Direct visualization of four diffusive LexA states controlling SOS response strength during antibiotic treatment

In bacteria, the key mechanism governing mutation, adaptation and survival upon DNA damage is the SOS response. Through autoproteolytic digestion triggered by single-stranded DNA caused by most antibiotics, the transcriptional repressor LexA controls over 50 SOS genes including DNA repair pathways and drivers of mutagenesis. Efforts to inhibit this response and thereby combat antibiotic resistance rely on a broad understanding of its behavior in vivo, which is still limited. Here, we develop a single-molecule localization microscopy assay to directly visualize LexA mobility in Escherichia coli and monitor the SOS response on the level of transcription factor activity. We identify four diffusive populations and monitor their temporal evolution upon ciprofloxacin-induced continuous DNA damage. With LexA mutants, we assign target bound, non-specifically DNA bound, freely diffusing and cleaved repressors. We develop a strategy to count LexA in fixed cells at different time points after antibiotic stress and combine the time-evolution of LexA sub-populations and the repressor’s overall abundance. Through fitting a detailed kinetic model we obtain in vivo synthesis, cleavage and binding rates and determined that the regulatory feedback system reaches a new equilibrium in ∼100 min. LexA concentrations showed non-constant heterogeneity during SOS response and designate LexA expression, and thereby regulation of downstream SOS proteins, as drivers of evolutionary adaptation. Even under low antibiotic stress, we observed a strong SOS response on the LexA level, suggestion that small amounts of antibiotics can trigger adaptation in E. coli.


Introduction
Mechanisms of bacterial resistance to antibiotics include removing drugs via various efflux pumps, acquiring resistance genes encoding for drug-inactivating enzymes, or generating mutations in drug target proteins (1). In Escherichia coli and many other bacterial species, acquisition of resistance genes or mutations of drug target genes are results of the SOS response, a gene regulatory network that specifically responds to DNA damage, a downstream effect of nearly every antibiotic (2). Despite decades of research, how this regulatory scheme responds to different instances of DNA damage still lacks a global understanding and is hard to predict, in part due to difficulty of monitoring first steps of SOS induction in living cells. Orchestrated by the transcriptional repressor LexA, over 50 genes involved in DNA repair, mutagenesis, cell cycle control as well as several unknown functions are co-regulated (3). The SOS response is initiated through the exposure of single-stranded DNA (ssDNA), which is a product of nuclease complexes such as RecBCD processing DNA damage (4). Free monomers of RecA are recruited to ssDNA and rapidly polymerize along it (5). The resulting filament can induce autoproteolytic cleavage of the dimeric LexA repressor (6,7), leading to net dissociation from operator sites and expression of SOS genes such as sulA, uvrA, and umuCD (3) (Fig. 1a). Since only freely diffusing LexA dimers are susceptible to RecA-mediated autoproteolytic digestion (8), LexA DNA binding kinetics are determinant of the gene expression profile following DNA damage (9). Cleaved LexA fragments are thought to be unstable in the cytoplasm and quickly degraded by multiple proteases recognizing peptide motifs exposed after cleavage (10).
LexA represses both the lexA and recA genes in a double negative feedback. Together with the availability of the inducer ssDNA being highly incidental, the expression of SOS genes is nuanced and likely subject to stochastic fluctuations with a high cell-to-cell variability (11,12). This complexity makes it difficult to predict bacterial behavior under antibiotic challenges. A lack of timescales, molecular quantities and kinetics of individual constituents in vivo still blur our understanding of sub-cellular dynamics under stress. Many conventional SOS response assays rely on transcriptional reporters under the control of promoters that become active only after LexA cleavage (9,11,13), or on bulk measurements that cannot capture population heterogeneity. More recently, live-cell single-molecule microscopy has developed into a powerful tool in bacteriology because it addresses spatial and temporal scales appropriate for the small size of bacteria (14,15). Subpopulations of diffusing species can be resolved, and kinetic rates extracted from time course experiments. Fixed-cell single-molecule experiments provide insight into subcellular localization (16) and copy numbers of proteins of interest (17)(18)(19). Here, we characterize LexA mobility, quantity and heterogeneity in situ in unstressed cells and upon ciprofloxacin treatment with three different antibiotic concentrations reaching from 0.15× minimal inhibitory concentration (MIC) to 6×MIC. We capture molecule-to-molecule, as well as cell-to-cell variations in living and fixed bacteria using single-molecule tracking together with photoactivated localization microscopy (smtPALM). We identify four diffusive sub-populations, assign molecular functions using mutant LexA proteins and measure their time evolution. Complementing these live cell data, we develop an optimized single-molecule counting technique in E. coli. This approach allows us to quantify absolute LexA numbers in single cells and define the predominant location of LexA proteins within the E. coli cell. Combining live and fixed cell data, we devise a kinetic model which shows that under continuous antibiotic stress, copy numbers of individual LexA populations reach a new, unexpectedly high equilibrium, even under the lowest antibiotic stress. Our model provides for the first time in vivo LexA synthesis, cleavage, degradation and binding rates that are partially dependent on the antibiotic dosage. Finally, single-cell analysis reveals a homogeneous initial response to ciprofloxacin, and increased heterogeneity during late SOS response. We anticipate that this data and further experiments will help to shed more light on the bacterial SOS response and strategies to understand the development of antibiotic resistances.

Results
LexA assumes four diffusive states in E. coli SOS gene transcription requires unbinding of the transcriptional repressor LexA. It is known that upon presence of single-stranded DNA, a RecA filament forms and triggers autocatalytic proteolysis of LexA and, as a result, a reduced occupancy of LexA at its transcription repression sites (Fig. 1a). Yet, little is known about the response kinetics of the LexA-SOS system to stress, in particular to antibiotics. To observe the bacterial SOS response in real-time, we developed an in vivo single-molecule reporter system on the mobility of LexA. We hypothesized at least two distinct LexA mobilities, a target site bound state and a freely diffusing state.
To test this hypothesis, we replaced the chromosomal lexA gene with a C-terminal lexA-PAmCherry fusion in E. coli MG1655. A structural analysis of LexA bound with its N-terminal domain to DNA (20) suggested that LexA function would be minimally disturbed by extending the Cterminal domain with a short six amino acid linker sequence prior to a photoactivatable fluorescent tag (Fig. 1b). The resulting strain showed normal growth, formed elongated filamentous cells under SOS response of equal dimensions as the wildtype and retained its susceptibility to ciprofloxacin (CIP), indicating a functional LexA-PAmCherry fusion that still allows repressor dimerization (Fig. S1a-d). Using a weak photoactivation with 405 nm illumination, a small number of LexA-PAmCherry (termed LexA wt hereafter) repressors were fluorescent and single-molecule tracking was possible with an exposure time of 20 ms (Fig. 1c). Since clustering artifacts are sometimes observed with FPs of the mCherry family (19), we confirmed similar localization patterns of LexA-Dendra2 (Fig.  S1e), an FP tag that is reported to be strictly monomeric (21). In unstressed E. coli, we then localized (22) individual molecules and tracked (23) their movements until photobleaching occurred (Fig. 1c).
For each molecule, we calculated the distance traveled between consecutive frames and generated a probability distribution of mean distances per frame per track to observe the extent of diffusive variety (Fig. 1d, Fig. S2). Surprisingly, three distinct peaks were observed in unstressed cells with inter-frame distances of approximately 55, 100 and 180 nm. Additionally, a broad tail at larger distances per frame appeared, indicating potentially four mobility states of LexA in unstressed cells. While this observation indicates a rich diffusive landscape of LexA, the actual area explored by the molecules cannot be readily quantified from mean distance traveled distributions. We therefore calculated apparent diffusion coefficients ( * ) for each trajectory from the change in mean squared displacement over time (see Methods, Fig. S2). The resulting distributions of apparent diffusion coefficients spanned four orders of magnitude (Fig. 2a, Fig. S3a). We fitted logarithmic gamma functionbased models with varying numbers of populations using the * probability distribution (see Methods) and revealed with the Bayesian information criterion (BIC) an optimum of four states (Fig. 2a). When we stressed the cells with the antibiotic ciprofloxacin (CIP), which is known to activate the SOS response (24)(25)(26), the fastest population was strongly increased suggesting that this population represents cleaved repressors. Interestingly, the mean distance traveled per frame, as well as the apparent diffusion coefficients, showed only negligible shifts between all experiments, even during antibiotic stress (Fig. S3a). Therefore, we pooled all data sets and determined four global apparent diffusion coefficients, " * = 0.025 µm 2 s -1 , # * = 0.152 µm 2 s -1 , $ * = 0.677 µm 2 s -1 and % * = 2.67 µm 2 s -1 (Fig. 2a). We further applied an independent method to estimate the number of populations and their * values. The user unbiased, Bayesian inference based algorithm SMAUG (27) collapsed from initially ten populations to a four-population model for both unstressed and stressed cells (Fig. 2c, Fig. S3b). The resulting diffusion coefficients agreed well with the logarithmic gamma functions fit to the diffusion coefficient histograms, yet it remained unclear what biological roles the four diffusive states represent.

LexA mutants reveal identities of four diffusive states
We devised a mutation-based strategy to identify the nature of the four observed states. We designed three LexA mutants containing the PAmCherry fusion: (i) LexA E45K , which was reported to abolish specific binding to the recA SOS box (28) and most likely other LexA operators but retains non-specific DNA binding; (ii) LexA R28A, N41A, E45K (LexA 3x ), a previously unreported mutant, which should have a strongly reduced DNA affinity since two key residues involved in specific interactions with nucleobases (N41, E45) and one residue involved in backbone interaction (R28) were replaced (20); (iii) and LexA S119A , which is known to have an inactive catalytic center that renders the protein non-cleavable (29). We suspected the first two mutants to be lethal for E. coli due to their direct interference in the regulatory suppression of SOS genes. Therefore, we expressed LexA E45K and LexA 3x from Plac at the lacZ locus in addition to the untagged chromosomal lexA. The S119A mutation was inserted at the native locus on the chromosome (30) to serve as a negative control for SOS induction. We imaged all mutants under the same conditions as LexA wt in unstressed cells, obtained localizations and tracked single molecules. We subsequently plotted the mean distance traveled per frame for all three mutants and used these distributions to assign biological functions to each population (Fig. 2e).
LexA E45K shows a dominant peak at 100 nm mean distance traveled per frame, which corresponds very well to the second population of LexA wt . Knowing that LexA E45K binds to DNA but weakly to target sites compared to LexA wt (28), we infer that the second peak arises from DNA-associated LexA molecules, i.e. molecules that undergo a diffusional search along the chromosome to find their target site. The strong reduction in the 55 nm peak in this mutant suggests that the 55 nm peak represents target-bound LexA. The LexA 3x mutant showed a dominant peak at 180 nm mean distance per frame, coinciding perfectly with the third peak in the LexA wt population. Considering that DNA binding is largely abolished in LexA 3x , we assign this mean frame-to-frame distance to freely diffusing LexA dimers unassociated with the nucleoid. To identify the fourth and fastest population, which is underrepresented in unstressed cells, we treated E. coli with 20 ng/ml CIP for 45 min to induce a strong SOS response. Although this last population has no sharp peak in the mean distance traveled histograms, it is increasing and further expanding to larger mean distances upon stress, whereas the other populations diminish. We infer this population to be cleavage fragments (LexA wt C-terminal domain fragments).
Next, we analyzed the LexA * distributions of all mutant strains and quantified the relative abundance of each of the four diffusive populations and plotted their fractions (Fig. 2d). Upon antibiotic stress with 20 ng/ml CIP for 45 min, there is a strong increase in the fastest population. This population has a major contribution only in stressed cells, as expected for the increased concentration of cleavage fragments during SOS response. Target bound molecules, on the other hand, disappear almost entirely during stress, which is largely expected since unbinding of LexA is the major determinant of SOS gene expression. In contrast, the SOS response deficient LexA S119A displayed only a minor difference between stressed and unstressed conditions. In the LexA 3x mutant, the target bound fraction dropped to the levels of SOS induction as expected. LexA E45K showed only a small decrease in this population, most likely due to its residual affinity to stronger SOS boxes (28). It should be noted that, although the mutants are expressed from Plac at likely much higher levels than LexA wt from its native locus, heterodimer formation of untagged chromosomal LexA and the LexA 3x and LexA E45K mutants cannot be excluded and might contribute to the target bound and DNA-bound populations. Overall, these results are in line with the qualitative observations based on the mean distance traveled histograms (Fig. 2e) and fit expectations for the respective biological function. In summary, we have identified four diffusive modes of LexA in live E. coli cells: target bound ( " * ≈ 0.025 µm 2 s -1 ), non-specifically DNA bound and most likely target searching ( # * ≈ 0.152 µm 2 s -1 ), cytoplasmic diffusing and not DNA associated ( $ * ≈ 0.677 µm 2 s -1 ), and cleaved LexA fragments ( % * ≈ 2.67 µm 2 s -1 ).

Dosage-dependent change in LexA dynamics upon ciprofloxacin treatment
In order to understand the dynamic regulation of LexA, we investigated the time-dependent change of each individual population during SOS response of different strengths. We determined the minimal inhibitory CIP concentration under our growth conditions to be ~3 ng/ml (Fig. S1c), similar to previously reported values (31,32). We restricted the treatment of E. coli with CIP to the exponential growth phase, since stationary phase cultures are less susceptible (33,34). Cells were stressed with three different concentrations, 0.5, 3.0 and 20 ng/ml, i.e. ~0.15×, 1×, 6× the MIC and imaged at eight incremental time points, 0, 10, 25, 45, 60, 90, 120 and 180 min for approximately 3.5 min. At least three independent biological replicates per time point and CIP concentration were recorded. For each experiment, we determined the * of LexA wt and the corresponding proportions of molecules in each of the four states.
Corresponding histograms and fits for representative time points are shown in Fig. 3a for 20 ng/ml. We then plotted the fractions of each population over time for the three tested CIP concentrations (Fig. 3b-e).
The variance between the biological replicates (dots in Fig. 3b-e) is small, illustrating high reproducibility. For all CIP concentrations, the target bound LexA wt fraction declined rapidly during the first 45 min of stress, suggesting a fast response to DNA damage (Fig. 3b). DNA associated LexA wt dimers declined as well within the first 45 min, but not as drastically (Fig. 3c). In contrast, the LexA wt population of free dimers increased over time under all conditions (Fig. 3d). Cleavage fragments also increased rapidly and with a steeper slope at increasing CIP concentrations. However, since absolute LexA numbers change drastically during SOS response (see single-molecule counting below, Fig. 4c), kinetic rates such as cleavage and binding cannot be derived from relative population proportions only.

Single-molecule counting of LexA during SOS response
To obtain accurate single-cell LexA copy numbers during antibiotic challenge, and to obtain a full kinetic description of SOS repression, we applied single-molecule counting to quantify LexA wt . In fixed E. coli cells, we imaged LexA wt using PALM until most FPs were bleached and only sparse photoactivation (approximately one localization per cell in 20 frames) was visible. After localization, we employed a counting strategy that is based on two previous approaches. First, an iterative algorithm (17) was used to extract the number of molecules within a small radius (Fig. 4a). This procedure requires knowledge of the photophysical parameters of PAmCherry, which were unknown for in situ experiments. We therefore applied a model of PAmCherry photophysics from activation, blinking and bleaching kinetics (Fig. S4a) inside fixed E. coli cells and determined all necessary parameters directly under our experimental conditions (Tab. S1, Fig. S4b-d). With these parameters at hand, we obtained spatially resolved fluorescence time traces (23) and predicted the number of single LexA proteins within one time trace based on iterative optimal-tc molecular counting as described by Lee et al. (17) (Fig. S4e, see also Methods). All methods to determine absolute protein counts using only light emitting labels are biased by the detection efficiency of the respective fluorescent protein or dye (35). Improper folding, premature entry into the dark state and out-of-focus FPs or dyes can lead to a significantly large undetectable fraction. Knowledge of the stoichiometry of a labeled protein complex can be harnessed to determine this fraction (18,36,37). We introduced a known stoichiometry into the experimental system by labeling the well-characterized, strictly monomeric (38) inner membrane protein LacY with one or two copies of PAmCherry in tandem (tdPAmCherry). Both constructs showed clear membrane localization and LacY-tdPAmCherry portrayed significantly more double events within a single spot than LacY-PAmCherry, as determined with our counting algorithm (Fig. S4f). Using a global binomial fit, we determined a detection efficiency of 47.9 ± 6.6 %, which is much higher than previously shown for PAmCherry in E. coli (19), but in the same range as reported in Xenopus oocytes (36). We therefore corrected apparent single-cell counts by a factor of 2.09.
We applied this improved single-molecule counting method in fixed cells which grew under the same conditions as previously described for the live cell experiments. Raw LexA copy numbers per individual cell first decreased quickly, but then strongly increased during antibiotic stress (Fig. S3d). Before any CIP stress was applied, we detected 916 LexA molecules per cell ( Fig. S3d), slightly lower than early estimates for E. coli MG1655 (6). This number converts to 458 dimers and approximately 108 target bound repressors using our estimated fraction for this population (23.6 %, Fig. 2d). This is in agreement with 57-102 reported LexA binding sites in the E. coli genome (3).
Previous studies observed that the SOS response leads to a phase of nucleoid compaction and replication inhibition (39), followed by DNA dispersion (40) and possibly resumption of replication. Filamentous E. coli therefore may contain multiple chromosomes (41) and the cytoplasmic content of several normal-sized cells. To account for this possibility, we decoupled LexA copy numbers from cell size and cycle by normalizing each count with cellular area derived from brightfield images. Distributions of LexA concentrations remained unimodal throughout the SOS response and could be approximated with a lognormal probability density function (Fig. 4b, Fig. 6b). This allowed us to determine the expected value, which we used as the number of LexA proteins per cell area for each condition (Fig. 4c). We observed a fast, CIP concentration-dependent degradation of LexA wt within the first 25 min, where minimal levels of 100-150 molecules per µm 2 were reached (depending on antibiotic dosage), corresponding to ~300-500 molecules per cell on average. Given that at least 57 SOS genes require at least two LexA monomers for repression, such low numbers cannot sustain SOS repression. Accordingly, rapid degradation is followed by strong new synthesis due to net dissociation of the repressor from its own operator and subsequent lexA expression. This fast initial degradation also underscores that the LexA C-terminal cleavage fragment, which remains fused to PAmCherry after auto-proteolytic cleavage, is efficiently degraded by the corresponding proteases. At 20 ng/ml CIP, the concentration of LexA wt molecules per cell increased after 200 min incubation to 4-fold of the unstressed level (Fig. 4c). Interestingly, a strong increase was also observed at 0.5 ng/ml CIP (0.15×MIC), indicating a potent SOS response even at low continuous antibiotic dosage.
LexA wt counts over time contain both degradation and synthesis of new LexA wt and can be modeled using a simple three-state reaction scheme with irreversible steps. Central is the visible state , where the molecules are detectable using fixed-cell PALM (Fig. 5a, see also Methods). The influx to this state + represents the new synthesis of LexA wt while the outflux , * represents the apparent degradation rate of all LexA states together ( ). From the time evolution of our first set of experiments in live E. coli, we extracted the LexA wt cleavage fragment probability function -( ) (Fig. 3e) and could therefore determine the degradation rate of LexA wt fragments , (see Methods). We tested different response functions for +,/01 ( ) and found that a simple logistic function (Methods, Eq. 3) describes the delayed new synthesis well ( Fig. 4c and d, left). Increasing CIP stress lead to a faster response time (Fig. 5g) and stronger increase in the synthesis rate followed by a higher synthesis saturation speed, creating independent new equilibria of the regulatory network. For the degradation rate , , we initially assumed a time-and stress-independent degradation rate, which could not describe our data well (Fig. S6a). By introducing a stress-dependent response function ,,/01 * ( ) (Methods, Eq. 1iii) for the degradation rate, a better description of the experimental data with minimal number of parameters could be achieved. Since there is insufficient information available for the regulation of E. coli degradation complexes, we assumed a simple linear increase of the degradation rate followed by a stress-dependent saturation at time , (Fig. 4d, Fig. S5b). The degradation speed , ( ) = 2 ( ) • , ( ) • [ ] at the new equilibrium agrees with the synthesis of LexA wt monomers at ~1600/min at 20 ng/ml CIP. We can conclude that the SOS response reacts to different external stress levels within 100 min (Fig. 5g) and returns the system to equilibrium within 110-150 min, even when the stress level exceeds the MIC 6-fold and the cells will likely not recover. Having this quantitative data at hand, we proceeded to dissect the regulatory feedback further using the four diffusive states of LexA wt .

A kinetic model of transitions between LexA diffusive states
To determine in vivo interconversion rates between the four diffusive states, we expanded the coarsegrained state of visible molecules to four diffusive states: target-bound (T), DNA-bound (D), cytoplasmic (C) and LexA wt C-terminal fragments (F) (Fig. 5b). The single-molecule counting data allowed us to convert the time evolution of probabilities into molecular densities (LexA wt per µm 2 ) for each CIP concentration (Fig. 5c). In our initial assumption, we coupled all four states with each other through differential equations. Based on earlier reports (8), the cleavage reaction to LexA wt fragments is only possible from cytoplasmic LexA wt and irreversible, therefore we could simplify the set of equations (Methods, Eq. 6). We then assumed reversible transitions between the remaining three states, C, T and D.
All transitions between C, T, D, and F depend on the population of the outgoing state, except that C will be provided with the influx from new synthesis and F will be depleted by degradation. Both, synthesis and degradation were determined by the fit result of the counting data in the previous section. Using global optimization considering all tracking data sets at the same time and deriving errors by drawing iteratively from the pool of biological replicates, optimal rates for each transition were determined using a reduced 4 # criterion for the fit quality. In order to reproduce our data, the transition rateneeded to be time-dependent, which is plausible because CIP stress generates time-dependent DNA damage and ssDNA exposure, leading to time-dependent auto-proteolytic cleavage. We modeled the increasing fragmentation rate -( ) similar to , ( ) with a ramp function (Methods, Eq. 5iii, Fig. 5d, Fig. S6b). Using this model adjustment, we could reproduce in a global approach for each CIP concentration the LexA wt densities of the four states (Fig. 5c). The different transition rates between C, T and D covered about two orders of magnitude (Fig. 5e), while each replicate condition produced a similar set of rates (gray dots in Fig. 5e), suggesting high reproducibility. Surprisingly, our model revealed a low transition rate from D to T, which could be reasoned with current models of target search in the genome, that a mere 1D search in DNA is unlikely to succeed in a rapid target binding (42). This is further supported by the relatively high transition rate from C to T, which we initially assumed to be low considering the number of LexA binding sites and the genome size of E. coli. Furthermore, the transition rate from T to D appeared to be neglectable, which might indicate that the direct dissociation to the cytoplasm is preferred over the back transition to the DNA-bound state. Overall, the equilibrium between the cytoplasmic and the target bound state 567 was ≈0.28, indicating a bias towards a cytoplasmic population and regular exchange of transcriptional repressors (Fig. 5f). Noteworthy, our model assumed that the transitions between C, D and T are independent of CIP concentration, and that CIP stress affects only the synthesis speed +,/01 ( ), the fragmentation rate -,/01 ( ) and the degradation rate ,,/01 ( ). The combination of these together with the binding and unbinding kinetics of LexA wt to DNA and its target site lead to differential response times after CIP exposure in E. coli. While the response time delay, the time lag between initial LexA cleavage and new synthesis, is ~80 min at sub-MIC (0.5 ng/ml CIP) stress, the cells responded after ~40 min at 6×MIC (20.0 ng/ml) CIP under slow growth conditions in minimal medium.

Cell-to-cell heterogeneity during SOS response
Within the SOS network, heterogeneity in repressor copy numbers might arise from several processes including stochasticity or availability in RecA filamentation and subsequent LexA proteolysis, on-off binding rates of the LexA repressor on its own promoter (9) or transcriptional bursting during lexA expression itself (43). Time-resolved single-cell repressor counts and concentrations revealed varying amounts of heterogeneity throughout the SOS response (Fig. 4b, Fig. S3d). Notably, varying concentrations between individual cells were visually discernible in PALM images of fixed cells (Fig. 6a). For E. coli, the scaling of protein density variance # with mean protein density has previously been described with the power law # ∝ ".9 (44,45). We observed that during the SOS response # of [LexA] follows a power-law scaling, but with a larger exponent of 2.33 indicating unusually large heterogeneity (Fig. 6b). This is likely due to the self-regulatory feedback of LexA. Our data also allowed us to quantify the time-resolved heterogeneity by calculating the coefficient of variation from log-normal fits to [LexA wt ] ( [LexA wt ] ) and cell length distributions ( length ), using = 4 B ! − 1 with # corresponding to the variance of the log-normal distribution. The CV yielded a relative measure of variance at each time point of CIP stress (Fig. 6c). The cell length decreased initially after 10 min of CIP treatment at all concentrations (Fig. S1f), likely due to rapid arrest of cell division, however, the length monotonically increased over time for all [CIP] conditions, independently of CIP concentration. In contrast, the heterogeneity of [LexA wt ] showed a strong drop within the first hour of SOS response compared to the steady state of unstressed cells under all antibiotic concentrations. In the second hour of incubation, [LexA wt ] displayed a brief peak and at longer CIP incubation times [LexA wt ] stabilized approximately at the unstressed level, indicating a new stable feedback. Since the first hour is dominated by LexA loss rather than synthesis (Fig. 4c), the decrease in cell-to-cell variation within this period and the subsequent increase with more repressors being synthesized (Fig. 4d) indicate LexA unbinding and synthesis as the major sources of variability, rather than signaling events upstream.

Discussion
The underlying mechanism of SOS response activation (2, 3), as well as the gene expression profile of SOS activated cells (46) have been extensively studied. Regulatory steps leading to these patterns, kinetics of regulation in living cells, as well as cell-to-cell variation of SOS induction are still lacking a global understanding. Here, we studied the dynamics of the master-regulator of the SOS response, LexA, in nonstressed cells as well as during continuous DNA damage with the antibiotic ciprofloxacin. We used singlemolecule tracking in live cells, single-molecule counting in fixed cells and a set of mutants to characterize the stress response under low, medium and high antibiotic stress. We present here the course of SOS response activation and feedback regulation on the level of binding, unbinding, cleavage and synthesis of the master repressor LexA itself.
Four diffusive states, even in unstressed cells, represent a surprising variety in the LexA mobility landscape. By comparing several mutants of the repressor in their diffusive pattern, we identified the four states as target bound, non-specifically DNA bound, cytoplasmic, and cleaved LexA fragments. The nonspecifically DNA bound state is supported by previous reports that prior to finding the target sequence and firmly binding to it, repressors often associate with the DNA in a sequence non-specific manner and perform a 1D target search, as previously shown for the lac repressor (47,48). Tight binding to operator sites results in an apparent diffusion coefficient " * close to zero, defined by minimal movement of DNA within bacterial cells (49,50). The number of tightly bound repressors quickly decreased already after 10 min of CIP treatment (Fig. 5c), showcasing the prompt response to antibiotic stress and DNA damage under exponentially growing conditions. Our quantitative model suggests that every ~6 min, LexA is unbinding the target bound state to the cytoplasm, which allows for the short reaction time. This rapid regulation was previously difficult to capture on the cellular level due to the time delay inherent to indirect fluorescent reporters, though observed on the mRNA level for several SOS genes (46), well in line with our finding. The target-bound population decreased more rapidly when the bacteria were exposed to higher concentrations of CIP (Fig. 5c). This dose-response relationship of the SOS response has been previously observed for pulses of UV damage (6,9), but is not well described for continuous antibiotics exposure. Counting of LexA levels during CIP stress agreed qualitatively with previously reported pulsed UV exposure stress (6,(51)(52)(53). Surprisingly, even in unstressed cells, we found about 4 % of LexA in the cleaved fragment population, suggesting a low level of LexA fragmentation under normal growth conditions with a small, but detectable LexA turnover.
Both the target bound and the non-specifically DNA bound state quickly diminish during CIP exposure (Fig. 5c), as overall cellular LexA concentration drops and cleavage and degradation dominate during the early SOS response, especially at above-MIC antibiotic concentrations. Interestingly, we observe that particularly the target bound LexA population recovers during late SOS response, as an immense amount of LexA up to 800 molecules per µm 2 is synthesized and cytoplasmic concentrations increase. A new equilibrium is reached after 100-120 min, depending on CIP concentration, as LexA synthesis balances continuous cleavage. It follows that E. coli returns to repressing SOS genes before intense mutagenesis and cell-cycle inhibition lead to death, assuming resistance-granting mutagenesis took place within the time frame of maximum upregulation. At sub-MIC CIP, this recovery is significantly slower, suggesting the bacterial attempt to carry out mutagenesis and adaptation in a more controlled fashion.
By applying a simple kinetic model (Fig. 5b) to this time-course data, we were able to determine the key parameters fully describing LexA action in vivo. The rates associated with operator binding represent mean rates over all LexA binding sites, which display large variations in binding affinity (9). They did not show variation under CIP stress, and we therefore propose that cleavage, degradation and synthesis rates are the major determinants of LexA abundance during SOS response. We determined a maximum cleavage rateas 4.3 min -1 (Fig. 5d), well in line with maximum cleavage rates of 3.6-4.2 min -1 measured in vitro (54,55). This rate is higher for higher CIP concentrations likely due to increased cytoplasmic LexA availability and formation of RecA* filaments with increasing DNA damage (Fig. 5d). Degradation of LexA fragments is mediated by the ClpXP protease complex (10). Our results suggest that this process must be highly efficient in vivo, given the high degradation rates (3.5-11.5 min -1 ) that explain the fast decay of total LexA in the early SOS response, as well as counter the accumulation of cleavage fragments (Fig. 4d). Averaged PALM images reveal localization of LexA towards the pole regions ( Supplementary Information, Fig. S5), which is also where ClpXP resides during heat shock stress to dissolve protein aggregates that are occluded from the nucleoid (56). This localization might also stem from freshly synthesized repressors still in proximity of ribosomes (57). We note however that we found no evidence of LexA aggregates in single cells, and the average images (Fig. S5) merely present trends of preferential localization overall. Interestingly, the LexA wt saturation rate for synthesis at 20 ng/ml CIP is ~1,600 LexA wt per minute for a 444 amino acid (aa) protein.
Taking into account previous reports of translation rates of ~15 aa/s (58), this would mean that ~800 ribosomes are occupied with LexA wt synthesis, which is 2 % of all available ribosomes in E. coli (57) to maintain the new equilibrium at high stress conditions.
Cell-to-cell heterogeneity is a major driver of microbial evolution and thought to play an important role in antibiotic resistance acquisition (59). Within the SOS response, heterogeneity has been observed before with fluorescent reporters expressed from the SOS promoters (13,60). Reporting directly on single-cell protein levels with lexA expressed from the native genomic locus, we showed large LexA copy number heterogeneities, and thereby likely heterogeneity of downstream transcriptional output, which varies during antibiotic challenge (Fig. 6). An initial decrease of the highlights a uniform response to initial damage. Downstream events such as noisy gene expression from SOS promoters (12) likely lead to increased heterogeneity during the later response and with it, chances of population survival increase rather than those of a single cell. Our data further suggests that regular un-and rebinding of LexA occurs on the order of ~10 min in unstressed cells, likely causing sporadic expression of SOS genes and might thereby increase mutagenesis events that lead to persistence (61, 62) even before antibiotic exposure.
In conclusion, we directly observed individual states of the SOS response master regulator over time with single-molecule tracking and quantitative PALM during constant ciprofloxacin stress. We discovered that the response kinetics of individual processes differ greatly with increasing stress, however, E. coli manages to re-establish a new equilibrium under all tested conditions within ~100 min. We further provide regulatory timescales and precise LexA quantities that help to better understand the bacterial response to DNA damaging antibiotics and might contribute to developing new strategies for SOS response inhibition. In the future, our in vivo quantities can help to parametrize more complex simulations of the whole SOS network to finally achieve a systems-level understanding of this intriguing network. The combined approach of single-molecule tracking and counting can be adapted to a range of different proteins to monitor molecular sub-populations and corresponding expression changes in a precise manner.

Bacterial strain construction
To tag all genes at their endogenous locus, the gene for PAmCherry was cloned into the plasmid pR6K-lox71-cm-lox66 by ligation into a unique BstAPI restriction site. For LexA mutants that were integrated at the lacZ locus, the lexA gene was amplified from the E. coli MG1655 genome by colony PCR and cloned into pR6K-PAmCherry-lox71-cm-lox66 using the In-Fusion ® HD cloning kit (Clontech). Mutations were introduced using the QuikChange II Site-Directed Mutagenesis Kit (Agilent). A targeting cassette including ~50 bp homology to the target region on either end was amplified by PCR. We described the construction of the genomic LexA S119A mutation previously (30). Recombineering (63) was carried out using a protocol adapted from (64). E. coli MG1655 was transformed with pSC101-BAD-gbaA, where Redgba expression was induced with 0.25 % L-arabinose. 250 ng of the targeting cassette were electroporated into competent cells. The temperature-sensitive plasmid was removed by incubation at 37 °C. The genotype of successfully engineered clones was verified by colony PCR and sequencing. The chloramphenicol resistance gene was recycled using Cre recombination from the temperature-sensitive plasmid pSC101-BAD-Cre.

Culture conditions and sample preparation
Bacterial cultures were grown in M9 minimal medium (1 x M9 salts [Sigma], 1 mM MgSO4, 0.1 mM CaCl2, 0.4 % glucose) supplemented with 0.001 % biotin and thiamine. Autoclaved 1.5 ml tubes with a punctured lid were used for incubation in an Eppendorf ThermoMixer ® at 37 °C and 950 rpm. For imaging, cultures were streaked on LB plates without antibiotics from a glycerol stock. 1 ml M9 cultures were inoculated from the plate and grown over night. The cultures were diluted 36-fold into 1.44 ml fresh M9 medium and grown until exponential phase for 3.5 h. If applicable, the lactose operon was induced with 150 µM IPTG at the beginning of incubation for imaging of LexA mutants at the lacZ locus or LacY-PAmCherry, and with 17 µM for LacY tandem constructs. Bacteria were then treated with CIP and incubation was continued as indicated. For live-cell experiments, cultures were then centrifuged for 30 s at 7,300 g, most of the medium was removed and the pellet was resuspended in an appropriate amount of M9. 1.5 mm thick coverslips were cleaned at least twice by sonicating for 15 min in 5 % Mucasol, 15 min in ethanol and drying with nitrogen gas. An agar pad containing M9 medium as well as CIP, if applicable, was prepared according to (65). 2 µl of the concentrated cell suspension were placed on top of a clean coverslip, covered by the agarpad and immobilized by adding another coverslip on top and pressing gently. For fixed-cell experiments, cultures were grown as described above, cooled on ice for 10 min and incubated in 4 % paraformaldehyde in PBS, pH 7 for 35 min at room temperature, then washed twice with PBS and stored at 4 °C. Prior to imaging, dark red Fluospheres 0.2 µm (Thermo Fisher) were diluted 2,000-fold into the concentrated cell suspension and the sample was assembled as described above.

Data acquisition
PALM movies were acquired at room temperature on a Nikon Ti-E STORM/PALM microscope equipped with a 1.49 NA 100 x TIRF objective (Nikon) and Andor iXon Ultra 897 EMCCD camera. PAmCherry was continuously activated with a 405 nm laser and excited at 561 nm with 28 mW (measured after the objective) under near-TIRF conditions. The 405 nm activation laser was increased over the course of a movie following a Fermi function as described previously (17). Emission light was filtered by a 605/70 bandpass for fixed-cell movies or by a 575 longpass (AHF) for live-cell experiments to collect more photons from diffusing PAmCherry fusions. For single-molecule tracking experiments, around 10,000 frames were recorded at 20 ms exposure time. Fixed-cell PALM movie length varied according to the protein copy number between 20,000 and 30,000 frames. Brightfield images of the same field of view were taken after PALM acquisition.

Raw data processing
Raw movies were processed using SMAP (22) with settings for 2D localization (parameters listed in Tab. S2). The shape of the canonical point spread function was calibrated from 20 z-stacks (10 nm step size) of dark red fluorescent beads under the exact experimental conditions. Cells were segmented from brightfield images using Oufti (66). Localizations were then grouped based on the E. coli outlines using custom-written MATLAB script.

Live-cell data processing
The tracking software swift (23) was used with the parameters listed in Tab. S2 to obtain LexA-PAmCherry trajectories. Tracks with less than four and more than 50 localizations were discarded. To create histograms from the mean distance traveled per frame, we took the mean of all step lengths within a track and weighted the histogram according to the number of steps (Fig. S2). Apparent diffusion coefficients were calculated from track fragments of four localizations in length (Fig. S2). If a track was at least eight localizations long, a maximum of three fragments were recovered from a single track. Apparent diffusion coefficients ( * ) were extracted from mean squared displacement ( ) over time lag ( ) curves using linear fitting according to The was calculated for each using the following equation, with C and C being coordinates of the consecutive localizations making up a trajectory.
Distributions of * were fitted with analytical equations as first described by Vrljic et al. (67), composed of linear combinations of gamma-distributions: with C and C * being the probability and average apparent diffusion constant of state , respectively, and being the number of steps, in this case three (four localizations). The fits were performed and displayed at logarithmic x-axis using a linear combination of log-transformed gamma distributions.
Maximum likelihood estimation (MLE) was realized in MATLAB and the Bayesian information criterium ( ) was determined directly from the maximum value of the likelihood function M with being the number of free parameters and being the sample size.
= ln( ) − 2 ln ( M ) * distributions from unstressed wildtype cells were fitted in this way to determine the optimal size of the analytical model based on a minimized . A four-population model was found most probable, which was confirmed by applying SMAUG (27) to the same dataset (Fig. S2). The four apparent diffusion coefficients were determined from pooled * values, and globally fitted with a four-population model. Standard deviations were determined from 50 bootstrapping iterations by randomly drawing m datapoints from each dataset with replacement; m is the size of the smallest dataset. The four * parameters obtained in this way were fixed and only " -$ fitted to single biological replicates. Biological errors were based on standard deviations of at least three biological replicates. Additionally, data from all replicates within one dataset were pooled and fitted again to obtain more accurate, global amplitudes. The sample sizes together with mean distance traveled and * distributions of all live-cell data collected are recorded in Fig S3.

Fixed-cell data processing
For fixed-cell movies, sample drift was corrected using red-shifted fluorescent beads as suggested recently (68). A custom implementation of the "DriftCorrectionFiducial" plugin from PALMsiever (69) was employed to directly shift PAmCherry localizations based on smoothed frame-to-frame translation of the fiducial markers. Cells were manually sorted into dividing and non-dividing based on the presence of an indentation at the cell mid. Single-molecule localization images were rendered with the ThunderSTORM plugin for ImageJ (70).

Extraction of in situ photophysical parameters of PAmCherry
Fluorescence time series of active fixed PA-FPs were extracted from raw movies by swift (23) using the following set of parameters: exp_displacement = 55 nm, max_displacement = 125 nm, max_blinking_duration = 10 frames, precision = 55 nm, exp_noise_rate = 10 %, p_switch = 0, p_bleach = 0.0001 and p_blink = 0, where the latter two parameters were set to zero to avoid the connection of fluorescent traces interrupted by dark frames. Next, the lengths of all fluorescence segments were sorted in a histogram (Fig. S4b). The resulting on distribution is well described by the sum of two exponential functions (R 2 = 0.99): 1 + α with and 1/(1 + ) being the fractions of segments with rate " and # , respectively. The corresponding average rate 〈 〉 is directly connected to the sum of the bleaching rate O , and the transition rate from the active to the dark state P . In order to obtain the recovery rate 4 , from the dark to the active state, the spatial positions of the segments were correlated: all segments with a distance smaller than 125 nm were connected. From the resulting time traces a off histogram was collected from the length of fluorescence gaps (Fig. S4c). The resulting distribution contains a mixture of blinking events and activation of new PA-FPs within the same radius and is well described by a sum of three exponential functions (R 2 = 0.96): While the biggest two relaxation rates, 4" and 4# (>1 s -1 ) most likely correspond to the recovery of the PA-FPs from the dark to the active state, the smallest relaxation rate R * of about 0.1 s -1 refers to the activation of new fluorescence proteins. The ratio of the two species is given by 4 . To account for the new activation of PA-FPs, a blinking tolerance time 5 = 750 ms was chosen from the off distribution (Fig. S4c). Subsequently, the number of blinking events were collected from the separated fluorescence time traces and sorted in an blink histogram (Fig. S4d), which was then analyzed as described earlier (17). The obtained kinetic parameters are listed in Tab. S1. For further counting experiments, the reappearance probability reappear = ∆ 〈 off 〉 ⁄ , the blinking probability blink = ∆ 〈 on 〉 ⁄ and the bleaching probability bleach = O ∆ ⁄ were calculated and used as experimentally determined input parameters for swift.

Single-molecule counting
In order to quantify the number of molecules per localization spot of the recorded movie, first trajectories were built with swift using the parameters as in the previous section. From the localization list, an activation profile (number of active molecules per frame) was accumulated (Fig. S4e, top) and described using polynomial fits. Next, the calibration curve 5,Z[7 ( mol ) was obtained from Monte Carlo simulations using the photophysical parameters of PAmCherry (Tab. S1) as previously described (17), where mol denotes the number of simulated molecules and 5,Z[7 the optimal blinking tolerance time, where over-and undercounting cancel out each other. Briefly, in the Monte Carlo simulation, mol was varied from 2 to 100 molecules. For every iteration, mol ×5000 fluorescence traces were created by first drawing activation frames from the approximated activation profile (Fig. S4e, top). Subsequently, for every molecule a sequence of active and dark dwell times was drawn using the experimentally derived on , off and blink distributions ( Fig. S4b-d). The resulting mol ×5000 traces were randomly merged to simulate mol ×5000 molecules per localization spot. The optimal blinking tolerance time 5,Z[7 was then chosen such that the average number of molecules per spot matched the simulated number of molecules (Fig. S4e, bottom). Revisiting the localization list, localizations with a distance smaller than 55 nm were combined to a single time trace. By applying the iterative 5,Z[7 counting algorithm to the combined time traces as presented by Lee et al. (17) we finally derived the corresponding number of molecules per localization spot with minimal bias error.

Detectable fraction of PAmCherry molecules in E. coli
To extract a detectable fraction of PAmCherry for correction of LexA-PAmCherry counts, we expressed LacY-PAmCherry and LacY-tdPAmCherry from the original chromosomal locus in two E. coli strains. Well-separated signals were achieved by extremely low expression from Plac using 17 µM IPTG. After single-molecule localization and counting as described above, we extracted the number of molecules per individual spot for each LacY construct. To reduce the error from non-matured or misfolded proteins, we restricted our analysis to a 200 nm wide region along the cell outline, which is where LacY localization is expected and predominately occurred when induced with a higher IPTG concentration of 150 µM (Fig. S5).
As previously described (18), we built two histograms from the number of molecules per spot and applied a global binomial weighted least-square fit neglecting the first bin at = 0 (Fig. S6). This resulted in a detectable fraction = 0.479 ± 0.066 (one σ confidence interval).

Cell alignment
To create images of several cells stacked on top of each other to infer average localizations of LexA, HupA and LacY, we used the python package ColiCoords (71). First, E. coli outlines from non-dividing cells obtained using oufti were converted into binary images. These binaries, the corresponding brightfield images and PALM localization tables were then processed with ColiCoords functions to project localizations for all cells of a single condition into a synthetic cell with average dimensions. The resulting localization table was exported and visualized using the dscatter algorithm (72).

LexA synthesis, degradation model
The single-molecule counting time courses were modelled with a single population ("visible") for each stress condition. Synthesis of new molecules as well as the degradation of visible molecules over time were considered by + and , * (Eq. 1, Fig. 5a). The apparent degradation rate , * , on the other hand, is defined as the product of the proportion of cleaved fragments 2,/01 ( ) and the degradation rate ,,/01 ( ) (Eq. 1). In order to disentangle the degradation rate from the product, the fractions of cleaved fragments derived by the single-molecule tracking measurements were fitted with a single exponential (Eq. 5) and incorporated in the counting fit.
Here, 2,/01 denotes the exponential time constant, and 2,/01 (0) and ∆ 2,/01 are the probability of cleaved fragments in absence of stress at = 0 and the change of the probability over time, respectively.
Since the temporal behavior of ,,/01 was unclear, three different scenarios were considered (Eq. 1): i) A stress independent degradation rate, where all conditions and time points share the same rate. ii) A time invariant but stress dependent degradation rate.
iii) A step function with shared zero stress rate and response time but increasing maximal degradation rate.
Fig . S6a shows the resulting ,,/01 ( ) and + ( ) curves of global fits for the three scenarios. The corresponding fitting curves for the time evolution of visible molecules is exemplary shown for the stress condition [CIP] = 0.5 ng/ml for every scenario in the bottom panel. The fit quality was quantified by the reduced Chi-square c 4 # , which also takes the number of fit parameters into account. The overall c 4 # appears similar for the different scenarios with a value of around 20, however, the first case shows a significant overshoot in the beginning of the curve, followed by an increasing residual at larger . The introduction of three different degradation rates in scenario ii) led to a decreased sum of squares of residuals for the cost of two more fitting parameters, indicating that , also depends on the concentration of CIP. Since an equal degradation rate is expected at zero stress, a shared degradation rate ,G at = 0 and saturation time , were introduced in scenario iii) leading to a smaller sum of squared residuals together with the reduction of the overshoot in the beginning of the curve. Response time delays (Fig. 5g) were approximated from the difference of the characteristic time of an exponential fit of the first part of [ ] /01 ( ) and the actual response time of the respective +,/01 ( ) function.

Kinetic model for individual LexA populations
The LexA tracking data were modeled by four populations: target bound (T), DNA bound (D), cytoplasmic (C) and cleavage fragments (F). While LexA synthesis and degradation rates +,/01 ( ) and ,,/01 ( ) were derived from the counting data, the interconversion between the individual populations is described by the rates P5 , 5P , P7 , 7P , 75 , 57 , -(see Fig. 5b). As a first step, all rates were assumed to be independent on stress condition and constant over time. (ii) -,G.9 < -,$ < -,#G were used for the different CIP concentrations as a second scenario (Eq. 6ii). The corresponding fit led to a reduction of c 4 # (Fig. S6b, mid panels). A shared cleavage rate at zero stress -G together with saturation time -, were introduced, similar to the degradation rate. In this third scenario, c 4 # was further reduced. The final fit of scenario iii) also revealed that the interconversion rate from the target to the DNA bound state, 7P , was close to zero and could therefore be neglected (bold in Eq. 6). In order to account for the random and systematic error of the extracted rates, bootstrapping was implemented in the fitting procedure, where for each time point of the tracking data a set of experimentally obtained * histograms was drawn from the pool of biological replicates. The resulting rates and ratio of rates, 567 and 56P , for each bootstrapping iteration are shown in Fig. 5e (gray) together with the best estimator of the combined replicates (black).

LexA mainly localizes outside the nucleoid
Visual inspection of fixed-cell LexA PALM images suggested a seemingly uniform distribution of LexA in single cells (Fig. 6a). To reveal a possible preferential localization that might not be detectable in single cells due to too low LexA counts, we averaged LexA distributions over many cells (Fig. S5). We used separate strains with reference markers to determine LexA densities relative to the nucleoid (HU-PAmCherry) and membrane (LacY-PAmCherry). The three strains were imaged using PALM after fixation at 0, 60, 90 and 180 min with 3 ng/ml CIP stress. We used ColiCoords (71) to align localizations based on E. coli outlines from brightfield images (66). The average positioning of LacY along the cell periphery suggests a relatively high precision of this diffraction-limited method (Fig. S5). HU portrayed distributions within the cell center of unstressed cells in the region where the nucleoid is expected, in agreement with earlier reports (73,74). Even under long stress, we observed a single, but diffuse DNA mass in the cell center. This is well in agreement with earlier reports for fluoroquinolone antibiotics (39,75), but different from UV stress that can cause multiple segregated nucleoid-like structures in filamentous E. coli during late SOS response (40,41). Interestingly, the average LexA wt position does not colocalize with HU. In our 2D projection, LexA wt explored a larger area, presumably including the cytoplasmic region between nucleoid and membrane. In fact, areas of particularly high LexA abundance appear outside of the highdensity nucleoid regions. This was emphasized further throughout the SOS response and especially pronounced in images after 90 and 180 min CIP-stress. Such average localization agrees well with our single-molecule tracking analysis showing a high abundance of cytoplasmic and cleaved vs. DNAassociated repressors.  Raw PALM movies are processed with SMAP (22) to fit a PSF model to PAmCherry signals. The resulting localizations are then linked in time using the tracking software swift (23). Each trajectory can then be 1) analyzed with SMAUG or 2) subjected to a simple mean inter-frame-distance analysis or 3) split into four localizations long segments to determine apparent diffusion coefficients from linear mean squared displacement fits.