Summary
Dynamic control of cell polarity is of critical importance for many aspects of cellular development and motility. In Myxococcus xanthus, a G-protein and its cognate GTPase-activating protein establish a polarity axis that defines the direction of movement of the cell and which can be rapidly inverted by the Frz chemosensory system. Although vital for collective cell behaviours, how Frz triggers this switch has remained unknown. Here, we use genetics, imaging and mathematical modelling to show that Frz controls polarity reversals via a gated relaxation oscillator. FrzX, which we newly identify as the primary Frz output, provides the gating and thus acts as the trigger for reversals. Slow relocalisation of the polarity protein RomR then creates a refractory period during which another switch cannot be triggered. A secondary Frz output, FrzZ, decreases this delay allowing rapid reversals when required. This architecture thus results in a highly tunable switch that allows a wide range of motility responses.
Introduction
Periodic dynamics are pervasive in biology with examples ranging from circadian rhythms to brain activity and from the cell cycle to multicellular development1. Study of rhythmic processes in microbes has often been particularly insightful due to the simpler nature of the system dynamics. Classic examples include the Escherichia coli Min system regulating cell division positioning and the circadian Kai oscillator in cyanobacteria2,3.
Rhythmic processes can be particularly important in microbes for the regulation of cell motility. In the bacterium Myxococcus xanthus, back and forth movements (reversals) are not only important for the motile dynamics of isolated cells but are also critical for the regulation of multicellular behaviours, fruiting body formation and rippling during the invasion and consumption of prey cell colonies4. The function of periodic reversals is especially evident during rippling, the accordion-like wave movements of large cell groups, where each cell of a wave reverses upon collision with a cell of an opposite incoming wave5. This large-scale order has been proposed to emerge from the synchronisation of an intracellular compass (called Frz) by cell-cell contacts5,6. However, in other contexts M. xanthus reversals can be aperiodic4, and thus the underlying mechanism that generates reversals must be able to create richer dynamics than simple oscillations. In this study, we use an interdisciplinary approach combining genetics, live imaging and mathematical modelling, to elucidate this underlying mechanism, dissecting how Frz controls dynamic polarity in individual cells. Such an interdisciplinary strategy is essential to properly dissect how the individual molecular components fit together to generate coherent dynamics and rapid switching.
Myxococcus cells employ two motility systems depending on the context, both of which are assembled at the leading cell pole. The S-motility complex functions within large cell groups and consists of a Type-IV pilus that deploys to pull the cell forward7 (Figure 1A), while the A-motility complex traffics toward the lagging cell pole, propelling the cells as it becomes adhered at so-called bacterial focal adhesions8 (Figure 1A). Thus at the molecular level, cell reversals are provoked by the rapid activation of the motility complexes at the opposite cell pole (Figure 1A). The genetic control of cell reversals involves a chimeric circuit composed of bacterial Che-like proteins and a eukaryotic Ras-like regulation system (Figure 1A). Spatial activation of A-and S-motility depends on a single regulator, MglA, a G-protein of the Ras superfamily, which binds to the leading cell pole in its active GTP-bound form and recruits key proteins of each motility system9–12 (Figure 1A). The activity of MglA is regulated by MglB, a GTPase Activating Protein (GAP) that binds to MglA in a 2:1 stoichiometry to activate the transition from polar-localised MglA-GTP to cytoplasmic MglA-GDP13. Since MglB localises to the lagging cell pole, its GAP activity is spatially regulated, blocking access of MglA to the lagging pole. This MglAB polarity axis can be inverted on a timescale of 30-60 seconds, leading to cell reversals9,12.
The mechanism by which polarity is switched is, however, still not understood despite intense investigation. Upstream, the switch is controlled by the Frz chemosensory-like system, which forms signalling arrays at discrete positions along the bacterial nucleoid14, and connects to the CheA-type kinase FrzE. Following activation (by as yet unknown physiological signals, possibly cell-cell contacts), FrzE dimers have been proposed to phosphorylate several downstream Response Regulator (RR) domain proteins: the cognate FrzE RR domain FrzERR, the tandem RR protein FrzZ and the RR domain of RomR (RomRRR)4,15–17,14 (Figure 1A). The respective contribution of each RR domain has been RR investigated by genetic analysis, suggesting that the central output of the pathway is RomRRR 4,18 FrzERR and FrzZ act as accessory domains that impact the signal flow negatively and positively, respectively (Figure 1A). Specifically, FrzERR acts as a phosphate sink preventing noisy activation of the system at low stimulation levels4,14. On the contrary, the non-essential FrzZ protein amplifies the system efficiency by an as-yet undetermined mechanism4 (Figure 1A). However, contrary to FrzERR and FrzZ15,16, it has not been shown experimentally that RomRRR is a direct substrate of the FrzE kinase. In motile cells, RomR interacts with MglA-GTP and is essential for MglA’s polar localisation19,20. However, RomR also interacts with MglB at the lagging cell pole19,20. While the exact function of the RomR localisation pattern is not understood, RomR is known to be essential for cell reversals4. Therefore, direct phosphorylation of RomR has been proposed to connect Frz signalling to the MglAB polarity complex.
In this study, we identify for the first time the link between Frz and the polarity proteins. We find that Frz, via its newly discovered primary output FrzX, acts as the trigger for a new type of biological oscillator: a gated relaxation oscillator. Here, we use the terminology of electronic circuits, where ‘gated’ refers to the requirement for an input signal, in this case FrzX, to trigger reversals21. The oscillator itself consist of the polarity proteins MglA, MglB and RomR where RomR sets the concentration of MglA both at the leading and lagging poles. The slow dynamics of RomR further introduces a refractory period (relaxation time) immediately after a switch during which time another reversal cannot be triggered. However, Frz is able to overcome this minimum period to achieve rapid reversals when required via the action of its secondary output FrzZ, explaining the previously observed accessory function of FrzZ. This unique system design allows a wide range of responses to variations in incoming signals.
Results
MglA and MglB rapidly switch their polar localisation when cells reverse
Polar switching only occurs in the presence of all three polarity proteins MglA, MglB and RomR, indicating that they are all part of the same oscillatory circuit. However, how the phosphorylation of RomR could control the switch is not known4,18. To investigate this mechanism, we first determined the sequence of events that leads to switching, performing high-time resolution fluorescence microscopy using YFP fusions to MglA and MglB12 (Figure 1B,C), followed by quantitative image analysis (see Supplementary Information). In this assay, both proteins re-localised at the time of reversals as previously described12, with switching timescales (i.e. the time necessary for the entire protein fluorescent cluster to switch pole, see Figure S1A, Methods) of 45 ± 20 s (n=12) for MglA-YFP and 90 ± 30 s (n=19) for MglB-YFP (Figure 1D). Fluorescence Recovery After Photobleaching (FRAP) revealed the polar dissociation of MglA and MglB is rapid with mean recovery times of 4 s (n=51) and 6 s (n=20) respectively (Figure 1E, Figure S1B, Methods). The MglA and MglB recovery times were not substantially affected in frz mutants (Figure S1C,D), suggesting that Frz signalling does not directly modulate the affinity of MglA and MglB for the poles. Analysis of a dual colour strain expressing both MglA-YFP and MglB-mCherry12 revealed that when cells reverse, both proteins co-localise during a short time window and MglA is the first protein to re-localise during a given reversal (observed in 10 out of n=10 events, Figure 1F). This suggests that overcoming the repelling action of MglB triggers a reversal event (Figure 1F)
A three-protein relaxation oscillator model of the reversal cycle
We next turned to mathematical modelling to investigate how interactions between MglA, MglB and RomR could generate the oscillations. Our initial mathematical model incorporated observations from the previous section, as well as those previously published (Supplementary Information). In particular, we assumed that MglA and MglB exert bidirectional antagonistic effects such that each protein excludes the other protein from the pole, with local concentrations determining which protein is dominant over the other at a given pole (Figure 2A,B Supplementary information). This could be explained if immediately after a reversal, MglB efficiently inhibits polar MglA-GTP by stimulating GTP hydrolysis9,12 returning MglA to the cytoplasm in the GDP form. However, as the cell gets closer to the next reversal, MglB also sequesters RomR progressively, and this interaction in turn increases the recruitment rate of MglA-GTP19,20. Eventually MglB inhibition of MglA becomes saturated when RomR accumulates to sufficient levels (Figure 2B). At this point, excess MglA-GTP could effectively replace MglB if the MglA-MglB interaction detaches MglB from the pole (Supplementary Information). MglB would thus be displaced to the other pole where MglA-GTP levels are significantly lower, allowing the process to begin again. This process would be greatly facilitated if MglB has an affinity for itself (through a cooperative self-interaction). Consistent with this hypothesis, structural studies indicate that MglB can form tetramers13. Furthermore, MglB is monopolar in an mglA romR mutant20, a localisation pattern that could be explained if MglB cooperatively forms polar oligomers similar to, for example, the hub protein PopZ22,23. We therefore incorporated into the model an affinity of MglB for itself. The equations describing the interactions in Figure 2A (solid and non-solid arrows) are presented in Figure 2C.
We solved this system of equations numerically and found that the system could indeed exhibit oscillations, with the MglA and MglB profiles qualitatively similar to the experimental curves (Figure 2D). Specifically, the oscillations were driven by RomR binding to MglB and then recruiting MglA, with switching provoked when RomR reaches a critical threshold at the lagging pole. This driving could be seen explicitly by manually varying the asymmetry in polar RomR levels and observing the effect on polar MglB localization (Figure 2E). We also observed that oscillations only took place if the dynamics of RomR occurred on a timescale longer than that for MglA and MglB. We further found that, in this case, the slower RomR timescale set the cycle duration (defined as the time between two successive polarity switching events) (Figure 2F). These properties are characteristic of a relaxation oscillator, in which oscillations are due to, and set by, a component of the system with dynamics much slower than the others. Indeed, from simulations we found a linear relationship between the timescale of RomR dynamics and the cycle duration (Figure 2F). Thus, if phosphorylation of RomR by the FrzE kinase (Figure 2A) alters the (slow) timescale of RomR dynamics, then the model suggests that this regulation would specify the cycle duration (Figure 2D,F).
RomR dynamics do not time the reversal cycle
We next tested if our experimental observations of RomR are indeed consistent with the slow dynamics predicted by the model. We found that RomR switching indeed occurred on longer timescales than MglA and MglB (mean 160 s, Figure 1D) with a mean FRAP recovery time of 28s, slower than that measured for both MglA and MglB (Figure 1E). Unexpectedly however, in WT cells RomR switching dynamics were not correlated to reversals and RomR-GFP accumulated stably at the lagging pole before the cell reversed (Figure 2G). In fact, the timescale of RomR switching was largely constant and did not vary significantly as a function of the cycle duration (Figure 2F). These results suggest that switching cannot be solely regulated by the slow dynamics of RomR, a conclusion that questions whether RomR is indeed a substrate of the FrzE kinase.
We therefore tested if the receiver domain of RomR (RomRRR, Figure S2A) is phosphorylated by FrzE in vitro. Consistent with published results15, purified FrzE phosphorylated FrzZ very efficiently, achieving 100% transfer less than 2 min after the proteins were mixed (Figure 3A). However, under the same conditions, neither full length RomR nor RomRRR were significantly phosphorylated even after 8 min incubation (Figure 3A, Figure S2B).
Since we obtained no evidence for RomR phosphorylation in vitro, we revisited the impact of point mutations on the conserved D53 residue of RomRRR in vivo18 by substituting romR with a romRPD53E (phospho-mimicking mutation) or romRD53N (phospho-ablative mutation). To quantitatively measure the impact of the point mutations on the reversal frequency, we scored single cell reversals of both mutants as compared to the WT in a microfluidic device where the level of Frz activation can be controlled by Isoamylalcohol (IAA), a known Frz activator4 (see methods). Surprisingly, the romRD53E and the romRD53N mutants showed no detectable defect and had a reversal frequency comparable to the WT (Figure 3B). In addition, the romRD53E frzZ and romRD53N frzZ double mutants showed reversals similar to the frzZ mutant4 (Figure 3B), while it is known that the romR frzZ double mutant does not reverse, similar to the romR mutant4. Thus, the presence of RomR, but not its phosphorylation, is required for reversals. Consistently, the RomR point mutant strains showed no developmental defects: both the romRD53E and romRD53N point mutants formed fruiting bodies on hard surfaces, showing that the phosphorylation of RomR is not critical for multicellular development (Figure S2C). We therefore conclude that RomR is required for reversals, presumably because it is needed for the polar localisation of MglA but its phosphorylation is not involved in the control of the switch. Furthermore, since FrzE can still trigger reversals when the frzZ gene is deleted and/or when the RomRRR receiver domain is mutated, these results implicate an as yet unidentified response regulator in the reversal process.
Identification of a new target of the FrzE kinase
To identify the missing regulator, we reasoned that it should share structural similarities with FrzZ, which is directly phosphorylated by FrzE. The search of close FrzZ homologs identified the product of the MXAN_5688 gene as a predicted single domain response regulator protein with high sequence homologies to the FrzZ1 domain (Figure 3C). In addition, a homolog of MXAN_5688 is encoded in proximity to a frz-type operon in Anaeromyxobacter species, which contains both a FrzZ and an MXAN_5688 homolog (Figure S3A). To test if the protein encoded by the MXAN_5688 locus is a direct target of FrzE, we purified the protein (named FrzX) and tested its phosphorylation in vitro. Co-incubation between the FrzE kinase domain and FrzX led to the complete disappearance of phosphorylated FrzE even after 30 sec of co-incubation, suggesting that phosphotransfer had occurred (Figure 3D). However, no band corresponding to phosphorylated FrzX could be detected. The phosphorylated state of RR domains with high auto-phosphatase activity can be difficult to capture on SDS-PAGE gels24,25. Therefore, to test whether FrzE indeed phosphorylates FrzX, we repeated the phosphotransfer assay in the presence of a FrzX variant carrying a non-phosphorylatable D55A mutation, where D55 is the predicted phosphorylatable Asp (Figure 3C,D). Under these conditions, FrzE remained phosphorylated even after 8 min co-incubation (Figure 3D), suggesting that FrzX is indeed a direct target of the FrzE kinase.
FrzX is the missing Frz Response Regulator protein
Similar to a frzE-null mutant, a frzX-null mutant formed typical “frizzy” tangled filaments instead of fruiting bodies on developmental agar plates (Figure 3E). The deletion of frzX could be complemented with a frzX allele but not with a fizXD55A allele, showing that the phosphorylation of FrzX is essential for its function (Figure S3B,C). FrzX is central to Frz signalling because neither a frzX mutant nor a frzX frzZ double mutant were rescued by the addition of IAA (Figure 3E). By contrast, IAA addition can rescue the absence of FrzZ, implying that, despite its signal amplification properties, FrzZ is a less critical component of the reversal apparatus4 (Figure 3E).
To show directly that FrzX acts in the regulation of reversals, we measured the reversal frequency of the frzX mutant in a single cell assay that measures IAA and Frz-dependent protein switching directly4 (FrzS-YFP). This methodology can thus unambiguously distinguish bona fide reversals from other movements such as stick-slip motions (these motions occur at a low level adding noise to standard reversal scoring assays4, see Methods). As expected, the frzX mutant failed to reverse, similar to a frzE kinase mutant (Figure 3F), but dissimilar to the frzZ mutant which does still reverse in this assay, albeit at a lower frequency, in the presence of IAA (Figure 3F). These results again place FrzX in a more central position in the reversal mechanism as compared to FrzZ.
To prove this central function of FrzX in a definitive manner, we tested its contribution in a strain with a hyper-signaling state of the FrzE kinase (termed the frzon mutation4,26, where the cells hyper-reverse due to constitutive activation by the Frz receptor (FrzCD). These reversals can be detected in our single cell assay in the absence of IAA (Figure 3G). A frzonfrzZ mutant still reversed, although again at a lower frequency since FrzZ is needed for optimal signalling activity4. In contrast, both a frzon frzX and a frzon frzX frzZ mutant failed to reverse (Figure 3G). We conclude that FrzX acts genetically downstream from FrzZ and, unlike FrzZ, is absolutely required for the transmission of FrzE signals to the downstream polarity proteins.
The phosphorylated form of FrzX localises to the lagging cell pole in an MglB-dependent manner
To understand how FrzX provokes cellular reversals downstream from the FrzE kinase, we first tested how deleting frzX affects the localisation of MglA-YFP, MglB-YFP and RomR-GFP. In a frzX mutant, these proteins were correctly localised at their respective poles (Figure S4A) but they did not switch poles, consistent with FrzX being essential for reversals. Thus, FrzX is only required for the dynamic switching of the polarity proteins.
We next constructed a functional N-terminal GFP-FrzX fusion (Figure S3D) to investigate where FrzX localises. We found that GFP-FrzX was present diffusely in the cytoplasm when Frz-signalling is at low level (Figure 4A). However, the addition of IAA induced the appearance of a clear polar focus (Figure 4A). This polar localisation was fully abrogated in a frzE mutant in the presence of IAA (Figure 4A). These results suggest that phosphorylation of FrzX by FrzE is required for polar localisation.
To identify a possible FrzX target at the pole, we next investigated the localisation of GFP-FrzX in the polarity protein mutants, mglA, romR, mglB and frzZ. Except for the mglB mutant, GFP-FrzX was polarly localised in all mutants (Figure 4B, although a slight reduction was also observed in the mglA mutant), suggesting that either MglB or an MglB-interacting protein is a polar target for FrzX. Finally, consistent with this probable interaction with MglB or an MglB-interacting partner, GFP-FrzX accumulated at the lagging cell pole between reversals (see below).
RomR and FrzX both act to provoke reversals
To determine how FrzX and RomR act at the lagging cell pole to provoke reversals, we more closely investigated their localisation dynamics during the reversal cycle. Because the polar localisation of FrzX can only be observed at high Frz signalling levels, we performed all the GFP-FrzX localisation assays in the presence of either IAA or a frzon mutation (similar results were obtained in both conditions). Remarkably, in these Frz-activated cells, reversals coincided with a peak accumulation of GFP-FrzX, suggesting that FrzX triggers cell reversals (Figure 5A,B and Figure S5A).
We next tested how GFP-FrzX localises in the absence of FrzZ, again either in the presence of IAA or in a frzon background. Remarkably, in both conditions, GFP-FrzX still localised to the lagging cell pole but its accumulation no longer coincided with cell reversals (Figure 5C,D and Figure S5B), suggesting that another component is needed for reversals in a frzZ mutant. To test if this component could be RomR, we further analyzed RomR-GFP dynamics in Frz-activated cells (Figure 5C and Figure S5C). Indeed, the maximum accumulation of RomR-GFP was strongly correlated with reversals (Figure 5D). Consistent with this, the distribution of the RomR switching timescale coincides with that of the cycle duration in a frzon frzZ background (Figure 5E). However, as observed previously, the RomR switching timescale is not significantly correlated with reversals in the wildtype background (Figure 2F, Figure 5E). Taken together the results suggest that both RomR and FrzX function together at the lagging pole to provoke reversals, but which of the two provides the final trigger depends on which is limiting: FrzX in WT but RomR when frzZ is missing.
FrzZ overcomes a refractory period set by the dynamics of RomR
In cells where Frz-signaling is at maximum level, RomR dynamics set a minimum reversal frequency and faster reversals require FrzZ. This function is evident when RomR dynamics are analysed in WT cells in a frzon background (Figure 5F) and compared to frzon frzZ (Figure 5G). In frzon cells, switching is also correlated to RomR levels at the lagging cell pole but, contrarily to frzon frzZ cells, it does not require the entire RomR population to localise to the lagging pole and occurs at a much lower threshold (Figure 5G). This result is confirmed in a dual labelled strain expressing functional GFP-FrzX and RomR-mCherry (RomR-mCh), fusions in which reversals coincide both with peak accumulations of GFP-FrzX and low amplitude changes of RomR-mCh at the lagging cell pole (Figure S5D).
Thus, FrzZ overcomes a limit set by the slow dynamics of RomR, accounting for the previously documented positive effect of FrzZ on the reversal frequency. How FrzZ performs this function is not known. FrzZ localises to the leading cell pole in a FrzE phosphorylation- and MglA-dependent manner17, opposite to GFP-FrzX (Figure 5H, Figure S4B). Furthermore, FrzZ and FrzX localise independently to the cell poles (Figure 4B and Figure S4B). In the next section, we will use these results together with mathematical modelling to propose a mechanism for FrzZ function.
A gated relaxation oscillator model of the polarity switching mechanism, incorporating the functions of FrzX and FrzZ
The above results show that the reversal switch requires the combined action of phosphorylated FrzX and RomR at the lagging pole. By gradually accumulating at the lagging pole via its interaction with MglB, RomR primes the cell for the next reversal. The kinetics of RomR relocalisation therefore introduce a refractory or relaxation period during which it is not possible to effect a reversal until sufficient RomR has accumulated. However, the above mechanism is critically incomplete to provoke the switch, since FrzX is also required as a trigger.
To test whether a combined mechanism involving FrzX can explain the reversal switch, we added the dynamics of FrzX~P to our earlier mathematical model. A simple and thermodynamically consistent mode of action of FrzX~P is to mediate the inhibitory effect proposed in our earlier model of MglA-GTP on the polar binding of MglB (Figure 2A and Supplementary Information). Based on our experimental data, we assume that FrzX~P is recruited to the pole by MglB (Figure 4B). The interactions between MglA, MglB, RomR and FrzX and the associated differential equations are presented in Figures 6A,B. Solving the equations led to the expected properties: in WT cells, the re-localisation of RomR introduced a refractory period and primed the reversal event, which was eventually provoked by the action of FrzX~P (Figure 6C). The polarity module can therefore be decomposed into two components: the MglA/MglB/RomR relaxation oscillator, with these oscillations “gated” by a FrzX~P trigger (Figure 6A), together forming a gated relaxation oscillator.
We next simulated a frzon background, with constitutively high levels of FrzX~P (Supplementary Information) (Figure S6A). Switching is now more rapid, with reversals happening on a timescale faster than the intrinsic RomR dynamics (Figure 6C), leading to only weak RomR oscillations. Due to the high levels of FrzX~P, the required threshold of RomR is reduced so much that, immediately after a reversal, the new lagging pole already has sufficient RomR (and thus MglA) bound for another reversal. Since reversals occur with approximately symmetrical RomR levels at both poles (Figure S6A), consistent with our experimental observation (Figure 5G), the trigger function of FrzX~P is then clearly revealed (Figure S6A). In a frzon background, the system is still effectively a relaxation oscillator, but where now FrzX~P rather than RomR acts as the slow component. To further confirm that dynamical changes in RomR levels are inessential, we simulated artificially constant and symmetric RomR in the frzon background (Figure S6B). As expected, reversals still occurred, demonstrating the key trigger role of FrzX~P.
We next used our simulations to investigate the effect of deleting frzZ. Given that FrzZ~P localises to the leading pole and promotes reversals, we considered two possibilities for its mode of action: (i) FrzZ~P promotes the polar switching of MglA by accelerating the re-localisation of RomR, or (ii) FrzZ~P favors the unbinding of MglA from the leading pole without affecting the dynamics of RomR, by, for example, dissociating MglA from RomR. These two options were incorporated into the model implicitly by alterations in the kinetic parameters. We found that option (i) is likely incorrect, because removing FrzZ from the model in the frzon background (and thus simulating a frzon frzZ background) resulted in a more symmetric RomR distribution at the poles (compare Figure S6A,C), whilst we observed the opposite experimentally (compare Figure 5C and 5F). We therefore pursued option (ii) (Figure 6A).
In a simulated frzon frzZ background, using option (ii), we found that the reversal switch now became dependent on RomR accumulation to a sufficiently high level at the lagging pole (Figure 6D), as observed experimentally (Figure 5C,D). In this case, the FrzX~P trigger is quickly primed, but with slower MglA dynamics, RomR must now accumulate to high levels to recruit enough MglA to provoke the switch, similar to our original relaxation oscillator model. This reasoning was confirmed when we again simulated artificially constant and symmetric RomR: unlike in the frzon background simulated above, no reversals were seen, confirming the key role of RomR dynamics (Figure S6D). The resulting increase in RomR asymmetry in a frzon background due to the removal of FrzZ seen in our simulations (compare Figure 6D and Figure S6A) was also consistent with our experimental observations (compare Figure 5C and Figure 5F).
Finally, we found that in the absence of FrzZ alone, and thus slower MglA dynamics than the wild-type, simulated reversals were only obtained with sustained FrzX activity (Figure S6E). This result was consistent with previous observations and the restoring effect of IAA to the frzZ mutant4 (Figure 3E, Figure S5B,C).
Overall, the modified model has rationalized our findings on RomR and FrzX: the system behaves like a gated relaxation oscillator with FrzX acting as the gate or trigger. The relaxation property means that stimulation by FrzX~P is only effective if sufficient time has passed since the previous switch to allow RomR to prime the lagging pole, by recruiting MglA at a sufficiently high rate. However, in contrast to the standard gated oscillators in electronics21, which return to a default state, the system here remains in its current state after removal of the input (FrzX~P). Furthermore, both the experimental data and simulations suggest that FrzZ~P increases the MglA off-rate, thus decreasing the threshold of RomR required to prime the pole for a reversal. This effect shortens the RomR refractory period, allowing for more frequent reversals.
Discussion
In this work, we have systematically dissected the dynamics of the Myxococcus polarity module. Using a combination of mathematical modelling and experiments, we discovered that our original three-protein relaxation oscillator model, where Frz signalling enters through modulation of the RomR dynamical timescale, was too simple. This result motivated our experimental search for an additional Frz response regulator protein, leading to the identification of FrzX. Subsequent characterisation of the role of FrzX, then led to an improved model in which FrzX acts as the trigger of a gated relaxation oscillator. This model successfully accounts for many features of the polarity switching dynamics in Myxococcus.
Controlling reversals in this way combines many of the advantages of both a switch and an oscillator. The presence of a relaxation oscillator naturally causes the polarity apparatus to reverse poles, an essential feature. However, direct control of the relaxation oscillator period would require the tuning of a continuous variable (the RomR timescale), a nontrivial task if a wide response range is to be obtained. Employing a gating mechanism bypasses these constraints and only requires that the levels of the input (FrzX~P) exceed a given threshold when a reversal is required and stay below it otherwise. Furthermore, the presence of the refractory period may also be advantageous. Unlike swimming bacteria, which can change their direction of movement in 3D (usually via tumbling), Myxococcus has a binary choice: reverse or not. A refractory period can ensure that a cell cannot be stimulated again immediately after it reversed which could be important for cooperative motility behaviors. Indeed, mathematical models have predicted that, in addition to an internal biochemical clock, a refractory period is required for rippling behaviour6,27–29. We have shown that this refractory period is shortened when Frz signalling is high, but is lengthened by the absence of FrzZ. Such fine-tuned control is clearly important because the frzZ mutant is defective in most developmental processes.
Another necessary consequence of our gated switch mechanism is that the system becomes sensitive to variations in the level of FrzX~P. Assuming that the pool of FrzX does not vary abruptly between cells, these fluctuations could be introduced not only by varying levels of FrzE activity but also due to the existence of a high auto-phosphatase activity of FrzX, as suggested by our inability to capture FrzX~P on SDS-PAGE gels (Figure 3D). These effects could be important because wild-type Myxococcus cells show a broad distribution of reversal frequencies4, but all mutants with narrow distributions, be they in the fast (frzon) or slow (frzZ) ranges, are severely impaired in development30.
We have found that RomR acts as an oscillating scaffold protein, regulating the polar concentration of MglA. Our data indicates that RomR is never fully localised to the lagging cell pole, which likely explains why MglA remains attached to the leading cell pole even if the majority of RomR localises to the opposite pole. We have further proposed that FrzX~P could be responsible for triggering the inhibitory effect of MglA-GTP on MglB (see Supplementary Information for further discussion). Note, however, that FrzX alone cannot be the long sought after MglA Guanine nucleotide Exchange Factor (GEF) because MglA is active in absence of FrzX. Moreover, we cannot of course exclude a more complex sequence of triggering events occurring downstream from FrzX, perhaps involving as yet unidentified polar proteins.
In conclusion, the Myxococcus polarity system forms a new type of genetic circuit in which two polar response regulators mediate two distinct controls. One (RomR) ramps up slowly as part of a relaxation oscillator and must exceed a critical level, while the other (FrzX~P) then acts as a critical checkpoint or gate to trigger a reversal. This flexible gated relaxation oscillator architecture, incorporating a checkpoint into an oscillator, allows a wide range of reversal dynamics in response to environmental signals. It is therefore likely that this type of regulation also occurs in other rhythmic biological systems.
Methods
Bacterial strains, growth conditions and genetic constructs
Strains, plasmids and primers used for this study are listed in Tables S1, S2 and S3. All genetic mutants were constructed in the Myxococcus xanthus DZ2 strain30. M. xanthus DZ2 was grown at 32°C in CYE rich media, as previously described30. Plasmids were introduced in M. xanthus by electroporation. Mutants and transformants were obtained by homologous recombination based on a previously reported method30. Complementation, expression of the fusion and mutant proteins were either obtained by ectopic integration of the genes of interest at the Mx8-phage attachment site12 under the control of their own promoter in appropriate deletion backgrounds, or by expression from the endogenous locus (Table S2). Clean replacement and deletions were constructed as previously reported.
The plasmid to replace frzX contains an insert encompassing 850 bp upstream from the frzX coding sequence to 850 bp immediately downstream of the frzX coding sequence and synthesized into the pBluescriptII SK(+) plasmid by Biomatik. This plasmid was then digested by HindIII/EcoRI restriction enzymes and the insert was ligated into the pBJ114 vector.
For clean replacement of the romR gene by romR-sfgfp at the endogenous locus, pBJ114-romR-sfgfp was constructed by amplifying and fusing 850 bp upstream from the romR stop codon, the sf-gfp gene and 850 bp immediately downstream from the romR coding sequence, by overlap PCR. The resulting PCR product was digested by the EcoRI/HindIII restriction enzymes and ligated into the pBJ114 vector. The insert was verified by sequencing.
The plasmids carrying the romRD53E/N point mutations were constructed by PCR with oligonucleotides carrying the mutation amplifying a fragment encompassing 500 bp upstream from the mutation site with a fragment encompassing 1000 bp downstream from the point mutation. The two fragments were fused by overlap PCR, digested by the HindIII/Xbal restriction enzymes and cloned into the pBJ114 plasmid. The insert was verified by sequencing.
For replacement of the frzZ gene by frzZ-mcherry at the locus, pBJ114-frzZ-mcherry was constructed by amplifying independently 857 bp encompassing the 5’ end of frzZ and the mcherry gene. The two fragments were fused by overlap PCR. The resulting PCR product was digested by the BamHI/EcoRI restriction enzymes and ligated into the pBJ114 vector. The insert was verified by sequencing.
Complementation of the frzX deletion was obtained by expressing frzX under the control of its own promoter from the pSWU30 plasmid, an integrating plasmid that recombines at the Mx8 site. A fragment encompassing frzX and the upstream 200 bp sequence containing the promoter was digested using the EcoRI/BamHI restriction enzymes and ligated into the pSWU30 vector. pSWU19-frzXD55A was constructed with the same external primers as the frzX complementation, but with internal overlapping primers carrying the point mutation. The fragments were fused using overlap PCR. The resulting fragment was digested and ligated into pSWU19, a pSWU30 derivative containing a Kanamycin resistance cassette12.
GFP-FrzX was expressed in a frzX deletion background by expressing sfGFP-frzX from the frzX promoter integrated at the Mx8 site. For this, the frzX promoter region upstream was fused upstream from the sf-gfp gene, itself fused in-frame with the frzX gene. The resulting PCR product was digested using the BamHI/EcoRI restriction enzyme and ligated into the pSWU19 vector.
Phenotypic assays
Development assays were performed as previously described30. Cells were grown up to exponential phase and concentrated at Optical Density OD = 5 in TPM buffer (10 mM Tris-HCl, pH 7.6, 8 mM MgSO4 and 1 mM KH2PO4). Then they were spotted (10 μL) on CF 1.5% agar plate. Colonies were photographed after 72 h of incubation at 32°C. Developmental assays in the presence of Isoamyl alcohol (IAA, Sigma Aldrich) were performed similarly, except that plates also contained IAA at appropriate concentrations.
Cloning, expression and purification of M. xanthus Frz system proteins
The cloning, expression and purification of M. xanthus Frz system proteins were performed as previously described4. Briefly, the genes encoding FrzZ, FrzX, RomR and RomRRR were amplified by PCR using M. xanthus DZ2 chromosomal DNA as a template, with the forward and reverse primers listed in Table S3. The amplified product was digested with the appropriate restriction enzymes, and ligated into either pETPhos or pGEX. All constructs were verified by DNA sequencing. The generated plasmids were used to transform E. coli BL21(DE3)Star cells in order to overexpress His-tagged or GST-tagged proteins. Recombinant strains harboring the different constructs were used to inoculate 400 ml of LB medium supplemented with glucose (1 mg/mL) and ampicillin (100 μg/ml). The resulting cultures were incubated at 25°C with shaking until the optical density of the culture reached an OD = 0.6. IPTG (0.5 mM final) was added to induce overexpression, and growth was continued for 3 extra hours at 25°C. Purification of the His-tagged/GST-tagged recombinant proteins was performed as described by the manufacturer (Clontech/GE Healthcare).
In vitro autophosphorylation assay
The in vitro phosphorylation assay was performed as described4,15, with E. coli purified recombinant proteins. Briefly, 4 μg of FrzEkinase was incubated with 1 μg of FrzA and increasing concentrations (0.5 to 7 μg) of FrzCD in 25 μl of buffer P (50 mM Tris-HCl, pH 7.5; 1 mM DTT; 5 mM MgCl2; 50mM KCl; 5 mM EDTA; 50μM ATP, 10% glycerol) supplemented with 200 μCi ml-1 (65 nM) of [γ-33P]ATP (PerkinElmer, 3000 Ci mmol-1) for 10 minutes at room temperature in order to obtain the optimal FrzEkinase autophosphorylation activity. Each reaction mixture was stopped by addition of 5 × Laemmli and quickly loaded onto SDS-PAGE gel. After electrophoresis, proteins were revealed using Coomassie Brilliant Blue before gel drying. Radioactive proteins were visualized by autoradiography using direct exposure to film (Carestream).
Fluorescence microscopy
Time-lapse experiments were performed as previously described4, using an automated and inverted epifluorescence microscope TE2000-E-PFS (Nikon, France), with a 100×/1.4 DLL objective and a CoolSNAP HQ2 camera (Photometrics). The microscope is equipped with “The Perfect Focus System” (PFS) that automatically maintains focus so that the point of interest within a specimen is always kept in sharp focus at all times, in spite of any mechanical or thermal perturbations. Images were recorded with Metamorph software (Molecular Devices). All fluorescence images were acquired with a minimal exposure time to minimize bleaching and phototoxicity effects.
FRAP experiments
Image acquisition and FRAP measurements were performed on a custom-made upright monolithic aluminum microscope31 with a 100 × /1.49 N.A. objective (Nikon), iXon DU-897 cooled EMCCD camera (Andor Technology), and a homemade LabView software package (National Instruments).
Photobleaching was achieved by focusing an argon ion laser to a diffraction-limited spot on the specimen for a pulse of ≈5 s. Wide-field fluorescent images of the cells were acquired before and after photobleaching by custom time-lapse recording of digital images with 16-bit grey levels. Images of both wild-type MglA-YFP cells and MglB-YFP cells were obtained every 0.4 s for 30 s. Images of wild-type RomR-GFP cells were obtained every 10 s for 4 min.
Bioinformatics
Genomic contexts: close FrzX homologs identified by BLAST were analysed using Microbial Genomic Context Viewer (http://mgcv.cmbi.ru.nl/). Protein sequence alignment was performed using Mafft (https://toolkit.tuebingen.mpg.de/mafft) and Ali2D for secondary structure prediction (https://toolkit.tuebingen.mpg.de/ali2d).
Mathematical modelling
The model is described by a set of ordinary differential equations. The equations were solved numerically using the ode45 solver in Matlab (The Mathworks Inc.). We mimicked signalling from the Frz system to the response regulator FrzX using a square wave smoothened with the smooth function. The bifurcation diagram was created using the matcont toolbox (https://matcont.sourceforge.io). See main text and Supplementary Information for detailed description and justification.
Quantification and Statistical Analysis
Reversal scoring assays
Reversals were scored using previously described microfluidic single cell carboxymethylcellulose based assays, allowing modulation of Frz-signaling intensity with IAA4. In this assay, cells are moving using the S-motility system and reversals are scored in the presence of IAA (0.1% or 0.15%) or without IAA (for mutants with a frzon mutation). For this, homemade PDMS glass microfluidic chambers32 were treated with 0.015% carboxymethylcellulose after extensive washing of the glass slide with water. For each experiment, 1 mL of a CYE grown culture of OD = 0.5–1 was injected directly into the chamber and the cells were allowed to settle for 5 min. Motility was assayed after the chamber was washed with TPM 1mM CaCl2 buffer4. IAA solutions made in TPM 1mM CaCl2 buffer at appropriate concentrations (0.1% or 0.15%) were injected directly into the channels. Reversals were scored using two different analyses, since rapid directional changes unlinked to reversals but linked to motility engine activity (so-called stick-slip motions4,33) can occur infrequently accounting for a low number of false positives. In mutants with no stick-slip motions, directional changes were monitored in contrast images acquired every 15 s for 30 min (see below) with 0.15% IAA, or without for mutants carrying the frzon mutation. To discriminate stick-slip motions from bona fide reversals in certain mutants, oscillations of FrzS-YFP proteins were scored instead of directional movements in the presence of 0.1% IAA (see below). This method has proven particularly accurate in determining the effect of a given gene in reversal control4. Here, we use this method to unambiguously characterise the role of FrzX.
Cell tracking
Image analysis was performed with a specific library of functions written in Python and adapted from available plugins in FIJI/ImageJ34. Cells were detected by thresholding the phase contrast images after stabilization. Cell were tracked by calculating all object distances between two consecutive frames and selecting the nearest objects. The computed trajectories were systematically verified manually and, when errors were encountered, the trajectories were removed. The analysis of the trajectories was performed using a Python script that calculates the angle formed by the line segments between the center of the cell at time t, the center at time t-1 and the center at time t-1.
Directional changes were scored as reversals when cells switched their direction of movement, and the angle between segments was less than 90°. For non-reversing strains, the reversal frequency was calculated by dividing the number of directional changes by the number of tracked frames, and, since images were acquired every 15s, this number was multiplied by 240 to generate a reversal frequency per hour and plotted. For strains that frequently reversed, the mean time between two reversals for each cell was plotted. Plotting was performed using the software R (http://www.R-project.org/).
To further discriminate bona fide reversal events from stick-slip motions, the fluorescence intensity of FrzS-YFP was measured at cell poles over time. For each cell that was tracked, the fluorescence intensity and reversal profiles were correlated to distinguish bona fide reversals from stick-slip events with the R software. When a directional change was not correlated to a switch in fluorescence intensity, this change was discarded as a stick-slip event. The reversal frequency was then calculated by dividing the number of bona fide reversals by the number of tracked frames, and, since images were acquired every 15s, this number was multiplied by 240 to generate a reversal frequency per hour and plotted.
Statistics were performed using R: the Wilcoxon test was used when the number of cells was less than 40 in at least one of the two populations compared, while the student test (t-test) was used when the numbers of cells was higher than 40.
Generating single cell traces
Tracking of fluorescent polar clusters was performed manually with the MTrackJ plugin under FIJI after background subtraction and using a local cursor snapping to detect the maximum of fluorescence intensity at a pole. Normalized fluorescence intensities were calculated by normalizing the difference in polar signal by its maximum absolute value: I=(Pole1-Pole2)/max(abs(Pole 1-Pole 2)).
Switching timescales
Measurement of the timescale of polar switching, i.e. how long it takes a fluorescent foci to switch poles, was performed using an automated method under the FIJI/ImageJ plugin MicrobeJ35. Cell outlines and tracks were obtained based on phase contrast images and used to extract the subcellular fluorescence (using the ‘profile’ option). In this methodology, MicrobeJ performs a projection of the fluorescent signal onto the medial axis of the cell, returning the projected signal at discrete points along this axis (beginning and ending at each pole, and approximately 1 pixel apart). These discrete points define the boundary of transverse segments along the medial axis. The R script determines, for each cell on each frame, the area A(i) and the total fluorescent signal S(i) of each segment i. The sum of these values are the cross-sectional cell area (A_cell) and the total fluorescence of the cell respectively. The mean fluorescence intensity of the cell (Int_cell) is the latter divided by the former. The polar regions were defined to be the first and last 5 segments of the cell and the corresponding mean polar fluorescence intensities, P1 and P2, are given by dividing the sum of the fluorescent signal, S(i), of these segments by the sum of the corresponding segment areas A(i). The mean cytoplasmic (CYTO) fluorescence intensity was defined as the summed intensity of the remaining segments divided by the sum of the corresponding segment areas. A correction for background fluorescence was made by subtracting the background intensity (extracted from the MicrobeJ output). A photobleaching correction was also added by normalizing to the whole cell intensity (Int_cell). We removed the effect of autofluorescence and diffuse cytoplasmic signal by subtracting CYTO from P1 and P2. We denote these corrected mean polar intensities by Y1 and Y2, respectively.
We found that working with the difference between the two polar intensities was less noisy than looking at the poles individually and we define the normalised difference as Y=(Y1-Y2)/(Y1+Y2). The profile, Y was then smoothened using a Savitzky-Golay filter (Fig. S1D, upper plot). Nevertheless, variation in Y made it difficult to say when precisely a switch began and ended in all cases. However, one time point that can be determined robustly is the time of maximum (or minimum) slope, i.e. the time at which the signal changes fastest. We therefore used this measure as the basis of our approach. To calculate the slope maxima and minima, we used a Savitzky-Golay derivative filter to calculate a smoothened derivative directly from the unsmoothed profile (Fig. S1D, lower plot). We also take the time period between consecutive minima/maxima to define individual cycles (and the cycle duration). This generally agrees with the times of parity in the signal between the poles. We define the switching timescale to be the duration of the switch if the signal were to change continuously at its maximum measured rate. This is calculated as twice the maximum absolute value of Y within a cycle divided by the absolute value of the maxima/minima of the derivative (Fig. S1D). Note that each cycle has two associated switching timescales.
Correlating fluorescence intensities and reversals
To correlate fluorescence intensities and reversals, the time interval between a reversal, detected by the first time frame where a directional change can be measured, and the maximum of fluorescence intensity of a given GFP/mCherry fusion was scored for each reversal event (n). Negative time values were given if the maximum intensity was measured before a reversal and positive time values were given if the maximum intensity was measured after a reversal. A zero value means that a fluorescence maximum is observed exactly at the reversal detection time. Note that due to phototoxicity and photobleaching, the time resolution of the measurements is 30 s and thus detection of the exact reversal time has a resolution equal to this interval.
FRAP analysis
The analysis of FRAP data was performed using a custom MATLAB script. Data stored as multiplane tiff images were read in and presented to the user to select a region of interest as well as the bleached region. After background subtraction, the mean intensity within the region of interest was corrected for acquisition bleaching by multiply the intensities by an exponential exp(kt), the coefficient, k, having being obtained by fitting to the acquisition bleaching curve of another cell. Finally, we normalized to a prebleach intensity of 1. The resulting curves were fit using non-linear least squares to the equation f(t)=a*(1-exp(-b*t))+c, where a is a measure of the amplitude of the recovery, b is the inverse of the timescale of recovery and c is the fraction of the initial intensity that was not bleached.
Other than the intensity in the bright focus near the pole, the background intensity in the cell is uniform along the long axis of the cell, even at the fastest timescales that we investigated (2.5 frames/second). As described in the Supporting Information section describing the three compartment model, this implies that the timescale of FRAP recovery is dominated not by the diffusion of free protein through the cytoplasm, but the binding and unbinding kinetics. Following the work of Sprague et al.36, we interpret the constant b from each cell to be an estimate of koff. The half-time of recovery, t1/2, is ln(2)/b.
Statistics were performed using R: the Wilcoxon test was used when the number of cells (n) was less than 40 in at least one of the two populations compared, and the student test (t-test) was used for a number of cells higher than 40.
Author contributions
Conceptualization, MG, SMM, EM, SL, MH and TM; Methodology, MG, SMM, EM, SL, VM, MH and TM.; Investigation, MG, SMM, EM, SL, LM, GB and YZ; Writing - Original Draft, MH and TM; Writing - Review & Editing, MG, SMM and EM; Visualization: MG, SMM, EM, SL, LE, MH and TM; Funding Acquisition, MH and TM; Resources, BB, RV, JS and MV; Mathematical analysis: SMM and MH; Supervision, MH and TM.
Supplemental figure titles and legends
Figure S1: Recovery times of polarity proteins MglA-YFP, MglB-YFP and RomR-GFP. Related to Figure 1.
(A) A schematic of the switching timescale measurement. The normalised difference between polar signals, Y, is determined from time-lapse analysis (upper plot, blue dots). Savitzky-Golay filters are used to obtain a smoothed profile (upper plot, red line) and a smoothed profile of the derivative (lower plot, blue line). The duration of a switching cycle is defined to be the time between a peak and subsequent (or preceding) valley in the derivative profile (indicated for the first cycle by shading and crosses). Since the derivative is simply the angle between the tangent (black dashed lines) to the profile and the x-axis (blue triangles), we can use values of the maxima/minima of the derivative to define appropriate timescales: the two switching timescales associated with each cycle are defined to be twice the maximum absolute value, M, of (smoothened) Y within each cycle divided by the absolute value of the minimum/maximum of the derivative profile (S).
(B) Top: Example of single-cell recovery after photobleaching for each polarity protein. The fluorescence intensity dynamics in the bleached regions (blue crosses and lines), corrected for bleaching, were fit to exponential curves (red lines) by non-linear least squares fitting. Bottom: Timelapse images (0.4 s time frame for MglA-YFP and MglB-YFP, 10 s time frame for RomR-GFP) of single-cell recovery after photobleaching.
(C) MglA-YFP and (D) MglB-YFP recovery times as determined by FRAP in WT, frzon and frzE mutants. The lower and upper boundaries of the boxes correspond to the 25% and 75% percentiles, respectively. The median is shown as a red line and the whiskers represent the 10% and 90% percentiles.
Figure S2: RomR is not phosphorylated by FrzE. Related to Figure 3.
(A) Schematic of RomR domain structure.
(B) RomRRR is not phosphorylated by the FrzE kinase in vitro. Autoradiogram of P32-labelled FrzE in the presence of RomRRR.
(C) Developmental phenotypic assays showing the absence of fruiting body formation in a romR mutant. romR is essential for fruiting body formation but point mutations at the phosphorylatable aspartate of the RomR response regulator domain do not affect fruiting body formation. Scale bar: 1 mm.
Figure S3: FrzX is a target of FrzE and is essential for reversals. Related to Figure 3.
(A) Genomic context of genes encoding FrzX and FrzX-like proteins in the Myxococcalesand Anaeromyxobacter species.
(B) and (C) Fruiting body formation of (B) WT, frzX mutant and frzX mutant complemented with an ectopic copy of the frzX gene, (C) an ectopic copy of the fizXD55A gene and an ectopic copy of the gfp-frzX gene. Scale bar: 1 mm.
Figure S4: Localization dependencies between the frz proteins and the polarity proteins. Related to Figure 4
(A) Images showing localization of MglA-YFP, MglB-YFP, RomR-GFP in the frzX mutant. Scale bar = 2 μm.
(B) Images showing localization of FrzZ-GFP in the WT and frzE and frzX mutants. Scale bar = 2 μm.
Figure S5: Dynamics of GFP-FrzX and RomR-GFP in a frzon background and a frzZ background in the presence of IAA. Related to Figure 5.
(A) Top: time lapse images of GFP-FrzX dynamics from a single reversing cell in a frzon background (30 s time frames). Bottom: difference in intensity of GFP-FrzX between the two poles normalized to maximum absolute value of the difference. R: Reversals, detected by a clear directional change of the cell. Scale bar = 2 μm.
(B),(C) and (D) Same as (A) but for (B) GFP-FrzX with 0.1% IAA in a frzZ background (15 s time frames), (C) RomR-GFP with 0.1% IAA in a frzZ background and (D) GFP-FrzX (green trace) and RomR-mCh (red trace) in a WT background with 0.3% IAA (30 s time frames). Scale bar = 2 μm
Figure S6: Simulated polarity protein dynamics. Related to Figure 6.
(A) Simulated profiles of MglA, MglB, RomR and FrzX~P, generated by the equations in Figure 6B, showing the difference in polar levels in the frzon background. Phosphorylation of FrzX~P is continuous. For all panels, dashed lines are as in Figure 2D. See Supplementary Information for parameter values.
(B) Simulated profiles in frzon cells as in (A) but with RomR levels held constant and symmetric. Asymmetry in polar RomR is not required for oscillations.
(C) Simulated profiles in frzon frzZ cells, assuming FrzZ promotes RomR unbinding (option (i) of main text). Parameters are same as in (A) but with a one order of magnitude lower rate of RomR unbinding.
(D) Simulated profiles in frz0n frzZ cells (with option (ii) of main text) as in Figure 6D, but with RomR levels held constant and symmetric. In this case, asymmetry in polar RomR is clearly required for oscillations.
(E) Simulated profiles in frzZ cells (option (ii) of main text). Shown is the effect of phosphorylation pulses of differing durations (1.3, 2 and 3 mins). Unlike the wild-type, a 1.3 min pulse is not sufficient to induce a switch, nor is a 2 min pulse. However, a 3 min pulse (or greater) is sufficient and induces a polar switch if it occurs when sufficient RomR has accumulated at the lagging pole (indicated by the shaded region). See Supplementary Information for parameter values and justification for modelling FrzX activity as pulsatile.
Supplemental tables
Table S1. Bacterial strains used in this study. Related to STAR Methods
Table S2. Plasmids used in this study. Related to STAR Methods
Table S3. Primers used in this study. Related to STAR Methods
Acknowledgments
We wish to thank Lotte Sogaard-Andersen and Ulrich Gerland for discussions and Victor Sourjik for comments on the manuscript. MG was the recipient of an ARC fellowship (DOC20140601482). EM is the recipient of an AMIDEX “Académie d’excellence” thesis fellowship (n°ANR-11-IDEX-0001-02). SL is funded by an ANR program “BACTOCOMPASS” TM is the recipient of an ERC starting grant “DOME 261105” and an ANR program “BACTOCOMPASS”. RV was supported by the French Infrastructure for Integrated Structural Biology (FRISBI) ANR-10-INBS-05.