Figure 1.
Decision Making in lambda phage.
A: The role of the and
promoters involved in lambda phage decision. Dashed lines denote transcriptional events that require no activation while solid lines denote transcriptional events that require activation. B: Schematic of the core genetic network involved in lysis-lysogeny decision. CI gene promotes itself and represses the other genes. Cro represses everything, while CII promotes CI. C: Rate of lysogeny as observed from experimental observations in Zeng et al. [24] as a function of viral concentration for different MOI. D: Rate of lysogeny as a function of MOI for different volumes. Bacterial volumes and viral concentrations are expressed in arbitrary units using the normalized cell lengths following Zeng et al. [24].
Figure 2.
(A) Illustration of a stochastic trajectory of CII proteins from time of infection to decision. We consider the decision criteria as to whether the area under the curve of CII (light blue area) is above , or equivalently average
is above
over a particular length of time
. This criteria is outlined in flow diagram B.
Figure 3.
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.
Figure 4.
How the Relationship Between Noise and Threshold Level Affect the Decision.
(A) Rate of lysogeny across different threshold values for basic model. Blue line: MOI = 1, V = 1; Green line: MOI = 2, V = 2; Orange dashed line: ; Pink and yellow dashed lines: Theoretical approximations for the rate for MOI = 1, V = 1 and MOI = 2, V = 2 respectively. (B) How changing the level of noise for same MOI affects the outcome at a high threshold (green line,
above the mean), threshold at
(yellow line) and low threshold (blue line,
below the mean). (C) How the MOI affects the rate of lysogeny at a high threshold (green line,
above the mean), threshold at
(yellow line) and low threshold (blue line,
below the mean). The phenomenological rate
is shown for a typical unit cell volume using
. (orange dashed line).
Figure 5.
Robustness of our results with respect to variations in model assumptions and parameters.
(A) Rate of lysogeny across different threshold values for model with CII tetramers instead of dimers, phage replication (deterministically doubling every 3 minutes for the first 15 minutes) and CI self repression. Blue line: MOI, V
; green line: MOI
, V
. (B) Global sensitivity analysis using 200 different parameter sets chosen by randomly varying all parameters within a factor of 2 or 10 of their nominal values. Rate of lysogeny for MOI
, V
against MOI
, V
are plotted with blue dots for changes by a factor of 2 and green dots for changes by a factor of 10. The orange dashed line represents the point where rate for MOI
, V
is equal to MOI
, V
. The rate of lysogeny for each parameter set is estimated using 500 stochastic simulations with a decision threshold set at
above the mean
value for that parameter set.
Figure 6.
Average CII concentrations for different rates of diffusion. (A) MOI = 1, V = 1, phage at centre (,
); (B) MOI = 2, V = 2, phage at centre (
,
); (C) MOI = 2, V = 2, phages at a quarter and three quarter of the cell length (
,
); (D) MOI = 2, V = 2, phage at cell poles (
,
). Average [CII] with for non-spatial model (blue line) shown alongside spatial model (yellow lines). Results based on
simulations. (E) Rate of lysogeny across different threshold values for spatial model with original diffusion rates (solid lines). Results are shown alongside the non-spatial results (dashed lines).
Figure 7.
The Role of Cell Cycle Effects.
(A) Method for determining cell growth rate. Measurements are taken at 2 time points, the first frame and final frame. The final frame is determined by the event. For an uninfected cell (grey) this is the point at which the cell divides. For an infected cell it is the point at which a decision of lysis (green) or lysogeny (red) has been made. The growth rate was calculated using where
is the time between the first frame and the final frame. (B) Observed growth rates at different MOI. (C) Effect of cell growth on rate of lysogeny by considering dilution only. Fast rate
and slow rate
. (D) Effect of growth rate on rate of lysogeny when also considering possible changes in transcription rates. Growth rate modulation of transcription rate are similar to the study by Klumpp et al. [33], with a two fold enhancement in the slower transcription rate case.
Figure 8.
The Effect of Growth Media on Rate of Lysogeny.
(A) Division time for cells infected with lambda phage. For MOI this is the division time of the cell, for MOI
this is the division time for infected cells that choose lysogeny. (B) Effect of growth rate on rate of lysogeny in different growth media. Here, simulations compared the rate of lysogeny in cells of the same size with different MOI. Growth rate modulation of transcription rate are similar to the study by Klumpp et al. [33].
Table 1.
Model Parameters.