Simulating the temporal modulation of inducible DNA damage response in Escherichia coli

Non-equilibrium repressor binding kinetics link DNA damage dose to transcriptional timing within the SOS gene network

Biochemical pathways are often genetically encoded as simple transcription regulation networks, where one transcription factor regulates the expression of multiple genes in a pathway. The relative timing of each promoter’s activation and shut-off within the network can impact physiology. In the DNA damage repair pathway (known as the SOS response) of Escherichia coli, approximately 40 genes are regulated by the LexA repressor. After a DNA damaging event, LexA degradation triggers SOS gene transcription, which is temporally separated into subsets of ‘early’, ‘middle’, and ‘late’ genes. Although this feature plays an important role in regulating the SOS response, both the range of this separation and its underlying mechanism are not experimentally defined. Here we show that, at low doses of DNA damage, the timing of promoter activities is not separated. Instead, timing differences only emerge at higher levels of DNA damage and increase as a function of DNA damage dose. To understand mechanism, we derived a series of synthetic SOS gene promoters which vary in LexA-operator binding kinetics, but are otherwise identical, and then studied their activity over a large dose-range of DNA damage. In distinction to established models based on rapid equilibrium assumptions, the data best fit a kinetic model of repressor occupancy at promoters, where the drop in cellular LexA levels associated with higher doses of DNA damage leads to non-equilibrium binding kinetics of LexA at operators. Operators with slow LexA binding kinetics achieve their minimal occupancy state at later times than operators with fast binding kinetics, resulting in a time separation of peak promoter activity between genes. These data provide insight into this remarkable feature of the SOS pathway by demonstrating how a single transcription factor can be employed to control the relative timing of each gene’s transcription as a function of stimulus dose.

As the precise timing of gene expression is critical for cells to respond and adapt to new environments, it is important to understand the underlying mechanisms which control this timing. In this report, we studied the timing of transcription for genes in the bacterial DNA damage repair pathway (known as the SOS response), a regulatory system where each gene is controlled by the same transcriptional repressor, LexA. By specifically isolating the role of the LexA binding interaction at SOS gene promoters, we found a relationship between the amount of DNA damage incurred by the cell, LexA binding kinetics at a promoter, and the timing of promoter activation. Our data fit a kinetic model that reveals how a disequilibrium between the LexA-operator binding reaction and cellular LexA concentrations causes timing differences between genes to emerge only at higher doses of DNA damage. Taken together, we show that non-equilibrium DNA binding kinetics is the mechanism by which a single transcription factor can modulate timing differences across an entire network of genes as a function of stimulus dose.

Single-molecule DNA repair in live bacteria

Cellular DNA damage is reversed by balanced repair pathways that avoid accumulation of toxic intermediates. Despite their importance, the organization of DNA repair pathways and the function of repair enzymes in vivo have remained unclear because of the inability to directly observe individual reactions in living cells. Here, we used photoactivation, localization, and tracking in live Escherichia coli to directly visualize single fluorescent labeled DNA polymerase I (Pol) and ligase (Lig) molecules searching for DNA gaps and nicks, performing transient reactions, and releasing their products. Our general approach provides enzymatic rates and copy numbers, substrate-search times, diffusion characteristics, and the spatial distribution of reaction sites, at the single-cell level, all in one measurement. Single repair events last 2.1 s (Pol) and 2.5 s (Lig), respectively. Pol and Lig activities increased fivefold over the basal level within minutes of DNA methylation damage; their rates were limited by upstream base excision repair pathway steps. Pol and Lig spent >80% of their time searching for free substrates, thereby minimizing both the number and lifetime of toxic repair intermediates. We integrated these single-molecule observations to generate a quantitative, systems-level description of a model repair pathway in vivo.

Optimality in DNA repair

DNA within cells is subject to damage from various sources. Organisms have evolved a number of mechanisms to repair DNA damage. The activity of repair enzymes carries its own risk, however, because the repair of two nearby lesions may lead to the breakup of DNA and result in cell death. We propose a mathematical theory of the damage and repair process in the important scenario where lesions are caused in bursts. We use this model to show that there is an optimum level of repair enzymes within cells which optimises the cell's response to damage. This optimal level is explained as the best trade-off between fast repair and a low probability of causing double-stranded breaks. We derive our results analytically and test them using stochastic simulations, and compare our predictions with current biological knowledge.

Stochastic analysis of the SOS response in Escherichia coli

BACKGROUND

DNA damage in Escherichia coli evokes a response mechanism called the SOS response. The genetic circuit of this mechanism includes the genes recA and lexA, which regulate each other via a mixed feedback loop involving transcriptional regulation and protein-protein interaction. Under normal conditions, recA is transcriptionally repressed by LexA, which also functions as an auto-repressor. In presence of DNA damage, RecA proteins recognize stalled replication forks and participate in the DNA repair process. Under these conditions, RecA marks LexA for fast degradation. Generally, such mixed feedback loops are known to exhibit either bi-stability or a single steady state. However, when the dynamics of the SOS system following DNA damage was recently studied in single cells, ordered peaks were observed in the promoter activity of both genes (Friedman et al., 2005, PLoS Biol. 3(7):e238). This surprising phenomenon was masked in previous studies of cell populations. Previous attempts to explain these results harnessed additional genes to the system and deployed complex deterministic mathematical models that were only partially successful in explaining the results.

METHODOLOGY/PRINCIPAL FINDINGS

Here we apply stochastic methods, which are better suited for dynamic simulations of single cells. We show that a simple model, involving only the basic components of the circuit, is sufficient to explain the peaks in the promoter activities of recA and lexA. Notably, deterministic simulations of the same model do not produce peaks in the promoter activities.

CONCLUSION/SIGNIFICANCE

We conclude that the double negative mixed feedback loop with auto-repression accounts for the experimentally observed peaks in the promoter activities. In addition to explaining the experimental results, this result shows that including additional regulations in a mixed feedback loop may dramatically change the dynamic functionality of this regulatory module. Furthermore, our results suggests that stochastic fluctuations strongly affect the qualitative behavior of important regulatory modules even under biologically relevant conditions, thus emphasizing the importance of stochastic analysis of regulatory circuits.

Fluence-response dynamics of the UV-induced SOS response in Escherichia coli

Bacteria in nature often suffer sudden stresses, such as ultraviolet (UV) irradiation, nutrient deprivation, and chemotoxins that would cause DNA damage and DNA replication failure, which in turn trigger SOS response. According to the strength and duration of the stress, the SOS system not only repairs DNA damage but also induces mutagenesis, so as to adapt to the changing environment. The key proteins in charge of mutagenesis are UmuD and UmuD'. In this paper, we quantitatively measure the growth rate and cellular levels of proteins UmuD and UmuD' in Escherichia coli after various fluences of UV irradiation. To compare with the experimental observations, an ordinary differential equation model is built to describe the SOS response. Considering the fact that the DNA lesions affect cellular protein production and replication origination, the simulation results fit well with the experimental data. Our results show how the fluence of UV irradiation determines the dynamics of the inducing signal and the mutation frequency of the cell.