MinC oscillates in rotational or symmetric patterns in branched cells.
To evaluate the predictive and explanatory powers of current models of Min action and division control, it was necessary to examine the behavior of Min proteins in non-rod-shaped cells. E. coli
AV23-1 (with penicillin binding proteins [PBPs] 5 and 7 deleted) grows as branched and aberrantly shaped cells (39
) and provided a suitable suite of nonuniform shapes in which to observe the behaviors of these proteins. Especially useful were those cells that exhibited branches of different lengths. In these cells, four modes of Min oscillations were possible (Fig. ). The Min proteins could rotate clockwise or counterclockwise from branch to branch (Fig. ), back and forth between two branches (Fig. ), symmetrically between two halves of the cell (Fig. ), or randomly among any of the branches (Fig. ). To determine which of these oscillatory modes predominated, a GFP-MinC fusion protein encoded on plasmid pYLS49-2 was expressed in E. coli
AV23-1 and its behavior over time was observed in cells whose shapes were significantly different from that of normal uniform rods. Of these, we analyzed only those cells in which there were two or more complete cycles of oscillation that could be captured before fluorescence bleaching reduced the signal to an unacceptable level.
FIG. 1. Potential Min protein oscillation patterns in branched E. coli cells. (A) Clockwise and counterclockwise oscillations. The red and green arrows denote completely independent Min motions. (B) Back-and-forth movement between two branches. Min proteins proceed (more ...)
In branched cells having three or more distinct poles, GFP-MinC moved around the cells in one of two patterns: either MinC rotated from branch to branch in a repetitive cycle that progressed clockwise (Fig. ) or counterclockwise (Fig. ) or MinC oscillated symmetrically from one half of the cell to the other (Fig. ). Out of 24 cells that exhibited repeated oscillatory cycles, in 67% (16
) MinC moved either clockwise or counterclockwise and in 33% (8
) MinC oscillated symmetrically. In no case did the direction of GFP-MinC reverse itself over the time of observation (4 min). That is, once the direction of oscillation was established in a particular cell, MinC movement did not change from clockwise to counterclockwise or vice versa. In addition, GFP-MinC oscillated in the classical manner (moving symmetrically from one end of the cell to the other and dividing the cell into halves) in cells with simple bifurcations of a pole and in a few cells in which the branches formed distinct tubular extensions from the main body (Fig. ). The only discernible trait that determined the pattern of MinC oscillations (clockwise/counterclockwise versus symmetrical) was the length of the branches. Oscillation was symmetrical if two of the visible poles were very close to one another (e.g., in cells with bifurcated poles); otherwise, MinC moved from pole to pole in sequence. In a few cells with symmetrical oscillations, MinC sometimes exhibited a slightly longer “dwell time” at one branch at the bifurcated end of the cell (Fig. ), suggesting that there may be an intermediate stage in which symmetrical oscillations transition to the clockwise or counterclockwise mode.
FIG. 2. GFP-MinC oscillation patterns in abnormally shaped E. coli cells. E. coli strains were transformed with plasmid pYLS49-2, from which GFP-MinC and untagged MinD and MinE were induced by the addition of 10 μM IPTG. Each strain was incubated at 37°C (more ...)
Regarding the motion of Min proteins in branched cells, the clockwise and counterclockwise motions are equivalent because movement between branches is relative to the observer. That is, the observed direction depends on whether the cell landed “face up” or “face down” on the agar surface—in one case the observer would see the Min proteins travel clockwise, and in the other case they would move counterclockwise. In either case, the Min proteins could choose an oscillation direction at random or there might be a rule governing the exact sequence with which the proteins visited each branch. An example of the latter possibility would be if Min movement proceeded directionally from the shortest branch to the middle-size branch and finally to the longest and then back again to the shortest. However, when we measured the lengths of branches among cells exhibiting clockwise or counterclockwise oscillation, there was no correlation of branch length and rotation of Min within the cell. That is, the number of cells with Min oscillations progressing from short to intermediate to long branches was approximately the same as the number of cells in which oscillations moved from long to intermediate to short branches. It appeared, then, that the choice of rotation was either random or, at the very least, not robustly dictated by branch length.
A final possibility was that the observed oscillatory patterns were due to an artifact arising from the mixing of GFP-MinC fusion proteins with the wild-type (nonfused) MinCDE proteins expressed from the chromosome. To rule this out, we observed the oscillation of GFP-MinC in E. coli AV62-1K, from which the chromosomal minCDE genes had been deleted. The same patterns of oscillation were seen in these cells (Fig. ) as in E. coli AV23-1, which expressed wild-type Min proteins from the chromosome (Fig. ). Thus, the fusion proteins were reporting Min oscillations accurately regardless of subunit mixing between the two forms.
MinD mimics the oscillation patterns of MinC.
In normal rod-shaped E. coli
cells, MinD oscillations match those of MinC, although the accumulations are more dispersed (31
). To confirm that MinC and MinD maintained the same relationship in branched cells with multiple poles, we observed the oscillation of GFP-MinD in E. coli
AV23-1 (with PBPs 5 and 7 deleted). As expected, MinD movement mimicked the patterns exhibited by MinC in cells exhibiting two or three cycles of oscillation (Fig. ). In 7 of 12 cases, GFP-MinD rotated from branch to branch in a repetitive cycle that progressed clockwise or counterclockwise in cells having three or more poles (Fig. ), while in the remaining 5 instances, GFP-MinD moved symmetrically from end to end in cells with small bifurcations at one pole (Fig. ). MinD was not as clearly confined to the poles as was MinC (Fig. ). Instead, as MinD moved from pole to pole, the protein extended further toward the middle of the cell, whereas MinC was concentrated strongly at the polar tips (Fig. ). Once again, the patterns were identical in strains with or without wild-type MinCDE proteins expressed from the chromosome (Fig. ). Thus, MinD oscillations consistently followed the behavior of MinC in abnormal cells, as it did in normal rod-shaped cells (not shown).
FIG. 3. GFP-MinD oscillation patterns in abnormally shaped E. coli cells. E. coli strains were transformed with plasmid pFX9, from which GFP-MinD was induced by the addition of 10 μM IPTG, and the cells were treated as described in the legend to Fig. (more ...) MinE oscillates in rotational or symmetric patterns.
The MinE protein helps disassemble the MinCD complex, thereby driving the oscillatory behavior of MinCD in normally shaped cells (31
). Since the motions of MinC and MinD were similar to one another in branched cells, we expected that MinE oscillations would follow the same patterns. To determine if MinE movement paralleled the rotational motions of MinCD, we expressed MinE-YFP in E. coli
AV23-1 and observed how it functioned in abnormally shaped cells.
In cells with long branches of approximately equal lengths, MinE moved around the cells in a clockwise or counterclockwise manner (Fig. ). However, the behavior of MinE-YFP differed somewhat from that of MinCD. Instead of being confined mostly to a single branch, MinE concentrations remained high in two branches simultaneously, with the third branch exhibiting a much lower intensity of MinE. This “low MinE concentration” migrated from branch to branch in a rotational manner (e.g., counterclockwise in Fig. ), while MinE protein was distributed between the other two branches in a manner that followed the cyclical oscillations of MinD. Except for this quantitative difference, the rotational behavior of MinE followed a pathway qualitatively similar to that of MinC and MinD.
FIG. 4. MinE-YFP oscillation patterns in E. coli AV23-1 (with PBPs 5 and 7 deleted). E. coli strains were transformed with plasmid pFX55, from which MinE-YFP was induced by the addition of 10 μM IPTG, and the cells were treated as described in the legend (more ...)
In contrast to the above, in misshapen cells with one or two short branches (in 13 of 13 cases) MinE-YFP oscillated symmetrically from one half of the cell to the other half (Fig. ). The distribution of MinE in these cells was distinguished from the distributions of MinC and MinD in that during the course of its oscillation, MinE-YFP often covered more than half of the cell (Fig. ), whereas MinC and MinD were confined within less than one half of these types of cells. It seemed possible that MinE might not reproduce the motions of MinCD because it moved more slowly than the other two proteins in abnormally shaped cells. If so, then its period of oscillation would be expected to be significantly different. However, each of the Min proteins required approximately 60 to 120 s to complete one oscillation cycle (the time required to return to the starting pole) (not shown). The concordance of these times suggested that the movements of all three Min proteins were coordinated even in oddly shaped cells (8
One other trivial explanation for the discrepancies between the patterns followed by MinE and MinCD could have been that fusing the protein to YFP made MinE behave differently than when MinC and MinD were fused to GFP. Therefore, we examined the oscillations of YFP-MinD and MinE-CFP simultaneously in the same cell. When the two fusion proteins were expressed from plasmid pYLS68 in a cell having one very short branch between two very long ones, both MinD and MinE oscillated in a “back-and-forth” motion with a peak of concentrated MinE lagging behind in the branch just vacated by MinD (Fig. ). These results were consistent with the behavior of each protein when tested individually, indicating that the relative motions of MinE and MinD remained similar in each other's presence and were not artifacts related to the type of fusion protein.
FIG. 5. Oscillation patterns of YFP-MinD and MinE-CFP expressed simultaneously in branched E. coli cells. E. coli strains were transformed with plasmid pYLS68, from which the expression of both YFP-MinD and MinE-CFP was induced by the addition of 10 μM (more ...) Placement of division sites in branched cells.
To determine how cell morphology affected localization of the division plane in aberrantly shaped E. coli cells, we observed individual cells growing on an agar surface by using time-lapse photomicroscopy. In cells having at least three prominent branches (Y shaped), division always occurred near the center of the cell at the junction of these branches, usually via asymmetric invagination of the division furrow near the base of one branch (Fig. ). In addition, successive division events sequentially separated one branch at a time from the original cell (Fig. ). This was especially clear when a single cell could be followed through three or four divisions (Fig. ). In this case, the cell completed its first division at 40 min (at the junction of the three branches), division in a second branch was completed at 68 min, and release of the third branch occurred at 96 min (Fig. ). This sequence of events left a curiously shaped, slightly pinched, rectangular cell whose sides were derived mostly from previous septation events (Fig. , 108 min). This central localization of division sites was not surprising because one would expect septation to occur where the concentration of MinC was at its minimum, and therefore, the observed results were consistent with the pattern of Min protein oscillation.
FIG. 6. Cell division in aberrantly shaped E. coli cells. Overnight cultures of E. coli AV23-1 (with PBPs 5 and 7 deleted) were diluted 1:50 in LB medium and incubated for 1 h at 37°C. A cell suspension was transferred onto the surface of LB agar in a (more ...)
What could not be answered by the above-mentioned approach was how the specific septation sites were chosen so that branches were released one at a time. Since the positioning of FtsZ polymers determines the location of the division site, we followed the time-dependent placement of FtsZ-GFP rings in aberrantly shaped E. coli AV42-2K cells (with PBPs 5 and 7 deleted). Figure presents two typical examples of how FtsZ rings formed in this population. In one case, FtsZ rings began to form at each of two sites near the branch points (Fig. , -min frame). However, soon afterward, the FtsZ ring confined itself to only one of the branches (Fig. , -min frame), and this ring constricted to release the branch as a newborn cell (Fig. , 10- to 20-min frames).
FIG. 7. FtsZ ring assembly in branched and aberrantly shaped E. coli cells. Overnight cultures of E. coli AV42-2K were diluted 1:100 in LB medium containing ampicillin (25 μg/ml). After 30 min of incubation at 37°C, 10 μM IPTG was added (more ...)
Similarly, in a second example, an FtsZ ring formed near the center of a branched cell and division occurred close to the junction of the three branches (Fig. , 0-min frame). An interesting phenomenon was captured in the Y-shaped daughter cell that resulted from this division event. In this cell, two FtsZ rings began to form at the junction of the three branches (Fig. , 30-min frame), but one ring disappeared and left a single Z ring at right angles to one of the branches (Fig. , 36-min frame). Surprisingly, this ring did not persist but “flipped” from one branch to the other (Fig. , 36- and 42-min frames), after which the cell initiated constriction (Fig. , 60-min frame) and completed septation (Fig. , 78-min frame). Finally, the two-branched daughter cell from this second division event formed two FtsZ rings near the branch junction of the original cell (Fig. , 90-min frame). In this case, both rings persisted, but constriction and cell division took place at only one ring at a time. The first FtsZ ring constricted and released the branch as a daughter cell (Fig. , 96-min frame), after which the second FtsZ ring began to constrict (Fig. , 108-min frame), leading to a second division event (Fig. , 114-min frame). This event was consistent with the previous observation that successive divisions released each branch in turn.
The results suggest that MinCD oscillation in branched cells creates a broad MinC-free zone that gives the cell leeway to place FtsZ rings at more than one position. In this centralized area, a single ring may move from one branch to the other before constriction begins. On the other hand, if multiple rings form, one may disappear while the other persists and constricts, or (in larger cells) both may persist with constriction proceeding at each one in turn.
Relative branch lengths determine Min protein dynamics in the reaction-diffusion model.
Mathematical modeling has been useful in mimicking the motions of Min proteins in simple rod-shaped cells and cocci (9
). Specifically, a deterministic numerical reaction-diffusion model accurately reproduces the experimentally observed oscillatory patterns in both wild-type and filamentous rod-shaped cells and cocci (13
). We applied a stochastic version of this model to predict the movement of Min proteins in branched cells to see if this approach could accurately describe the rotational and symmetric oscillatory behaviors in cells having more complicated geometries. As in the study by Kerr et al. (15
), the reaction-diffusion cycles were implemented as stochastic processes with probabilities proportional to their rate constants (13
). We chose as case studies cell geometries that we expected would result in each of the first three oscillatory patterns in Fig. , since these cell types typified the observed behaviors of Min proteins in aberrantly shaped E. coli
cells. The cases fell into three broad categories: (i) cells with three branches that were roughly equal in length and that exhibited clockwise/counterclockwise Min movement (Fig. ), (ii) cells with one long and two short branches that exhibited symmetric movement (Fig. ), and (iii) cells with one short and two long branches that exhibited back-and-forth motion (Fig. ).
FIG. 8. Stochastic simulations of clockwise (I), symmetric (II), and back-and-forth (III) MinD/E oscillations in branched cells. In each of the sections is a cartoon of the shape of the model cell in which the motion of the Min proteins was simulated. In case (more ...)
First, we modeled the movements of MinD and MinE in a cell with three branches of nearly equal lengths (Fig. ). Monte Carlo simulations followed the positions of the five different states of these proteins within the cytoplasm or on the membrane along the length of the virtual cell as time progressed (Fig. ). These data were also used to predict the microscopically visible patterns that would be observed when using fluorescent versions of MinD (Fig. ) or MinE (Fig. ), assuming that the fluorescence intensity from a single molecule has a Gaussian distribution with a width of 200 nm. In this simulation, movement of MinD and MinE from branch to branch progressed in a clockwise direction (Fig. ). (Note that if viewed from the rear, the projected motion would be clockwise, which is consistent with what is observed for real cells, which can land on an agar surface in either of two orientations. More importantly, though, other simulations with the same initial conditions displayed counterclockwise rotations, indicating that noise can play a role in determining the direction of the oscillations.) The majority of MinD proteins start in the longest branch at time zero and migrate in succession to the shortest and middle branches with a pole-to-pole time of about 30 s (Fig. ). This rotational pattern was similar to the MinC and MinD oscillations observed in real cells (Fig. and Fig. , respectively), and as noted, the distribution of MinD was not always completely confined to the poles (Fig. and 8IC at 30 and 90 s).
The physical origin of these oscillations can be understood using the same conceptual framework developed for explaining Min behavior in rod-shaped cells (9
). A linear instability in the coupled reaction-diffusion system has a characteristic wavelength that generates (i) the accumulation of Min proteins at alternating poles in wild-type cells and (ii) a repetitive pattern of Min protein accumulation at sites spaced every 8 to 10 μm along the length of filamentous cells (13
). In the branched cell of Fig. , once an oscillation is initiated by fluctuations in local protein concentrations, the rotational pattern persists, because as MinD moves from pole 1 to pole 2, the residual and relatively high concentration of MinE at the first pole biases MinD to bypass pole 1 and accumulate instead at pole 3. This mechanism is evident in Fig. (t
= 30 s), where MinD is found predominantly in the shortest branch while a high concentration of MinE remains in the longest branch (Fig. , t
= 30 s), effectively blocking the return of MinD to the longest branch and thereby perpetuating the rotational direction of oscillation. Similar situations are visible in Fig. at 60 s and 90 s.
The projected movement of MinD and MinE was different in a virtual cell having two branches of equal length plus a third that was much longer (Fig. ). Here, the majority of MinD proteins began in the long branch (t = 0 s and 30 s), migrated away from this pole to populate both short branches at the opposite end of the cell (t = 60 s), and returned to the pole of the long branch after a total period of about 90 s. Though partitioning of the MinD population into the two short branches was not equal, both received a significant fraction of the MinD proteins. The difference in length between the long and short branches mandates that MinD accumulations in the short branches are disassembled before a new MinD polar zone is completed in the long branch, thereby perpetuating the symmetry of the oscillations. This symmetric pattern was similar to MinD and MinE oscillations observed in real cells (Fig. and , respectively).
Finally, a third pattern of oscillation was observed in simulated cells having two long branches of roughly equal lengths plus a third that was much shorter (Fig. ). In this case, the Min proteins moved alternately between the poles of the two long branches, but with a temporary (very brief) accumulation in the short branch as the proteins traveled to each of the far poles, similar to real cells (Fig. ). In the simulation, MinD and MinE molecules were initially distributed equally between the two long branches, but the system rapidly evolved into the alternating pattern shown. This back-and-forth movement (Fig. ) between the distal poles of a long cell with an intervening short branch is in direct contrast to the “doubled” pattern of oscillations observed in previous experiments using uniformly smooth rod-shaped filaments ~10 μm long. There, in cells with no intervening branch, the Min proteins did not move from one end of the elongated cell to the other. Instead, the oscillation pattern was dramatically different in that the proteins behaved as though the structure consisted of two cells, each approximately one-half the length of the whole. In such elongated cells, the Min proteins accumulated simultaneously at both poles, followed by accumulation at a site near the middle of the cell, after which the Min molecules returned to the two poles, thereby creating parallel oscillations within a single filament (13
). We verified that in simulated rod-shaped cells of the same length, equivalent and symmetrically “doubled” oscillations occurred around the centers of these elongated cells when MinD and MinE were initially distributed equally near the two poles (not shown). These results show that the “doubled” oscillation pattern in a single elongated cell can be broken in a cell possessing an additional branch. In sum, then, the simulations and experimental observations strongly suggest that Min protein oscillations depend on and respond to changes in the geometry of bacterial cells.