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Stochastic cellular fate decision making by multiple infecting lambda phage.

Robb ML, Shahrezaei V - PLoS ONE (2014)

Bottom Line: Here, we attempt to provide a mechanistic explanation of these results using a simple stochastic model of the lambda phage genetic network.Several potential factors including intrinsic gene expression noise, spatial dynamics and cell-cycle effects are investigated.However, simulations suggest spatial segregation of phage particles does not play a significant role.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Imperial College, London, United Kingdom.

ABSTRACT
Bacteriophage lambda is a classic system for the study of cellular decision making. Both experiments and mathematical models have demonstrated the importance of viral concentration in the lysis-lysogeny decision outcome in lambda phage. However, a recent experimental study using single cell and single phage resolution reported that cells with the same viral concentrations but different numbers of infecting phage (multiplicity of infection) can have markedly different rates of lysogeny. Thus the decision depends on not only viral concentration, but also directly on the number of infecting phage. Here, we attempt to provide a mechanistic explanation of these results using a simple stochastic model of the lambda phage genetic network. Several potential factors including intrinsic gene expression noise, spatial dynamics and cell-cycle effects are investigated. We find that interplay between the level of intrinsic noise and viral protein decision threshold is a major factor that produces dependence on multiplicity of infection. However, simulations suggest spatial segregation of phage particles does not play a significant role. Cellular image processing is used to re-analyse the original time-lapse movies from the recent study and it is found that higher numbers of infecting phage reduce the cell elongation rate. This could also contribute to the observed phenomena as cellular growth rate can affect transcription rates. Our model further predicts that rate of lysogeny is dependent on bacterial growth rate, which can be experimentally tested. Our study provides new insight on the mechanisms of individual phage decision making. More generally, our results are relevant for the understanding of gene-dosage compensation in cellular systems.

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Average Stochastic Trajectories of [CII] over time interval  for stochastic non-spatial model.Mean trajectories shown (blue line)  standard deviations (cream shaded region), alongside the deterministic trajectory (turquoise line). One stochastic trajectory from the data is also shown in green. (A) MOI = 1, V = 1 (,). (B) MOI = 2, V = 2 (, ). Results calculated based on  simulations. (C) Distribution of  showing a low threshold (purple dashed line), threshold at mean (brown dashed line) and high threshold (yellow dashed line). This illustrates that the area under the curve exceeding the threshold is larger for MOI = 2, V = 2 for the low threshold, equal areas for the threshold at the mean and larger area for MOI = 1, V = 1 for the high threshold.
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pone-0103636-g003: Average Stochastic Trajectories of [CII] over time interval for stochastic non-spatial model.Mean trajectories shown (blue line) standard deviations (cream shaded region), alongside the deterministic trajectory (turquoise line). One stochastic trajectory from the data is also shown in green. (A) MOI = 1, V = 1 (,). (B) MOI = 2, V = 2 (, ). Results calculated based on simulations. (C) Distribution of showing a low threshold (purple dashed line), threshold at mean (brown dashed line) and high threshold (yellow dashed line). This illustrates that the area under the curve exceeding the threshold is larger for MOI = 2, V = 2 for the low threshold, equal areas for the threshold at the mean and larger area for MOI = 1, V = 1 for the high threshold.

Mentions: In order to obtain insights to the role of MOI on the decision making process, we focus initially on the difference between cells with MOI and MOI at VC (). Figure 3 A and B show traces of a single stochastic trajectory and of the average [CII] based on stochastic simulations. We find similar mean [CII] for both case of MOI, V (, ) and MOI, V (, ). However, as shown in Figure 3 variation in the MOI case is significantly larger than for MOI, since it has more intrinsic noise due to having lower copy numbers of genes and other biomolecules. This is demonstrated further in Figure 3C. The rate of lysogeny is determined by the specific choice of the decision threshold and time point . We choose minutes, which is a reasonable choice given the timescales in which decisions occur as observed in [24]. However, our results are not sensitive to specific choice of (results not shown). If we choose we find similar probabilities of lysogeny for the two cases. Interestingly, we find that for the rate of lysogeny is higher for MOI than for MOI, whereas for the rate of lysogeny is higher for MOI than for MOI (Figure 4A). Since the average CII is similar for the MOI and MOI cases, the observed difference in the rate of lysogeny should be due to different levels of noise in CII. With larger noise a higher (lower) threshold than the average is exceeded more (less) frequently, as illustrated in Figure 3C.


Stochastic cellular fate decision making by multiple infecting lambda phage.

Robb ML, Shahrezaei V - PLoS ONE (2014)

Average Stochastic Trajectories of [CII] over time interval  for stochastic non-spatial model.Mean trajectories shown (blue line)  standard deviations (cream shaded region), alongside the deterministic trajectory (turquoise line). One stochastic trajectory from the data is also shown in green. (A) MOI = 1, V = 1 (,). (B) MOI = 2, V = 2 (, ). Results calculated based on  simulations. (C) Distribution of  showing a low threshold (purple dashed line), threshold at mean (brown dashed line) and high threshold (yellow dashed line). This illustrates that the area under the curve exceeding the threshold is larger for MOI = 2, V = 2 for the low threshold, equal areas for the threshold at the mean and larger area for MOI = 1, V = 1 for the high threshold.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4126663&req=5

pone-0103636-g003: Average Stochastic Trajectories of [CII] over time interval for stochastic non-spatial model.Mean trajectories shown (blue line) standard deviations (cream shaded region), alongside the deterministic trajectory (turquoise line). One stochastic trajectory from the data is also shown in green. (A) MOI = 1, V = 1 (,). (B) MOI = 2, V = 2 (, ). Results calculated based on simulations. (C) Distribution of showing a low threshold (purple dashed line), threshold at mean (brown dashed line) and high threshold (yellow dashed line). This illustrates that the area under the curve exceeding the threshold is larger for MOI = 2, V = 2 for the low threshold, equal areas for the threshold at the mean and larger area for MOI = 1, V = 1 for the high threshold.
Mentions: In order to obtain insights to the role of MOI on the decision making process, we focus initially on the difference between cells with MOI and MOI at VC (). Figure 3 A and B show traces of a single stochastic trajectory and of the average [CII] based on stochastic simulations. We find similar mean [CII] for both case of MOI, V (, ) and MOI, V (, ). However, as shown in Figure 3 variation in the MOI case is significantly larger than for MOI, since it has more intrinsic noise due to having lower copy numbers of genes and other biomolecules. This is demonstrated further in Figure 3C. The rate of lysogeny is determined by the specific choice of the decision threshold and time point . We choose minutes, which is a reasonable choice given the timescales in which decisions occur as observed in [24]. However, our results are not sensitive to specific choice of (results not shown). If we choose we find similar probabilities of lysogeny for the two cases. Interestingly, we find that for the rate of lysogeny is higher for MOI than for MOI, whereas for the rate of lysogeny is higher for MOI than for MOI (Figure 4A). Since the average CII is similar for the MOI and MOI cases, the observed difference in the rate of lysogeny should be due to different levels of noise in CII. With larger noise a higher (lower) threshold than the average is exceeded more (less) frequently, as illustrated in Figure 3C.

Bottom Line: Here, we attempt to provide a mechanistic explanation of these results using a simple stochastic model of the lambda phage genetic network.Several potential factors including intrinsic gene expression noise, spatial dynamics and cell-cycle effects are investigated.However, simulations suggest spatial segregation of phage particles does not play a significant role.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Imperial College, London, United Kingdom.

ABSTRACT
Bacteriophage lambda is a classic system for the study of cellular decision making. Both experiments and mathematical models have demonstrated the importance of viral concentration in the lysis-lysogeny decision outcome in lambda phage. However, a recent experimental study using single cell and single phage resolution reported that cells with the same viral concentrations but different numbers of infecting phage (multiplicity of infection) can have markedly different rates of lysogeny. Thus the decision depends on not only viral concentration, but also directly on the number of infecting phage. Here, we attempt to provide a mechanistic explanation of these results using a simple stochastic model of the lambda phage genetic network. Several potential factors including intrinsic gene expression noise, spatial dynamics and cell-cycle effects are investigated. We find that interplay between the level of intrinsic noise and viral protein decision threshold is a major factor that produces dependence on multiplicity of infection. However, simulations suggest spatial segregation of phage particles does not play a significant role. Cellular image processing is used to re-analyse the original time-lapse movies from the recent study and it is found that higher numbers of infecting phage reduce the cell elongation rate. This could also contribute to the observed phenomena as cellular growth rate can affect transcription rates. Our model further predicts that rate of lysogeny is dependent on bacterial growth rate, which can be experimentally tested. Our study provides new insight on the mechanisms of individual phage decision making. More generally, our results are relevant for the understanding of gene-dosage compensation in cellular systems.

Show MeSH
Related in: MedlinePlus