Single-cell analysis of lambda immunity regulation

Lytic/Lysogenic Transition as a Life-History Switch

The transition between lytic and lysogenic life cycles is the most important feature of the life-history of temperate viruses. To explain this transition, an optimal life-history model is offered based a discrete-time formulation of phage/bacteria population dynamics that features infection of bacteria by Poisson sampling of virions from the environment. The time step is the viral latency period. In this model, density-dependent viral absorption onto the bacterial surface produces virus/bacteria coexistence and density dependence in bacterial growth is not needed. The formula for the transition between lytic and lysogenic phases is termed the 'fitness switch'. According to the model, the virus switches from lytic to lysogenic when its population grows faster as prophage than as virions produced by lysis of the infected cells, and conversely for the switch from lysogenic to lytic. A prophage that benefits the bacterium it infects automatically incurs lower fitness upon exiting the bacterial genome, resulting in its becoming locked into the bacterial genome in what is termed here as a 'prophage lock'. The fitness switch qualitatively predicts the ecogeographic rule that environmental enrichment leads to microbialization with a concomitant increase in lysogeny, fluctuating environmental conditions promote virus-mediated horizontal gene transfer, and prophage-containing bacteria can integrate into the microbiome of a eukaryotic host forming a functionally integrated tripartite holobiont. These predictions accord more with the 'Piggyback-the-Winner' hypothesis than with the 'Kill-the-Winner' hypothesis in virus ecology.

Biological Properties of 12 Newly Isolated Acinetobacter baumannii-Specific Bacteriophages

Infections with the opportunistic Gram-negative bacterium Acinetobacter baumannii pose a serious threat today, which is aggravated by the growing problem of multi-drug resistance among bacteria, caused by the overuse of antibiotics. Treatment of infections caused by antibiotic-resistant A. baumannii strains with the use of phage therapy is not only a promising alternative, but sometimes the only option. Therefore, phages specific for clinical multi-drug resistant A. baumannii were searched for in environmental, municipal, and hospital wastewater samples collected from different locations in Poland. The conducted research allowed us to determine the biological properties and morphology of the tested phages. As a result of our research, 12 phages specific for A. baumannii, 11 of which turned out to be temperate and only one lytic, were isolated. Their lytic spectra ranged from 11 to 75%. The plaques formed by most phages were small and transparent, while one of them formed relatively large plaques with a clearly marked 'halo' effect. Based on Transmission Electron Microscopy (TEM), most of our phages have been classified as siphoviruses (only one phage was classified as a podovirus). All phages have icosahedral capsid symmetry, and 11 of them have a long tail. Optimal multiplicity of infections (MOIs) and the adsorption rate were also determined. MOI values varied depending on the phage-from 0.001 to 10. Based on similarities to known bacteriophages, our A. baumannii-specific phages have been proposed to belong to the Beijerinckvirinae and Junivirinae subfamilies. This study provides an additional tool in the fight against this important pathogen and may boost the interest in phage therapy as an alternative and supplement to the current antibiotics.

A conserved signaling pathway activates bacterial CBASS immune signaling in response to DNA damage

To protect themselves from the constant threat of bacteriophage (phage) infection, bacteria have evolved diverse immune systems including restriction-modification, CRISPR-Cas, and many others. Here, we describe the discovery of a two-protein transcriptional regulator module associated with hundreds of CBASS immune systems and demonstrate that this module drives the expression of its associated CBASS system in response to DNA damage. We show that the helix-turn-helix transcriptional repressor CapH binds the promoter region of its associated CBASS system to repress transcription until it is cleaved by the metallopeptidase CapP. CapP is activated in vitro by single-stranded DNA, and in cells by DNA-damaging drugs. Together, CapH and CapP drive increased expression of their associated CBASS system in response to DNA damage. We identify CapH- and CapP-related proteins associated with diverse known and putative bacterial immune systems including DISARM and Pycsar antiphage operons. Overall, our data highlight a mechanism by which bacterial immune systems can sense and respond to a universal signal of cell stress, potentially enabling multiple immune systems to mount a coordinated defensive response against an invading pathogen.

Protection of bacteriophage-sensitive Escherichia coli by lysogens

Some viruses that infect bacteria, temperate bacteriophages, can confer immunity to infection by the same virus. Here we report λ-immune bacteria could protect λ-sensitive bacteria from killing by phage λ in mixed culture. The protection depended on the extent to which the immune bacteria were able to adsorb the phage. Reconciling modeling with experiment led to identifying a decline in protection as bacteria stopped growing. Adsorption of λ was compromised by inhibition of bacterial energy metabolism, explaining the loss of protection as bacterial growth ceased.

Bacteriophage λ is a temperate virus infecting the bacterium Escherichia coli. Temperate phages have the ability to form lysogens where the prophage is maintained in the infected bacterium in a largely quiescent state. The lysogen becomes immune to superinfection by λ by blocking the development of the superinfecting phage. Here we report the λ lysogen not only protected itself from killing by λ phages but also protected λ-sensitive bacteria in mixed culture. This protection required that the lysogen was able to adsorb the superinfecting λ phages. The protection was also sensitive to the growth state of the mixed culture, and the λ lysogen lost efficiency in protecting λ-sensitive bacteria as it stopped growing. A mutant of the λ tail protein, λJ, was not subject to this loss of protection. Adsorption of λ having the wild-type J protein but not the mutant λJ protein to E. coli was inhibited by interference with bacterial energy metabolism. The last observation suggests wild-type λ preferentially infects bacteria with competent energy metabolism.

Bacteriophage λ RexA and RexB Functions Assist the Transition from Lysogeny to Lytic Growth

The CI and Cro repressors of bacteriophage λ create a bistable switch between lysogenic and lytic growth. In λ lysogens, CI repressor expressed from the P_RM promoter blocks expression of the lytic promoters P_L and P_R to allow stable maintenance of the lysogenic state. When lysogens are induced, CI repressor is inactivated and Cro repressor is expressed from the lytic P_R promoter. Cro repressor blocks P_RM transcription and CI repressor synthesis to ensure that the lytic state proceeds. RexA and RexB proteins, like CI, are expressed from the P_RM promoter in λ lysogens; RexB is also expressed from a second promoter, P_LIT , embedded in rexA. Here we show that RexA binds CI repressor and assists the transition from lysogenic to lytic growth, using both intact lysogens and defective prophages with reporter genes under control of the lytic P_L and P_R promoters. Once lytic growth begins, if the bistable switch does return to the immune state, RexA expression lessens the probability that it will remain there, thus stabilizing the lytic state and activation of the lytic P_L  and P_R  promoters. RexB modulates the effect of RexA and may also help establish phage DNA replication as lytic growth ensues.

Cell fate potentials and switching kinetics uncovered in a classic bistable genetic switch

Bistable switches are common gene regulatory motifs directing two mutually exclusive cell fates. Theoretical studies suggest that bistable switches are sufficient to encode more than two cell fates without rewiring the circuitry due to the non-equilibrium, heterogeneous cellular environment. However, such a scenario has not been experimentally observed. Here by developing a new, dual single-molecule gene-expression reporting system, we find that for the two mutually repressing transcription factors CI and Cro in the classic bistable bacteriophage λ switch, there exist two new production states, in which neither CI nor Cro is produced, or both CI and Cro are produced. We construct the corresponding potential landscape and map the transition kinetics among the four production states. These findings uncover cell fate potentials beyond the classical picture of bistable switches, and open a new window to explore the genetic and environmental origins of the cell fate decision-making process in gene regulatory networks.

Prophages and Growth Dynamics Confound Experimental Results with Antibiotic-Tolerant Persister Cells

Bacterial persisters are phenotypic variants that survive antibiotic treatment in a dormant state and can be formed by multiple pathways. We recently proposed that the second messenger (p)ppGpp drives Escherichia coli persister formation through protease Lon and activation of toxin-antitoxin (TA) modules. This model found considerable support among researchers studying persisters but also generated controversy as part of recent debates in the field. In this study, we therefore used our previous work as a model to critically examine common experimental procedures to understand and overcome the inconsistencies often observed between results of different laboratories. Our results show that seemingly simple antibiotic killing assays are very sensitive to variations in culture conditions and bacterial growth phase. Additionally, we found that some assay conditions cause the killing of antibiotic-tolerant persisters via induction of cryptic prophages. Similarly, the inadvertent infection of mutant strains with bacteriophage ϕ80, a notorious laboratory contaminant, apparently caused several of the phenotypes that we reported in our previous studies. We therefore reconstructed all infected mutants and probed the validity of our model of persister formation in a refined assay setup that uses robust culture conditions and unravels the dynamics of persister cells through all bacterial growth stages. Our results confirm the importance of (p)ppGpp and Lon but no longer support a role of TA modules in E. coli persister formation under unstressed conditions. We anticipate that the results and approaches reported in our study will lay the ground for future work in the field.IMPORTANCE The recalcitrance of antibiotic-tolerant persister cells is thought to cause relapsing infections and antibiotic treatment failure in various clinical setups. Previous studies identified multiple genetic pathways involved in persister formation but also revealed reproducibility problems that sparked controversies about adequate tools to study persister cells. In this study, we unraveled how typical antibiotic killing assays often fail to capture the biology of persisters and instead give widely differing results based on poorly controlled experimental parameters and artifacts caused by cryptic as well as contaminant prophages. We therefore established a new, robust assay that enabled us to follow the dynamics of persister cells through all growth stages of bacterial cultures without distortions by bacteriophages. This system also favored adequate comparisons of mutant strains with aberrant growth phenotypes. We anticipate that our results will contribute to a robust, common basis for future studies on the formation and eradication of antibiotic-tolerant persisters.

In silico Evolution of Lysis-Lysogeny Strategies Reproduces Observed Lysogeny Propensities in Temperate Bacteriophages

Bacteriophages are the most abundant organisms on the planet and both lytic and temperate phages play key roles as shapers of ecosystems and drivers of bacterial evolution. Temperate phages can choose between (i) lysis: exploiting their bacterial hosts by producing multiple phage particles and releasing them by lysing the host cell, and (ii) lysogeny: establishing a potentially mutually beneficial relationship with the host by integrating their chromosome into the host cell's genome. Temperate phages exhibit lysogeny propensities in the curiously narrow range of 5–15%. For some temperate phages, the propensity is further regulated by the multiplicity of infection, such that single infections go predominantly lytic while multiple infections go predominantly lysogenic. We ask whether these observations can be explained by selection pressures in environments where multiple phage variants compete for the same host. Our models of pairwise competition, between phage variants that differ only in their propensity to lysogenize, predict the optimal lysogeny propensity to fall within the experimentally observed range. This prediction is robust to large variation in parameters such as the phage infection rate, burst size, decision rate, as well as bacterial growth rate, and initial phage to bacteria ratio. When we compete phage variants whose lysogeny strategies are allowed to depend upon multiplicity of infection, we find that the optimal strategy is one which switches from full lysis for single infections to full lysogeny for multiple infections. Previous attempts to explain lysogeny propensity have argued for bet-hedging that optimizes the response to fluctuating environmental conditions. Our results suggest that there is an additional selection pressure for lysogeny propensity within phage populations infecting a bacterial host, independent of environmental conditions.

Models of life: epigenetics, diversity and cycles

This review emphasizes aspects of biology that can be understood through repeated applications of simple causal rules. The selected topics include perspectives on gene regulation, phage lambda development, epigenetics, microbial ecology, as well as model approaches to diversity and to punctuated equilibrium in evolution. Two outstanding features are repeatedly described. One is the minimal number of rules to sustain specific states of complex systems for a long time. The other is the collapse of such states and the subsequent dynamical cycle of situations that restitute the system to a potentially new metastable state.

Cell fate decisions emerge as phages cooperate or compete inside their host

The system of the bacterium Escherichia coli and its virus, bacteriophage lambda, is paradigmatic for gene regulation in cell-fate development, yet insight about its mechanisms and complexities are limited due to insufficient resolution of study. Here we develop a 4-colour fluorescence reporter system at the single-virus level, combined with computational models to unravel both the interactions between phages and how individual phages determine cellular fates. We find that phages cooperate during lysogenization, compete among each other during lysis, and that confusion between the two pathways occasionally occurs. Additionally, we observe that phage DNAs have fluctuating cellular arrival times and vie for resources to replicate, enabling the interplay during different developmental paths, where each phage genome may make an individual decision. These varied strategies could separate the selection for replication-optimizing beneficial mutations during lysis from sequence diversification during lysogeny, allowing rapid adaptation of phage populations for various environments.

Supercoiling biases the formation of loops involved in gene regulation

The function of DNA as a repository of genetic information is well-known. The post-genomic effort is to understand how this information-containing filament is chaperoned to manage its compaction and topological states. Indeed, the activities of enzymes that transcribe, replicate, or repair DNA are regulated to a large degree by access. Proteins that act at a distance along the filament by binding at one site and contacting another site, perhaps as part of a bigger complex, create loops that constitute topological domains and influence regulation. DNA loops and plectonemes are not necessarily spontaneous, especially large loops under tension for which high energy is required to bring their ends together, or small loops that require accessory proteins to facilitate DNA bending. However, the torsion in stiff filaments such as DNA dramatically modulates the topology, driving it from extended and genetically accessible to more looped and compact, genetically secured forms. Furthermore, there are accessory factors that bias the response of the DNA filament to supercoiling. For example, small molecules like polyamines, which neutralize the negative charge repulsions along the phosphate backbone, enhance flexibility and promote writhe over twist in response to torsion. Such increased flexibility likely pushes the topological equilibrium from twist toward writhe at tensions thought to exist in vivo. A predictable corollary is that stiffening DNA antagonizes looping and bending. Certain sequences are known to be more or less flexible or to exhibit curvature, and this may affect interactions with binding proteins. In vivo all of these factors operate simultaneously on DNA that is generally negatively supercoiled to some degree. Therefore, in order to better understand gene regulation that involves protein-mediated DNA loops, it is critical to understand the thermodynamics and kinetics of looping in DNA that is under tension, negatively supercoiled, and perhaps exposed to molecules that alter elasticity. Recent experiments quantitatively reveal how much negatively supercoiling DNA lowers the free energy of looping, possibly biasing the operation of genetic switches.

Effect of Intrinsic Noise on the Phenotype of Cell Populations Featuring Solution Multiplicity: An Artificial lac Operon Network Paradigm

Heterogeneity in cell populations originates from two fundamentally different sources: the uneven distribution of intracellular content during cell division, and the stochastic fluctuations of regulatory molecules existing in small amounts. Discrete stochastic models can incorporate both sources of cell heterogeneity with sufficient accuracy in the description of an isogenic cell population; however, they lack efficiency when a systems level analysis is required, due to substantial computational requirements. In this work, we study the effect of cell heterogeneity in the behaviour of isogenic cell populations carrying the genetic network of lac operon, which exhibits solution multiplicity over a wide range of extracellular conditions. For such systems, the strategy of performing solely direct temporal solutions is a prohibitive task, since a large ensemble of initial states needs to be tested in order to drive the system--through long time simulations--to possible co-existing steady state solutions. We implement a multiscale computational framework, the so-called "equation-free" methodology, which enables the performance of numerical tasks, such as the computation of coarse steady state solutions and coarse bifurcation analysis. Dynamically stable and unstable solutions are computed and the effect of intrinsic noise on the range of bistability is efficiently investigated. The results are compared with the homogeneous model, which neglects all sources of heterogeneity, with the deterministic cell population balance model, as well as with a stochastic model neglecting the heterogeneity originating from intrinsic noise effects. We show that when the effect of intrinsic source of heterogeneity is intensified, the bistability range shifts towards higher extracellular inducer concentration values.

Well-temperate phage: optimal bet-hedging against local environmental collapses

Upon infection of their bacterial hosts temperate phages must chose between lysogenic and lytic developmental strategies. Here we apply the game-theoretic bet-hedging strategy introduced by Kelly to derive the optimal lysogenic fraction of the total population of phages as a function of frequency and intensity of environmental downturns affecting the lytic subpopulation. "Well-temperate" phage from our title is characterized by the best long-term population growth rate. We show that it is realized when the lysogenization frequency is approximately equal to the probability of lytic population collapse. We further predict the existence of sharp boundaries in system's environmental, ecological, and biophysical parameters separating the regions where this temperate strategy is optimal from those dominated by purely virulent or dormant (purely lysogenic) strategies. We show that the virulent strategy works best for phages with large diversity of hosts, and access to multiple independent environments reachable by diffusion. Conversely, progressively more temperate or even dormant strategies are favored in the environments, that are subject to frequent and severe temporal downturns.

DNA supercoiling: a regulatory signal for the λ repressor

Topoisomerases, polymerases, and the chirality introduced by the binding of histones or nucleoid-associated proteins affect DNA supercoiling in vivo. However, supercoiling is not just a by-product of DNA metabolism. Supercoiling is an indicator of cell health, it modifies the accessibility of chromatin, and coordinates the transcription of genes. This suggests that regulatory, protein-mediated loops in DNA may sense supercoiling of the genome in which they are embedded. The λ repressor (CI) maintains the quiescent (lysogenic) transcriptome of bacteriophage λ in infected Escherichia coli. CI-mediated looping prevents overexpression of the repressor protein to preserve sensitivity to conditions that trigger virulence (lysis). Experiments were performed to assess how well the CI-mediated DNA loop traps superhelicity and determine whether supercoiling enhances CI-mediated DNA looping. CI oligomers partitioned plasmids into topological domains and prevented the passage of supercoiling between them. Furthermore, in single DNA molecules stretched and twisted with magnetic tweezers, levels of superhelical density confined in CI-mediated DNA loops ranged from -15% or +11%. Finally, in DNA under tensions that may occur in vivo, supercoiling lowered the free energy of loop formation and was essential for DNA looping. Supercoiling-enhanced looping can influence the maintenance of lysogeny in the λ repressor system; it can encode sensitivity to the energy level of the cell and creates independent topological domains of distinct superhelical density.

Tethered particle analysis of supercoiled circular DNA using peptide nucleic acid handles

This protocol describes how to monitor individual naturally supercoiled circular DNA plasmids bound via peptide nucleic acid (PNA) handles between a bead and a surface. The protocol was developed for single-molecule investigation of the dynamics of supercoiled DNA, and it allows the investigation of both the dynamics of the molecule itself and of its interactions with a regulatory protein. Two bis-PNA clamps designed to bind with extremely high affinity to predetermined homopurine sequence sites in supercoiled DNA are prepared: one conjugated with digoxigenin for attachment to an anti-digoxigenin-coated glass cover slide, and one conjugated with biotin for attachment to a submicron-sized streptavidin-coated polystyrene bead. Plasmids are constructed, purified and incubated with the PNA handles. The dynamics of the construct is analyzed by tracking the tethered bead using video microscopy: less supercoiling results in more movement, and more supercoiling results in less movement. In contrast to other single-molecule methodologies, the current methodology allows for studying DNA in its naturally supercoiled state with constant linking number and constant writhe. The protocol has potential for use in studying the influence of supercoils on the dynamics of DNA and its associated proteins, e.g., topoisomerase. The procedure takes ~4 weeks.

Commitment to lysogeny is preceded by a prolonged period of sensitivity to the late lytic regulator Q in bacteriophage λ

A key event in development is the irreversible commitment to a particular cell fate, which may be concurrent with or delayed with respect to the initial cell fate decision. In this work, we use the paradigmatic bacteriophage λ lysis-lysogeny decision circuit to study the timing of commitment. The lysis-lysogeny decision is made based on the expression trajectory of CII. The chosen developmental strategy is manifested by repression of the pR and pL promoters by CI (lysogeny) or by antitermination of late gene expression by Q (lysis). We found that expression of Q in trans from a plasmid at the time of infection resulted in a uniform lytic decision. Furthermore, expression of Q up to 50 min after infection results in lysis of the majority of cells which initially chose lysogenic development. In contrast, expression of Q in cells containing a single chromosomal prophage had no effect on cell growth, indicating commitment to lysogeny. Notably, if the prophage was present in 10 plasmid-borne copies, Q expression resulted in lytic development, suggesting that the cellular phage chromosome number is the critical determinant of the timing of lysogenic commitment. Based on our results, we conclude that (i) the lysogenic decision made by the CI-Cro switch soon after infection can be overruled by ectopic Q expression at least for a time equivalent to one phage life cycle, (ii) the presence of multiple λ chromosomes is a prerequisite for a successful Q-mediated switch from lysogenic to lytic development, and (iii) phage chromosomes within the same cell can reach different decisions.

Effect of supercoiling on the λ switch

The lysogenic state of the λ switch is exceptionally stable, still, it is capable of responding to DNA-damage and rapidly enter the lytic state. We invented an assay where PNA mediated tethering of a plasmid allowed for single molecule investigations of the effect of supercoiling on the efficiency of the epigenetic λ switch. Compared with non-supercoiled DNA, the presence of supercoils enhances the CI-mediated DNA looping probability and renders the transition between the looped and unlooped states steeper, thus increasing the Hill coefficient. Interestingly, the transition occurs exactly at the CI concentration corresponding to the minimum number of CI molecules capable of maintaining the pRM-repressed state. Based on these results we propose that supercoiling maintains the pRM-repressible state as CI concentration decline during induction and thus prevent autoregulation of cI from interfering with induction.

DNA supercoiling enhances cooperativity and efficiency of an epigenetic switch

Bacteriophage λ stably maintains its dormant prophage state but efficiently enters lytic development in response to DNA damage. The mediator of these processes is the λ repressor protein, CI, and its interactions with λ operator DNA. This λ switch is a model on the basis of which epigenetic switch regulation is understood. Using single molecule analysis, we directly examined the stability of the CI-operator structure in its natural, supercoiled state. We marked positions adjacent to the λ operators with peptide nucleic acids and monitored their movement by tethered particle tracking. Compared with relaxed DNA, the presence of supercoils greatly enhances juxtaposition probability. Also, the efficiency and cooperativity of the λ switch is significantly increased in the supercoiled system compared with a linear assay, increasing the Hill coefficient.

Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions

The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.

The lysis-lysogeny decision of bacteriophage 933W: a 933W repressor-mediated long-distance loop has no role in regulating 933W P(RM) activity

Our data show that unlike bacteriophage λ, repressor bound at O(L) of bacteriophage 933W has no role in regulation of 933W repressor occupancy of 933W O(R)3 or the transcriptional activity of 933W P(RM). This finding suggests that a cooperative long-range loop between repressor tetramers bound at O(R) and O(L) does not form in bacteriophage 933W. Nonetheless, 933W forms lysogens, and 933W prophage display a threshold response to UV induction similar to related lambdoid phages. Hence, the long-range loop thought to be important for constructing a threshold response in lambdoid bacteriophages is dispensable. The lack of a loop requires bacteriophage 933W to use a novel strategy in regulating its lysis-lysogeny decisions. As part of this strategy, the difference between the repressor concentrations needed to bind O(R)2 and activate 933W P(RM) transcription or bind O(R)3 and repress transcription from P(RM) is <2-fold. Consequently, P(RM) is never fully activated, reaching only ∼25% of the maximum possible level of repressor-dependent activation before repressor-mediated repression occurs. The 933W repressor also apparently does not bind cooperatively to the individual sites in O(R) and O(L). This scenario explains how, in the absence of DNA looping, bacteriophage 933W displays a threshold effect in response to DNA damage and suggests how 933W lysogens behave as "hair triggers" with spontaneous induction occurring to a greater extent in this phage than in other lambdoid phages.

Minimal gene regulatory circuits for a lysis-lysogeny choice in the presence of noise

Gene regulatory networks (GRNs) that make reliable decisions should have design features to cope with random fluctuations in the levels or activities of biological molecules. The phage λ GRN makes a lysis-lysogeny decision informed by the number of phages infecting the cell. To analyse the design of decision making GRNs, we generated random in silico GRNs comprised of two or three transcriptional regulators and selected those able to perform a λ-like decision in the presence of noise. Various two-protein networks analogous to the λ CI-Cro GRN worked in noise-less conditions but failed when noise was introduced. Adding a λ CII-like protein significantly improved robustness to noise. CII relieves the CI-like protein of its 'decider' function, allowing CI to be optimized as a decision 'maintainer'. CII's lysogenic decider function was improved by its instability and rapid removal once the decision was taken, preventing its interference with maintenance. A more reliable decision also resulted from simulated co-transcription of the genes for CII and the Cro-like protein, which correlates fluctuations in these opposing decider functions and makes their ratio less noisy. Thus, the λ decision network contains design features for reducing and resisting noise.

Stability and instability in the lysogenic state of phage lambda

Complex gene regulatory circuits exhibit emergent properties that are difficult to predict from the behavior of the components. One such property is the stability of regulatory states. Here we analyze the stability of the lysogenic state of phage λ. In this state, the virus maintains a stable association with the host, and the lytic functions of the virus are repressed by the viral CI repressor. This state readily switches to the lytic pathway when the host SOS system is induced. A low level of SOS-dependent switching occurs without an overt stimulus. We found that the intrinsic rate of switching to the lytic pathway, measured in a host lacking the SOS response, was almost undetectably low, probably less than 10(-8)/generation. We surmise that this low rate has not been selected directly during evolution but results from optimizing the rate of switching in a wild-type host over the natural range of SOS-inducing conditions. We also analyzed a mutant, λprm240, in which the promoter controlling CI expression was weakened, rendering lysogens unstable. Strikingly, the intrinsic stability of λprm240 lysogens depended markedly on the growth conditions; lysogens grown in minimal medium were nearly stable but switched at high rates when grown in rich medium. These effects on stability likely reflect corresponding effects on the strength of the prm240 promoter, measured in an uncoupled assay system. Several derivatives of λprm240 with altered stabilities were characterized. This mutant and its derivatives afford a model system for further analysis of stability.

Fixed points and limit cycles in the population dynamics of lysogenic viruses and their hosts

Starting with stochastic rate equations for the fundamental interactions between microbes and their viruses, we derive a mean-field theory for the population dynamics of microbe-virus systems, including the effects of lysogeny. In the absence of lysogeny, our model is a generalization of that proposed phenomenologically by Weitz and Dushoff. In the presence of lysogeny, we analyze the possible states of the system, identifying a limit cycle, which we interpret physically. To test the robustness of our mean-field calculations to demographic fluctuations, we have compared our results with stochastic simulations using the Gillespie algorithm. Finally, we estimate the range of parameters that delineate the various steady states of our model.

Lambda-prophage induction modeled as a cooperative failure mode of lytic repression

We analyze a system-level model for lytic repression of lambda phage in E. coli using reliability theory, showing that the repressor circuit comprises four redundant components whose failure mode is prophage induction. Our model reflects the specific biochemical mechanisms involved in regulation, including long-range cooperative binding, and its detailed predictions for prophage induction in E. coli under ultraviolet radiation are in good agreement with experimental data.

DNA looping provides stability and robustness to the bacteriophage lambda switch

The bistable gene regulatory switch controlling the transition from lysogeny to lysis in bacteriophage lambda presents a unique challenge to quantitative modeling. Despite extensive characterization of this regulatory network, the origin of the extreme stability of the lysogenic state remains unclear. We have constructed a stochastic model for this switch. Using Forward Flux Sampling simulations, we show that this model predicts an extremely low rate of spontaneous prophage induction in a recA mutant, in agreement with experimental observations. In our model, the DNA loop formed by octamerization of CI bound to the O(L) and O(R) operator regions is crucial for stability, allowing the lysogenic state to remain stable even when a large fraction of the total CI is depleted by nonspecific binding to genomic DNA. DNA looping also ensures that the switch is robust to mutations in the order of the O(R) binding sites. Our results suggest that DNA looping can provide a mechanism to maintain a stable lysogenic state in the face of a range of challenges including noisy gene expression, nonspecific DNA binding, and operator site mutations.

A novel assay based on fluorescence microscopy and image processing for determining phenotypic distributions of rod-shaped bacteria

Cell population balance (CPB) models can account for the phenotypic heterogeneity that characterizes isogenic cell populations. To utilize the predictive power of these models, however, we must determine the single-cell reaction and division rates as well as the partition probability density function of the cell population. These functions can be obtained through the Collins-Richmond inverse CPB modeling methodology, if we know the phenotypic distributions of (a) the overall cell population, (b) the dividing cell subpopulation, and (c) the newborn cell subpopulation. This study presents the development of a novel assay that combines fluorescence microscopy and image processing to determine these distributions. The method is generally applicable to rod-shaped cells dividing through the formation of a characteristic constriction. Morphological criteria were developed for the automatic identification of dividing cells and validated through direct comparison with manually obtained measurements. The newborn cell subpopulation was obtained from the corresponding dividing cell subpopulation by collecting information from the two compartments separated by the constriction. The method was applied to E. coli cells carrying the genetic toggle network with a green fluorescent marker. Our measurements for the overall cell population were in excellent agreement with the distributions obtained via flow cytometry. The new assay constitutes a powerful tool that can be used in conjunction with inverse CPB modeling to rigorously quantify single-cell behavior from data collected from highly heterogeneous cell populations.

The bacteriophage lambda CI protein finds an asymmetric solution

The CI protein of bacteriophage lambda (lambdaCI) is both a repressor and activator of transcription that has served as a model for understanding how gene regulatory proteins work. A dimeric DNA-binding protein, lambdaCI also forms higher-order oligomers that allow it to bind cooperatively to both adjacent and nonadjacent operator sites within the phage genome. The ability of phage lambda to transition efficiently from one program of gene expression to another depends upon the formation of these higher-order protein-DNA complexes. A recently determined crystal structure of a DNA-bound lambdaCI dimer reveals that the two subunits of the dimer adopt different conformations. This unexpected asymmetry helps explain how these higher-order complexes are assembled.

Collective decision making in bacterial viruses

For many bacterial viruses, the choice of whether to kill host cells or enter a latent state depends on the multiplicity of coinfection. Here, we present a mathematical theory of how bacterial viruses can make collective decisions concerning the fate of infected cells. We base our theory on mechanistic models of gene regulatory dynamics. Unlike most previous work, we treat the copy number of viral genes as variable. Increasing the viral copy number increases the rate of transcription of viral mRNAs. When viral regulation of cell fate includes nonlinear feedback loops, very small changes in transcriptional rates can lead to dramatic changes in steady-state gene expression. Hence, we prove that deterministic decisions can be reached, e.g., lysis or latency, depending on the cellular multiplicity of infection within a broad class of gene regulatory models of viral decision-making. Comparisons of a parameterized version of the model with molecular studies of the decision structure in the temperate bacteriophage lambda are consistent with our conclusions. Because the model is general, it suggests that bacterial viruses can respond adaptively to changes in population dynamics, and that features of collective decision-making in viruses are evolvable life history traits.

Cro's role in the CI Cro bistable switch is critical for {lambda}'s transition from lysogeny to lytic development

CI represses cro; Cro represses cI. This double negative feedback loop is the core of the classical CI-Cro epigenetic switch of bacteriophage lambda. Despite the classical status of this switch, the role in lambda development of Cro repression of the P(RM) promoter for CI has remained unclear. To address this, we created binding site mutations that strongly impaired Cro repression of P(RM) with only minimal effects on CI regulation of P(RM). These mutations had little impact on lambda development after infection but strongly inhibited the transition from lysogeny to the lytic pathway. We demonstrate that following inactivation of CI by ultraviolet treatment of lysogens, repression of P(RM) by Cro is needed to prevent synthesis of new CI that would otherwise significantly impede lytic development. Thus a bistable CI-Cro circuit reinforces the commitment to a developmental transition.

From single-cell genetic architecture to cell population dynamics: quantitatively decomposing the effects of different population heterogeneity sources for a genetic network with positive feedback architecture

Phenotypic cell-to-cell variability or cell population heterogeneity originates from two fundamentally different sources: unequal partitioning of cellular material at cell division and stochastic fluctuations associated with intracellular reactions. We developed a mathematical and computational framework that can quantitatively isolate both heterogeneity sources and applied it to a genetic network with positive feedback architecture. The framework consists of three vastly different mathematical formulations: a), a continuum model, which completely neglects population heterogeneity; b), a deterministic cell population balance model, which accounts for population heterogeneity originating only from unequal partitioning at cell division; and c), a fully stochastic model accommodating both sources of population heterogeneity. The framework enables the quantitative decomposition of the effects of the different population heterogeneity sources on system behavior. Our results indicate the importance of cell population heterogeneity in accurately predicting even average population properties. Moreover, we find that unequal partitioning at cell division and sharp division rates shrink the region of the parameter space where the population exhibits bistable behavior, a characteristic feature of networks with positive feedback architecture. In addition, intrinsic noise at the single-cell level due to slow operator fluctuations and small numbers of molecules further contributes toward the shrinkage of the bistability regime at the cell population level. Finally, the effect of intrinsic noise at the cell population level was found to be markedly different than at the single-cell level, emphasizing the importance of simulating entire cell populations and not just individual cells to understand the complex interplay between single-cell genetic architecture and behavior at the cell population level.

Noise in timing and precision of gene activities in a genetic cascade

The timing of events along the induction cascade of bacteriophage lambda is independent of UV dose and displays increased relative temporal precision with cascade progression.

This behavior is reproduced by a model of a cascade consisting of independent steps that shows that higher temporal precision can be attained by a cascade consisting of a large number of fast steps.

The observed cell-cell variability in cascade timing is not due to differences in uniform dilation of intervals between events among cells, but rather to the independent distribution of interval durations within the cascade, consistently with the modular architecture of the lambda genome.

The single-cell time lapse study reveals a bistable regime at low UV doses in which some cells are induced while others are not, evidence for a commitment point beyond which lysis will occur, and an unexpected shutoff of the lambda pR promoter.

Stochasticity or noise, an inherent property of all biological networks, is often manifested by different phenotypic behaviors in clonal populations of cells (Raser and O'Shea, 2005). Noise can arise, for instance, from sources such as cell–cell variations in small numbers of regulatory molecules or from the stochastic nature of molecular interactions (Paulsson, 2005). Besides affecting the number of molecules in a cell, noise may also lead to variability in timing of particular events along a given pathway. In this work, we studied temporal noise in the induction cascade of phage lambda.

Infection of a bacterial cell by bacteriophage lambda can lead to two different fates (Ptashne, 2004; Dodd et al, 2005; Oppenheim et al, 2005): the phage can either multiply inside the host leading to its eventual lysis and the generation of progeny virions (the lytic pathway) or, alternatively, it can integrate its genome into the host's genome (prophage state), replicating passively with the latter (the lysogenic pathway). The prophage state is highly stable, being maintained by a phage-encoded repressor, which shuts off phage genes leading to lytic growth. However, the lytic pathway can be induced in a lysogenic cell, through the activation of the bacterial SOS response to DNA damage (Little, 1996), for example by UV irradiation. Once activated, the SOS response results in cleavage of the lambda repressor, leading to expression of the phage early and late genes, and culminating in the lysis of the host cell.

The lambda induction cascade has been extensively characterized over the years. We built upon this knowledge to tap the cascade at different points and quantitatively analyze the progressive loss of temporal coherence between cells, as different stages along the cascade are executed, following synchronous induction. Using time-lapse microscopy, we monitored the time of activation of early and late genes in individual cells using lambda pR and pR′-tR′ promoter-GFP fusions, respectively, by means of reporter plasmids, and finally the time of lysis. Sample results are shown in Figure 2.

At low UV levels (5 J/m²), the network exhibits bistability: only approximately 40% of the bacteria lyse, whereas the others continue to divide, following a lag period. At high UV levels (20 J/m²), almost all bacteria lyse. We found that the timing of events in cells that lyse is independent of UV dose. This is in contrast to the known behavior of the SOS network (Friedman et al, 2005), indicating that these two networks proceed independently. Following induction, a surprising shutoff in the activity of the pR promoter is observed in all cells (see Figure 2). Furthermore, the data show that whereas early genes are expressed in all cells irrespective of cell fate, late genes are expressed only in the lysing cells, indicating that similar to infection, a specific commitment checkpoint is operating.

To characterize the temporal variability in a cell population, we used the coefficient of variation, defined as the non-dimensional ratio of the standard deviation and the mean time of occurrence of a particular event. We studied the changes in both standard deviation and coefficient of variation in timing of various events along the lambda induction cascade, from the expression of the early genes to the ultimate lysis of the cells. As shown in Figure 6, the absolute noise as measured by the standard deviation increases as the cascade progresses. In contrast, the coefficient of variation, which measures variability relative to the time of occurrence, decreases. Simple theoretical considerations described in the text yield a necessary and sufficient condition for a monotonic decrease in the coefficient of variation. Higher temporal precision can be achieved when the cascade is composed of a large number of fast steps.

Further support for the independence of network modules is furnished by a correlation analysis of the times of occurrence of different steps along the lytic cascade. This analysis also indicates that the variability in lysis time is not due to differences in the global rate of cascade progression, but probably to random fluctuations in the execution time of the various cascade stages. Indeed, phage lambda gene expression architecture is well known to have evolved from a number of independent regulatory modules (Hendrix, 2003).

Biological developmental pathways require proper timing of gene expression. We investigated timing variations of defined steps along the lytic cascade of bacteriophage λ. Gene expression was followed in individual lysogenic cells, after induction with a pulse of UV irradiation. At low UV doses, some cells undergo partial induction and eventually divide, whereas others follow the lytic pathway. The timing of events in cells committed to lysis is independent of the level of activation of the SOS response, suggesting that the lambda network proceeds autonomously after induction. An increased loss of temporal coherence of specific events from prophage induction to lysis is observed, even though the coefficient of variation of timing fluctuations decreases. The observed temporal variations are not due to cell factors uniformly dilating the timing of execution of the cascade. This behavior is reproduced by a simple model composed of independent stages, which for a given mean duration predicts higher temporal precision, when a cascade consists of a large number of steps. Evidence for the independence of regulatory modules in the network is presented.

A quantitative study of lambda-phage SWITCH and its components

We propose what we believe is a new model to quantitatively describe the lambda-phage SWITCH system. The model incorporates facilitated transfer mechanism of transcription factor, which can be simplified into a two-step reaction. We first sequentially obtain two indispensable parameters by fitting our model to experimental data of two simple systems, and then apply them to study the natural lambda-SWITCH system. By incorporating the facilitated transfer mechanism, we find that in RecA(-) host Escherichia coli, the wild-type lambda-lysogenic state is in a monostable regime rather than in a bistable regime. Furthermore, the model explains the weak role of Cro protein and probably sheds light on the evolution of lambda-Cro protein, which is known to be structurally distinct from the other Cros in lambdoid family members.

Microbial cell individuality and the underlying sources of heterogeneity

Single cells in genetically homogeneous microbial cultures exhibit marked phenotypic individuality, a biological phenomenon that is considered to bolster the fitness of populations. Major phenotypes that are characterized by heterogeneity span the breadth of microbiology, in fields ranging from pathogenicity to ecology. The cell cycle, cell ageing and epigenetic regulation are proven drivers of heterogeneity in several of the best-known phenotypic examples. However, the full contribution of factors such as stochastic gene expression is yet to be realized.

Detailed genomic analysis of the Wbeta and gamma phages infecting Bacillus anthracis: implications for evolution of environmental fitness and antibiotic resistance

Phage-mediated lysis has been an essential laboratory tool for rapidly identifying Bacillus anthracis for more than 40 years, relying on the gamma phage derivative of a Bacillus cereus prophage called W. The complete genomic sequences of the temperate W phage, referred to as Wbeta, and its lytic variant gamma were determined and found to encode 53 open reading frames each, spanning 40,864 bp and 37,373 bp, respectively. Direct comparison of the genomes showed that gamma evolved through mutations at key loci controlling host recognition, lysogenic growth, and possibly host phenotypic modification. Included are a cluster of point mutations at the gp14 tail fiber locus of gamma, encoding a protein that, when fused to green fluorescent protein, binds specifically to B. anthracis. A large 2,003-bp deletion was also identified at the gamma lysogeny module, explaining its shift from a temperate to a lytic lifestyle. Finally, evidence of recombination was observed at a dicistronic Wbeta locus, encoding putative bacterial cell surface-modifying proteins, replaced in gamma with a locus, likely obtained from a B. anthracis prophage, encoding demonstrable fosfomycin resistance. Reverse transcriptase PCR analysis confirmed strong induction at the dicistronic Wbeta locus and at four other phage loci in B. anthracis and/or B. cereus lysogens. In all, this study represents the first genomic and functional description of two historically important phages and is part of a broader investigation into contributions of phage to the B. anthracis life cycle. Initial findings suggest that lysogeny of B. anthracis promotes ecological adaptation, rather than virulence, as with other gram-positive pathogens.

Switches in Bacteriophage Lambda Development

The lysis-lysogeny decision of bacteriophage lambda (lambda) is a paradigm for developmental genetic networks. There are three key features, which characterize the network. First, after infection of the host bacterium, a decision between lytic or lysogenic development is made that is dependent upon environmental signals and the number of infecting phages per cell. Second, the lysogenic prophage state is very stable. Third, the prophage enters lytic development in response to DNA-damaging agents. The CI and Cro regulators define the lysogenic and lytic states, respectively, as a bistable genetic switch. Whereas CI maintains a stable lysogenic state, recent studies indicate that Cro sets the lytic course not by directly blocking CI expression but indirectly by lowering levels of CII which activates cI transcription. We discuss how a relatively simple phage like lambda employs a complex genetic network in decision-making processes, providing a challenge for theoretical modeling.

Revisited gene regulation in bacteriophage lambda

The contribution of bacteriophage lambda to gene control research is far from over. A revised model of the lambda genetic switch includes extra cooperativity through octamerization of the cI repressor protein, mediated by long-range DNA looping. Structural analysis reveals remarkably subtle transcriptional activation by cI. The action of cI, activation by cII, and aspects of antitermination by N and Q all confirm the utility and versatility of simple, weak adhesive interactions mediated by nucleic acid tethers. New genetic and quantitative analysis of the lambda gene network is challenging cherished ideas about how complex behaviours emerge from this regulatory system.

On the role of Cro in lambda prophage induction

The lysogenic state of bacteriophage lambda is exceptionally stable yet the prophage is readily induced in response to DNA damage. This delicate epigenetic switch is believed to be regulated by two proteins; the lysogenic maintenance promoting protein CI and the early lytic protein Cro. First, we confirm, in the native configuration, the previous observation that the DNA loop mediated by oligomerization of CI bound to two distinct operator regions (O(L) and O(R)), increases repression of the early lytic promoters and is important for stable maintenance of lysogeny. Second, we show that the presence of the cro gene might be unimportant for the lysogenic to lytic switch during induction of the lambda prophage. We revisit the idea that Cro's primary role in induction is instead to mediate weak repression of the early lytic promoters.

Nonspecific binding of the OR repressors CI and Cro of bacteriophage λ

We estimate the Gibbs free energy for nonspecific binding (DeltaGNSB) to the Escherichia coli DNA for two regulatory proteins of the lambda phage, CI and Cro. By means of a statistical-mechanical approach, we calculate the cI and cro activities associated with the operator OR of an introduced lambda phage genome (prophage). In this statistical model we apply in vitro-measured binding free energies to fit in vivo experimental data for cI and cro activities, respectively, where DeltaGNSB is introduced as a free (fitting) parameter. Without nonspecific binding included in the model, the quality of the description is fairly poor, whereas data are nicely correlating with our model with nonspecific binding included over the entire data range. The obtained values of DeltaGNSB are -4.1+/-0.9 kcal/mol, for CI, and -4.2+/-0.8 kcal/mol, for Cro. In particular, in a lysogen (approximately 250 CI monomers per cell) we conclude that 86% of the total CI in the cell is nonspecifically bound, leaving on average around 10 CI dimers freely available in the E. coli cytoplasma. These findings corroborate the view that due to low free cellular particle numbers a dynamical analysis of genetic regulation at OR and comparable systems should include a stochastic component. In addition, we perform a stability analysis of the OR system in the presence of nonspecific binding.