Population and evolutionary dynamics of phage therapy. Levin,B.R., Bull,J.J. (2004). J. Nat. Rev. Microbiol 2:166-173.Following a sixty-year hiatus in western medicine, bacteriophages (phages) are again being advocated for treating and preventing bacterial infections. Are attempts to use phages for clinical and environmental applications more likely to succeed now than in the past? Will phage therapy and prophylaxis suffer the same fates as antibiotics--treatment failure due to acquired resistance and ever-increasing frequencies of resistant pathogens? Here, the population and evolutionary dynamics of bacterial-phage interactions that are relevant to phage therapy and prophylaxis are reviewed and illustrated with computer simulations. [TOP OF PAGE]
Bacterial debris—an ecological mechanism for coexistence of bacteria and their viruses. Rabinovitch,A., Aviram,I., Zaritsky,A. (2003). J. Theor. Biol. 224:377-383.A model of bacteria and phage survival is developed based on the idea of shielding by bacterial debris in the system. This model is mathematically formulated by a set of four nonlinear difference equations for susceptible bacteria, contaminated bacteria, bacterial debris and phages. Simulation results show the possibility of survival, and domains of existence of stable and unstable solutions. [TOP OF PAGE]
On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment. Carletti,M. (2002). Math. Biosci. 175:117-131.In this paper we extend the deterministic model for the epidemics induced by virulent phages on bacteria in marine environment introduced by Beretta and Kuang [Math. Biosci. 149 (1998) 57], allowing random fluctuations around the positive equilibrium. The stochastic stability properties of the model are investigated both analytically and numerically suggesting that the deterministic model is robust with respect to stochastic perturbations. [TOP OF PAGE]
Overcoming the phage replication threshold: a mathematical model with implications for phage therapy. Kasman,L.M., Kasman,A., Westwater,C., Dolan,J., Schmidt,M.G., Norris,J.S. (2002). J. Virol. 76:5557-5564.Prior observations of phage-host systems in vitro have led to the conclusion that susceptible host cell populations must reach a critical density before phage replication can occur. Such a replication threshold density would have broad implications for the therapeutic use of phage. In this report, we demonstrate experimentally that no such replication threshold exists and explain the previous data used to support the existence of the threshold in terms of a classical model of the kinetics of colloidal particle interactions in solution. This result leads us to conclude that the frequently used measure of multiplicity of infection (MOI), computed as the ratio of the number of phage to the number of cells, is generally inappropriate for situations in which cell concentrations are less than 10(7)/ml. In its place, we propose an alternative measure, MOI(actual), that takes into account the cell concentration and adsorption time. Properties of this function are elucidated that explain the demonstrated usefulness of MOI at high cell densities, as well as some unexpected consequences at low concentrations. In addition, the concept of MOI(actual) allows us to write simple formulas for computing practical quantities, such as the number of phage sufficient to infect 99.99% of host cells at arbitrary concentrations. [TOP OF PAGE]
Bacteriophage T4 development in Escherichia coli is growth rate-dependent. Rabinovitch,A., Fishov,I., Hadas,H., Einav,M., Zaritsky,A. (2002). J. Theor. Biol. 216:1-4.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. [TOP OF PAGE]
Bacteriophage latent-period evolution as a response to resource availability. Abedon,S.T., Herschler,T.D., Stopar,D. (2001). Appl. Environ. Microbiol. 67:4233-4241.Bacteriophages (phages) modify microbial communities by lysing hosts, transferring genetic material, and effecting lysogenicconversion. 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 inhost quantity and host quality, and in modeling strategy can affectpredictions. First we compare two published models of phage growth,which differ primarily in terms of how they model the kineticsof phage adsorption; one is a computer simulation and the otheris an explicit calculation. At higher host quantities (~108 cells/ml), both models closely predict experimentally determinedphage population growth rates. At lower host quantities (107 cells/ml), the computer simulation continues to closely predictphage growth rates, but the explicit model does not. Next we concentrateon predictions of latent-period optima. A latent-period optimumis the latent period that maximizes the population growth of aspecific phage growing in the presence of a specific quantityand quality of host cells. Both models predict similar latent-periodoptima at higher host densities (e.g., 17 min at 108 cells/ml). At lower host densities, however, the computer simulationpredicts latent-period optima that are much shorter than thosesuggested by explicit calculations (e.g., 90 versus 1,250 minat 105 cells/ml). Finally, we consider the impact of host quality onphage latent-period evolution. By taking care to differentiatelatent-period phenotypic plasticity from latent-period evolution,we argue that the impact of host quality on phage latent-periodevolution may be relativelysmall. [TOP OF PAGE]
Effects of bacteriophages on the population dynamics of four strains of pelagic marine bacteria. Middelboe,M., Hagstrom,A., Blackburn,N., Sinn,B., Fischer,U., Borch,N.H., Pinhassi,J., Simu,K., Lorenz,M.G. (2001). Microb. Ecol. 42:395-406.Viral lysis of specific bacterial populations has been suggested to be an important factor for structuring marine bacterioplankton communities. In the present study, the influence of bacteriophages on the diversity and population dynamics of four marine bacterial phage-host systems was studied experimentally in continuous cultures and theoretically by a mathematical model. By use of whole genome DNA hybridization toward community DNA, we analyzed the dynamics of individual bacterial host populations in response to the addition of their specific phage in continuous cultures of mixed bacterial assemblages. In these experiments, viral lysis had only temporary effects on the dynamics and diversity of the individual bacterial host species. Following the initial lysis of sensitive host cells, growth of phage-resistant clones of the added bacteria resulted in a distribution of bacterial strains in the phage-enriched culture that was similar to that in the control culture without phages after about 50-60 h incubation. Consequently, after a time frame of 5-10 generations after lysis, it was the interspecies competition rather than viral lysis of specific bacterial strains that was the driving force in the regulation of bacterial species composition in these experiments. The clonal diversity, on the other hand, was strongly influenced by viral activity, since the clonal composition of the four species in the phage-enriched culture changed completely from phage-sensitive to phage-resistant clones. The model simulation predicted that viral lysis had a strong impact on the population dynamics, the species composition, and the clonal composition of the bacterial community over longer time scales (weeks). However, according to the model, the overall density of bacteria in the system was not affected by phages, since resistant clones complemented the fluctuations caused by viral lysis. Based on the model analysis, we therefore suggest that viral lysis can have a strong influence on the dynamics of bacterial populations in planktonic marine systems. [TOP OF PAGE]
Linking genetic change to community evolution: insights from studies of bacteria and bacteriophage. Bohannan,B.J.M., Lenski,R.E. (2000). Ecol. Lett. 3:362-377.A major goal of community ecology is to link biological processes at lower scales with community patterns. Microbial communities are especially powerful model systems for making these links. In this article, we review recent studies of laboratory communities of bacteria and bacteriophage (viruses that infect bacteria). We focus on the ecology and evolution of bacteriophage-resistance as a case study demonstrating the relationship between specific genes, individual interactions, population dynamics, community structure, and evolutionary change. In laboratory communities of bacteria and bacteriophage, bacteria rapidly evolve resistance to bacteriophage infection. Different resistance mutations produce distinct resistance phenotypes, differing, for example, in whether resistance is partial or complete, in the magnitude of the physiological cost associated with resistance, and in whether the mutation can be countered by a host-range mutation in the bacteriophage. These differences determine whether a mutant can invade, the effect its invasion has on the population dynamics of sensitive bacteria and phage, and the resulting structure of the community. All of these effects, in turn, govern the community's response to environmental change and its subsequent evolution. [TOP OF PAGE]
The relative importance of competition and predation varies with productivity in a model community. Bohannan,B.J.M., Lenski,R.E. (2000). Am. Nat. 156:329-340.Recent theory predicts thatproductivity can influence therelative importance of predationand competition in determiningpatterns in abundance, diversity,and community structure. Inlow-productivity systems, competition ispredicted to be themajor influence on communitypatterns, while at highproductivity, the major influenceis predicted to bepredation. We directly testedthis theory using alaboratory model community. Ourmodel community consisted ofthe bacteriophage T2 (avirus that feeds onEscherichia coli) and two populationsof E. coli, in glucose-limitedchemostats. One E. coli populationconsisted of individuals thatwere sensitive to predationby T2 (“vulnerable” E. coli),and the other populationconsisted of individuals thatwere partially resistant topredation by T2 (“lessvulnerable” E. coli). We manipulatedproductivity in this experimentby running replicate chemostatswith different input concentrationsof glucose. Our observationswere consistent with theoreticalpredictions. We observed thedecline of the morevulnerable prey population athigher productivity but notat lower productivity, andthe decline of theless vulnerable prey populationat lower productivity butnot at higher productivity.However, the rate ofdecline in some replicateswas slower than predicted,and extinctions were notobserved during the experiments,contrary to theoretical predictions.We present some testablehypotheses that might explainthe slow rate ofdecline observed. [TOP OF PAGE]
Mathematical analysis of growth and interaction dynamics of streptomycetes and a bacteriophage in soil. Burroughs,N.J., Marsh,P., Wellington,E.M.H. (2000). Appl. Environ. Microbiol. 66:3868-3877.We observed the infection cycle of the temperate actinophage KC301 in relation to the growth of its host Streptomyces lividans TK24 in sterile soil microcosms. Despite a large increase in phage population following germination of host spores, there was no observable impact on host population numbers as measured by direct plate counts. The only change in the host population following infection was the establishment of a small subpopulation of KC301 lysogens. The interaction of S. lividans and KC301 in soil was analyzed with a population-dynamic mathematical model to determine the underlying mechanisms of this low susceptibility to phage attack relative to aquatic environments. This analysis suggests that the soil environment is a highly significant component of the phage-host interaction, an idea consistent with earlier observations on the importance of the environment in determining host growth and phage-host dynamics. Our results demonstrate that the accepted phage-host interaction and host life cycle, as determined from agar plate studies and liquid culture, is sufficient for quantitative agreement with observations in soil, using soil-determined rates. There are four significant effects of the soil environment: (i) newly germinated spores are more susceptible to phage lysis than are hyphae of developed mycelia, (ii) substrate mycelia in mature colonies adsorb about 98% of the total phage protecting susceptible young hyphae from infection, (iii) the burst size of KC301 is large in soil (> 150, 90% confidence) relative to that observed in liquid culture (120, standard error of the mean (SEM), 6), and (iv) there is no measurable impact on the host in terms of reduced growth by the phage. We hypothesize that spatial heterogeneity is the principal cause of these effects and is the primary determinant in bacterial escape of phage lysis in soil. [TOP OF PAGE]
Toward antiviral strategies that resist viral escape. Endy,D., Yin,J. (2000). Antimicrob. Agents Chemother. 44:1097-1099.We studied the effect on viral growth of drugs targeting different virus functions using a computer simulation for the intracellular growth of bacteriophage T7. We found that drugs targeting components of negative-feedback loops gain effectiveness against mutant viruses that attenuate the drug-target interaction. The greater inhibition of such mutants than of the wild type suggests a drug design strategy that would hinder the development of drug resistance. [TOP OF PAGE]
Bacterial growth rate and marine virus–host dynamics. Middelboe,M. (2000). Microb. Ecol. 40:114-124.The dynamics of a marine virus–host system were investigated at different steady state growth rates in chemostat cultures and the data were analyzed using a simple model. The virus–host interactions showed strong dependence on host cell growth rate. The duration of the infection cycle and the virus burst size were found to depend on bacterial growth rate, and the rate of cell lysis and virus production were positively correlated with steady state growth rate in the cultures (r2 > 0.96, p < 0.05). At bacterial growth rates of 0.02 to 0.10 h-1 in the chemostats the virus burst size increased from 12 ± 4 to 56 ± 4, and the latent period decreased from 2.0 to 1.7 h. Resistant clones of the host strain were present in the cultures from the beginning of the experiment and replaced the sensitive host cells following viral lysis in the cultures. Regrowth of resistant cells correlated significantly (r2 = 1.000, p < 0.02) with the lysis rate of sensitive cells, indicating that release of viral lysates stimulated growth of the non-infected, resistant cells. The constructed model was suitable for simulating the observed dynamics of the sensitive host cells, viruses and resistant clones in the cultures. The model was therefore used in an attempt to predict the dynamics of this virus–host interaction in a natural marine environment during a certain set of growth conditions. The simulation indicated that a steady state relationship between the specific viruses and sensitive and resistant bacterial clones may occur at densities that are reasonable to assume for natural environments. The study demonstrates that basic characterization and modeling of specific virus–host interactions may improve our understanding of the behavior of bacteria and viruses in natural systems. [TOP OF PAGE]
Virus Dynamics: Mathematical Principles of Immunology and Virology. Nowak,M.A., May,R.M. (2000). [TOP OF PAGE]
Analysis of two-stage continuous operation of Escherichia coli containing bacteriophage lambda vector. Park,S.H., Park,T.H. (2000). Bioprocess Engineering 23:557-563.Bacteriophage lambda containing a cloned-gene is stably maintained in Escherichia coli in the lysogenic state while it is replicated and it overproduces a recombinant protein product in the lytic state. The host cell is eventually lysed in the lytic state. The kinetics of cell lysis and production induction were studied and are reported in this article through model equations. In two-stage continuous operation, the first tank is maintained in the lysogenic state for cell growth and cloned-gene stability while the second tank is in the lytic state for the overproduction of cloned-gene product. Individual cells in the second tank have different extent of the induction for product formation, since each has a different residence time. The different residence time for individual cells was taken into account using a population model. The numerical results show good agreement with the experimental data for the prediction of dilution rate in the second tank which gives the maximum product concentration. [TOP OF PAGE]
Elements of a theory for the mechanisms controlling abundance, diversity, and biogeochemical role of lytic bacterial viruses in aquatic systems. Thingstad,T.F. (2000). Limnol. Oceanogr. 45:1320-1328.Mechanisms controlling virus abundance and partitioning of loss of bacterial production between viral lysis and protozoan predation are discussed within the framework of an idealized Lotka-Volterra-type model. This combines nonselective protozoan predation with host-selective viral lysis of bacteria. The analysis leads to a reciprocal relationship between bacterial diversity and viruses, in which coexistence of competing bacterial species is ensured by the presence of viruses that “kill the winner,” whereas the differences in substrate affinity between the coexisting bacterial species determine viral abundance. The ability of the model to reproduce published observations, such as an approximate 1:10 ratio between bacterial and viral abundance, and the ability of viral lysis to account for 10-50% of bacterial loss are discussed. [TOP OF PAGE]
Effect of prey heterogeneity on the response of a food chain to resource enrichment. Bohannan,B.J.M., Lenski,R.E. (1999). Am. Nat. 153:73-82.We demonstrated that the presence of invulnerable prey can result in a shift in the balance between top-down and bottom-up control of a model food chain. Our model food chain consisted of the bacterium Escherichia coli and the bacteriophage T4 (a virus that feeds on E. coli) in chemostats supplied with different concentrations of glucose. The E. coli population consisted of individuals that were susceptible to predation by T4 (“edible” E. coli) and individuals that were resistant to predation by T4 (“inedible” E. coli). The equilibrium density of a hetergeneous prey population (consisting of edible and inedible E. coli) increased strongly in response to an enrichment of its resources. This response consisted of an increase in the inedible fraction of the prey population but no change in the edible fraction. In contrast, a homogeneous prey population (edible E. coli only) increased only marginally. The equilibrium density of the predator population (bacteriophage T4) did not significantly increase in response to enrichment when its prey were heterogeneous, but it increased when its prey were homogeneous. [TOP OF PAGE]
Bacterial lysis by phage--a theoretical model. Rabinovitch,A., Zaritsky,A., Fishov,I., Einav,M., Hadas,H. (1999). J. Theor. Biol. 201:209-213.The similarity to materials corrosion is invoked to develop a model for phage-infected bacterial lysis based on the statistics of extremes. The importance of cell size, envelope thickness and lysozyme eclipse time on the final probability distribution of lysis is considered. Experiments are suggested to test the model. [TOP OF PAGE]
Model for bacteriophage T4 development in Escherichia coli. Rabinovitch,A., Hadas,H., Einav,M., Melamed,Z., Zaritsky,A. (1999). J. Bacteriol. 181:1677-1683.Mathematical relations for the number of mature T4 bacteriophages, both inside and after lysis of an Escherichia coli cell, as a function of time after infection by a single phage were obtained, with the following five parameters: delay time until the first T4 is completed inside the bacterium (eclipse period, nu) and its standard deviation (sigma), the rate at which the number of ripe T4 increases inside the bacterium during the rise period (alpha), and the time when the bacterium bursts (mu) and its standard deviation (beta). Burst size [B = alpha(mu - nu)], the number of phages released from an infected bacterium, is thus a dependent parameter. A least-squares program was used to derive the values of the parameters for a variety of experimental results obtained with wild-type T4 in E. coli B/r under different growth conditions and manipulations (H. Hadas, M. Einav, I. Fishov, and A. Zaritsky, Microbiology 143:179-185, 1997). A “destruction parameter” (zeta) was added to take care of the adverse effect of chloroform on phage survival. The overall agreement between the model and the experiment is quite good. The dependence of the derived parameters on growth conditions can be used to predict phage development under other
experimental manipulations. [TOP OF PAGE]
Amplification and spread of viruses in a growing plaque. You,L., Yin,J. (1999). J. Theor. Biol. 200:365-373.The two-dimensional propagation of viruses through a “lawn” of receptive hosts, commonly called plaque growth, reflects the dynamics of interactions between viruses and host cells. Here we treat the amplification of viruses during plaque growth as a reaction-diffusion system, where interactions among the virus, uninfected host cells, and virus-producing host-virus complexes are accounted for using rates of viral adsorption to and desorption from the host-cell surface, rates of reproduction and release of progeny viruses by lysis of the host, and by the coupling of these reactions with diffusion of free virus within the agar support. Numerical solution of the system shows the development of a traveling wave of reproducing viruses, where the velocity of the wave is governed by the kinetic and diffusion parameters. The model has been applied to predict the propagation velocity of a bacteriophage plaque. Different mechanisms may account for the dependence of this velocity on the host density during early stages of a growing plaque. The model provides a means to explore how changes in the virus-host interactions may be manifest in a growing plaque. [TOP OF PAGE]
Modeling and analysis of a marine bacteriophage infection. Beretta,E., Kuang,Y. (1998). Math. Biosci. 149:57-76.A mathematical model for the marine bacteriophage infection is proposed and its essential mathematical features are analyzed. Since bacteriophage infection induces bacterial lysis which releases into the marine environment, on the average, 'b' viruses per cell, the parameter b epsilon (1, t infinity) or 'virus replication factor' is chosen as the main parameter on which the dynamics of the infection depends. We proved that a threshold b* exists beyond which the endemic equilibrium bifurcates from the free disease one. Still, for increasing b values the endemic equilibrium bifurcates toward a periodic solution. We proved that a compact attractor set omega within the positive cone exists and within omega the free disease equilibrium is globally stable whenever b < or = b*, whereas it becomes a strong uniform repeller for b > b*. A concluding discussion with numerical simulation is then presented. [TOP OF PAGE]
Significance of lysogeny in the marine environment: studies with isolates and a model of lysogenic phage production. Jiang,S.C., Paul,J.H. (1998). Microb. Ecol. 35:235-243.The importance of lysogeny in marine microbial populations is just beginning to be understood. To determine the abundance of lysogens in bacterial populations, we studied the occurrence of lysogenic bacteria among bacterial isolates from a variety of marine environments. More than 116 bacteria isolated on artificial seawater nutrient agar plates were tested for the presence of inducible prophage by mitomycin C and UV radiation. Induction was determined as a decrease in culture absorbance at 600 nm, after treatment with inducing agents. Samples in which optical density decreased or remained the same after induction were further examined by transmission electron microscopy, for the presence of virus-like particles. More than 40% of the bacterial isolates contained inducible prophage, as determined by mitomycin C induction. A higher percentage of lysogenic bacteria was found in isolates from oligotrophic environments, compared to coastal or estuarine environments. These studies suggest that lysogenic bacteria are important components in marine microbial populations. However, a mathematical model based on viral and bacterial abundance and production rates suggests that, under normal conditions, lysogenic viral production contributes less than 0.02% of total viral production. Therefore, lysogens in the marine environment may serve as a source of viruses and only contribute significantly to viral production during natural induction events. [TOP OF PAGE]
A theoretical approach to structuring mechanisms in the pelagic food web. Thingstad,T.F. (1998). Hydrobioligia 363:59-72.In the literature there is a commonly used idealized concept of the food web structure in the pelagic photic zone food web, based to a large extent on size dependent relationships. An outline is here given of how the elementary size-related physical laws of diffusion and sinking, combined with the assumption of predators being size selective in their choice of prey, give a theoretical foundation for this type of structure. It is shown how such a theoretical fundament makes it possible to relate a broad specter of phenomena within one generic and consistent framework. Phenomena such as Hutchinson's and Goldman's paradoxes, the influence of nutrients and water column stability on the balance between microbial and classical food webs, bacterial carbon consumption, new production and export of DOC and POC to the aphotic zone, eutrophication and diversity, can all be approached from this perspective. By including host-specific viruses, this approach gives a hierarchical structure to the control of diversity with nutrient content controlling the maximum size of the photic zone community, size selectivity of predators regulating how the nutrient is distributed between size-groups of osmotrophic and phagotrophic organisms, and viral host specificity regulating how the nutrients within a size group is distributed between host groups. I also briefly discuss how some biological strategies may be successful by not conforming to the normal rules of such a framework. Analyzing the behavior of these idealized systems is thus claimed to facilitate our understanding of the behavior of complex natural food webs. [TOP OF PAGE]
Effect of resource enrichment on a chemostat community of bacteria and bacteriophage. Bohannan,B.J.M., Lenski,R.E. (1997). Ecology 78:2303-2315.We determined the responses of a model laboratory community to resource enrichment and compared these responses to the predictions of prey-dependent and ratio-dependent food chain models. Our model community consisted of Escherichia coli B and bacteriophage T4 in chemostats supplied with different concentrations of glucose. We observed the following responses to enrichment: (1) a large and highly significant increase in the equilibrium population density of the predator, bacteriophage T4, (2) a small but significant increase in the equilibrium population density of the prey, E. coli, and (3) a large and highly significant decrease in the stability of both the predator and prey populations. These responses were better predicted by a prey-dependent model (altered to include a time delay between consumption and reproduction by predators) than by a ratio-dependent model. Enrichment had a large effect on evolutionary change in our system. Enrichment significantly decreased the amount of time required for mutants of E. coli that were resistant to predation by bacteriophage to appear in the chemostats. Enrichment also significantly increased the rate at which these bacteriophage-resistant mutants invaded the chemostats. These results were also better predicted by the prey-dependent model. Invasion by bacteriophage-resistant mutants had a large effect on the subsequent population dynamics of both predator and prey. Both the equilibrium density and stability of the E. coli population increased following invasion, and the population shifted from being primarily limited by predators to being primarily limited by resources. After invasion by the mutants, the T4 population decreased in equilibrium density, and.the population cycled with an increased period. These results were compared to the predictions of a ratio-dependent model and a prey-dependent model altered to include T4-resistant mutants. The dynamics of this community were better predicted by the modified prey-dependent model; however, this model was more complex mathematically than the simpler ratio-dependent model. [TOP OF PAGE]
Intracellular kinetics of a growing virus: A genetically-structured simulation for bacteriophage T7. Endy,D., Kong,D., Yin,J. (1997). Biotech. Bioeng. 55:375-389.Viruses have evolved to efficiently direct the resources of their hosts toward their own reproduction. A quantitative understanding of viral growth will help researchers develop antiviral strategies, design metabolic pathways, construct vectors for gene therapy, and engineer molecular systems that self-assemble. As a model system we examine here the growth of bacteriophage T7 in Escherichia coli using a chemical-kinetic framework. Data published over the last three decades on the genetics, physiology, and biophysics of phage T7 are incorporated into a genetically structures simulation that accounts for entry of hte T7 genome into its host, expression of T7 genes, replication of T7 DNA, assembly of T7 procapsids, and packaging of T7 DNA to finally produce intact T7 progeny. Good agreement is found between the simulated behavior and experimental observations for the shift in transcription capacity from the host to the phage, the initation times of phage protein synthesis, and the intracellular assembly of both wild-type phage and a fast-growing deletion mutant. The simulation is utilized to predict the effect of antisense molecules targetted to different T7 mRNA. Further, a postulated mechanism for the down regulation of T7 transcription in vivo is quantitatively examined and shown to agree with available data. The simulation is found to be a useful tool for exploring and understanding the dyanamics of virus growth at the molecular level. [TOP OF PAGE]
Theoretical models for control of bacterial growth rate, abundance, diversity and carbon demand. Thingstad,T.F., Lignell,R. (1997). Aquat. Microb. Ecol. 13:19-27.Our conceptual understanding of the role of heterotrophic bacteria in pelagic ecosystems and in ocean biogeochemical cycles is closely Linked to our understanding of how their growth rate, abundance, and diversity is controlled. Here we discuss consequences of the simplifying assumption that there are only 5 potentially important interactions between heterotrophic bacteria and their biological and chemical environment. We consider 3 possible types of growth rate limitation: (1) organic carbon, (2) inorganic phosphate, and (3) organic and inorganic nitrogen; and 2 types of cell losses: (1) predation by heterotrophic flagellates, or (2) lysis by infectious viruses. Incorporating this into simple food web structures, we discuss 4 classes of models, 2 based on carbon limitation and 2 based on mineral nutrient limitation of bacterial growth rate. Bacterial abundance is assumed to be controlled by protozoan predation in all cases. For each class, we derive expressions describing bacterial carbon demand, and discuss the control of bacterial carbon demand, growth rate and diversity. It is shown how models predicting an ecosystem production of dissolved organic carbon (DOG) exceeding bacterial carbon demand may be constructed assuming either a low degradability of the DOG, or mineral nutrient limitation of bacterial growth rate. For 2 classes of models, infectious viruses are shown to affect neither growth rate nor abundance of the steady state bacterial community. For all 4 classes of models, viruses are suggested to control diversity of the steady state bacterial community. [TOP OF PAGE]
Accumulation of degradable DOC in surface waters: Is it caused by a malfunctioning microbial loop? Thingstad,T.F., Hagstrom,A., Rassoulzadegan,F. (1997). Limnol. Oceanogr. 42:398-404.Recent literature indicates that dissolved organic carbon (DOC) may accumulate in productive surface waters. Such accumulation will allow export of DOC to the aphotic zone by diffusion and downwelling. As an alternative to models based on low degradability, we here propose a mechanism where bacterial carbon consumption is restricted due to food web mechanisms controlling both growth and biomass of the bacteria: growth rate is kept low by bacteria-phytoplankton competition for mineral nutrients, and biomass is kept low by bacterial predators. With such a mechanism, otherwise degradable material may accumulate and become subject both to chemical transformation and vertical transport. The steady-states of a model describing the interactions between heterotrophic bacteria, phytoplankton, and bacterivorous protozoa is used to explore how the balance between DOC production and consumption shifts along a gradient from oligotrophy to eutrophy. [TOP OF PAGE]
Imaging the propagation of viruses. Lee,Y., Yin,J. (1996). Biotech. Bioeng. 52:438-442.The propagation of viruses in a growing plaque has been measured using a digital image acquisition and analysis system. Plaques of phage T7 incubated at 37°C and illuminated against a dark field emerged as dark growing spots against a background of host bacteria. Images of the growth were acquired using a charge-coupled device (CCD) camera at 1-h intervals over 24 h. The first 10 h of plaque development coincided with rapid growth of the agar-immobilized Escherichia coli host, measured as a reduction in gray value. Following this period, the average radial velocity of plaque growth remained constant at 0.059 mm/h while the standard deviation about this velocity increased. These results suggest the suitability of the system for spatially resolving the dynamics of viral evolution during plaque growth. [TOP OF PAGE]
Phage therapy revisited: the population biology of a bacterial infection and its treatment with bacteriophage and antibiotics. Levin,B.R., Bull,J.J. (1996). Am. Nat. 147:881-898.Phage therapy is the use of bacterial viruses (bacteriophage) to treat bacterial infections. It has been practiced sporadically on humans and domestic animals for nearly 75 yr. Nevertheless, phage therapy has remained outside the mainstream of modern medicine, presumably because of doubts about its efficacy, and possibly because it was eclipsed by antibiotics and other chemotherapeutic agents. In this report, we develop the study of phage therapy and antibiotic therapy as a population biological phenomenon-the dynamic interaction of bacteria with a predator (phage) or a toxic chemical (antibiotic) inside a host whose immune and other defenses also affect the interaction. Our goal is to identify the conditions under which phage and antibiotics can successfully control a bacterial infection and when they cannot. We review data published in the 1980s by H. Williams Smith and J. B. Huggins on the use of phage and antibiotics to control lethal, systemic infections of Escherichia coli in experimentally inoculated mice. We show that some of their observations can be accommodated by a quantitative model that invokes known or plausible assumptions about host defenses and the interactions of bacteria with phage and antibiotics; some observations remain unexplained by the model. Our analysis identifies several hypotheses about the population dynamics of phage and antibiotic therapy that can be tested experimentally. Included among these are hypotheses that account for variation in the efficacy of the different phages employed by Smith and Huggins and why, in their study, phages were more effective than antibiotics. [TOP OF PAGE]
Evolution of the genetic switch in temperate bacteriophage. I. Basic theory. Mittler,J.E. (1996). J. Theor. Biol. 179:161-172.While the molecular mechanisms underlying lysogeny and induction in bacteriophage have been intensely studied, relatively little has been done to relate these findings to their presumed selective functions. To explore the ecological basis for these traits, I have used a resource-based model for competition between bacteriophage with different probabilities of lysogeny and different spontaneous induction rates. In any given habitat the fitness of a phage will depend on the inputs of sensitive cells and nutrient resources. In equable environments (modeled here using chemostats with constant inputs of nutrients and sensitive cells), bacteriophage with low probabilities of lysogeny and low induction rates can always invade when rare and will generally be good competitors. In variable environments (chemostats with seasonal inputs), bacteriophage with higher probabilities of lysogeny and higher induction rates are favored. In both equable and variable environments, the ability of a phage to invade when rare will depend on the properties of the resident phage, and it is possible for phages with divergent parameter values to coexist. The modeling suggests that bacteriophage that have evolved moderately low induction and lysogeny rates will be able to “hedge their bets” against environmental change without sacrificing the ability to compete well in a constant environment. Implications of this theory for understanding the molecular basis of gene regulation in temperate bacteriophage and other viruses are discussed. [TOP OF PAGE]
A model on the production of temperate phages in continuous culture. Noack,D. (1996). pp. 233-241. In AnonymousContinuous Cultivation of Microorganisms, Proceedings of the Fourth Symposium. ???, ??? [TOP OF PAGE]
Host-parasite persistence: the role of spatial refuges in stabilizing bacteria-phage interactions. Schrag,S., Mittler,J.E. (1996). Am. Nat. 148:348-347.We manipulated a bacteria-phage model system to investigate empirical and theoretical conditions allowing for the coexistence of an Escherichia coli host with each of two virulent phage species, a T1-like phage (T1X) and lambda-vir. In minimal medium in the laboratory, bacteria coexisted with each phage species in continuous (chemostat) culture; however, in serial culture, T1X rapidly became extinct in all cases and lambda-vir became extinct in most cases. When we refined a previously developed mechanistic model of bacteria-phage interactions in continuous culture, this model failed to predict our laboratory observations of long-term stability of bacteria and phage in chemostats. A serial transfer version of this model, however, came much closer to predicting bacteria-phage dynamics. To investigate why models of continuous culture failed, we tested hypotheses for phage persistence by manipulating experimental culture conditions. We found that wall populations of bacteria strongly influenced the stability of both phage species. When wall populations were not allowed to develop in chemostats, both phage species became extinct rapidly; conversely, when wall populations were allowed to develop in serial transfer, both phage species showed evidence of long-term persistence. The final percentage of sensitive bacteria was significantly higher in walls than in liquid populations, suggesting that glass surfaces did indeed act as a spatial refuge for sensitive bacteria. In addition, serial transfer of bacteria and phage on agar surfaces produced more stable interactions than in liquid. We discuss these results in light of previous observations of bacteria-phage interactions and in the broader context of parasite-host and predator-prey coexistence conditions. [TOP OF PAGE]
Can phage defence maintain colicin plasmids in Escherichia coli? Feldgarden,M., Golden,S., Wilson,H., Riley,M.A. (1995). Microbiology 141:2977-2984.We examined the role of plasmid-based phage defence in maintaining plasmids, using colicin plasmids in Escherichia coli as a model system. Experimental data indicated that the possession of a colicin plasmid can confer limited protection against bacteriophages. A continuous culture model, using these experimental values, indicated that the observed limited protection alone could selectively maintain colicin plasmids, without requiring a competitive advantage due to colicinogeny. Phage defence might explain the current maintenance of colicin plasmids, given the naturally occurring high levels of resistance to colicins. This model also suggests that many plasmids might be maintained in natural populations, in part, by phage resistance, including 'cryptic' plasmids for which no phenotype is known. [TOP OF PAGE]
Population dynamics in the co-culture of Shigella flexneri 1b original strain and its antigenic 3b mutant carrying a prophage. Lachowicz,T.M., Dziadkowiec,D., Kopocinska,I., Kopocinski,B. (1995). Microbios 83:89-106.The antigenic mutant Shigella flexneri 3b showed selective prevalence when subcultured with the original strain 1b. Mathematical analysis of such co-cultures showed that the dynamics of bacterial growth may be described by equations of the Lotka-Volterra type. The analysis of serial cultivations suggests that parameters of the equations may be realizations of random variables characterizing strains and media. The mutant carries a prophage lethal for the original strain. Distinctive features of the growth of these strains alone and in co-culture may be successfully explained by the differences in growth parameters, without phage inference. The concurrence model connected only with the existence of the phage is not sufficient. A complete description of the dynamics of the co-culture is obtained by the connection of the assumptions of two models: strains in competition and growth of strains with phage, given the random character of the parameters. [TOP OF PAGE]
A continuous culture model to examine factors that affect transduction among Pseudomonas aeruginosa strains in freshwater environments. Replicon,J., Frankfater,A., Miller,R.V. (1995). Appl. Environ. Microbiol. 61:3359-3366.Transduction among Pseudomonas aeruginosa strains was observed in continuous cultures operated under environmentally relevant generation times, cell densities, and phage-to-bacterium ratios, suggesting its importance as a natural mechanism of gene transfer. Transduction was quantified by the transfer of the Tra super(-) Mob super(-) plasmid Rms149 from a plasmid-bearing strain to an F116 lysogen that served as both the recipient and source of transducing phages. In control experiments in which transduction was prevented, there was a reduction in the phenotype of the mock transductant over time. However, in experiments in which transduction was permitted, the proportion of transductants in the population increased over time. These data suggest that transduction can maintain a phenotype for an extended period of time in a population from which it would otherwise be lost. Changes in the numbers of transductants were analyzed by a two-part mathematical model, which consisted of terms for the selection of the transductant's phenotype and for the formation of new transductants. Transduction rates ranged from 10 super(-9) to 10 super(-6) per total viable cell count per ml per generation and increased with both the recipient concentration and the phage-to-bacterium ratio. These observations indicate an increased opportunity for transduction to occur when the interacting components are in greater abundance. [TOP OF PAGE]
Period dependent selection in continuous culture of viruses in a periodic environment. Aita,T., Husimi,Y. (1994). J. Theor. Biol. 168:281-289.Selection in a cellstat culture of two mutant strains of a bacteriophage under periodically fluctuating temperature was analyzed mathematically and numerically. Each of the two viral strains (P-1 and P-2) was assumed to have a different Arrhenius activation energy for its reproduction reaction. A phase diagram of the final state in the continuous culture was drawn. The most noticeable was that there were both P-1-only and P-2-only phases of competitive exclusion depending on the period of oscillation and the dilution rate. The period-dependent selection was proved that it was based on the feedback effect via the host-population change. At a short period of oscillation, the strain with larger arithmetic average fitness ultimately dominated in the population; on the other hand, at a long period of oscillation, the strain with larger geometric average fitness ultimately dominated. There was a co-existence phase between the two exclusion phases. The results suggest the feasibility of a method to escape from trapping at local optima on a fitness landscape in evolutionary molecular engineering. [TOP OF PAGE]
Modeling the role of viral disease in recurrent phytoplankton blooms. Beltrami,E., Carroll,T.O. (1994). J. Math. Biol. 32:857-863.The recurrent pattern of some phytoplankton species can vary considerably from year to year. Recent experimental work suggests that the contamination of algal cells by viruses can serve as a regulatory mechanism in bloom dynamics. A simple trophic model is proposed that includes virus-induced mortality, and it mimics the actual bloom patterns of several species. The model results are compared to actual data by a combination of nonlinear forecasting techniques. [TOP OF PAGE]
Virus coagulation in aqueous environments. Grant,S.B. (1994). Environ. Sci. Technol. 28:928-933.A mathematical model is presented for the temporal decline in total infectious units caused by simultaneous first-order inactivation and Brownian coagulation of viruses in an aqueous environment. On the basis of published physicochemical and biological constants for poliovirus, human immunodeficiency virus, and indigenous marine and freshwater bacteriophage, the model predicts that virion-virion coagulation is negligible in most aquatic systems. This analysis provides a framework for investigating the effect of coagulation and inactivation on viral infectivity and for developing more sophisticated models of virus survival outside the host cell. [TOP OF PAGE]
Marine viral ecology: Incorporation of bacteriophage into the microbial planktonic food web paradigm. Murray,A.G., Eldridge,P.M. (1994). J. Plankton. Res. 16:627-641.In the decade since the microbial loop was defined by Azam et al. (Mar. Ecol. Prog. Ser., 59, 1-17, 1983), the importance of the interaction between microbial organisms and the larger planktonic animals has been a subject of controversy. Until recently, grazing was considered to be the major fate of bacterial production. Now, however, viruses are seen to have an important role in microbial processes. We describe how growth and recycling parameters affect the transfer of bacterial production through a microbial loop model that includes viruses. The loop is very inefficient for all reasonable conditions, but its relative importance as a source of mesozooplankton nutrition is variable. The model demonstrates that in mesotrophic coastal waters, the microbial loop is unlikely to supply more than a minor component of mesozooplankton nutrition, a proposition that is supported by accumulating evidence. For oligotrophic pelagic waters, the model indicates that in the absence of viruses the microbial loop, despite its low efficiency, may provide an important resource for mesozooplankton. Bacterial production, without viral mortality, is also relatively important in the case of direct exploitation by salps. Under these conditions, bacteria account for 10-30% of mesozooplankton nutrition. With high levels of bacteriophage activity, zooplankton production is generally reduced by 5-15%. We thus conclude that bacteriophages could significantly affect mesozooplanktonic and, hence, exploitable marine production. [TOP OF PAGE]
Viral dynamics II: A model of the interaction of ultraviolet light and mixing processes on virus survival in seawater. Murray,A.G., Jackson,G.A. (1993). Mar. Ecol. Prog. Ser. 102:105-114.Viruses are an important component in the functioning of marine ecosystems. They are especially vulnerable at the stage when they are free particles seeking a new host. A major factor in viral mortality during this phase is the presence of ultraviolet (UV) radiation. UV radiation penetrates only a short distance into the water column because of a very high attenuation coefficient. Processes that move viruses to the surface change their UV exposure. We have modelled the mortality of viruses subject to UV radiation by means of a Lagrangian Monte-Carlo type model that incorporates viral movements within the mixed layer. For viruses with a given UV-induced surface mortality, mixed-layer depth and UV attenuation coefficient are important factors in their water column mortality. Other more subtle factors can also affect viral mortality: nature of the diurnal thermocline; type of mixing; and the time of day that they are released into the water. Viruses not subject to mixing have their mortality rate enhanced by internal wave motion, although the absolute mortality rates may remain low. Increased UV irradiance associated with atmospheric ozone depletion could significantly change viral mortality in polar environments. UV-induced mortality can be comparable to that from biological factors such as virucidal bacteria. [TOP OF PAGE]
Nucleic acids from the host bacterium as a major source of nucleotides for three marine bacteriophages. Wikner,J., Vallino,J.J., Steward,G.F., Smith,D.C., Azam,F. (1993). FEMS Microbiol. Ecol. 12:237-248.The incorporation of 32P-phosphorus into marine bacteriophage nucleic acid was studied in culture experiments to investigate the source of nucleotides used by the phage. We consistently found that the 32P-specific activity in the phage genome increased during the 11 h incubation and was low relative to the specific activity in the medium, averaging 21% (.+-. SD 5.9) for the three phage isolates. This was in accordance with a mathematical model where most of the nucleotides for phage DNA synthesis were derived from the host cell nucleic acid rather than de novo synthesis. We propose that this metabolic strategy may be common among marine phages, as an adaptation to a nutrient poor environment. Consequently, the contribution of free DNA to the dissolved fraction through phage lysis of bacteria, may be less than previously thought. Also during radiolabelling of bacteriophages in natural water samples, isotope dilution may be dependent on the specific growth rate of the bacterial host. [TOP OF PAGE]
Bacteriophage-host interactions in aquatic systems. Miller,R.V., Sayler,G.S. (1992). pp. 176-193. In In Wellington,E.M.H. and van Elsas,J.D. (eds.), Genetic Interactions among Microorganisms in the Natural Environment. Pergamon Press, Oxford. Recently, bacterial virus (bacteriophage) concentrations in many aquatic environments have been reported to be one to two orders of magnitude higher than bacterioplankton (Bergh et al., 1989, Børsheim et al., 1990; Bratbak etal., 1990; Proctor & Fuhrman, 1990). These observations have brought into question many of our conclusions about the ecology of aquatic microbial populations. Is bacterial abundance really controlled by viral infection and not by heterotrophic nanoplanktonic predators as has been previously thought? Is the make-up of bacterial communities controlled by bacteriophage susceptibility? Is gene transfer of chromosomal and extrachromosomal DNA by transduction a viable method for the reassortment of natural gene pools in aquatic microbial populations? Will alterations to the environment which alter the flux of solar UV radiation have an effect on interactions between aquatic bacteriophages and their bacterial host populations? Even though phage-host interactions have not been investigated in any great detail in aquatic environments, there are data that suggest each of these questions may be answered in the affirmative. In this review, we survey the available literature pertinent to assessing the roles of environmental viruses in determining microbial community structure and diversity in aquatic ecosystems. [TOP OF PAGE]
Viral dynamics: A model of the effects of size, shape, motion, and abundance of single-celled planktonic organisms and other particles. Murray,A.G., Jackson,G.A. (1992). Mar. Ecol. Prog. Ser. 89:103-116.The transport of aquatic viruses to particles can be described in terms of diffusive transport from solution. Such transport is influenced by motion of the water relative to the particle. Because transport rate is determined purely by physical factors it is independent of whether the particle is a host or non-host organism. The low viral diffusivity relative to that for dissolved nutrients makes transport enhancement from organism swimming more important for viruses. The virus contact rate with bacteria is relatively unaffected by such motions because of small bacterial sizes. Transport rates for phytoplankton and protozoa can increase over an order of magnitude when swimming motions are considered. Although larger organisms have much higher transport rates per individual, their far lower concentrations in sea water should make small organisms the preferred targets for viruses. Rates of host-virus interactions in culture are closely related to predictions from transport theory. There is a fairly close relationship between bacterial populations and virus disappearance rates in the marine environment, suggesting that non-host organisms are a major cause of viral mortality at the higher ionic strengths typical of sea water. Other factors, such as UV radiation, must also be included when estimating viral mortality in seawater. [TOP OF PAGE]
Replication of viruses in a growing plaque: A reaction-diffusion model. Yin,J., McCaskill,J.S. (1992). Biophys. J. 61:1540-1549.An understanding of viral replication process commonly referred to as “plaque growth” is developed in the context of a reaction-diffusion model. the interactions among three components: the virus, the healthy host, and the infected host are represented using rates of viral adsorption and desorption to the cell surface, replication and release by host lysis, and difdusion. The solution to the full model reveals a maximum in the dependency of the velocity of viral propagation on its equilibrium adsorption constant, suggesting that conditions can be chosen where viruses which adsorb poorly to their hosts will replicate faster in plaques than those which adsorb well. ¶ Analytic expressions for the propagation velocity as a function of the kinetic and diffusion parameters are presented for the limiting cases of equilibrated adsorption, slow adsorption, fast adsorption, and large virus yields. Hindered diffusion at high host concentrations must be included for quantitative agreement with experimental data. [TOP OF PAGE]
Selection for lysis inhibition in bacteriophage. Abedon,S.T. (1990). J. Theor. Biol. 146:501-511.For Escherichia coli cells that have been infected by T-even bacteriophages (phages T2, T4, and T6), the adsorption of a second T-even phage results in an increase in the length of the original phage infection and an associated increase in the number of phages produced by the same infected cell. This is a phage encoded response called lysis inhibition. In this study the ecological significance of lysis inhibition is explored. In particular it is argued that lysis inhibition is an adaptive response to environments containing high concentrations of infected cells and low concentrations of uninfected cells. [TOP OF PAGE]
Selection for bacteriophage latent period length by bacterial density: A theoretical examination. Abedon,S.T. (1989). Microb. Ecol. 18:79-88.In bacteriophage (phage), rapid and efficient intracellular progeny production is of obvious benefit. A short latent period is not. All else being equal, a longer latent period utilizes host cell resources more completely. Using established parameters of phage growth, a simulation of three successive phage lysis cycles is presented. I have found that high, but not low, host cell densities can select for short latent periods. This results from phage with short latent periods more rapidly establishing multiple parallel infections at high host cell concentrations, whereas phage with long latent periods are restricted to growth within a single cell over the same period. This implies that phage with short latent periods habitually grow in environments that are rich in host cells. [TOP OF PAGE]
Selection and evolution of bacteriophages in cellstat. Husimi,Y. (1989). Adv. Biophys. 25:1-43.Objectives of this work were as follows: 1. to establish a laboratory experimental system utilizable in a biophysical approach to molecular evolution; and 2. to provide real world parameters to theories of molecular evolution, especially to Eigen's theory of quasi-species. Secretion type bacteriophage fd of E. coli, closely related phages and artifactual chimera phages of fd, and a virulent Q beta of E. coli were cultured continuously in a specially designed fermenter called a “cellstat”. A phage is cultured in a flow of host bacterial cells. Due to its high dilution rate, the mutant cell could not be selected in a cell stat. It was therefore recognized that the cellstat is suitable for study of the selection and evolution process of a bacteriophage . . . [ABSTRACT NOT COMPLETE]. [TOP OF PAGE]
Dynamics of interactions between bacteria and virulent bacteriophage. Lenski,R.E. (1988). Adv. Microbial. Ecol. 10:1-44.The interactions of bacteria and their viruses (bacteriophage) are, by and large, ones of trophic exploitation. In fact, “phage” is derived from the Greek word for “devour.” Using the criteria of relative size, the interactions can be defined as parasitism (Bull and Slater, 1982). Because replication by most virulent phage necessarily results in bacterial death, these interactions could also be called predation. Certain interactions could even be termed mutualistic, as some temperate phage encode phenotypic characteristics that are of direct benefit to their hosts. Semantics adide, the fundamental ecological question that I will attempt to address in this chapter is: What role do bacteriophage infections play in limiting the abundance of bacteria? ¶ Such a broad question cannot be answered using any single approach or line of evidence. Therefore, I have chosen to organize this chapter in a hierarchical manner, moving from mathematical models, throught simple laboratory communities, and finally to much more complex communities in natural settings. But first it is necessary to review the basic biological features of the itneractions between bacteria and pahge, as revealed by the extraordinary advanceds in the areas of microbial genetics and molecular biology. This research provides a precise methodological and conceptual framework for examining ecological hypotheses, probably unrivaled for any other parasite-host interaction. the same features of the phage-bacteria system that have been so valuable in nonecological research also contribute to its power in addressing fundamental ecological questions: specifically, ease of culture and sampling, high population densities, and short generation times. In fact, generations are so short that it becomes imperartive to consider the effects of evolutionary change on population dynamics, even over the course of short-term experiments. [TOP OF PAGE]
Computer simulation of T3/T7 phage infection using lag times. Buchholtz,F., Schneider,F.W. (1987). Biophys. Chem. 26:171-179.A minimal mechanism is proposed which describes the transcriptional and translational processes for four phage proteins (RNA polymerase, DNase, primase and DNA polymerase) involved in T3/T7 DNA replication. Phage DNA replication is also included. It is shown how lag times may be incorporated into a kinetic mechanism. The distinct three-stage transport of phage DNA into the bacterial host (E. coli) is considered. DNA transport is assumed to be rate-determining for the transcription class I and II proteins. Transcriptional and translational lag times have been calculated on the basis of available gene mapping of T7 phages. The kinetic behavior of T7 and T3 phage infection is practically identical. The hydrolysis of bacterial DNA by phage DNase (endonuclease and exonuclease) as well as the subsequent phosphorylation to the deoxymononucleoside triphosphates are assumed to be rate-determining in phage DNA replication. Good agreement with experiment is obtained by computer simulations. [note: figure 1 gives a good view of the relative rates of DNA replication, phage production, phage release, and the production of various enzymes over the course of an infection.]. [TOP OF PAGE]
Modelling the interaction of Streptomycetes and their phage. Manchester,L. (1986). University of Liverpool. [TOP OF PAGE]
Constraints on the coevolution of bacteria and virulent phage: A model, some experiments, and predictions for natural communities. Lenski,R.E., Levin,B.R. (1985). Am. Nat. 125:585-602.One view of the coevolution of parasites and their hosts is that of a gene-for-gene arms race between host defenses and parasite counterdefences. We have incorporated mutations into a model of the ecological interactions between bacteria and virulent phage to determine rates of mutation that would be consistent with this scenario. The model assumes an open habitat (e.g., a chemostat) in which virulent phage and sensitive bacteria can coexist. Equilibrium densities of bacteria and phage are inversely proportional to the efficiency with which phage irreversibly adsorb to their hosts. The absolute rate at which mutations appear is proportional to the product of habitat size, population density, rate of increase, and mutation rate. ¶ The bacterium Escherichia coli B readily evolved resistance to virulent phage T4 in our chemostat experiments. Approximately 100 h was required for the appearance, establishment, and attainment of a resourse-limited population of these T4-resistant mutants; this time period is close to that predicted from the model when the parameters of the model are estimated independently. No hostrange phage T4 mutants appeared, yet the phage persisted even after the resistant bacteria had become resource-limited. We hypothesized that the failure to observe corresponding phage mutants indicates mutational constraints on the coevolutionary potential of this phage. We also hypothesized that the persistence of the wild-type phage indicates the presence of a minority population of sensitive bacteria that persists because of selective constraints which produce a competitive disadvantage for resistant baceria under resource-limiting conditions. Both of these hypotheses were verified. Host-range T4 mutants occurred at a rate on the order of 10-12 or less, and could not be expected in the chemostats for several years. T4-sensitive and -resistant bacteria had very nearly the same exponential growth rates, but at steady state the latter had approximately a 50% disadvantage. ¶ We also examined the interactions of E. coli B and virulent phages T2, T5, and T7 for evidence of selective and mutational constraints on the bacteria and phage, respectively. Under the conditions of our experiments, T2-resistant and T7-resistant (but not T4-resistant) bacteria also had clear competitive disadvantages to sensitive bacteria udner resource-limiting conditions. We were able to isolate T2 and T7 (but not T5) host-range mutants. Even with T2 and T7, however, we could not select indefinitely for host-range mutants active against higher-order resistant bacteria. This general asymmetry in the coevolutionary potential of bacteria and phage occurs becuase mutations conferring resistance may arise by either the loss or alteration of gene function, while host-range mutations depend on specific alterations of gene function. ¶ These constraints preclude observing endless arms races between baceria and virulent phage. Instead, because of the asymmetry in coevolutionary potential of these hosts and parasites, we anticipated that natural communities of coliform bacteria and virulent coliphage are dominated by bacterial clones resistant to all co-occurring virulent phage. If virulent pahge to which the dominant clones are sensitive should appear, then bacteria will either rapidly evolve resistance or be replaced by existing clones resistant to the phage. Thus, the role of virulent phage in structuring communities of bacteria is seen as important in determining clonal composition but uninportant in determining bacterial densities. [TOP OF PAGE]
Bacteria and phage: A model system for the study of the ecology and co-evolution of hosts and parasites. Levin,B.R., Lenski,R.E. (1985). pp. 227-242. In In Rollinson,D. and Anderson,R.M. (eds.), Ecology and Genetics of Host-Parasite Interactions. Academic Press, London. The results are reviewed of theoretical and experimental investigations of the population biology of bacteria and bacteriophage, emphasizing those apsects of general interest in the study of host-parasite ecology and evolution. ¶ 1) Existence conditions: the conditions are considered udner which phage can invade bacterial populations and will stably co-exist with these hosts. Particular emphasis is given to the effects of phage resistant bacterial clones on these communities, and hypotheses are presented to account for the observation that experimental populations of bacteria and virulent phage are more stable than anticipated from theory. ¶ 2) Co-evolution: The nature and effects of selection on the interacting populations of bacteria and phage are examined. Evidence is presented that the resulting co-evolution is a constrained process, rather than the indefinite gene-for-gene arms race previously postulated. ¶ 3) Latency: Temperate bacteriophage are analogous to the latent virusses of eukaryotes. We critically discuss three classes of hypotheses for the ecological conditions and selective pressures responsible for the evolution and maintenance of temperate (as opposed to virulent) modes of phage reproduction. ¶ 4) Immunity: Bacterial restriction-modification systems are similar to the immune systems of higher organisms. The hypothesis is considered that restriction-modification systems evolved nad are maintained for the defence against phage infection and we speculate on the effects of this type of immune system on the population dynamics of bacteria and phage. ¶ 5) Coda: This review is concluded with a brief consideration of the use of phage for the biological control of bacteria. [TOP OF PAGE]
The population biology of bacterial viruses: Why be temperate. Stewart,F.M., Levin,B.R. (1984). Theor. Pop. Biol. 26:93-117.A model of the interaction between populations of temerate 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 demonstrted 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 evalulated. Two hypothesesfor the “advantage of temperance” are championed. (1) As a consequence of the allelopathic effects of diffusing phages, 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. [TOP OF PAGE]
Coevolution in bacteria and their viruses and plasmids. Levin,B.R., Lenski,R.E. (1983). pp. 99-127. In In Futuyama,D.J. and Slatkin,M. (eds.), Coevolution. Sinauer Associates, Inc., Sunderland, Massachusetts. [no abstract]. [TOP OF PAGE]
Some theoretical aspects of protein coevolution in the ecosystem “phage-bacteria”. II. The deterministic model of microevolution. Rodin,S.N., Ratner,V.A. (1983). J. Theor. Biol. 100:197-210.[TOP OF PAGE]
Some theoretical aspects of protein coevolution in the ecosystem of “phage-bacteria”. I. The problem. Rodin,S.N., Ratner,V.A. (1983). J. Theor. Biol. 100:185-195.[TOP OF PAGE]
Appendix: a model of plaque formation. Kaplan,D.A., Naumovski,L., Rothschild,B., Collier,R.J. (1981). Gene 13:221-225.Equations describing plaque formation in soft agar have been based on certain simplifying assumptions, for which data are presented. The derived equations permit one to calculate (i) average plaque size as a function of the initial density of indicator cells (Do), (ii) the number of cells lysed per plaque as a function of Do, and (iii) the cumulative number of cells lysed at various stages of plaque development. The calculated values agree well with those determined experimentally. [TOP OF PAGE]
[Theoretical model of the predator-prey interaction kinetics between “Bdellovibrio bacteriovoru”s and “escherichia coli “(author's transl)]. Marchand,A., Gabignon,O. (1981). ANNALES DE MICROBIOLOGIE 132 B:321-336.A theoretical model is suggested in order to explain the main features of the interaction kinetics between the micropredator Bdellovibrio bacteriovorus and its prey Escherichia coli. Three parametes are used in this model: the incubation time T, the fixation rate constant k, and the predator multiplication factor a. Their values can be determined from the experimental variations of the total predator concentration p, and the total density of preys (c + c'). An experimental study of the predation kinetics was performed at various temperatures (25-40 degrees C) and in media with different Ca++ and Mg++ concentrations. From the values of parameters obtained, theoretical prey and predator density curves were computer-simulated; they agree satisfactorily with the experimental curves. The parameters values are quite reasonable and in good agreement with previous findings. [TOP OF PAGE]
Mathematical models for continuous culture growth dynamics of mixed populations subsisting on a heterogeneous resource base. II. Predation and trophic structure. Smouse,P.E. (1981). Theor. Pop. Biol. 20:127-149.[TOP OF PAGE]
Mathematical models for continuous culture growth dynamics of mixed populations subsisting on a heterogeneous resource base. I. Simple competition. Smouse,P.E. (1980). Theor. Pop. Biol. 17:16-36.[TOP OF PAGE]
Diffusion-controlled reactions on spherical surfaces: Applications to bacteriophage fiber attachment. Bloomfield,V.A., Prager,S. (1979). Biophys. J. 27:447-453.[TOP OF PAGE]
Determination of the biological parameters of bacterium-phage complexes. Gaspar,S., Ronto,G., Muller,G. (1979). Z Allg Mikrobiol 19:163-169.The authors present a method of measurement and evaluation for continuous cultures of bacteria infected by virulent phages. By the comparison of the model describing the phage-bacterium interaction and their own experimental data they determined the following biological parameter values characterizing the interaction: the adsorption rate (mu), the expectation of the latency period (T) and its standard deviation ((sigma), the time required for lysis (d), the infection efficiency (eta) and the average burst size (C). The parameters were used for the determination of optimal cultivating conditions (maximum phage yield). [TOP OF PAGE]
Resource limited growth, competition, and predation: A model and experimental studies with bacteria and bacteriophage. Levin,B.R., Stewart,F.M., Chao,L. (1977). Am. Nat. 111:3-24.We present a model of resource-limited population growth, competition, and predation based on what we believe to be biologically realistic assumptions about the relationship between resources and the growth of primary consumers and about the interaction of the primary consumers with the predators that prey upon them. Consideration is given to an equable habitat in which resources are continually supplied and wastes are continually removed. The general properties of this model are exmanined and two specific cases are studied in some detail: (i) one resource, one prey, and one predator, and (ii) one resource, two prey, and one predator. Particular consideration is given to the conditions which will permit the continued coexistance of the itneracting populations. In conceiving this model we were guided by the specific case of bactera and their virulent viruses. To study its validity we compare the theoretical predictions with the experimental results from continuous-culture populations of the bacterium E. coli and the phage T2. ¶ Structurally stable equilibria with all populations coexisting are possible when the number of distinct predator populations is not more than the number of distinct prey populations and the number of the latter is not more than the sum of the number of resources and the number of predator populations. ¶ For one resource, one prey, and one predator threre are stable states of coexistance. Given specific resource utilization functions, the levels of these equilibria or oscillations and the range of parameter values required for stability can be determined. ¶ In situations where a stable equilibrium exists for the one predator-one prey system, a second population of primary consumers which is totally resistant to predation can also be maintained. Sufficient conditions for this to occur are that the resistant population have a lower intrinsic growth rate than the sensitive but that the former can, nevertheless, survive and multiply living on the resources present in the one predator-one prey system. If, however, this second species of primary consumer becomes slightly sensitive to predation, it may then entirely displace the original sensitive population. ¶ Stable equilibria were observed in glusose minimal continuous cultures containing T2 sensitive E. coli B and T2 phage. The equilibrium concentration of glucose and the densities of the populations were similar to those predicted by the model. However, with the estimated values of the parameters, the experimental system fell in the range where the model predicted the oscillations would increase to the pont where the populations would eventually become extinct. ¶ Stable equilibria were also observed for a glucose-limited chemostat culture containing T2 phage together with a T2-sensitive clone of E. coli B and a T2-resistant strain of E. coli K12. This system fulfilled the conditions under which the theory predicts that stable coexistance will occur. ¶ We discuss the validity of this model as a general analogue of resource limited growth, competition, and predation in planktonoic species. We also consider the implications of these theoretical and experimental results for the general theory of competition and predation and for the specific problem of coexistance for bacteria and their virulent viruses. [TOP OF PAGE]
Dynamics of the interaction between “predator” and “prey” under flowing conditions. (Russian). Nazar\cprime ev,O.E. (1975). Dinamika Sistem 7:148-156 (168).Author's summary: “We consider a mathematical model of the interaction dynamics between `predator' and `prey' under flowing conditions, using the example of interaction between bacteriophages and bacteria. The essential difference of the model from standard models of small type is the fact that in this model a time lag is introduced, characterizing the time the phage stays in the bacterium (latency period). For the model in question we determine stationary states, construct a $D$-partitioning of the density of two parameters, determine the domain of stability of stationary states and show the character of the transition processes when the system goes into a stationary condition.”. [TOP OF PAGE]
On the distribution of inanimate marks over a linear birth-and-death process. Morgan,B.J.T. (1974). Journal of Applied Probability 11:423-436.[TOP OF PAGE]
Studies of the bacteriophage kinetics of multicellular systems: a statistical model for the estimation of burst size per cell in streptococci. Barron,B.A., Fischetti,V.A., Zabriskie,J.B. (1970). J. Appl. Bacteriol. 33:436-442.The determination of burst size is chaining or clustering bacteria involves experimental variables that must be considered in estimating burst size/cell and in contrasting the results of different experiments. Whereas the Poisson distribution is the model for single cell host systems, the statistical model presented here provides a method for evaluating the probability of obtaining a plate that reflects the lysis of more than one cell. [TOP OF PAGE]
Age dependent stochastic models for phage reproduction. Srinivasan,S.K., Rangan,A. (1970). Journal of Applied Probability 7:251-261.Authors' summary: “The problem of age specific bacteriophage growth is dealt with, using the product density approach. Expressions for the product densities, taking into account the intermediate stages of transformations from the vegetative phage to mature phage, are also given.”. [TOP OF PAGE]
Direct solution of Markovian phage attachment to bacteria in suspension. Chang,M.L., Chang,T.S. (1969). Math. Biosci. 5:9-18.A Markov process of phage attachment to bacteria in suspension is considered. For such a stochastic process, the probabilities P(n0, n1, . . . , nr; v0; t) of n0, n1, . . . , nr bacteria having 0, 1, . . . , r phages attached to them (where r is the maximum number of phages that can be attached to a bacterium) and v0 unattached phages at t >= 0 are related by a rather complicated differential-difference equation. This article presents a direct solution of such a stochastic process with contrained random variables. [TOP OF PAGE]
Some new results in the mathematical theory of phage-reproduction. Puri,P.S., Prem,S. (1969). Journal of Applied Probability 6:493-504.In the theory of phage reproduction, the mathematical models considered thus far (see Gani [5]) assume that the bacterial burst occurs a fixed time after infection, after a fixed number of generations of pahge multiplication, or when the number of mature bacteriophages has reached a fixed threshold. In the present paper, a more realistic assumption is considered: given that until time t the bacterial burst has not taken place, its occurrence between t and t + Dt is a random event with probability f(• | t)Dt + o(t), where f is a non-negative and non-decreasing function of the number X(t) of vegetative phages and of Z(t), the number of mature bacteriophages at time t. More specifically it is assumed that f = b(t)X(t) + c(t)Z(t) with b(t),c(t)>=0. Here X(t) denotes the survivors in a linear birth and death process and Z(t) the number of deaths until time t. The joint distribution of XTand ZT, the respective numbers of vegetative and mature bacteriophages at the burst time is considered. The distribution of ZT is then fitted to some observed data of Delbrück[2]. [TOP OF PAGE]
On an extension of Gani's model for attachment of phages to bacteria. Bhat,B.R. (1968). Journal of Applied Probability 5:572-578.In recent papers Yassky (1962) and Gani (1965) have considered respectively deterministic and stochastic models for the attachment of pahges to bacteria. Following Brenner's (1965 [sic, should read 1955]) conjecture they assumed that there is a maximum, S (say) to the number of phages that can be attachhed to a bacterium. In this note, Gani's (1965) results will be obtained starting from a different set of assumptions. This modification enables us to consider the case when S is a random variable, which probably is a more realistic assumption. Some remarks on the problem of estimation for the latter model are given in Section 3. [TOP OF PAGE]
A model on the production of temperate phages in continuous culture. Noack,D. (1968). pp. 233-241. In AnonymousContinuous Cultivation of Microorganisms (Proc. 4th Symp). [TOP OF PAGE]
A regulatory model for steady-state conditions in populations of lysogenic bacteria. Noack,D. (1968). J. Theor. Biol. 18:1-18.[TOP OF PAGE]
Estimation of the parameter in the stochastic model for phage attachment to bacteria. Srivastava,R.C. (1968). Annals of Mathematical Statistics 39:183-192.[TOP OF PAGE]
Some aspects of the stochastic model for the attachment of phages to bacteria. Srivastava,R.C. (1967). Journal of Applied Probability 4:9-18.[TOP OF PAGE]
Stochastic phage attachment to bacteria. Gani,J. (1965). Biometrics 21:134-139.[no abstract]. [TOP OF PAGE]
Some birth-death and mutation models for phage reproduction. Gani,J., Yeo,G.F. (1965). Journal of Applied Probability 2:150-161.[TOP OF PAGE]
Stochastic Models For Bacteriophage. Gani,J. (1965). Methuen & Co. Ltd., London.The use of mathematical methods in biology may be traced back to Galton's work on “Co-relations” at the end of the nineteenth century, or if demographic studies are included as part of biology, to Graunt's “Bills of Mortality” at the turn of the seventeenth century. Write, Mather, Mal,cot, Kimura, Moran, Gause, Lotka, Neyman, McKendrick, Bailey, Bartlett, D.G. Kendall, among others, spring to mind as important contributors to such diverse fields as the correlation of biological characteristics, the analysis of agricultural and biological experiments, mathematical genetics, animal ecology and epidemic theory. Following on the quantitative work of Schlesinger, Delbrück, Dulbecco and Luria in this area of bacterial virology in the 1930's and 40's, the use of stochastic models of bacteriophage is only in its early stages. It is my hope that the following review will arouse the interest of research workers in applied mathematics and statistics in this fascinating area, and possibly suggest new (if somewhat complex) stachastic processes for study. It is also my belief that closer collaboration between experimental virologists and their mathematical and statistical colleagues may well lead to serious advances in virology. [TOP OF PAGE]
A model for chemical mutagenesis in bacteriophage. Kimball,A.W. (1965). Biometrics 21:875-889.[TOP OF PAGE]
A model for phage attachment to bacteria with death and reproduction. Gani,J., Nagai,T. (1964). Annals of Mathematical Statistics 35, 1835. In a bacterial colony of initial size n0 subject to attack by v0 bacteriophage, suppose that at any time t > 0, there are n uninfected bacteria, N bacteria with one or more phages attached to them, and v unattached phages. ¶ Approximate deterministic equations for these can be derived
where l, al are phage attachment rates to uninfected and infected bacteria respectively (a < 1), b is the bacterial reproduction rate, m the bacterial death rate from phage infection, and K the number of phages produced when an infected bacterium dies. ¶ These equations are discussed, and assuming a solution for the v can be found, whether exact or approximate, it is shown that a stochastic model may be set up for n, N, such that their joint probability of generating function can be obtained. [this is the entire publication]. [TOP OF PAGE]
The growth of viral plaques during the enlargement phase. Koch,A.L. (1964). J. Theor. Biol. 6:413-431.The kinetics of the enlargement phase of plaque development are considered. It is shown that the plaque diameter increases and depends primarily on the square root of the diffusion constant divided by the square root of the lag period. Additional theoretical treatment of the shielding influence of the recipient cells is presented. Literature observations made with bacterial, animal, and plant viruses are then compared with the theory. [TOP OF PAGE]
Models for a bacterial growth process with removals. Gani,J. (1963). Journal of the Royal Statistical Society. Series B (Statistical Methodology) 25:140-149.The paper considers the extinction of a bacterial colony subject to phage infection. A description of the biological process leads to the construction of a simplified model from which it is possible to derive the probability generation function (p.g.f.) for surviving bacteria in terms of repeated contour integrals. The distribution of phage offspring released by a single bacterium, and of bacterial infections due to these phages, are discussed. For bacterial birth and birth-death processes, it is possible to express the p.g.f. for surviving bacteria explicitly; this is done by first obtaining the p.g.f. conditional on numbers of bacterial infections, and then summing over all such possible infections. [TOP OF PAGE]
On uncertainties inherent in the determination of the efficiency of collision between virus particle and cells. Ogston,A.G. (1963). Biochim. Biophys. Acta 66:279-281.Several authors (VALENTINE AND ALLISON, TOLMACH AND STENT AND WOLLMAN) have recently concluded, or regarded it as established, that the efficiency of collision of virus particles with cells is near unity. In fact the methods used can only give meaningful values for the collision efficiency if this is less than 10-3-10-6, and are insensitive to higher values. Apart from this limitation, uncertainties in the kinetic theory of liquids prevents the exact measurement of collision efficiency under any conditions... One must conclude, therefore, that even in the most favourable case of collision with small spherical objects, the collision efficiency can be measured only if it is considerably less than 10-3. Even so, the value would be subject to a considerable uncertainty because of our prsent lack of exact knowledge of such microscopic quantities as the jump-length and the jump-frequency. [TOP OF PAGE]
The extinction of a bacterial colony by phages: A branching process with deterministic removals. Gani,J. (1962). Biometrika 49:272-276.This paper discusses two simple branching models for the extinction of a bacterial colony infected by phages. Their treatment by discrete time Markov chain methods does not appear to lead to simple explicit solutions. However, for one of the branching models a generating function method yields direct solutions for the probabilities of first extinction of the colony, as well as the probability of i survivals. The probability of eventual extinction of the bacteria is considered, and the paper concludes with extensions of the previous results to the case of unequal and random time intervals. [TOP OF PAGE]
A simple population model for phage reproduction. Gani,J. (1962). Bull. Math. Statist. 10:1-3.In a recent paper on phage crosses, Hershey (1958) has raised a number of interesting problems in population and genetic processes. A very simplified model of phage reproduction may be imagined as follows: at time t=0 let n phage particles be released in a medium containing N>n bacteria, and penetrate (infect) some bacteria, each with a probability 0<p<1 of success. Only the bacteria free of phages reproduce in an ordinary birth-death process with contant parameters l>m>0; meanwhile in any infected bacterium, the number of pahges may be considered to grow in a birst process with parameter a. Wen exactly r phages are produced, the bacterium dies, and releases these particles; they immediately infect more bacteria, and the process continues until all bactreria are killed. We are interested in the time of extinction T of the bacteria. [TOP OF PAGE]
An approximate stochastic model for phage reproduction in a bacterium. Gani,J. (1962). J. Aust. Math. Soc. 2:478-483.[TOP OF PAGE]
The clone size distribution of mutants arising from a steady-state pool of vegetative phage. Steinberg,C., Stahl,F. (1961). J. Theor. Biol. 1:488-497.[TOP OF PAGE]
Encounter efficiency of coliphage-bacterium interaction. Koch,A.L. (1960). Biochim. Biophys. Acta 39:311-318.A collision theory treatment for the adsorption of virus by host bacteria has been combinded with an extension of the Smoluchowski diffusion limited coagulation equation. From these considerations, the conclusion that the collision efficiency may approach unity is not found warranted. The effects of various types of mixing on the adsorption rate constant are discussed. Under conditions of diffusion limitation the effects of Brownian motion and sedimentation in the earth's gravitational field are considered and shown to be small though significant. More vigorous mixing is produced by laboratory aeration procedures and results in an increase in the diffusion limited rate. [TOP OF PAGE]
Frequency distribution of phage release in the one-step growth experiment. Adams,M.H., Wassermann,F. (1956). Virology 2:96-108.Phage release as a function of time in the one-step growth experiment is a close approximation to the integral of a normal frequency distribution. This suggests that the frequencies of bacterial lysis are normally distributed about a mean latent period. The use of the probit method to plot the data of the one-step growth experiment furnishes a sensitive method for studying nonrandom heterogeneity in a population of phage infected bacteria. Several examples of such nonrandome heterogeneity are presented and discussed. [TOP OF PAGE]
Thermodynamic and kinetic studies on the attachment of T1 bacteriophage to bacteria. Garen,A. (1954). Biochim. Biophys. Acta 14:163-172.The first phase of the invasion of E. coli strain B by T1 bacteriophage has been found to proceed in two distinct, consecutive steps1, 2, of which the first is a reversible binding of the phage to the bacterium through the interaction primarily of ionic groups on the two surfaces3, 4. Under optimal conditions at 37° C this reaction has a collision efficiency in the neighborhood of 100% (i.e., almost every random contact between reactants results in attachment). This high efficiency remains unchanged as the temperature is lowered from 37 to 2° C, showing that no significant activation energy is required. Reversible attachment is followed by an irreversible step, after which the phage can no longer be recovered as an infected particle. This step, in contrast to the preceeding one, requires around 18,000 calories/mole of activation energy, and yet also occurs with an almost 100% collision efficiency at 37° C. As will be shown in the present work, this result is a consequence of the stepwise nature of the reaction. [TOP OF PAGE]
An analysis of the mode of increase in number of intracellular phage particles at different temperatures. Bentzon,M.W., Maaløe,O., Rasch,G. (1952). Acta Pathologica et Microbiologica Scandinavica - Section B, Microbiology & Immunology 30:243-270.[TOP OF PAGE]
On the reliability of the Poisson distribution as a distribution of the number of phage particles infecting individual bacteria in a population. Dulbecco,R. (1949). Genetics 34:122-125.[no abstract]. [TOP OF PAGE]
