymorphous and consists of particles the genomes or which vary from each other by the "insert" located 6.8 +/- 0.6 kb from the end of molecule. The blot hybridization has demonstrated that the bacteriophage genome is not inserted into the chromosome of the lysogenic strain. Autonomous location of the phage genome in the host cell is suggested. The temperature and hydrogen ions concentration effects on bacteriophage phi T stability were studied. The conditions for phage suspension storage are described.     

The phage T4 uvs Y recombination protein stabilizes presynaptic filaments

The bacteriophage T4 uvsY protein is required for efficient recombination in T4-infected Escherichia coli cells. Previous in vitro work has shown that the purified uvsY protein is an accessory protein; it stimulates homologous pairing catalyzed by the phage uvsX protein (a RecA-like recombinase) under certain conditions. We show here that this effect can be traced, at least in part, to a UvsY-dependent stabilization of uvsX protein-single-stranded DNA complexes. These presynaptic filaments are one of the early obligatory intermediates in the strand exchange reaction between homologous single- and double-stranded DNAs. The mechanism of filament stabilization seems to involve a slower loss of UvsX subunits. A model that accounts for the data is presented in which both recombination proteins are incorporated into the presynaptic filament.     

Bacteriophage Typing of Clinically Isolated Serratia marcescens

A bacteriophage-typing scheme for the differentiation and classification of clinically isolated strains of Serratia marcescens was developed. Thirty-four Serratia bacteriophages were isolated from sewage and used to type 185 of 204 isolates (90.6%) of S. marcescens into 23 bacteriophage groups representing 71 types. Different bacteriophage types occurred at different intervals, suggesting that particular strains of S. marcescens are found at certain times. A correlation was found between inositol fermentation and bacteriophage type and between susceptibility to carbenicillin and bacteriophage type. However, there was no relationship between source of isolate and bacteriophage type. Bacteriophage typing of S. marcescens should provide a system which will aid in determining the origin of nosocomial Serratia infections.     

Three-dimensional reconstruction of bacterial viruses from electron microscopy data. Bacteriophage structure

The structure of bacteriophages from different groups is presented based on the data obtained by the three-dimensional reconstruction, optical diffraction and filtration and electron microscopy techniques. The study made possible to suggest the scheme for the mechanism of sheath molecules rearrangement at contraction of bacteriophage tail sheath, the model of bacteriophage FI-1 connector. The structural elements for difference and relation of various bacteriophages are demonstrated.     

Bacteriophage T4 development in Escherichia coli is growth rate dependent

Three independent parameters (eclipse and latent periods, and rate of ripening during the rise period) are essential and sufficient to describe bacteriophage development in its bacterial host. A general model to describe the classical "one-step growth" experiment [Rabinovitch et al. (1999a) J. Bacteriol.181, 1687-1683] allowed their calculations from experimental results obtained with T4 in Escherichia coli B/r under different growth conditions [Hadas et al. (1997) Microbiology143, 179-185]. It is found that all three parameters could be described by their dependence solely on the culture doubling time tau before infection. Their functional dependence on tau, derived by a best-fit analysis, was used to calculate burst size values. The latter agree well with the experimental results. The dependence of the derived parameters on growth conditions can be used to predict phage development under other experimental manipulations.     

Competition between plasmid-bearing and plasmid-free organisms in a chemostat with nutrient recycling and an inhibitor

The asymptotic behavior of solutions of a model for competition between plasmid-bearing and plasmid-free organisms in the chemostat with two distributed delays and an external inhibitor is considered. The model presents a refinement of the one considered by Lu and Hadeler [Z. Lu, K.P. Hadeler, Model of plasmid-bearing plasmid-free competition in the chemostat with nutrient recycling and an inhibitor, Math. Biosci. 167 (2000) p. 177]. The delays model the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition. Furthermore, it is assumed that there is inter-specific competition between the plasmid-bearing and plasmid-free organisms as well as intra-specific competition within each population. Conditions for boundedness of solutions and existence of non-negative equilibrium are given. Analysis of the extinction of the organisms, including plasmid-bearing and plasmid-free organisms, and the uniform persistence of the system are also carried out. By constructing appropriate Liapunov-like functionals, some sufficient conditions of global attractivity to the extinction equilibria are obtained and the combined effects of the delays and the inhibitor are studied.     

Maximization principles for frequency-dependent selection I: the one-locus two-allele case

In this article we study the one-locus two-allele version of the pairwise-interaction model of frequency-dependent selection in discrete and continuous time. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles. We provide a systematic approach that covers all possible facets of the dynamical behavior of the model, and we illustrate our results by concrete examples. We show that the mean fitness of the population is nondecreasing if the interaction coefficients are symmetric and positive. Moreover, monotonic convergence to the set of equilibria always occurs, which is not true if we also consider negative interaction coefficients. For asymmetric interaction, we provide necessary conditions when the mean fitness is nondecreasing and sufficient conditions when it is not. Furthermore, in discrete time, we show that limit cycles cannot occur, unless some interaction coefficients are negative.     

Cooperative DNA binding by lambda integration protein--a key component of specificity

Quantitative analysis of nitrocellulose filter binding data by the method of Clore, Gronenborn and Davies [(1982) J. Mol. Biol. 155, 447-466] has been used to show that lambda integration protein (Int) exhibits cooperativity in binding to specific recognition sites within the attachment site region (lambda attP) of bacteriophage lambda DNA. Optimal values of the equilibrium constant obtained were 3.0(+/- 1.0) X 10(10) M-1 for the P' site using a model of three sites with equal affinity and 1.9(+/- 0.4) X 10(10) M-1 for the P1 site on a two-site model. The value of the cooperativity parameter alpha is 172(+106)(-66) in all cases. The occurrence of a consensus recognition sequence is necessary but not sufficient for strong binding; cooperative interaction between Int molecules binding to adjacent members of an array of binding sites is also essential. The occurrence of binding site arrays distinguishes lambda attP very clearly from other DNA sequences containing single recognition sites by chance.