Introduction

RNA is an essential macromolecule in all living cells. Aside from messenger RNA (mRNA), transfer RNA (tRNA) and ribosomal RNA (rRNA), all of which are elemental to protein expression, additional RNA species play significant roles within cells, such as ribozymes, microRNAs and small nuclear RNAs contributing to catalysis, gene regulation and intron splicing, respectively1. RNA is susceptible to damage by processes such as alkylation, radiation and oxidation, in addition to RNA-specific damaging agents such as ribonucleases and ribotoxins2. As most abundant types of RNA are long-lived3, damage to them has potentially enduring effects. With repair likely to require less energy than de novo synthesis, RNA repair can provide an evolutionary advantage to cells4. To maintain vital functions, cells have therefore developed specific RNA repair mechanisms, such as AlkB, which repairs alkylative RNA damage in both humans and E. coli 5,6.

Here we investigate two RNA repair proteins, the RNA cyclase RtcA and the RNA ligase RtcB, which are conserved across all domains of life7. In metazoans and archaea, RtcB plays a well-defined role in tRNA ligation after intron excision and in the unfolded protein response8,9. In bacteria, however, the exact roles of Rtc are less known. Previous work on E. coli showed that Rtc plays roles in chemotaxis and motility10. In addition, Rtc has been shown to be key for maintenance of the translational apparatus of E. coli, where expression of Rtc is induced by oxidative damage or impairments to the translation apparatus, specifically, ribosome-targeting antibiotics and other translation-inhibiting agents such as colicin D10. The ligase RtcB has been implicated with tRNA and rRNA repair: increased degradation of tRNA in the absence of functional RtcB suggests that RtcB contributes to the repair of damaged tRNAs11,12,13, while other evidence suggests that RtcB also improves ribosome health through the re-ligation of fragmented rRNA with ribosomal damage accumulating in the absence of RtcB14,15. Another target of RtcB, the transfer messenger RNA ssrA, is involved in rescuing stalled ribosomes upon translation defects, further highlighting the importance of Rtc in maintaining translational activity11,16.

While rtcA and rtcB are widely conserved, E. coli and some closely related species, including Salmonella, Klebsiella and Shigella species, share a distinct regulation17, where the rtcBA genes are co-expressed from the same promoter under tight control of the regulator protein, RtcR. Transcribed divergently to rtcBA, RtcR completes the rtc locus7 (Fig. 1A). RtcR is a bacterial enhancer binding protein (bEBP), activation of which precedes rtcBA transcription following exposure to inducing conditions18,19. Upon expression, RtcBA can repair damaged RNA in a concerted healing and sealing procedure20, where RtcA cyclizes (heals) damaged RNA ends, and RtcB subsequently ligates (seals) cyclic phosphate termini with 5’-OH termini to repair the RNA perfectly14 (Figure 1B).

Fig. 1: rtcBA expression and Rtc-induced RNA repair in E. coli.

A The rtc locus contains three Rtc genes: rtcBA are co-expressed from a σ54-controlled promoter regulated by RtcR. RtcR contains three domains (right side of panel A). The CARF domain imposes negative regulation on the AAA+ domain; binding of an RNA with a 2’,3’-phosphate end to the CARF domain causes activation of the intrinsic ATPase activity of the AAA+ domain to produce active RtcR which initiates transcription of rtcBA. B Healthy RNA, with phosphodiester bonds linking adjacent RNAs, can be damaged to produce RNA with a 3’-phosphate end (damaged RNA). RtcA requires ATP to convert RNA with 3’-phosphate termini to 2’3’-cyclic phosphate termini (cyclized RNA). RtcB requires GTP to ligate 2’3’-cyclic phosphate with RNA 5’-OH termini (RNA for ligation) to complete the cycle and repair the RNA with a perfect phosphodiester bond (healthy RNA). C Treatment with a ribosome-targeting antibiotic will initially cause a reduction in growth but will also cause the onset of Rtc-induced resistance. Resistant cells stay alive despite the antibiotic and resume growth rendering the antibiotic ineffective (upper panel). If infections could be treated with a ribosome-targeting antibiotic in combination with an Rtc-inhibitor, Rtc-induced resistance may be avoided (lower panel).

The precise damage inflicted by Rtc-inducing antibiotics has not been fully characterised and may affect ribosomal or transfer RNAs21,22,23. Repair of the damaged RNA then enables expressing cells to restore translational activity and rescue growth amid antibiotic assault (Fig. 1C). The system thus affords cells with an intrinsic antibiotic resistance present only in cells expressing Rtc as a regulated stress response upon RNA damage24. The nature of Rtc-induced resistance is transient, as cells acquire resistance as and when Rtc is expressed. Therefore, cells are able to adapt to survive until the antibiotic challenge has passed or a permanent specific resistance mechanism is acquired25. Given the widespread use of ribosome-targeting antibiotics, which across England accounted for over 40% of clinical use in 202226, Rtc-induced antibiotic resistance could be contributing to the growing antimicrobial resistance problem.

Despite the importance of RNA repair across all domains of life, there has been little research on RNA repair in comparison to the more widely studied DNA repair systems. Given the uncertainty surrounding the role of Rtc within resistance, we developed a mathematical model of the E. coli rtcBA system to investigate the mechanistic action of RNA repair proteins in maintaining the translation apparatus and leading to induced antibiotic resistance. The model provides a computational framework to study Rtc-regulated RNA repair and gain a systemic understanding of its physiological implications.

We perform a comprehensive analysis of the Rtc model, which reveals a previously unknown trait of the Rtc system, namely that the regulatory mechanisms governing Rtc expression promote bistability. Bistability enables cells to adopt distinct expression phenotypes that can coexist across a range of conditions. Bistable responses have been linked with other phenotypes of antibiotic resistance, where isogenic cells can either be susceptible or resistant within the same environment27. The model predicts that cells expressing Rtc are able to counteract the damage and recover translational activity, whereas translation collapses in non-expressing cells. We provide experimental evidence which validates model predictions on cell-to-cell heterogeneity in rtc expression, and moreover, that expressing cells display higher translational activity upon exposure to a ribosome-targeting antibiotic. The findings suggest that Rtc-induced resistance to ribosome-targeting antibiotics may constitute a form of heteroresistance28.

Using the Rtc repair model, we computationally screen for molecular targets amenable to suppressing Rtc expression and locking cells in the susceptible state (Fig. 1C). Our computational analysis suggests that inhibition of the ligase RtcB as well as the transcriptional regulator RtcR result in effective suppression of RNA repair and translational recovery. Targeting the cyclase RtcA, in turn, only results in a reduction of Rtc expression, where cells can still recover translational activity. Motivated by these predictions, we then quantify ribosome concentration, as a readout of translational capacity, across single E. coli cells that were challenged with the ribosome-targeting antibiotic tetracycline. We find that cells lacking rtcB or rtcR indeed display a more severely affected translational capacity compared to those lacking rtcA. The data thus provide initial validation that RtcR or RtcB, rather than RtcA, present promising targets for inhibition aimed at reducing levels of heteroresistance.

Our work revealed a previously unknown form of resistance to commonly used antibiotics and thus inspires research to optimise usage of these drugs. The results highlight the potential of the computational toolkit we developed to generate testable hypotheses. We further identified specific molecular targets that may be inhibited in combination with ribosome-targeting antibiotics to increase the overall effectiveness of treatment. Considering the broad use of Rtc-inducing antibiotics and the high level of conservation of rtcBA across several clinically relevant bacterial pathogens, our results pinpoint a potential avenue to address the incidence of antibiotic resistance.

Results

A dynamic model of Rtc-regulated RNA repair

We developed a computational model of Rtc-regulated RNA repair in E. coli that describes the regulated expression of Rtc proteins and their dynamic action to heal and seal damaged RNA within the translation machinery (Fig. 2A). We model the expression of the three rtc genes by considering their transcription to mRNA and subsequent translation to proteins. Throughout, we assume that Rtc proteins act to repair damaged rRNA, but we also show that the same conclusions hold when Rtc maintains damaged tRNA (see SI). To this end, we model three distinct species of ribosomes: healthy ribosomes that can obtain breakage within their rRNA and become damaged ribosomes; upon interaction with RtcA, damaged ribosomes convert to what we call ‘tagged’ ribosomes, which are still considered to be damaged but have been pre-processed for final repair. These tagged ribosomes contain cyclized rRNA ends and serve as a substrate to RtcB for full repair to recover healthy ribosomes.

Fig. 2: Model of Rtc-regulated RNA repair.

A Model schematic. The model describes the dynamic interplay of the Rtc operon with a pool of damaged, healthy and tagged ribosomes. Tagged ribosomes, which contain rRNA with 2’,3’-cyclic phosphate ends, act as the ligand for RtcR to activate rtcBA transcription. RtcA converts damaged ribosomes (containing RNA with 3’-phosphate ends) to tagged ones, and RtcB converts tagged ribosomes to healthy ones. Healthy and tagged ribosomes feed back to Rtc expression via translation and RtcR-activation, respectively. B Dependent rates and their definitions. Parameter descriptions and values can be found in the SI.

Overall, the model considers nine molecular species, the three mRNAs, m**x, where x ∈ {R, B, A} stands for the different rtc genes, their corresponding proteins, p**x, as well as three species of translational RNA r**h, r**d and r**t, denoting healthy, damaged and tagged RNA, respectively. Translational RNA, which we sometimes refer to by RNA, may represent rRNA or tRNA. For brevity, main figures depict results of the rRNA model and equivalent results for the tRNA model are given in the SI. We model Rtc expression and the dynamic interaction of the Rtc repair proteins with the translational machinery via a set of ordinary differential equations. Below we detail the mechanistic assumptions we use to derive the rates of change for each of the variables, starting with the regulatory control of Rtc expression and followed by the repair steps underpinning the maintenance of translational RNA.

Rtc-regulated RNA repair

The biochemical mechanisms of RtcA and RtcB are well understood; RtcA performs RNA-end healing while RtcB is responsible for sealing RNAs. Despite this comprehensive understanding, the link between these mechanistic actions and their physiological significance in bacteria remains unclear. RtcA converts 3’-phosphate RNA ends to 2’,3’-cyclic phosphate termini (Fig. 1B). The process of cyclisation is carried out in a three-step reaction mechanism which relies upon the presence of ATP and Mn2+ ions17,29. RtcA can also cyclise 2’-phosphate ends but at a much slower rate than 3’ ends17. We primarily model RtcA action on 3’-phosphate ends, but also consider the action on 2’-phosphate ends by using the lower catalytic rate of cyclisation in the model.

RtcB ligates 2’,3’-cyclic phosphate termini with 5’-OH termini to produce a phosphodiester bond and repair the RNA perfectly (Fig. 1B), in a process dependent on GTP and Mn2+ 30,31,32. It has also been shown that RtcB can directly repair 3’-phosphate ends31, however, at a much slower rate than cyclisation by RtcA33 (cf. Table S1). When the two are co-expressed, as in the antibiotic response we consider, RtcA thus likely removes reactive 3’-phosphate ends before RtcB can, and so in the model we only consider the action of RtcB on 2’,3’-cyclic phosphate termini.

Alternatively, damage may directly yield 2’,3’-cyclic phosphate RNA ends34, in which case RtcA would not be required for repair. This scenario gives rise to much the same dynamics as the concerted repair of 3’-phosphate ends by RtcA and RtcB, because the cyclization by RtcA is extremely fast (see §S1.4.3 and Fig. S1). In addition, it has been shown that RtcA is required for RtcR activation11, and since rtcBA are co-expressed, here we assume that RtcA is necessary to produce the cyclic ligand for activation and substrate for RtcB.

The E. coli rtcBA system is induced by agents that challenge the translation apparatus, where both tRNA and rRNA may be targeted for damage10. Whilst ribosome-targeting antibiotics may not directly damage translational RNA, expression of stress-induced genes, such as mazF15, in response to cellular stress can cause rRNA damage. Similarly, oxidative stress can indirectly damage both tRNA and rRNA21,35,36. We can therefore model damage and repair on both rRNA within a ribosome and on tRNA. In the case of rRNA repair, RtcB has been shown to only interact with rRNA that is structurally intact within a ribosome14,15, suggesting that RtcB will not repair free rRNA that has been released from collapsed ribosomes. We thus model the repair of rRNA within structurally intact ribosomes.

Figure 2A shows how we model the presence of three distinct species of translational RNA, which are controlled by the action of RtcA, RtcB and damage. We assume that only healthy translational RNA is available for translation. Upon damage, healthy RNA becomes non-functional, damaged RNA which is converted to tagged RNA via RtcA. Tagged RNA is converted back to healthy RNA via the action of RtcB.

The dynamics of healthy RNA (r**h), damaged RNA (r**d) and tagged RNA (r**t) are described by the following differential equations:

$${\dot{r}}_{h}={k}_{{{{\rm{in}}}}}+{v}_{{{{\rm{rep}}}}}-{r}_{h}\cdot (\lambda+{k}_{{{{\rm{dam}}}}}),$$

(1)

$${\dot{r}}_{d}={r}_{h}\cdot {k}_{{{{\rm{dam}}}}}-{v}_{{{{\rm{tag}}}}}-{r}_{d}\cdot (\lambda+{d}_{r}),$$

(2)

$${\dot{r}}_{t}={v}_{{{{\rm{tag}}}}}-{v}_{{{{\rm{rep}}}}}-\lambda \cdot {r}_{t},$$

(3)

where (\dot{y}) denotes the rate of change in species ({y}). Rates that further depend on molecular species or parameters we denote by ({v}_{{{{\rm{process}}}}}^{(y)}), where subscripts indicate the process, and whenever clarification is required, superscripts indicate the affected molecular variable ({y}) (see Fig. 2B). We assume that there is a constant influx of healthy rRNA or tRNA at rate kin, and that ribosome-targeting antibiotics damage healthy RNA at a constant rate kdam. Damaged RNA contains 3’-phosphate RNA and is converted to tagged RNA through the action of RtcA with rate (v_{{\mathrm{tag}}}), or degraded with rate d**r. Tagged RNA contains 2’,3’-cyclic termini, which is both the product of the RtcA healing reaction and the RtcR-activating ligand. Tagged RNA is converted back to healthy RNA by the ligating action of RtcB at rate (v_{{\mathrm{rep}}}). All species are diluted by growth with rate (\lambda).

Equations (1)-(3) describe a dynamic pool of rRNA or tRNA, respectively, where different RNA states are governed by RtcA and RtcB as well as the addition of damage through antibiotic stress. Next we explain the assumptions underlying the dependence of Rtc expression upon ribosomal levels to give the full model of Rtc-regulated RNA repair (Fig. 2A).

The rtc operon

We consider transcription and translation of the three rtc genes. We assume that mRNA levels, m**x with x ∈ {A, B, R} for rtcA, rtcB and rtcR, respectively, are governed by production via transcription (({v}_{{{{\rm{tx}}}}}^{(x)})) and decay via dilution ((\lambda)) as well as mRNA degradation (d**m), giving rise to the differential equations

$${\dot{m}}_{x}={v}_{{{{\rm{tx}}}}}^{(x)}-{m}_{x}\cdot (\lambda+{d}_{m}).$$

(4)

Bacterial enhancer binding proteins, including RtcR, are often expressed from promoters regulated by σ70, which are a family of σ-factors associated with regulating housekeeping genes37. We therefore assume constitutive rtcR expression38, where the transcription rate ({v}_{{{{\rm{tx}}}}}^{{(R)}) only depends on physiological parameters of the cell (see Figs. 2B and SI). As rtcA and rtcB share a joint promoter, we assume that ({v}_{{{{\rm{tx}}}}}}{(A)}={v}_{{{{\rm{tx}}}}}^{(B)}) at all times.

Transcription of rtcBA is regulated by σ547. Unlike σ70-controlled promoters, which can initiate transcription spontaneously, σ54-regulation requires ATP to remodel the holoenzyme (RNAP:σ54) from the closed complex to the open complex so DNA can enter the RNAP active site39. RtcR provides ATP for formation of the open complex, but firstly requires its own activation11. Figure 1A shows the Rtc operon, including control of rtcBA expression through activation of RtcR, followed by the remodelling of the σ-factor containing holoenyzme.

Similar to the structure of other bacterial enhancer binding proteins, RtcR has three domains: a regulatory CARF (CRISPR-associated Rossman fold) domain, a DNA binding domain and an AAA+ domain40,41 (Fig. 1A). The CARF domain of RtcR imposes negative regulation on the AAA+ domain, evidenced by over-expression of an N-terminal deletion strain where expression of rtcBA was constitutively active7. To alleviate RtcR auto-inhibition, an unknown ligand binds the CARF domain to activate the AAA+ domain. This ligand could be a linear RNA molecule, a tRNA fragment or an RNA with 2’,3’-cyclic termini, as CARF domains are known to bind cyclic termini11,19,42. Therefore, in the model we assume that tagged RNA r**t, i.e. the product of the RtcA reaction which contains RNA with 2’,3’-cyclic termini, act as the ligand for RtcR activation (Fig. 1A).

Following ligand binding, RtcR oligomerises to form fully active RtcR with functional ATPase activity to remodel the holoenzyme for initiation of transcription of rtcBA11. Consequently, in the model we assume that RtcR acts as a hexamer, as is typical for bEBPs43, therefore requiring the cooperative binding of up to six ligands for full activation19,44. We model this cooperative binding with a Monod-Wyman-Changeux (MWC) model which describes the cooperative activation of proteins made up of identical subunits45 (see SI). By adjusting the MWC parameters, we include spontaneous activation of RtcR, and subsequent leaky transcription of rtcBA (see Supplementary Table S1). Therefore, when there is no damage, there can still be a baseline level of rtcBA expression, which accounts for the recent finding that RtcR activation requires the binding of a ligand in addition to the presence of both RtcA and RtcB11. The total rate of rtcBA transcription, ({v}_{{{{\rm{tx}}}}}^{{{{\rm{(BA)}}}}}), thus accounts for the rate of transcriptional initiation via RtcR,

$${\sigma }_{o}=\frac{{p}_{R}^{*}\cdot {v}_{{{{\rm{oc}}}}}}{{k}_{{{{\rm{diss}}}}}},$$

(5)

where ({v}_{{{{\rm{oc}}}}}=\frac{{V}_{\max }\cdot {{{\rm{ATP}}}}}{{K}_{m}+{{{\rm{ATP}}}}}), as well as physiological parameters that can impact the rate of transcriptional elongation (see Table in Fig. 2B and derivation in the SI).

Finally, we model each Rtc protein, p**x for x ∈ {A, B, R}, independently via

$${\dot{p}}_{x}={v}_{{{{\rm{tl}}}}}^{(x)}-\lambda \cdot {p}_{x}.$$

(6)

Here, we assume that protein decay is dominated by dilution and active degradation is negligible. The key difference between translational RNA representing rRNA vs tRNA is how their healthy forms, r**h, differentially impact translation. Ribosomes scale translation linearly by

$${v}_{{{{\rm{tl,rRNA}}}}}=({k}_{c}\cdot {r}_{h}\cdot {m}_{x})\cdot \frac{1}{{n}_{x}}\cdot \frac{{\gamma }_{\max }\cdot {{{\rm{ATP}}}}}{{\theta }_{{{{\rm{tl}}}}}+{{{\rm{ATP}}}}},$$

(7)

where the term in parentheses accounts for binding with mRNA and the remainder for translation elongation, which is scaled inversely with the length, n**x, of protein p**x. When r**h represents healthy tRNA, ribosome levels are considered constant, denoted by R, and r**h impacts translation elongation in a saturable manner by

$${v}_{{{{\rm{tl,tRNA}}}}}=({k}_{c}\cdot R\cdot {m}_{x})\cdot \frac{1}{{n}_{x}}\cdot \frac{{\gamma }_{\max }\cdot {{{\rm{ATP}}}}}{{\theta }_{{{{\rm{tl}}}}}+{{{\rm{ATP}}}}}\cdot \frac{{r}_{h}}{{\theta }_{t}+{r}_{h}}.$$

(8)

Equations (1)-(8) comprise the model of Rtc-regulated RNA repair. For brevity, we summarize the definition of rates in Fig. 2B and their derivation in the SI. Thanks to the mechanistic derivation of the rate equations, we were able to constrain most model parameters using literature values for E. coli (see SI §S2.2). Only three parameters—the rate of damage to healthy ribosomes, kdam, as well as the maximal transcription rates, ωr and ωba—remained unconstrained and formed the basis of the analysis that follows below.

The model of Rtc-regulated RNA repair describes how Rtc expression in E. coli adapts to damage to rRNA or tRNA and the subsequent actions of the Rtc proteins in maintaining translational RNA (Fig. 2A). It predicts the level of healthy rRNA or tRNA available to cells, based on their ability to induce Rtc expression to counter the imposed damage, and thus, the cellular capacity to sustain translational activity. We next set out to characterise the dynamic response landscape of Rtc expression and its consequences for the translational capacity of cells.

Robust bistability of the Rtc model suggests heterogeneous levels of growth rescue

Activation of the Rtc system is characterised by expression of the RtcBA proteins. We first investigated how Rtc expression adapts to the rate of damage imposed on cells. To this end, we performed a stability analysis of the model to determine the steady-state levels of Rtc and translational RNA species at various damage rates (see Methods).

We consider the absence of damage, i.e. kdam = 0, representative of wild-type E. coli where Rtc is not active. When damage rates increase, for example through the addition of a ribosome-targeting antibiotic, the model predicts an initial increase in steady-state RtcBA protein expression due to an adequate availability of healthy ribosomes (Figs. 3A and S2A). Preceding translation, transcription of rtcBA (Figs. S3C, S4C) occurs due to an increase in tagged RNA causing RtcR activation (Fig. 3A, S2A).

Fig. 3: Steady-state responses of the rRNA-repair model.

A Stability analysis: Bifurcation diagrams for the Rtc proteins (top) and rRNA species (bottom) show a range of damage rates (grey region) in which two stable cell states (solid lines) and one unstable steady-state (dashed lines) co-exist. If damage increases from initially low levels (below grey region), cells are predicted to enter the ‘Rtc-on’, resistant state (upper solid branch for all species but damaged and tagged rRNA, lower solid branch for latter) that enables rRNA repair, and consequently, maintenance of sufficiently high levels of healthy rRNA to sustain translational activity. Conversely, if damage decreases from initially high levels (above grey region), cells are predicted to remain in an ‘Rtc-off’ state (lower solid branch except for damaged and tagged rRNA), where RNA damage levels exceed the capacity of repair and prevent translation of Rtc proteins. B The system displays bistability across a range of parameter combinations. Purple regions represent combinations of ATP concentrations and dilution rates, that display bistability within the range of damage rates considered (0 to 0.8 min−1). Shades of purple indicate how the regions depend on the inducibility, i.e. the maximal transcription rate ωba, of the rtcBA genes, where higher inducibility supports bistability across a wider and increasing range of dilution conditions. C Parameter sensitivity: ATP-availability (top), dilution rate (middle) and maximal rtcBA transcription rate (bottom) impact the magnitude of Rtc expression and the region of bistability. Higher ATP concentrations and rtcBA transcription yield higher expression states, whereas dilution lowers expression. The region of bistability widens for higher ATP concentrations, and it shifts towards higher ranges of damage rates for lower rates of dilution and higher transcription. Grey lines indicate conditions where the region of bistability has shifted beyond damage rates of interest, and so the system is monostable within the considered range of damage. Unless stated otherwise, parameter values are given in Table S1. Source data are provided in the source data file.

Steady-state expression of RtcBA is predicted to peak when activation levels of RtcR* saturate (Fig. 3A). When damage rates increase further, steady-state RtcBA expression decreases as the levels of healthy ribosomes available for translation decline. Eventually, expression is predicted to collapse at high rates of damage, when there is no longer sufficient healthy RNA to sustain translation of the Rtc repair proteins. In the collapsed state there is a build up of damaged RNA due to a lack of sufficient RtcBA to carry out repair. RtcR expression, which was assumed to be constitutive, is less affected by the damage rate and follows declining levels of healthy RNA (Figs. 3A, S2A).

Interestingly, the stability analysis revealed that the Rtc model displays bistability across a range of damage rates. Bistability of a dynamical system denotes the co-existence of two stable steady-states for a given condition. When damage rates decrease from initially high levels (rates above the grey range in Fig. 3A), the system remains in the collapsed state even for damage rates (rates within the grey range) that allow Rtc expression in cells which previously experienced low damage (rates below the grey range). This phenomenon, whereby the system adopts one stable state over the other based upon a memory of previous conditions (in this case damage), is called hysteresis. It is a key feature of bistability and typically arises as a result of positive feedback, especially in combination with ultrasensitivity46, both of which are present in the Rtc system. Ultrasensitivity is exhibited through the cooperative activation of RtcR by tagged RNA, and positive feedback is exerted in the model at two stages: 1) through RtcA which is required to activate its own expression, and 2) through healthy RNA necessary for translation of the repair proteins.

The presence of bistability suggests that two distinct Rtc expression states can co-exist for a range of damage inflicted on cells for Rtc proteins and ribosome species (Fig. 3A). These cell states represent an Rtc-on state, where there is expression of rtcBA and repair of translational RNA, corresponding to resistant cells, and an Rtc-off state with insufficient healthy RNA to sustain protein expression, corresponding to susceptible cells. At damage rates within the bistable region (grey range in Fig. 3A), the system will enter the on-state if previous exposure to damage has been lower, and enter the off-state if previous exposure has been higher than levels within the bistable region. The model therefore suggests that for a range of damage conditions the structure of Rtc regulation promotes phenotypic heterogeneity, where resistant and susceptible cells can co-exist within a form of hetero-resistant cell population.

We next aimed to identify whether bistability was robust across a range of parameter conditions, or if it was specific to a small subset of conditions. We analysed the sensitivity of model predictions to variation in key parameters (see Methods), including the unknown maximal transcription rates of rtc genes, ωba and ωr, as well as the dilution rate λ and cellular ATP levels, which we could only loosely constrain within a physiological range due to their inherent variation.

Sensitivity analysis suggests that the Rtc system displays bistability robustly throughout a range of parameter conditions (Fig. 3B, C and S2B-C). Occurrence of bistability at any damage rate within the range we considered (between 0 and 0.8 min−1) was largely insensitive to ATP concentrations, however, low ATP concentrations affected the dilution rates that support bistability. Dilution rates that support bistability were further predicted to depend on inducibility of the rtc repair genes, where higher inducibility increases the range of dilution conditions that support bistable responses (Fig. 3B).

We further analysed how Rtc expression levels and the region of bistability, i.e. damage rates where resistant and susceptible cells are predicted to co-exist, depend on individual changes in parameter values. Figures 3C and S2C show the effect of cellular ATP concentration (top), dilution rate (middle), and maximal transcription rate of the rtcBA genes ωba (lower panel) on RtcB expression. Changes in the transcription rate of rtcR had qualitatively the same effect as changes in rtcBA transcription (Figs. S3B, S4B).

Higher ATP concentrations support higher overall expression in the Rtc-on state and widen the region of damage rates where bistability is displayed. The widening of the bistable region at high ATP levels largely resulted from an increase of its upper boundary, whereas the effect on its lower boundary was minor, explaining why bistabilit