Figure 1.
Schematic Representation of the SOS Network in E. coli, Including Proteins, Functional States of DNA, and Key Processes
The purple lines indicate transcriptional regulation, the red lines active degradation and proteolytic cleavage, and the green lines complex formation. The yellow shading highlights the proteins involved in mutagenesis, centered around the Pol V DNA polymerase, a complex consisting of an UmuD′ homodimer and UmuC.
Figure 2.
Mechanism for Measuring Damage
When the replication fork stalls at a lesion, a RecA filament (RecA*) is formed. Each filament exists for an average time τRecA*. For low lesion densities (A), the filament disassembles before the replication fork reaches the next lesion. In contrast, an extreme scenario is depicted in (B) where the lesion density is so high that the replication fork reaches the next lesion before the first filament disassembles. In this case, more than one RecA filament can be present on the DNA for some time, and the average RecA* concentration is correspondingly higher. For intermediate lesion densities, the average concentration of RecA* also increases with the lesion density, its value being determined by the interplay between the stall time (τstalled), distance between lesions (1/μ), speed of the fork on undamaged DNA (v), and the RecA filament lifetime (τRecA*) (see main text).
Figure 3.
Mutagenesis Subnetwork and Associated Dynamical Equations (Only Those Links Are Shown That Have Corresponding Terms in the Equations)
u, u′, and uhetd are the concentrations of UmuD, UmuD′, and UmuD–UmuD′ heterodimer, respectively. r* is the RecA* level. l is the LexA level. kf, kb, βu, Ku,γu, γdd′, γdil, C, and K are parameters (see Methods for their values). The equations describe (1) LexA repressed production of UmuD (highlighted in yellow), (2) RecA*-mediated cleavage of UmuD (highlighted in red), (3) heterodimerization of UmuD and UmuD′ (highlighted in green), (4) degradation of UmuD′ by ClpX when in the heterodimer, releasing UmuD (red), (5) dilution of all proteins due to cell growth/division (indicated by blue), and (6) formation of Pol V (green).
Figure 4.
Mechanism of Pol V to RecA* Feedback
The red line shows the progress in time of a replication fork on DNA with UV-induced lesions. Each yellow bar shows the time span of existence of the RecA filament formed when the fork encounters a lesion. In the absence of Pol V, each RecA filament disassembles before the next one is created. At a later time, when Pol V appears (light blue region), the stall time is substantially reduced, so that a new RecA filament is created before the previous one disassembles, hence the level of RecA* goes up.
Figure 5.
Activity of a Hypothetical LexA-Regulated Promoter, Parameterized as ∝1/(1+(LexA/100nM))
The blue curve is for default parameters with UV dose 20 J/m2. The position of the second peak coincides with the generation of Pol V and is due to the feedback between Pol V and RecA* levels, mediated by Pol V–assisted bypass of replication forks. The red curve is produced by averaging more than 200 runs of the model, each with a different value for the number of replication forks, Nf, uniformly distributed between 1 and 3 (Nf = 2 for the blue curve).
Figure 6.
Pol V Concentration as a Function of Time, Following an Instantaneous Pulse of UV at Time Zero, For Different UV Doses
Below a threshold of about 17 J/m2 there is no Pol V and, hence, no mutagenesis. The sharp onset of Pol V, in relation to both time and UV dose, is a direct consequence of the strong heterodimerization of UmuD–UmuD′. Thus, mutagenesis occurs only if the amount of UmuD′ exceeds that of UmuD, so that some free UmuD′ is left to generate Pol V.
Figure 7.
Temporal Profile of Pol V Following a UV Dose of 20 J/m2 as a Function of Various Parameters
(A) The three curves refer, respectively, to strong (Kdd′ = 0.01 nM, blue), medium (Kdd′ = 1 nM, red), and weak (Kdd′ = 100 nM, black) binding between UmuD and UmuD′.
(B) The effects of changing the binding constant between the UmuD′ homodimer and UmuC: as binding strength 1/K in Equation 12 increases (K = 100,10,1 nM for the green, blue, and red curves, respectively), the Pol V concentration saturates at the 200 nM value set by the maximum cellular level of UmuC.
(C) For strong binding (Kdd′ = 0.01 nM), the three curves show the effect of increasing the degradation rate γdd′ of UmuD′ by ClpX. As a default, the degradation rate is set equal to the dilution rate γdil (blue). The rate is half of the dilution rate for the red curve, whereas it is zero for the black curve. For the green curve, the degradation rate is double that of the dilution rate, which—at this level of UV damage—results in almost no Pol V.
(D) The effect of removing the Pol V to RecA* feedback. The blue curve is when there is feedback (as in Figure 7 A–C). The green curve is when there is no feedback, i.e., τstalled = τstalled(0), irrespective of the Pol V level.
Figure 8.
Saturation of Peak Promoter Activity at High UV Doses
(A) Height of the first (blue curve) and second (red curve) peaks in LexA-regulated promoter activity, averaged more than 200 runs each with a different value of Nf, uniformly distributed between 1 and 3 (other parameters remained fixed as in Figure 4) as a function of the UV dose. Red circles and blue triangles show the corresponding data from Figure 4C of [10]. To facilitate comparison, the height of the red (blue) curve was normalized to match the maximum experimentally observed peak activity.
(B) The peak heights as a function of UV dose for a single run with Nf = 2, with the same normalization as in (A). The saturation of peak heights for increasing UV doses in our model is a consequence of Equation 3.
Figure 9.
SOS Response to Prolonged UV Exposure
(A) LexA (blue) and RecA* (red) levels as a function of time in the presence of a continuous source of UV, which in 300 min (i.e., five cell generations) produces as many lesions as an instantaneous pulse of 20 J/m2.
(B) The presence or absence of mutagenesis in our model in response to a pulse of UV radiation of a given integral intensity (y-axis) and duration (x-axis). Mutagenesis was detected in the colored regions. The criterion for its detection was the Pol V level crossing a specified threshold: 0.1 nM (yellow region), 1 nM (orange region), and 10 nM (brown region).
Figure 10.
Summary of the Main Lessons of Our Model of the SOS Response and Mutagenesis