Lytic And Lysogenic Cycle Of Lambda Phage Pdf
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Here we address this question directly. We first quantify transcriptional regulation governing lysogenic maintenance using a single-cell fluorescence reporter. We then use the single-cell data to derive a stochastic theoretical model for the underlying regulatory network.
We use the model to predict the steady states of the system and then validate these predictions experimentally. Specifically, a regime of bistability, and the resulting hysteretic behavior, are observed. Beyond the steady states, the theoretical model successfully predicts the kinetics of switching from lysogeny to lysis.
Our results show how the physics-inspired concept of bistability can be reliably used to describe cellular phenotype, and how an experimentally-calibrated theoretical model can have accurate predictive power for cell-state switching. This is an open-access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The authors confirm that all data underlying the findings are fully available without restriction.
All relevant data are within the paper and its Supporting Information files. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
A scenario often encountered in living systems is that of a choice between two alternative cellular fates, driven by different gene expression patterns  — . A classical bacterial example is the decision whether or not to utilize a specific carbon source  , . In metazoans, the eventual fate of a cell is established through a cascade of such binary decision steps during development  , . Once a cellular state is chosen, the memory of that state can be inheritably maintained  — .
The life cycle of bacteriophage lambda has long served as a simple paradigm for a binary choice between alternative cell fates and the long-term maintenance of the selected state  ,  , . Upon infection of an E. Once chosen, the lysogenic state is extremely stable, lasting millions of cell generations under favorable conditions  , .
Lysogenic induction can be triggered by a cellular signal such as DNA damage  but can also occur spontaneously, due to fluctuations in gene expression  , .
The lysogenic state is maintained by a single transcription factor, CI a. As long as enough CI is present in the cell, transcription of the key lytic activator, Cro, is repressed while continuous CI production is maintained through autoregulation  , . If, however, CI levels drop below a critical level, transcription of cro from the P R promoter takes place, leading to halting of CI production and initiation of the lytic pathway  , .
After dimerization, both proteins regulate each other's transcription as well as their own. In the reporter system, the cI and cro transcripts also encode red and green fluorescent proteins, respectively, allowing the detection of P RM and P R activity in individual cells under the microscope. B—D Using temperature to control cellular state schematic.
As a result, the balance between CI production and elimination shifts as temperature is changed panel C , plotted as a function of the amount of active CI in the cell. In particular, in the example shown, as temperature increases the system moves from having a single, high-P RM state corresponding to lysogeny, at temperature 1 , to having two stable states high P RM , low P RM ; bistability, at temperature 2 and finally to a single, low-P RM state lytic-onset, at temperature 3.
In the region around 2, hysteretic behavior is expected with cells following the paths indicated by the arrows: Since both states are stable, cells will mostly stay in the state they were originally in. In other words, cell state is dependent on its history. Following the strict mathematical definition  ,  bistability means that the two gene-expression states coexist, and each is locally stable, i.
Such switch-inducing perturbations can be due to an external source for example, RecA-driven cleavage of CI  , or due to internal fluctuations . In a physical system, such fluctuations would be thermally driven. In living cells, copy-number fluctuations driven by biochemical stochasticity are believed to play an analogous role  ,  , . The bistability picture is further motivated by theoretical analysis of the gene regulatory circuit governing the maintenance of lysogeny  ,  ,  , .
This analysis takes into account the way cI transcription from P RM is modulated by the concentration of CI in the cell, and the balance of CI production and elimination by degradation or dilution by cell growth. Under plausible choices of model parameters, two stable states are predicted, corresponding to high lysogeny and low lysis levels of CI see Fig.
Following the lambda paradigm, bistability has been invoked for multiple systems exhibiting a binary choice of cell state  , . In a handful of examples, hysteretic behavior was experimentally demonstrated, providing strong evidence for true bistability see below  ,  , .
In most cases, however, the bistability picture was motivated by indirect evidence, such as the presence of positive feedback in the underlying regulatory network; in particular, a self-regulating, fate-determining transcription factor, which is commonly found in systems exhibiting long-term memory of cellular states  ,  , .
There are multiple reasons to doubt the validity of the bistability description: First, the mere existence of two distinct gene expression states does not immediately imply bistability. Both states simultaneously have to be locally stable for the system to be bistable . In contrast to this situation, some systems such as the yeast Gal1 promoter exhibit only a single gene expression state, but that state is modulated in response to external conditions .
Second, even if cells in both gene-expression states are simultaneously observed within the population co-existence , this still does not mean both states are locally stable. A bimodal population can be achieved by other means, such as large but very infrequent bursts of transcription  , .
Third, the fact that one of the lambda states lysis is inherently irreversible leads to cell death suggests that this state does not necessarily need to be stable to achieve its physiological purpose; instead, even a transient excursion from lysogeny to lysis would suffice for complete switching.
Finally, our current knowledge of gene regulation in the system—how P RM activity depends on CI and Cro amounts in the cell, in particular in the low CI regime—is not quantitative enough to unambiguously determine whether both the lysis and lysogeny states are locally stable. Specifically, one needs to quantify the population structure i. Most critically, establishing bistability requires demonstrating the existence of hysteresis , that is, the history dependence of cellular state.
Hysteresis would indicate the presence of two coexisting stable states, with a barrier in transitioning between them. Hysteresis is therefore a necessary consequence of the local stability of both of the lysogenic and lytic states.
The question of bistability in the lambda system thus remains open. Here we perform a quantitative characterization of the lambda lysogeny maintenance system using a two-color fluorescent reporter to measure the activity of the P RM and P R promoters in individual cells Fig. A temperature-sensitive mutant of CI  ,  —  is used to continuously control the gene-expression state of the cells.
We first measure the P RM -activity versus CI-concentration regulatory curve and use it to predict the steady states of the system. We find that a regime of bistability is expected.
This prediction is then verified experimentally. In particular, we find that hysteretic behavior is exhibited in the expected temperature range. Next, we measure the kinetics of switching from lysogeny to lysis. The observed kinetics again show good agreement with the theoretical prediction based on our measured parameters of stochastic gene expression in the system.
For the purpose of this study, we constructed a two-color reporter strain that allows us to quantify simultaneously, in individual cells, the activity of the two key promoters in the lysogeny maintenance circuit: P RM , from which cI is transcribed, and P R , from which cro is transcribed Fig.
In constructing this reporter, we followed the approach of . The region of the lambda genome governing the maintenance of lysogeny position — bp  , was inserted into the lac locus of the E. For reporting on the transcriptional activities of P RM and P R , genes encoding green GFP and red mCherry fluorescent proteins were fused to cro and cI , respectively, creating transcriptional fusions.
Unlike a true lysogen, however, the reporter strain does not contain the full viral genome and therefore actual lysis does not ensue in the latter case . The use of temperature as a control parameter in our system is depicted schematically in Fig.
The cI allele used in our reporter system is a temperature-sensitive mutant, cI  ,  — . As temperature is increased, however, an increasing fraction of CI proteins in the cell become non-functional  , . The result is that, by varying the temperature we can continuously change the balance of CI production and elimination Fig. Depending on the precise way in which P RM activity depends on CI concentration, three different regimes may be encountered as temperature is changed Fig.
The key to determining the steady states of the system, in particular the possible existence of bistability, is to be able to describe quantitatively the balance of CI production and elimination. We set out to quantify the autoregulatory response curve f x , which describes the activity of P RM f , number of proteins produced per generation time as a function of CI concentration in the cell x , number of active CI molecules per cell.
Note that the regulatory effect of Cro, which also regulates P RM  ,  , is only included implicitly here: Cro's presence when CI levels are low leads to a strong repression of P RM in that regime . This one-dimensional simplification may be justified by understanding that, at a given CI concentration, Cro will always adopt a single steady-state value, i. This implies that the steady-state P RM promoter activity can be written entirely as a function of CI level.
A A schematic of the switching experiment. Two variables were extracted: The time when switching at a constant rate begins designated the delay time and the average time at which a cell switches from lysogeny to lysis designated the mean switching time.
Each stair-step graph shows experimental data from a corresponding experiment. The dashed line is a fit to the observed biphasic behavior: delay followed by exponential switching. The fit was used to estimate the delay time and the mean switching time. Squares, experimental results and standard error from 3 independent experiments. Solid line and shaded region, results of the stochastic model and their estimated error.
Notation as in panel C. In other words, at each temperature, the mean cell fluorescence is proportional to P RM activity at the steady-state CI level at that temperature this proportionality constant may be set to 1 by measuring both fluorescence and P RM activity relative to their maximum values. We note that using the slightly different expressions from other studies  ,  ,  leads to similar results in our analysis below Table S1.
Using the relations above, we measured f x as follows. At each temperature, we measured the mean population fluorescence during exponential growth, F T. When two distinct populations were present see Fig. S1 in Text S1 , the mean fluorescence for each sub-population was estimated separately. The resulting estimate is depicted in Fig. As CI levels increase, P RM displays a cooperative super-linear increase in activity  ,  ,  ,  until a maximal activity is reached.
S2 in Text S1. The shaded region in Fig. Each data point was obtained by averaging over three independent experiments. Error bars represent the standard error of these three experiments. The inset depicts the same data in semi-logarithmic scale. Shaded region represents the confidence boundary of the theoretical prediction. The P RM activity of individual cells is plotted, for cultures grown initially at low temperature high P RM activity, top panel and cultures grown initially at high temperature low P RM activity, bottom panel.
Each dot represents one cell total cells randomly chosen from our data at each temperature. We also plot blue shaded area the estimated error in predicting the steady states see Text S1 based on the uncertainty in the fitting parameters of the P RM response-curve f x A similar error analysis was performed for the possible pleiotropic effects of changing the growth temperature, see Fig.
Here we address this question directly. We first quantify transcriptional regulation governing lysogenic maintenance using a single-cell fluorescence reporter. We then use the single-cell data to derive a stochastic theoretical model for the underlying regulatory network. We use the model to predict the steady states of the system and then validate these predictions experimentally. Specifically, a regime of bistability, and the resulting hysteretic behavior, are observed. Beyond the steady states, the theoretical model successfully predicts the kinetics of switching from lysogeny to lysis.
CI represses cro ; Cro represses cI. 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. CI simultaneously activates transcription of its own gene from P RM. This CI—Cro double negative feedback loop, augmented by direct CI positive feedback, provides stable and heritable alternative epigenetic states. Cro repression of P RM.
Viruses are infectious particles that cannot multiply on their own. View LyticAndLysogenicCycles. The lambda phage multiplies using lysogenic cycle, which does not cause the host cell to die. Similar, and at times, confusing, understanding the difference between both these cycles depends largely on studying each of them individually.
NCBI Bookshelf. An Introduction to Genetic Analysis. New York: W. Freeman;