In most known bacterial species, cell division starts with the forma on of the cytokine c ring, the Z-ring, at the cell's middle 1,2 . In Escherichia coli, the Z-ring consists of FtsZ protofilaments anchored to the inner membrane via FtsA and ZipA linker proteins. FtsZ protofilaments in the cytokine c ring are dynamic, undergoing a treadmilling mo on 3,4 . TEM and super-resolu on imaging have shown that the Z-ring consists of a sparse set of loosely associated filaments which are distributed in a narrow band (50 nm) around the midcell 5,6 . Forma on of the Z-ring depends on growth condi ons star ng mostly at cell birth in fast growth rates but being delayed when cells are grown in a poorer quality medium 7 . Despite the early presence of the Z-ring, the cells do not ini ate the onset of constric on concurrent with the forma on of the Z-ring. Instead, there is a delay that lasts about ¼ of the cell cycle in E. coli for a range of different growth condi ons 8,9 .
While the Z-ring is a prerequisite for cell division, the onset of constric on acts as an effec ve cell cycle checkpoint 10,11 . Despite this significance, the signal that triggers the onset of constric on in E. coli and other bacteria has remained undetermined. Prior to the onset of constric on, a number of essen al divisome proteins are recruited to the midcell. The order of recruitment of these proteins has been determined to be FtsE-FtsX and FtsKFtsQ-FtsB-FtsLFtsW-FtsIFtsN 12 . Deple on or inac va on of upstream proteins prevents the recruitment of all downstream components. FtsN is the last essen al component to arrive at the divisome, and it accumulates in a self-enhancing manner. Accordingly, it has been considered the trigger protein for cell division in E. coli [13][14][15][16][17][18][19][20][21] .
During the onset of constric on, a core divisome complex that includes the pep doglycan synthesizing unit FtsWI 22 separates from the treadmilling FtsZ protofilaments 23 . It has been proposed that this separa on and subsequent pep doglycan synthesis is due to the binding of FtsN to the FtsBQL complex that, in turn, ac vates FtsWI 19,24 . Before separa on, FtsBQL and FtsWI are either associated with sta onary FtsZ monomers or follow FtsZ treadmilling protofilaments via tracking their ends 23 by the diffusion-and-capture mechanism 25 . A different pathway to trigger the checkpoint has also been proposed, in which a change in the oligomeriza on state of FtsA ini ates the synthesis of septal cell wall 1,26,27 . FtsA, which shares its fold with ac n, forms oligomeric structures in vitro 28 . These structures include 12-mer minirings, curved arcs, and an parallel double filaments 20,29,30 . Of these higher-order structures, the experimental evidence in vivo exists only for the FtsA an parallel filaments 20 . It has been proposed that the onset of constric on is triggered by the transforma on of FtsA minirings to an parallel filaments 1 or, alterna vely, that mostly monomeric FtsA is driven to an parallel filament form as a result of FtsN binding 20 .
While the protein-protein interac ons between FtsN, FtsA, and other divisome proteins are needed to trigger the onset of constric on, it has remained unclear what causes the switching on of these interac ons during the cell cycle. There is no evidence of phosphoryla on nor any other post-transla onal or slow conforma onal changes of these proteins. As such, the protein-protein interac ons involved remain immutable in the cell cycle. On the other hand, E. coli and other bacteria have been observed to add approximately a constant length increment from one DNA replica on ini a on to the next 31 and from birth to division, irrespec ve of their birth length 32,33 . The la er phenomenon, referred to as the cell size adder, can be explained if cell division is triggered when a number of some protein in the cell reaches a threshold value 31,34,35 . Most different protein species in the cell appear to increase exponen ally during the cell cycle, being synthesized in propor on to cell volume. In principle, a cell could use one of these protein species as a proxy for all of them to determine that its content is approximately doubled before commi ng to division. We refer to this idea as the threshold accumula on model. A caveat here is that a cell cycle checkpoint is not at the division but at the onset of constric on 11,36 , and no cell size adder between consecu ve constric on ini a on events has been reported.
In addi on to approximately doubling its protein content, the cell needs to have a mechanism to verify that it has at least two copies of chromosomal DNA. Accordingly, one would expect the onset of division to be ghtly coupled to the replica on cycle 31,34,[37][38][39] . However, the ght coordina on between replica on and division cycles has been disputed 10,35,40 . Recent experiments and analysis have reconciled these views, indica ng that the replica on status appears to be only one of the input signals for the onset of constric on, and its effect becomes smaller at faster growth rates 11,36 . These ideas are captured in the concurrent processes model, where a replica on-related signal and threshold accumula on of an effector protein must both be present to trigger cell division 41,42 . The model leaves open what could be the actual effector protein. Si et al. proposed it to be FtsZ because the adder correla ons weakened in cells with downregulated FtsZ amount 35 . These authors furthermore found that the simpler threshold accumula on model describes their data. However, their work did not quan fy the downregulated FtsZ amount, and it was carried out in cells where the na ve FtsZ was replaced by FtsZ fluorescent fusion. It is expected that a sufficient downregula on of any of the essen al divisome proteins and likely also non-essen al ones would lead to a delay in the onset of constric on, to longer cells and a decrease in the adder correla ons.
A more conclusive determina on of whether the amount of FtsZ or some other division protein is limi ng for the cell division is therefore warranted.
Here, we inves gate what is the rate-limi ng component or process for the onset of constric on in E. coli at moderately fast growth rates using high throughput imaging in microfluidic devices and cell cycle modeling. We consider the protein concentra on rate-limi ng if its increase within the physiologically occurring range significantly accelerates the onset of constric on, at least transiently. Our data and modeling show that FtsZ is rate-limi ng for the onset of constric on, while FtsN is not. However, at high excess levels, FtsN does accelerate the onset of constric on. Furthermore, our data also show that FtsA is not rate-limi ng nor inhibitory in physiological condi ons, but it becomes inhibitory at 50% overexpression level. We propose a model for the onset of constric on that is consistent with these findings.
Our goal in this work was to develop a quan ta ve approach to determining if a protein is rate-limi ng for cell division. A decrease in concentra on/protein numbers of the rate-limi ng component should lead to delays in the cell division. However, a sufficiently large down-regula on of an essen al divisome component leads to the cessa on of the division process even if this component is not rate-limi ng in normal growth condi ons 43 . The downregula ng concentra on of an essen al but not rate-limi ng protein for cell division, by say 20%, may delay the division process, but at 10%, downregula on may s ll not be limi ng. Controlled and quan ta ve downregula on of this level of accuracy has not been achieved yet. Therefore, instead of downregula ng, we ra onalized that upregula on of the protein of interest should produce a more robust way of assessing if it is rate-limi ng for cell division. An upregula on within the physiologically occurring range should lead to a temporary increase in the ini a on rate of cell divisions if the component is rate-limi ng and have no effect if the component is not rate-limi ng. The caveat here is that a high upregula on is known to lead to cytotoxic effects. For example, significant overexpression of FtsA and FtsZ alone (more than 7-fold) leads to cessa on of cell division 44,45 .
Upregula on by a small amount and quan fica on of this amount is thus necessary. Furthermore, a aching a fluorescent fusion for the protein of interest to quan fy its concentra on/abundance may affect its func on so that the altered protein may become rate-limi ng due to its impaired func on, as shown below for FtsZ. Having these considera ons in mind, we upregulate in our experiments unlabeled protein in wild-type cells (the strain of interest -SOI) and use a strain with a fluorescent proxy on the same chip that expresses a fluorescent protein from the same locus under the same promoter and Shine-Dalgarno sequence (Reporter strain) (Fig. 1a). To calibrate the signal from the fluorescent reporter, we also added a third strain (Reference) which expressed the protein of interest fused to the same fluorescent protein as present in the Reporter strain. The Reference strain expresses this fusion protein cons tu vely from the na ve locus of the protein of interest. Using real-me signals from Reporter and Reference allows the calibra on of upregulated protein amounts in terms of the na ve protein concentra on (for details, see Methods, Determining Induced Protein Concentra ons). We used Western blo ng (Supplementary Fig. 1) to validate the method, finding comparable values from the fluorescence-based method and Western blo ng (Supplementary Table 5). We mixed SOI, Reporter, and Reference strains for quan ta ve fluorescence-based measurements and grew cells on a microfluidic mother-machine pla orm (Fig. 1b, c).
A er growing the cells for about six genera ons, we upregulated the protein of interest and monitored the change in protein concentra on in the cells (Fig. 1d), cell length at division, 𝐿𝑑, (Fig. 1e), and the doubling me, 𝑇𝑑, (Fig. 1f) as a func on of me from the upregula on of the protein of interest. We also determined ming, 𝑇𝑐, and the cell length, 𝐿𝑐, at the onset of constric on (Supplementary Fig. 2).
The data in Fig. 1e-f and Supplementary Fig. 2 is per nent to the upregula on of FtsZ from an extra copy from the -a achment (a B) site in moderately fast growth condi ons in a glucose-CAS medium. FtsZ upregula on by 1.96x (excess FtsZ 96%) leads to a step-like decrease in cell length by about 8% (Fig. 1e) and a transient decrease in doubling me ( me from cell birth to next division), with the shortest doubling mes being 13% shorter than before the protein upregula on (Fig. 1f). The observed speed-up in cell division frequency is qualita vely consistent with the idea that FtsZ is rate-limi ng for cell division in E. coli at faster growth rates. At the same me, we did not observe significant changes in cell lengths and cell cycle mings as a result of FtsZ upregula on in slow growth rates in alanine medium even at a much higher upregula on level (Supplementary Fig. 3). This finding is consistent with our earlier works 11,36 which show that replica on-related processes are dominantly rate-limi ng for E. coli cell division at slow growth rates rather than processes arising from protein abundances.
Since the focus of this work is to understand rate limita ons arising from protein abundances, the remainder of the work deals with moderately fast growth rates. Comparing the data in Figs. 1d and e, obtained at a moderately fast growth rate, shows that at higher overexpression levels, FtsZ ceases to be rate-limi ng because changes in cell length stop about 100 min a er the start of the induc on, while the FtsZ concentra on con nues to increase further for about 200 min. The cessa on of FtsZ being ratelimi ng during the upregula on can be more clearly seen by plo ng cell length as a func on of the normalized FtsZ concentra on, FtsZ , (Fig. 1g). Note that FtsZ is based on the normalized reporter signal, which is corrected for fluorophore matura on effects (see Methods). Here, we chose to measure the cell length at the onset of constric on rather than at the division because the former is the cell cycle checkpoint. The data show that as FtsZ starts to increase, the cell length at constric on decreases linearly in me, but when FtsZ exceeds about 1.7x of the na ve level, the decrease stops.
This is approximately the point when FtsZ ceases to be rate-limi ng for triggering the onset of constric on for all the cells in the cell popula on. To explain the changes in cell length upon FtsZ upregula on quan ta vely, we compared the data to the FtsZ threshold accumula on model proposed earlier 35 but with a modifica on that the FtsZ number threshold is reached at the onset of constric on rather than at the division (Fig. 1g). Assuming the FtsZ concentra on in this growth condi on is constant during the cell cycle yields a simple predic on 𝐿𝑐 𝐿𝑐 / FtsZ as indicated by a dashed line in Fig. 1g. Here 𝐿𝑐 is the cell length in WT cells without extra FtsZ. The predic on differs in two aspects from the experimental data: 1) the predicted line does not show a plateau at higher FtsZ values and 2) the slope of the curve at a small FtsZ is much higher than in the data.
We also performed upregula on measurements with two strains where the na ve FtsZ was replaced by FtsZ sandwich fusion to fluorescent mNeonGreen, FtsZmNG 46 . In one of these strains, the extra inducible copy inserted in the a B site carried FtsZmNG, while in the other strain, it contained the unlabeled FtsZ (as in SOI). Both strains were about 25% longer than the unlabeled SOI, consistent with earlier report 46 .
Upon upregula on of FtsZ, the cell length of both FtsZmNG labeled strains decreased about three mes more than unlabeled SOI, reaching as a result of upregula on about the same length as the WT cells (Supplementary Fig. 4a-d). Comparing cell lengths vs FtsZ data from these curves to the threshold accumula on model showed that this model be er fit the data from the labeled than from the unlabeled strain (Supplementary Fig. 4e-f). These results suggest that a fluorescent fusion to FtsZ reduces its func onality, and the reduced func onality of FtsZmNG makes it more limi ng than the WT FtsZ for the onset of constric on. However, the cell length defect can be corrected by higher expression of FtsZmNG.
The above comparison also poten ally explains why an earlier work 35 , where a strain with FtsZ sandwich fusion was used, concluded that the FtsZ threshold accumula on model applies.
The plateau region in cell length vs FtsZ data in unlabeled SOI strain indicates that in addi on to FtsZ accumula on, there could be an addi onal process that controls the onset of the constric on. This idea is captured by the concurrent processes model 36,41,42 , where one of the limi ng processes stems from FtsZ numbers reaching a threshold value in the cell, and the other limi ng process originates from the DNA replica on cycle. To compare the model to the experimental data, we used cell cycle parameters determined from the experiments and adjusted the threshold level for the FtsZ numbers and the me dura on when the replica on-related processes block the onset constric on using the measurement shown in Fig. 1d-g (for details see Methods, Modeling). A er these adjustments, the model quan ta vely explained the increase in fluorescent protein concentra on from the Reporter (Fig. 2a), step-like decrease in cell length (Fig. 2b, Supplementary Fig. 5a), and the transient decrease in mings for the onset of constric on (Fig. 2c) and cell division (Supplementary Fig. 5b). Note that to reproduce the change in steady state mings for the onset of constric on (𝑇𝑐) we needed to account for the increased constric on period (Δ𝑇𝑠 𝑇𝑑 𝑇𝑐) that resulted from FtsZ upregula on (Supplementary Fig. 6).
Qualita vely, the cell length and transient decrease in mings for the onset of constric on and division can be understood in the model because, at the higher synthesis rate of FtsZ, the cells reach the number threshold earlier in the cell cycle when their length is smaller. However, as the cells get smaller, the synthesis rate of FtsZ, which is propor onal to cell volume/length, decreases. The mings 𝑇𝑐 and 𝑇𝑑, therefore, shi back to their original values a er the comple on of one whole cell cycle that follows the upregula on of FtsZ (without accoun ng for increased Δ𝑇𝑠). The unchanged steady state mings 𝑇𝑐 and 𝑇𝑑 a er upregula on of FtsZ from their pre-induc on values can also be understood from the constancy of cell growth rates before and a er upregula on. However, as men oned above, we adjusted the basic model for the increased constric on period (𝑇𝑑 𝑇𝑐), which accompanies FtsZ upregula on. The increased constric on period shortens both 𝑇𝑐 and 𝑇𝑑 because more FtsZ accumulates during the longer constric on period in the previous cell cycle.
To test the model further, we carried out addi onal experiments where FtsZ concentra on at the final steady state differed from the one shown in Fig. 2a-c. The model predicts that because of the increase in the final FtsZ steady-state concentra on, the change in cell length at constric on approaches a minimal limi ng value, and the dura on of cell length change decreases (Fig. 2d). The minimal limi ng length is determined by replica on-related processes alone. Without any further parameter adjustments, the model qualita vely predicted the me-dependences of all measured quan es in both overexpression condi ons (Fig. 2e-f, Supplementary Fig. 78). At the quan ta ve level, however, the experimentally observed effect was smaller than the model predic on for the cell lengths at the onset of constric on in the low overexpression condi ons (1.57x) (Fig. 2e). The same was true also for the higher (3.2x) overexpression measurement (Fig. 2f). However, in this measurement, the effect appeared as incorrectly predicted 𝐿𝑐 value before upregula on. This is because, before the upregula on of FtsZ, there was a smaller leaky expression of FtsZ in high (3.2x) overexpression measurement ( FtsZ 1.02x) compared to the two lower FtsZ overexpression measurements ( FtsZ 1.10x). The model was thus unable to quan ta vely predict the effects arising from this leaky expression. The failure of the model to correctly predict cell length due to leaky expression of FtsZ was also evident when we compared the cell lengths from the Reporter strain, which has a na ve level of FtsZ, to the model (Supplementary Fig. 9). The behaviors in all overexpression levels can be summarized in the FtsZ tra on plot (Fig. 2g). The model can be seen to fit the data well, except for the FtsZ ≲ 1.1x and for FtsZ ≳ 2.3x. The devia on of the model for FtsZ ≳ 2.3x could be explained by the onset of cytotoxic/inhibitory effects of FtsZ overexpression, as has been observed earlier at higher expression levels 44 . Furthermore, at FtsZ 3.2x overexpression levels, about 1% of all divisions lead to mini cells, which is not accounted by the model. However, we did not observe mini cells at two lower overexpression levels.
While the devia on of the model from the experiments for FtsZ ≳ 2.3x was expected, the discrepancy at FtsZ ≲ 1.1x presents a more significant challenge for the model. A key characteris c of the concurrent processes model is a large cell length change for varia ons in FtsZ concentra on close to FtsZ 1.0x and decrease of this response as FtsZ increases (Fig. 2g). Such behavior is independent of model parameters. Failure of this predic on suggests that a number threshold postulated by the model may not accurately capture cellular response near the WT concentra on of FtsZ. Instead of a simple number-sensing mechanism, there could be a more complex response func on involved in the decision-making process that triggers the onset of constric on. At the same me, the model fits the data well at high overexpression condi ons, sugges ng that at a coarser level, the accumula on to threshold number provides a good, effec ve model to explain how the onset of constric on is triggered.
A comparison of data and model shows that the FtsZ amount in the cell is one of the rate-limi ng factors for the onset of constric on. The ques on then arises: how limi ng is FtsZ? As men oned above, the concentra on-dependent decrease in cell length plateaued at about 1.7x overexpression levels of FtsZ (Fig. 2g) indica ng that at this overexpression level, FtsZ is effec vely not limi ng the onset of constric on for any cell in a popula on. Alterna vely, the concurrent processes model allows us to es mate the probability that in each division FtsZ numbers are limi ng the onset of constric on. This probability as a func on of FtsZ is shown in Fig. 2h. The probability approaches zero at FtsZ 1.7x as expected from the previous argument. More importantly, the model predicts that FtsZ is limi ng in 68% divisions for the WT cells at the na ve level of FtsZ (i.e. FtsZ 1.0x). It is worth emphasizing that this number is as valid as the model. Since the model shows a smaller change in cell lengths than the experiment at low overexpression levels of FtsZ, 68% probability is likely an overes mate. Nevertheless, we can draw a rough es mate that for at least half of the cell divisions in WT cells in this moderately fast growth condi on, FtsZ numbers in the cell rate limit the onset of constric on.
Our analysis and modeling so far have focused on the total number of FtsZ molecules and their concentra ons in the cell. While this quan ty is sufficient to determine if FtsZ is rate-limi ng for the onset of constric on, the relevant molecular processes occur in the Z-ring. Therefore, FtsZ numbers in the Z-ring are also of interest. To inves gate the rela onship between FtsZ numbers in the Z-ring and total FtsZ numbers in the cell, we studied cells where the na ve sZ locus was replaced with the FtsZmNG fusion variant. These cells also had inducible extra copy FtsZmNG (strain JM276) or na ve FtsZ (strain JM275) expressed from the λ-a achment site as described earlier (Supplementary Fig. 4). As previously noted, these cells were longer than WT cells (Supplementary Fig. 4c). However, upregula ng FtsZmNG by 1.62x shortened the cells to approximately WT sizes, mi ga ng the apparent defect. In the majority of cells, the new Z-ring started to assemble concurrently with the dissocia on of the Z-ring in the mother cell, as reported before 7 . However, the ini al assembly can be transient in individual cells, with the Z-ring intermi ently dissocia ng 47 . We, therefore, defined two me points related to the assembly of the Zring: 𝑇𝑧, 1 marks the earliest me from cell birth when the first FtsZ assembly is present at the midcell, and 𝑇𝑧, 𝑝𝑒𝑟 the earliest me when a persistent Z-ring is present, remaining un l the cells are about to divide. The distribu ons of 𝑇𝑧, 1 and 𝑇𝑧, 𝑝𝑒𝑟 were both peaked at 𝑇𝑧 0 with a tail to longer mes (Supplementary Fig. 10a-b). Since the Z-ring forma on mostly coincides with the dissocia on of the old Zring in the mother cell, upregula on of FtsZmNG by 1.62x had a limited effect on either of these 𝑇𝑧 values (Supplementary Fig. 10a-c, f). The upregula on of FtsZ in these cells thus transiently shortened the delay from the Z-ring forma on to the onset of constric on (Supplementary Fig. 10d-e, g-h). This finding indicates that FtsZ concentra on in the cell directly affects the onset of constric on rather than accelera ng Z-ring forma on and thereby indirectly speeding up all downstream processes.
We then determined the total number of FtsZ in both the cell and in the Z-ring, where the la er was present (see Methods, Determining the Z-ring and N-ring-related parameters). The two numbers showed a high correla on (𝑅 0.89) for all cells with a detectable Z-ring, for a cell cycle period spanning from 𝑇𝑧, 𝑝𝑒𝑟 to 0.9𝑇𝑑 (Fig. 2i, Supplementary Fig. 11a-b). Note that for most cells 0.9𝑇𝑑 𝑇𝑐. The correla on between the total numbers of FtsZ molecules in the cell and those in the Z-ring was lower during the early and late stages of the cell cycle (Supplementary Fig. 11c-d). The same conclusion can be drawn from a different analysis where the excess FtsZ numbers at the midcell were correlated with the total number of FtsZ in the cell irrespec ve if the cells had a Z-ring or not (Supplementary Fig. 11e-h). These findings show that the amount of FtsZ in the Z-ring is determined by the total number of FtsZ in the cell throughout most of the cell cycle, except for a frac on of cells in early cell cycle stages without Z-ring and in the latest stages (𝑇 0.9𝑇𝑑) when the Z-ring started to dissociate. Therefore, the accumula on of FtsZ numbers to a threshold value in the cell, as postulated in the threshold accumula on and concurrent processes models, can be considered equivalent to the accumula on of FtsZ numbers to a threshold value in the Z-ring.
FtsN is not rate-limi ng for the onset of constric on.
Our modeling considered replica on the second limi ng process, but similar results can be obtained if, instead of replica on, another division-related protein limits the onset of constric on (Supplementary Fig. 12). Our earlier data indicate that at moderately fast growth condi ons, as used here, replica on is only a modestly limi ng factor for the onset of constric on 11,36 . Several recent works have argued that FtsN acts as a trigger for the onset of constric on [13][14][15][17][18][19][20]48 . Therefore, we also carried out the upregula on measurements for FtsN. In the first set of measurements, we upregulated FtsN concentra on by about 71% (Fig. 3a), which is similar to the FtsZ overexpression level in Fig. 1. Unlike for FtsZ, there was no systema c change in 𝐿𝑑, 𝐿𝑐, 𝑇𝑑 or 𝑇𝑐 upon overexpression of FtsN (Fig. 3b-c, Supplementary Fig. 13a-b).
In a two-sided Mann-Whitney test, 𝐿𝑐 and 𝐿𝑑 before and a er upregula on were not sta s cally significant (p-value > 0.2). We then repeated the measurements at a much higher upregula on level of FtsN (7.56x, Fig. 3d). In this case a clear decrease in cell length appeared (Fig. 3e, Supplementary Fig. 13cd) as observed earlier 49 . Combining these measurements in the FtsN tra on curve showed that cell length decreased approximately linearly with FtsN throughout the en re studied range (Fig. 3g).
However, the response of cell lengths to changes in FtsN was about ten mes less sensi ve than to changes in FtsZ . The same decrease in cell length was observed with the 7.56x upregula on of FtsN as with the 1.71x upregula on of FtsZ. To put these numbers into perspec ve, we determined FtsN concentra on in the cell cycle using previously reported Ypet-FtsN construct 9 . We es mate that the average concentra on varies only about 2 % ( 0.02x around its popula on-average value during the cell cycle (Supplementary Fig. 14a). At the same me, FtsN concentra on at the onset of constric on varies by 23% (0.23x) in the cell popula on (Supplementary Fig. 14b). Considering the la er number as the natural varia on of FtsN and using the slope from the tra on curve in Fig. 3g shows that the FtsN varia on in the cell popula on can account only for 10 nm varia on in 𝐿𝑐 while the varia on (standard devia on) of 𝐿𝑐 in cell popula on is 470 nm. Altogether, FtsN accelerates cell division at very high overexpression levels, but it is not rate-limi ng the onset of constric on under normal growth condi ons.
We also carried out FtsN upregula on measurements in a fluorescent fusion strain where a na ve copy of sN was replaced with Ypet-sN and an extra inducible Ypet-sN was cloned to the -a achment site.
While the upregula on of Ypet-FtsN does not also accelerate the onset of constric on at moderate expression levels (the final FtsN 1.48x, Supplementary Fig. 15a-e), the excess Ypet-FtsN at midcell nevertheless increases in these condi ons (Supplementary Fig. 16a). The fold-increase in the midcell Ypet-FtsN is larger in the late stages of the cell cycle (Supplementary Fig. 16b), similar to the increase in FtsZmNG when the la er is upregulated (Supplementary Fig. 16c-d). However, because of upregula on, excess Ypet-FtsN is also present at the midcell (N-ring) during the early cell cycle (Supplementary Fig. 16b). As observed previously in FtsA* (R286W) mutant cells 9 , the measurement here in WT FtsA background shows that earlier FtsN accumula on at midcell (Supplementary Fig. 15f-g) does not trigger the earlier onset of constric on (Supplementary Fig. 15d-e). The la er finding further supports the conclusion that FtsN is not rate-limi ng for the onset of constric on.
FtsA is the second most conserved bacterial cell division protein besides FtsZ 50 . At several-fold upregula on, FtsA is cytotoxic, preven ng the onset of constric on 45,51 . However, it is possible that at na ve levels, it is rate-limi ng for cell division like FtsZ because the two proteins are expressed from the adjacent genes in the same operon. To test this hypothesis, we carried out overexpression measurements also for FtsA (Fig. 4a). Contrarily to our hypothesis, FtsA in low overexpression condi ons (the final FtsA 1.6x) did not lead to a change in cell length and ming of the onset of constric on (Fig. 4bc) and of these parameters at the division (Supplementary Fig. 17a-b), sugges ng that FtsA is not ratelimi ng for cell division in normal growth condi ons. However, higher overexpression levels of FtsA (the final FtsA 2.4x) led to an increase in cell length (Fig. 4d, Supplementary Fig. 17d) but not the ming of the onset of constric on (Fig. 4e, Supplementary Fig. 17c). The length increase only occurred a er a dis nct delay (Supplementary Fig. 17e), confirming that at the low level of overexpression, FtsA is not inhibitory. The increase in cell length at higher overexpression levels is consistent with earlier reports 45,51,9,51 . Conver ng the me-dependent measurements to the FtsA tra on curve showed that FtsA inhibitory effects set in at about 1.6-1.7x overexpression levels (Fig. 4f). A 1.6-1.7x overexpression of [FtsA] beyond its mean value is likely beyond the natural varia on in a cell popula on as it is for FtsN. So, in a popula on, FtsA is not expected to be inhibitory for the vast majority or even in any cells in the popula on in regular growth condi ons.
The above data showed that while the cell length increased at high FtsA overexpression levels, there was effec vely no change in the ming for the onset of constric on. To understand why the increase in cell length is not accompanied by a transient increase in the ming for the onset of constric on, we modeled the FtsA upregula on measurements using the concurrent processes model. We considered an increase in FtsA to lead to a higher threshold level for FtsZ numbers at which they trigger the constric on. We assumed that the increase in the threshold level is propor onal to the excess FtsA , but only above FtsA 1.6x (based on Fig. 4f). Apart from this change, the model and the parameters were the same as in Fig. 2. The model reproduced the experimentally observed increase in cell lengths (Fig. 4d, Supplementary Fig. 17c). Notably, the model also showed, consistent with the experiment, that the ming for the onset of constric on was effec vely unchanged (Fig. 4e, Supplementary Fig. 17d). There is no dis nct increase in 𝑇𝑐 in the model because the threshold level for FtsZ to trigger the onset of constric on gradually increases as more FtsA is produced. The gradual increase in threshold level smears out the transient change in 𝑇𝑐 in a popula on average measurement. In contrast, in FtsZ upregula on measurements, the synthesis rate of FtsZ abruptly increases upon induc on, and a transient change in 𝑇𝑐 can be observed. Interes ngly, while the upregula on of FtsZ leads to a longer constric on period (Supplementary Fig. 6), the high level of upregula on of FtsA (the final FtsA 2.4x) shortens it (Supplementary Fig. 17f) even though at this level of overexpression, FtsA has an inhibitory effect on the onset of constric on.
Unlike FtsA, overexpression of its hypermorphic mutant FtsA* (R286W) is not known to cause cytotoxic effects and leads to short cell phenotype 52 . To quan fy its effects, we also upregulated FtsA* in the WT FtsA background (about 2.4x; Fig. 4g). Upregula on led to decreased cell length (Fig. 4h, Supplementary Fig. 18a-d) and a transient decrease in the ming for the onset of constric on that did not recover fully (Fig. 4i). The effect appeared in all aspects very similar to the ones from FtsZ upregula on measurements.
We overlayed the two measurements (Supplementary Fig. 18e-h), finding the effects of FtsZ and FtsA* upregula on almost indis nguishable from each other. Note the 𝐿𝑑 vs Time and 𝑇𝑑 vs Time curves are insensi ve to the amounts of protein upregula on in the range of concentra ons (cf. Fig. 2d). Since FtsZ and FtsA* have the same downstream effect, they may cause the same change in the divisome that is needed to trigger the onset of constric on.
Key proteins in the cell division in E. coli are the earliest-arriving components FtsZ and FtsA, and the last arriving essen al protein FtsN. Here, we inves gated if any of them are rate-limi ng for cell division by modestly upregula ng their concentra ons. Although the upregula on of these proteins has been carried out in the past, the increase of protein concentra ons in these measurements frequently far exceeded the physiologically relevant range and had not been precisely quan fied. Furthermore, cell length and division mings have been inferred at the me of division rather than at the onset of constric on. Such measurements overlook the possibility that increased levels of some proteins can change the constric on period in addi on to ming for the onset of constric on, as we observe for FtsZ (Supplementary Fig. 6)
and FtsA (Supplementary Fig. 17c-f). By addressing these limita ons, our measurements presented here show that FtsZ is rate-limi ng for cell division at moderately fast growth condi ons, whereas FtsN and FtsA are not.
While the rate-limi ng role of FtsZ in faster growth rates is expected based on earlier works 44,53 , the finding that FtsN is not rate-limi ng refutes the idea that it is the trigger protein. This no on does not mean that FtsN is not needed/essen al for the onset of constric on. Based on the terminology proposed earlier 43 , FtsN is a secondary rather than a primary cell cycle regulator. Clearly, the deple on of FtsN leads to cessa on of cell division. However, it is present in the cell in excess concentra on and ready to be incorporated into the divisome complex early on in an FtsA* background as was demonstrated earlier 9 .
The results from this earlier work, thus, showed that FtsN is not sequestered away by some yet-to-beiden fied protein interac ons in earlier stages of the cell cycle or undergoing some post-transla onal modifica ons before the onset of constric on. Instead, there is some other change in the upstream complex that needs to occur before FtsN can bind to the complex. Rather than being a trigger to the onset of constric on, the binding of FtsN to the divisome complex appears to be a consequence of some other event occurring before FtsN binds to FtsA.
What could this event be? Our data indicates that increase in FtsZ numbers in the cell and in the Z-ring drives this transi on. We used a previously published FtsZ polymeriza on model 54 to understand what effect an increase in FtsZ numbers and concentra on has on FtsZ protofilaments. Based on modeling, the excess FtsZ leads to an increased number of FtsZ protofilaments (Supplementary Fig. 19). The increase in filament number is approximately propor onal to the increase in FtsZ concentra on. At the same me, the increase in concentra on changes the filament length only weakly. More filaments of approximately the same length can be expected to lead to elevated filament bundling. Based on these arguments, we can infer that FtsZ protofilament bundling is needed for the onset of constric on.
There are several possibili es of what effect FtsZ protofilament bundling may have. A high local concentra on of FtsZ protofilaments due to bundling may cause a small inward bending of the plasma membrane, which may be needed to ini ate septal pep doglycan synthesis. The bending would be mediated by FtsA and ZipA. FtsA might have a dominant effect over ZipA because of its shorter disordered linker, which would bear a majority of the load from bending intrinsically curved FtsZ protofilaments 55 . It remains, however, unclear how the excess of FtsA could hinder and the excess of FtsA* mediate the force transduc on. Furthermore, the magnitude of the bending may not be significant in vivo, where the turgor pressure could oppose membrane deforma ons.
Alterna vely, FtsZ protofilament bundling can enforce a conforma onal change in FtsA, which in turn ac vates septal pep doglycan synthesis. Recent data indicate that for the la er to occur, FtsA an parallel filaments are needed 20 . The same work found that the transi on to an parallel filaments can be induced by adding high concentra ons of FtsN N-terminal cytoplasmic tail to the reac on mixture. Our data indicate that FtsN is not rate-limi ng in vivo, while FtsZ is. Accordingly, we propose that the transi on to FtsA an parallel conforma on is driven by FtsZ but not by FtsN.
In vivo measurements indicate that FtsA an parallel filaments are not thermodynamically favored compared to arcs and minirings when only FtsA alone is present in the reac on mixture 20,30 . We postulate that for the forma on of a FtsA an parallel filament, FtsZ protofilaments need to form at least a local doublet to nucleate FtsA an parallel filaments (Fig. 5a). A straight doublet of FtsZ protofilaments may force monomers and curved FtsA arcs to a straight (an parallel) filament conforma on. In this conforma on, 1:1 stoichiometry between FtsZ and FtsA locally holds where every C-terminal tail of FtsZ is bound to FtsA.
Based on the proposed model, these FtsZ C-terminal connec ons to FtsA drive the FtsA an parallel filament forma on. However, FtsZ protofilament doublets need to be parallel to stay together during treadmilling while FtsA oligomers are an parallel. This appears not to be a contradic on. We expect the free energy difference of FtsZ binding to the FtsA parallel strand compared to the an parallel strand to be minimal because FtsZ has a long and flexible C-terminal linker. Once FtsA an parallel filament nucleates, it is further stabilized by binding FtsN to it. The nuclea on and an parallel filament forma on can also be driven by FtsN alone without FtsZ doublets and bundles but at much higher concentra ons of FtsN than present in cells in vivo (Fig. 5b). The proposed mechanism works as if the arrival of FtsN to the divisome triggers the onset of constric on even though the actual mechanism is the conforma onal switch of FtsA induced by FtsZ protofilament bundling. The proposed mechanism does not contradict recent singlemolecule tracking data where some frac on of FtsBQL and FstIW complexes were found to move together with treadmilling FtsZ protofilaments 21,23 . These complexes can bind to mostly monomeric FtsA and follow treadmilling FtsZ protofilaments by diffusion and capture 25 . Furthermore, FtsZ doublets together with FtsA doublets have been observed in vitro experiments 56 (Fig. 2c in the reference) and can also be inferred from a different study that used an amphipathic helix dele on mutant of FtsA 57 .
Alterna vely, one could consider a mechanism where the onset of constric on is triggered by the transi on of FtsA minirings to its an parallel filament conforma on (Supplementary Fig. 20) 1 . The only difference between the two mechanisms is the ini al polymeriza on state and conforma on of FtsA (monomers and FtsA arcs vs minirings). FtsA minirings can be expected to be inhibitory for the onset of constric on because of the occlusion of the FtsW binding interface in this conforma on of FtsA 58 . If FtsA minirings were already present in cells in the na ve expression level of FtsA, then we would expect a con nuous increase in cell length as FtsA concentra on increases and more and more FtsA minirings form that are not competent for recrui ng downstream components. Instead, our data show an inhibitory effect arising from FtsA upregula on only at larger than 1.6x overexpression levels (Fig. 4f). We interpret the onset of inhibitory effects as a threshold for FtsA miniring forma on. Consistent with this idea, in vitro measurements have also shown a well-defined threshold for the FtsA miniring forma on as the concentra on of FtsA increases 27,30 .
FtsA* is defec ve in forming minirings 30 , and it was observed to transform more readily to an parallel filament conforma on in vivo in the presence of FtsN 20 . Expression of FtsA* could accelerate the onset of constric on, as observed in our measurements (Fig. 4h), because it prevents short FtsA arcs from forming, and this facilitates the nuclea on of FtsA an parallel filaments. So, its effect is similar to the one we observe in FtsZ upregulated condi ons (Supplementary Fig. 18e-h). Within this picture, both FtsA* and FtsZ overexpression facilitate the forma on of FtsA an parallel filaments. FtsA* achieves this by shortening FtsA oligomers and thereby lowering the ac va on barrier for nuclea on of FtsA an parallel filaments.
Altogether, our data is consistent with the model where an increase of FtsZ numbers in the cell cycle is one of the driving mechanisms for the onset of constric on at faster growth rates. The possible molecular pathway, which is consistent with our and other published data, involves the forma on of FtsZ bundles (doublets), which drive FtsA from a monomer and short arc form to an an parallel filament form. FtsA an parallel filament form is competent in the recruitment of FtsN, which ac vates the core divisome complex and starts the onset of constric on.
Although the exis ng data is consistent with the proposed model (Fig. 5a), alterna ve explana ons cannot be ruled out. To validate the model in Fig. 5a further, the existence of FtsZ protofilament doublets and bundles needs a more thorough in vivo verifica on. Also, in vitro measurements assessing the role of FtsZ protofilaments on the assembly of FtsA an parallel filaments would be valuable. Finally, the ques on also remains on how the core divisome complex, consis ng of FtsIW, FtsBQL, and FtsK, is exactly linked to FtsA an parallel filaments.
All E. coli strains used in the reported experiments are deriva ves of K12 BW27783 obtained from the Yale Coli Gene c Stock Center (CGSC#: 12119). Informa on on all strains and plasmids are listed in Supplementary Tables 1 and 2, respec vely. Oligonucleo de informa on is given in Supplementary Table 3.
For FtsZ and FtsN overexpression measurements, we constructed three strains: 1) the strain of interest (SOI) that overexpressed unlabeled gene of interest in addi on to the na ve one, 2) the Reporter strain that expresses fluorescent fusion protein instead of the gene of interest from the same genomic locus, 3) the reference strain that expresses fluorescent fusion to the gene of interest from its endogenous locus.
FtsZ under the control of an isopropyl-β-D-thiogalactoside (IPTG) inducible Ptac promoter was constructed.
Briefly, FtsZ was amplified from plasmid JW0093 3 using primers PR200 and PR201. The Ribosome Binding Sequence (RBS, TAGAGAAAGAGGAGAAATACTAG) was introduced in part of the forward primer in front of the sZ sequence. The resul ng insert (xbaI_RBS_ sZ_hindIII) was cloned into vector pEXT22 59 using restric on enzymes XbaI and HindIII. The same approach was also used for the Reporter plasmid expressing mNeonGreen (mNG) instead of sZ. In this case, mNG was amplified from plasmid pJM21 (Männik lab) using primers PR202 and PR203. The resul ng insert (xbaI_RBS_mNG_hindIII) was ligated into pEXT22 using restric on enzymes XbaI and HindIII and transformed into DH5α competent cells (Thermo Scien fic). A er verifica on by restric on analysis and DNA sequencing, the plasmids were transformed into the BW27783 strain, yielding strains JM237 (FtsZ expressing) and JM228 (mNG Reporter).
To obtain low-level FtsZ overexpression SOI (JM252) and corresponding Reporter mNG expressing strain (JM250), the DNA casse e of the lacI q -p Tac -sZ-aph from pEXT22-FtsZ was introduced into the λa achment (a B) site by λ-Red engineering 60 . For chromosome inser on, the lacI q -p Tac -sZ-aph casse e was amplified from plasmid pEXT22-FtsZ using primers (PR206/ PR207), each composed of a 42 (44)-bp sequence at the 5' end homologous to the a B region. The resul ng PCR product was treated with DpnI (NEB), gel purified using GeneJET Gel Extrac on and DNA Cleanup Micro Kit (Thermo Scien fic), and then electroporated into a JM217 strain containing pSIM5 60 that encodes λ-Red proteins. Kanamycin-resistant colonies were verified by using colony PCR with primers PR210 and PR211 (or PR212), followed by direct sequencing. The lacI q -p Tac -sZ-aph allele was then transduced from JM246 into BW27783 by P1 transduc on to generate strain JM252. In parallel, the same procedures were conducted to make the Reporter strain expressing mNG from the a B locus. Finally, the lacI q -p Tac -mNG-aph allele was transduced from JM248 into BW27783 to generate strain JM250. The reference strain (JM147) expresses endogenous FtsZmNG. The same reference strain was also used in the above-described experiments with pEXT22-FtsZ.
To construct a strain JM276 expressing the lacI q -p Tac -sZmNG-aph from the -a achment site, a similar approach to that described for the unlabeled FtsZ strain (JM252) was used, with the excep on that the sZmNG sequence was amplified from the HE1 strain expressing endogenous FtsZ sandwich fusion to fluorescent mNG (FtsZmNG) 46 . The construct was recombineered to WT strain, resul ng in strain JM261, and then transduced from JM261 into HE1, resul ng in strain JM276. To obtain a strain JM275, a lacI q -p Tac -sZ-aph allele in the -a achment site from the JM252 strain was transduced into the HE1 strain.
Strains for FtsN overexpression measurements. For FtsN over-expression strains (JM200, JM230), a plasmid expressing Ypet-FtsN (JM200) and unlabeled FtsN (JM230) under the control of an IPTG inducible weakened P trc promoter was constructed. Ypet-sN was amplified from the gDNA of the STK13 strain 11 using primers PR204 and PR205. The resul ng insert (ecoRI_RBS_ypet-sN_hindIII) was cloned into vector pDSW210 (JM149) using restric on enzymes EcoRI and HindIII. For unlabeled FtsN expression, sN was amplified from plasmid pDSW210-Ypet-FtsN using primers PR213 and PR205. The resul ng insert (xmaI_ sN_hindIII) was cloned into pDSW210-Ypet-FtsN (JM230) using restric on enzymes XmaI and HindIII. Also, the Reporter strain expressing plasmid pDSW210-Ypet was constructed in a similar way. In this case, ypet was amplified from pDSW210-Ypet-FtsN using primers PR204 and PR214. The resul ng insert (ecoRI_RBS_ypet_hindIII) was cloned into pDSW210-Ypet-FtsN (JM200) using restric on enzymes EcoRI and HindIII. To be able to compare expression levels of labeled and unlabeled FtsN strains, the same sequence, including RBS, was retained in front of the ypet sequence in pDSW210-Ypet (JM241), in front of sN expressed from pDSW210-FtsN (JM230), in front of ypet-sN expressed from pDSW210-Ypet-FtsN (JM200) as it is in upstream of na ve ypet-FtsN in strain STK13.
For low-level overexpression of FtsN and Ypet-FtsN, the DNA casse e sequences from respec ve plasmid constructs were inserted into the a B site by λ-Red engineering as described above for the sZ gene.
Briefly, the lacI q -p Trc -sN-bla and lacI q -p Trc -ypet-sN-bla casse e was amplified from a template plasmid pJM230 or pJM200, respec vely, using primers (PR208/ PR209) and electroporated into JM217 strain with pSIM5 plasmid. Ampicillin-resistant colonies were verified by colony PCR with primer pair PR210/PR211, followed by direct sequencing. In the final step, the resul ng alleles were transferred to BW27783 gene c background by P1 transduc on genera ng strains JM235 (inducible unlabeled FtsN at the a B site and endogenous mCherry-DnaN) and JM222 (inducible Ypet-FtsN at the a B site). Addi onally, the lacI q -p Trcypet-sN-bla allele was transferred to the STK13 expressing endogenous Ypet-FtsN and mCherry-DnaN, resul ng in the JM223 strain.
Strains for FtsA and FtsA* (FtsA R286W ) overexpression measurements. Plasmids expressing sA (pDSW210-sA, also known as pSEB306+) and sA* (pDSW210-sA * , also known as pSEB306*+) under an IPTG inducible promoter were transformed into BW27783 genera ng strains JM242 and JM243, respec vely. The strain JM149 containing pDSW210-GFP expressed GFP under an IPTG inducible promoter and was used as the Reporter. These three plasmids were described previously 61 . These upregula on measurements lacked reference strain because of an absence of genomically integrated fully func onal FtsA. Instead, Western blo ng was used to determine the final 𝐹𝑡𝑠𝐴 for 100 M IPTG induc on 9,61 for both FtsA (2.39x) and FtsA* (2.43x). The corresponding calibra on factor was also used to quan fy the expression level of FtsA in low overexpression condi ons (1.43x), where 30 M IPTG induc on was used.
For E. coli strain construc on, the cells were grown in lysogeny broth (LB) and appropriate selec ve an bio cs.
The new bacterial strains first described in this work are available from the corresponding author upon reasonable request.
For me-lapse imaging in microfluidic devices, the cells were cultured in M9 minimal media supplemented with 2 mM magnesium sulfate, 0.5% glucose as the carbon source, 0.5% casamino acids (CAS), and 1x trace metals mixture (Tre) at 28°C. In measurement where alanine was used as a carbon source, M9 minimal media was supplemented with 0.5% alanine (Millipore Sigma, MO) and 1x Tre. When appropriate, the medium was supplemented with 100 μg/ml ampicillin (Amp) or 40 μg/ml kanamycin (Kan). Amp and Kan concentra ons were reduced to 20 μg/ml when cells carried bla or aph integrated into the chromosome. For induc on, IPTG (30M, 100 M, 500 M, or 1 mM) was included in the media.
The strains were streaked on M9 minimal media agar plates supplemented with magnesium sulfate, glucose, CAS, Tre, and appropriate selec ve an bio cs. For the microscopy experiment, a colony from a fresh plate was inoculated into 3 ml of M9 minimal salt media supplemented with carbon source and addi ves described above. 40 µg/ml of Kan was added to grow strains JM147, JM228, and JM237. 100 µg/ml of Amp to grow strains JM149, JM230, JM241, JM242 and JM243. The cells were grown to an OD 600 of ~0.1 in a liquid medium and then concentrated ~100x by centrifuga on in the presence of 0.075 µg/ml of BSA (Bovine Serum Albumin; Millipore Sigma, MO) to minimize clumping of the cells. For the overexpression experiments, three strains -strain of interest (SOI), Reporter, and Reference were prepared the same way, mixed thoroughly in the Eppendorf tube before loading to PDMS (polydimethylsiloxane)based mother machine microfluidic device. The la er were prepared following a previously described procedure 62 . The concentrated mix of three strains was pipe ed onto the main flow channel of the mother machine device to populate the dead-end channels of the device for one hour. Next, a 10-ml syringe (Becton Dickinson, Fisher Scien fic) was prepared with fresh M9 growth medium with the carbon source, addi ves, BSA (0.075 µg/ml), and appropriate an bio cs when needed and mounted on NE-1000 Syringe Pump (New Era Pump Systems, NY). The tubing was connected to the device, and the flow of fresh M9 medium started and was kept at 6 µl/min during the en re experiment. The cells were le to grow in channels overnight (at least 14 hr) to ensure steady-state growth. Only the cells that are daughters of the mother cell (the cell at the end of the channel) will remain in the channel a er this period. This procedure thus ensures that cells in each channel are from only a single strain when the imaging starts. The next morning, two 10-ml syringes were prepared with fresh growth medium (to one syringe inducer IPTG was added) and mounted on separate NE-1000 Syringe Pumps. A T-junc on was formed with three pieces of tubing and a T-connector. Before applying IPTG to induce the expression of the gene of interest ( sZ, sN, sA or sA*) and the Reporter (mNeonGreen, Ypet or Gfp) from the extra copy at the a B site (or from the plasmid), cells were imaged in regular M9 media. A er 10 hours of imaging, the first pump with the regular media was turned off, and the second syringe pump containing regular media with IPTG was turned on without interrup ng imaging using a custom-made LabVIEW program. Altogether, cells were imaged for 22-26 hrs. For a list of all SOI, Reference, and Reporter strains and inducer IPTG concentra ons used in experiments see Supplementary Table 4.
A Nikon Ti-E inverted fluorescence microscope (Nikon Instruments, Japan) with a 100X NA 1.40 oil immersion phase-contrast objec ve (Nikon Instruments, Japan) was used to image the bacteria. Images were captured on an iXon DU897 EMCCD camera (Andor Technology, Ireland) and recorded using NIS-Elements so ware (Nikon Instruments, Japan). Fluorophores were excited by a 200W Hg lamp through ND4 and ND8 neutral density filters. Chroma 41001 and 41004 filter cubes (Chroma Technology Corp., VT)
were used to record mNeonGreen/Ypet and mCherry images, respec vely. A motorized stage (Prior Scien fic Inc., MA) and a Nikon Perfect Focus® system were u lized throughout me-lapse imaging. Images in M9 glucose-cas were obtained at 3 min frame rate. The typical exposure mes were 400 ms at an EM gain of 200 for mNeonGreen/Ypet and 400 ms without EM gain for the phase images. The mCherry signal was recorded before the FtsN upregula on experiment to dis nguish between strains JM235, STK13, and JM222 (expose me 250 ms at EM gain 200). mCherry signal was not recorded during the FtsN upregula on measurements.
MATLAB, along with the Image Analysis Toolbox and DipImage Toolbox (http://www.diplib.org/) and Python 3.11.4 with torch and torchvision packages (https://pytorch.org/) were used for image analysis. In all analyses of time-lapse recordings, corrections to subpixel shifts between different frames were applied first. These shifts were determined by correlating phase-contrast images in adjacent frames. Individual channel images were then cropped. A convolution neural network, referred to as the Omnipose 63 , was used for cell segmentation. The network was first trained on images obtained from the experimental setup used in this work. The resulting cell masks were then assembled into cell lineages using a custom MATLAB script. The same script also calculated the cell lengths based on these cell masks 64 .
To determine the induced protein concentrations, total fluorescence intensity from fluorescent fusion proteins of the Reporter and the Reference strains were determined as a function of time from cell images. The same fluorescent fusion (either mNeonGreen or Ypet) was used in both strains. To calculate the total intensity, the pixel values from 11 pixels (1.2 µm) wide band around the cell centerline were summed. This band is slightly wider than the cell (about 0.8 µm). The intensity was then normalized per pixel value. The same normalized intensity was also calculated for the unlabeled SOI, and the average value from the cell population from SOI was subtracted from the normalized intensities from the Reporter and the Reference strain populations at each binned timepoint. The per pixel normalized and backgroundcorrected intensity from the Reporter strain was then divided by the per pixel normalized and backgroundcorrected intensity from the Reference strain. Since the fluorescence from the Reference did not significantly vary in time, a single global value of the per pixel normalized and background-corrected intensity from the Reference strain was used for division. The resulting quantity is referred to as the Normalized Reporter Signal and is plotted in Fig. 1, 2a, 3a, 3d, 4a and 4g in the main Text. However, this quantity reflects the induced concentration of the mature fluorescent fusion protein in the Reporter strain, not the concentration of the total fluorescent fusion proteins in the Reporter. To determine this total concentration, we fitted the data in these plots to a previously described model 7 . The model has an analytic solution for the normalized mature protein concentration in the Reporter as a function of time:
where 𝑡 is the time of the induction, 𝑋 , is the concentration before induction including the leakage, Δ 𝑋 , is the increase of the normalized concentration as a result of induction, 𝜇 is the population-average growth rate, and 𝑘 is the maturation rate of the fluorescent protein. 𝑋 stands for FtsZ and FtsN. The solution before induction is 𝑋 , 𝑡 𝑋 , 𝑡 𝑡 . The maturation rate in these growth conditions (glucose-CAS medium in 28 °C) for mNeonGreen was determined to be 𝑘 0.029 min -1 previously 7 . For Ypet we used the same chloramphenicol treatment procedure as in 7,65 to find 𝑘 0.049 min -1 . We calculated the population average growth rate as 𝜇 𝑙𝑛 2 /𝑇 using 𝑇 value before induction. The above expression for 𝑋 Since the Reporter expressed the fluorescent reporter exactly from the same locus (the same promoter and ribosome binding site), the total fluorescent protein concentration can be taken to be equal to the total protein of interest concentration in the cells. This holds under the assumption that the protein of interest is not degraded. While FtsZ has significant degradation at lower growth rates by ClpXP protease, the degradation was undetectable in glucose-CAS medium 7 , which is used in this work.
There is no reference strain in FtsA and FtsA* upregulation measurements due to the lack of sufficiently 4.
The signal from the phase contrast images was used to determine the onset of constriction. The intensity line profiles along the long axes of the cell were averaged first, as described before 9 . The program then searched for the local maximum in this profile near the cell middle. The constriction timing was chosen as the earliest frame when the minimum was present, with an additional condition that this minimum persisted for at least two out of three measurement frames until the cell divided.
The mings for the Z-ring forma on were determined using fully automated analysis. To this end, the intensity line profiles from each frame of FtsZmNG signal were fi ed to a Gaussian. If the width of the fi ed peak (FWHM) of the Gaussian was between 200 and 1000 nm, and the peak was not more than 10% off from the cell center in terms of cell length, then this fi ng qualified as an accumula on. The ming for the first qualifying accumula on in the cell cycle determined ming 𝑇𝑧, 1. To determine the ming for the persistent Z-ring 𝑇𝑧, 𝑝𝑒𝑟 the accumula ons had to be present from this point onward un l the end of the cell cycle, but single frame misses were allowed. To find the number of FtsZ in the Z-ring (as in Fig. 2i, and Supplementary Fig. 11a-d), the integrated intensity from the Gaussian was calculated. Although the number of FtsZ in the Z-ring is in arbitrary units, these units are the same as those used for the total number of FtsZ. To find the excess number of FtsZ (as in Supplementary Fig. 11e-h and Fig. 16c) and FtsN molecules in the cell middle (as in Fig. 16a), integrated fluorescent intensity form a 0.75 µm wide band (7 pixels wide) centered at the midcell was calculated. From this integrated intensity, a cell background intensity was subtracted. The background intensity for subtrac on was also integrated from a 0.75 µm wide band (7 pixels wide). The la er band was centered at the ¼ posi on from the old pole of the cell. The non-fi ng-based and fi ng-based methods gave comparable results when a detectable Z-ring was present.
To independently verify the final normalized concentrations from the fluorescence-based measurements (the final 𝑋 ), we also determined these concentrations by Western blotting (Supplementary Fig. 1).
For the Western blotting of FtsZ, overnight cultures of JM252, JM147 and BW27783 cells were diluted to an OD600 of 0.005 in fresh M9 glucose-CAS medium and grown at 28℃ for about 5 hrs until reaching an OD600 of 0.04-0.05. The cultures were then diluted back to an OD600 of 0.005 in M9 glucose-CAS and divided into triplicate sets. To one set of JM252 cells, 500 µM of IPTG (Millipore Sigma, MO) was added.
Cells grown in the glucose-CAS medium were collected after 7 hours of induction, corresponding to an The collected cells were resuspended in an SDS sample buffer, the amount of which was adjusted according to the cell's OD, and boiled for 10 minutes before being loaded on the SDS-PAGE gel for analysis.
Western blo ng and detec on of FtsN were performed as described above, except for the primary an bodies. For FtsN detec on, 1:350 dilu on of the an -FtsN an serum (UK43; Lutkenhaus lab) in Odyssey blocking buffer was used.
The Western blot analysis for FtsA is from an earlier work 9 as the same extra copy construct and induc on was used in measurements here. Western blo ng and detec on of FtsA were performed as described above, except for the primary an bodies for which an an -FtsA serum was used at a final concentra on of 1:750 (UK54, Lutkenhaus lab).
To analyze the Western blot images, we first acquired intensity line profiles from each lane using ImageJ.
The line profiles had the same width for a given image and encompassed approximately the en re band.
To obtain the integrated intensi es from the bands, we fi ed the line profiles to one or two Gaussians with a background term in Origin Pro 2016. Two Gaussians were used to fit the FtsZ and FtsA signals where spurious bands were close to the band from the protein of interest (POI). The three measurements were then averaged and std calculated. The signal was then further normalized using the value obtained from the WT strain. For the final variance of the POI, the squares of the rela ve errors of POI and WT strains were summed. The error bar for POI is the square root of this final variance.
To further verify that the cell numbers contribu ng to each lane were the same, we also acquired reference bands from each Western blot (indicated by an asterisk in Supplementary Fig. 1). We chose the reference bands as high molecular weight bands, which could not have originated from the POI. The integrated intensi es from the reference band were acquired as described above for the POI bands. We also quan fied the protein abundances by dividing the signal from each lane from POI to that of the Reference.
The resul ng abundances were effec vely the same as when the reference bands were not used, but error bars were somewhat higher.
Western blot analysis shows about 15% lower overexpression levels for FtsN and 27% lower for FtsZ than the fluorescence-based measurements (Supplementary Table 5). This could be due to the degrada on of FtsZ and FtsN in the cells, unlike the fluorescent reporter, which is not expected to be degraded. Indeed, for FtsZ 10-50% degrada on during the cell cycle has been reported before 7,66 . The la er number depends on the growth rate of the cells being higher at lower growth rates 63 . On the other hand, the rela ve error for the Western blo ng results is about 30% for the final FtsZ and 25% for the final FtsN (Supplementary Table 5). Accoun ng for these errors, the difference between Western blot and fluorescence-based measurements is neglected.
We compare the experimental data to the concurrent processes model where the slowest of the two limi ng processes controls the start of septum forma on 36 rather than cell division 41,42 . Based on an earlier report 67 , we assume that the cell size (length) grows exponen ally with rate 𝜆 before the septum forma on starts. The cells grow with a different growth rate, 𝜆 , a er the onset of constric on. 𝜆 and 𝜆 is sampled from a normal distribu on with the mean value determined from experimental data as
⟨ ⟩ = 0.0126 min -1 . ⟨ ⟩ denotes the mean and the experimental data is from the 1.96x FtsZ overexpression experiment (Fig. 2a-c). The coefficient of varia on (CV) is fixed to be 0.
2 consistent with the CV observed for growth rate. The two limi ng processes are: 1. Inhibitory process related to DNA replica on that blocks the onset of constric on for a me 𝑇𝑖𝑐 that is measured from the ini a on of DNA replica on. 𝑇𝑖𝑐 is drawn from a normal distribu on with mean ⟨𝑇𝑖𝑐⟩ and CV 0.2 which is consistent with CV values of me variables. 2. FtsZ accumula on to a threshold amount. The amount of FtsZ (number) increases at a rate propor onal to the cell size i.e., 𝑠𝐿. The produc on rate of FtsZ, 𝑠, is fixed at the start of each cell cycle and is assumed to be normally distributed with mean ⟨𝑠⟩ 1+𝑠 (in units of ⟨𝜆 ⟩) and CV 0.2. 𝑠 is the leakage in FtsZ produc on before FtsZ is overexpressed. The upshi in FtsZ produc on is modeled as a step func on with the mean produc on rate increasing from 1+𝑠 to 1+𝑠 +𝑓 instantaneously. The factor 𝑓 is determined using the steady-state normalized concentra on of fluorescent protein in the Reporter strain. FtsZ accumulates to a threshold value drawn from a normal distribu on with a mean 𝑁 * and CV = 0.2. The values of the two model parameters ⟨𝑇𝑖𝑐⟩ and 𝑁 * are determined to be such that the average lengths at constric on before and a er 1.96x FtsZ overexpression match between simula ons and experiments. For a range of values of 𝑁 * and ⟨𝑇𝑖𝑐⟩, we find the value of the cost func on 𝐶 , , 1 , , 1 where 𝐿𝑐 , and 𝐿𝑐 , are the steady-state values of 𝐿𝑐 before and a er overexpression obtained from simula ons, respec vely. 𝐿𝑐 , and 𝐿𝑐 , are the steady state values of 𝐿𝑐 obtained from experiments. The cost func on has a minimum for ⟨𝑇𝑖𝑐⟩ 75.6 min and 𝑁 * 286 (Supplementary Fig. 21).
To simulate the DNA replica on cycle and constric on processes, we use previously specified models. The ini a on of DNA replica on is determined by an adder per origin model 31,34 where cells added a constant length increment per origin Δ from one ini a on of DNA replica on to the next. Δ is drawn from a normal distribu on with mean ⟨Δ ⟩ = 0.6 𝜇𝑚 and CV = 0.1 determined using experimental data in previous studies 11 . The cell division happens a er a me Δ𝑇𝑠 from the onset of constric on 68 . Δ𝑇𝑠 is normally distributed with a mean determined from experiments and is equal to ⟨𝑇𝑑 𝑇𝑐⟩ = 18.3 min and CV is fixed to be 0.2. The value of Δ𝑇𝑠 changes slightly (by 1.5 min) a er FtsZ overexpression (Supplementary Fig. 6). This is included as a step func on in ⟨Δ𝑇𝑠⟩ value. The cell divides on average symmetrically but with a noise in division ra o. The standard devia on in the division ra o is 0.03 69 .
The upshift in FtsZ production is obtained by monitoring the concentration of a mature reporter protein.
The reporter protein exists in two states-a mature state which is observed and an unmatured state. The protein goes from an unmatured to a mature state at a rate 𝑘 = 0.029 min -1 in FtsZ upregulation measurements. The total amount of the reporter protein is a proxy for the FtsZ amount. In the simulations, the amount of mature protein (𝑁 ) at each time step is 𝑘 𝑁 𝑁 , where is 𝑁 𝑁 is the amount of immature protein. Upon division, each daughter cell gets exactly half of the matured and total proteins.
We compared the results above to another model of cell division (Supplementary Fig. 12) where the two limi ng processes controlling it were: 1. FtsZ accumula on to a threshold (like in the previous model) and 2. another cell division-related protein accumula ng to a threshold amount (instead of the replica onrelated process being limi ng). The threshold amount was chosen by minimizing the cost func on 𝐶 above, keeping the rest of the parameters (including the FtsZ threshold 𝑁 * ) fixed. We assumed the same rela ve noise level in the threshold values for the other cell division-related protein as for FtsZ (CV = 0.2).
The minimiza on of the cost func on resulted in the threshold of 251 for the other division-related protein.
Comparing the concurrent processes model to FtsA upregula on measurements, we assumed, based on , ) for FtsA 1.6x and a constant value, 𝑁 𝑁 * , for FtsA 1.6x. Here, 𝑁 * 286 as used in simula ons of FtsZ upregula on. We adjust the coefficient of propor onality, 𝛼, manually to 0.07 (7%) to fit the 𝐿𝑐 vs me curve in Fig. 4d. All other parameters of the model are kept the same as in Fig. 2. Instead of directly simula ng the increase in FtsA , we used the formula from the fluorescence induc on model FtsA 1 FtsA , 1 1 exp 𝜇𝑡 as the la er approach matches well the corresponding average curve of the stochas c simula ons.
The custom MATLAB scripts used to analyze the data are available from Zenodo h ps://doi.org/10.5281/zenodo.13988793 64 . The codes to create concurrent processes modeling data are available also from Zenodo: h ps://doi.org/10.5281/zenodo.13987797 70 . constric on versus the normalized concentra on of FtsZ. The red points show data from SOI, and the green point corresponds to the Reporter strain. The dashed line represents the threshold accumula on model. The number of analyzed cells in panels d-g is N=7817 for the SOI and N=4948 for the Reporter strain. All error bars correspond to s.e.m. Source data are provided as a Source Data file.