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.