Emergent collective alignment gives competitive advantage to longer cells during range expansion

Domain: physics
Published: 2025-12-19
Editorial outcome: major_revision

Abstract
Bacterial competition shapes community architecture, yet a universally conserved determinant remains elusive. We show that cell aspect ratio – a simple morphological feature – confers a competitive advantage. Using growth-based range expansion experiments, we show that longer bacteria conquer the expanding front, even when initially in minority. Using an agent-based model of dividing bacteria, to isolate the effect of aspect ratio, we reveal that the takeover mechanism is collective alignment: groups of locally aligned bacteria form “nematic arms” bridging the central region of the colony to the expanding front. Once at the front, bacteria align parallel to it and block shorter bacteria from access to nutrients and space. We confirm this observation with single-cell experiments and further generalise our findings by introducing a generic continuum model of alignment-dominated competition, explaining both experimental and cell-based model observations. Moreover, we extend our predictions to spherical range expansions and confirm the competitive advantage, even though the effect is less pronounced than in surface-attached colonies. Our results uncover a simple, yet hitherto overlooked, mechanical mechanism determining the outcome of bacterial competition, which is potentially ubiquitous among various bacteria. Current advances in genetic engineering enable aspect ratio tuning as a mechanism with broad implications for biofilm control.

Introduction
Bacteria’s competition for nutrients and territory drives biofilm evolution1–4. The factors determining the outcome of competition among diverse bacterial species have a broad impact on a wide range of pathological5, environmental6, and microbiome interactions7. While motility-related traits8–11 and specific molecular mechanisms12,13 have been identified as potential winning attributes in bacteria.

Morphology is not always conserved from generation to generation, instead bacteria can change shape within a single generation, for example, during the infection of a host organism14 or as a response to shifts in nutritional composition15,16, osmolarity17, and temperature18; allowing them to spread effectively. It has also been found that rod-shaped bacteria dominate the base of a colony, indicating that cell shape is an important determinant of biofilm structure19. However, we still lack the full understanding of if and how cell shape affects competition during range expansion.

In this work, we find the aspect ratio to be a key determinant of competitive advantage. We show through range expansion experiments20, how longer bacteria consistently dominate the colony front. Agent-based modelling reveals that this dominance arises from emergent collective alignment: radially aligned nematic sectors extend from the colony centre to the front, which they overtake by aligning and growing along it. These findings are supported by single-cell resolution experiments and a continuum model of alignment-driven competition. Furthermore, we did spherical range expansions21 and concluded that the supremacy of longer bacteria is retained but weakened in a 3D configuration.

Results
Long bacteria win exclusively – even when outnumbered
We began by mixing two substrains of the non-motile Escherichia coli B: wild-type (WT) with a plasmid coding for green fluorescent protein (GFP) and an mreB mutant (AK) with a smaller aspect ratio (Table 1 and Supplementary Fig. S1) and with a plasmid coding for red fluorescent protein (RFP), see Fig. 1A. The mixture was inoculated on agar (1.5%) and resulted (after incubation) in a colony with three distinct regions from the centre and outwards (Fig. 1B): (i) the “homeland” where both strains were well mixed, (ii) a band thought to arise from the up-concentration of cells on the rim of the inoculation droplet (i.e., “coffee ring”22,23 in Supplementary Fig. S2), followed by (iii) a band where sectors merged. Strikingly, the WT (green) strain won over the shorter AK (magenta) during range expansion (outermost region of iii). We verified that these strains had similar growth rates (Supplementary Fig. S3A) and that takeover was independent of inoculation density (Supplementary Fig. S4). However, we found that the shorter strain had a growth advantage (in respect to the longer) in co-cultures (Supplementary Fig. S3B-C). Thus, WT wins in surface-attached colonies, even though this strain has a fitness disadvantage in liquid cultures.

To measure the strength of WT’s advantage, we assessed the competition outcome for different strain ratios ζ, which we defined as the inoculation density of the longer strain versus the shorter, quantified by optical density (OD600). We varied the ratio to identify the lower ζ-limit for WT to outcompete AK. However, for all tested strain ratios ζ (keeping combined inoculation density fixed), the longer strain (WT) consistently won over the shorter (AK) within the incubation time (20h), see Fig. 1B. The takeover was noticeably slower in the ζ = 0.001 case, where WT sectors (green) spread azimuthally while curving around cone-shaped regions of shorter bacteria (magenta). Due to the difference in cell volume (Table 1), the number of cells in the stationary phase with same OD600 value is ∼1.3 times higher for WT than for AK (Materials and Methods). However, because WT outcompetes AK even for the low strain ratios (ζ ≪ 1), this slight advantage (in numbers) of WT is not enough to explain the competition outcome. Together, these results showed that the longer WT bacteria outcompete the shorter AK strain, even when initially outnumbered.

To explore the robustness of the impact of the aspect ratio, we introduced an additional mreB mutant (AS) with an intermediate aspect ratio (Fig. 1A and Supplementary Fig. S3 and setup competition experiments over 3 days (Supplementary Fig. S5. We kept the colour-coding, such that longer cells expressed GFP (WT or AS) and shorter RFP (AS or AK), and found no systematic dependence on the colour (Supplementary Fig. S6). While the intermediate AS strain lost against the longer WT bacteria, this previously losing AS outcompeted the shorter AK strain. This indicates that the aspect ratio of individual bacteria is the determining factor for the competition outcome in dividing E. coli. To quantify the competitive strength, we segmented and filtered the image stacks to obtain 2D masks reconstituting a connected colony surface, where all pixels were assigned one and only one colour. Behind the expanding colony front, additional cell-layers are formed, so we investigated the cross-sections (Supplementary Fig. S7) to rule out any dramatic changes in the composition of cells along the vertical direction. On this mask, we defined the radial distance r(t), from the homeland boundary (i.e., the ring of high intensity of shorter cells). Then, we measured the strength S(r), defined by the re-scaled occupancy of the longer cell, such that S=1 (S= −1) signified that the longer (shorter) cells fully dominated. Fig. 1C is a heatmap of how ζ controls the strength, S(r), at the radial distance corresponding to the time point t1 = 1.5 days of incubation (Materials and Methods). The quantitative analyses confirmed that WT always wins over AK, even when initially outnumbered by as much as ζ = 0.001 (i.e., one in thousands). For AS/AK and WT/AS combinations, we found few successful formations of sectors of the longer strain for ζ ≤ 0.01, indicating that the outcome is highly stochastic for small ζ (Supplementary Fig. S5); averaging over several colonies resulted in S(r) ≲ 0. However, the sectors with longer bacteria tended to spread azimuthally with increasing r, indicating that they are likely to win the expanding front later on. In other words, the strain of longer aspect ratio could take over, if they succeeded in forming sectors early on (i.e., at small r).

Alignment-induced mechanism gives longer bacteria a mechanical winning advantage
The experimental results suggested cell aspect ratio to be the determinant of the outcome of bacterial competition in the monolayer front. In order to test if this is solely based on the mechanics of bacterial organisation, we simulated the range expansion in a minimal agent-based model (Materials and Methods), where surface adhesion dominates. Bacteria were modelled as non-motile repulsive particles expanding on a 2D surface. The particles grew with the same fixed rate (with stochasticity). We distinguished longer from shorter species by setting the length at division as lL and lS, respectively. By using a constant width of w=1, the aspect ratio (l/w) of these particles were lL and lS. We used an inoculation ratio, ζ = 0.25 (ratio of number of long species over short), such that shorter bacteria were in majority, and placed individual particles (either lL=8 or lS=3.5) randomly in a small region. We then let the cells grow and interact to expand over the 2D surface, as seen in Fig. 2A (Supplementary Movie 1).

After the homeland had reached uniform density and the radial expansion began, sector boundaries between populations are formed. Active forces cause elongated bacteria to align along these sector boundaries, a process known as active anchoring24–27. These interface boundaries orient the elongated bacteria into narrow channels28 along the radial vector, r, which connect the interior (homeland) to the outer rim of the colony, forming conduits through which the longer bacteria can reach the front. This channel-formation resulted in azimuthal spread of sectors of longer bacteria with increasing radial distance from the centre of the inoculation to the expanding front, r. As a result, the longer bacteria are deposited at the front, where they form localized bumps (t > 4 gen. in Fig. 2C and Supplementary Movie 1).

Once in front, they spread out29 and active forces result in a predominant azimuthal alignment (along the front) of the longer bacteria, as observed in Fig. 2B. See Supplementary Information for details on active anchoring. This alignment forms a barrier that suppresses the further expansion of the shorter bacteria. For comparison, we simulate a case in which short cells divide faster (Supplementary Fig. S9), and observe that this barrier does not form in that scenario.

To test the mechanism suggested by the cell-based model and to investigate how populations compete at the individual cell scale, we ran time-lapse experiments with single-cell resolution. E. coli colonies were inoculated from a suspension of WT/AK in equal proportions (ζ=1). We imaged the growth at the colony front over time t, as shown in Fig. 2C (Supplementary Movie 2) and for additional time-lapses (Supplementary Figs. S10, 11, Supplementary Movies 3, 4). Individual bacteria were segmented and their orientation was determined and the angle, θ, to the expanding colony front (i.e., 90∘ to r) in three equidistant regions of r was measured (Fig. 2D). In agreement with the alignment-induced mechanical mechanism suggested by the agent-based model, we found that the winning WT bacteria align along r (inside the colony) or along the expanding colony front, once the cell monolayer becomes confluent (Supplementary Fig. S11). Furthermore, the nematic order parameter, q, which is a measurement of local orientational alignment30, was calculated for every bacterium relative to its 8 closest neighbours, as extensively reported for bacterial monocultures8,31–35. The distribution of q was analysed at three different time points: t ∈ {2.5, 4.5, 6.5} h in Fig. 2E. The distributions of WT and AK strains did not differ significantly after 2.5h, but they differed increasingly after 4.5 and 6.5h. The distributions account for the visual observations in Fig. 2C that WT cells align with each other, while AK’s alignment was weak. Together, model predictions and experimental quantifications show how the longer WT are squeezed by small clusters of growing AK cells and form channels of (radially) aligned bacteria. When they reach the colony front, they align with the expanding front and start dividing along the tangential direction. In this way, WT cut their shorter AK counterparts off from both nutrients and space.

To emphasise the generic mechanical nature of this takeover mechanism – set by aspect ratio affecting torques and enhanced by stronger local alignment of the longer bacteria – we also employed a continuum model of a bi-phasic active nematic, where we took the two different bacteria types into account with an additional phase field order parameter ϕ, where ϕ > 0 (ϕ < 0) corresponded to longer (shorter) bacteria regions modelled with a higher (lower) elastic constant and extensile activity (which mimics the dipolar force of division, without changing the actual biomass at the front36,37). It is well established that both orientational elasticity and extensile division activity are higher for higher aspect ratios38,39. We observed that even when the front is mostly populated by shorter bacteria, the phase corresponding to the more elongated bacteria eventually overtakes the shorter (Supplementary Fig. S12). Importantly, this phase segregation is solely driven by activity, stemming from cell divisions and differences between aspect ratios, without any free-energy-driven phase separation. Remarkably, the bacteria of longer phase take over the front by forming aligned channels to the interfaces, due to differences in torque and local alignment resulting in “active anchoring” at the front24, in agreement with both the cell-based model and experimental observations (Fig. 2A, C). Consequently, the bacteria of longer phases spread at the interface, as they aligned more strongly with it, due to their higher elastic constant. We note that no radial expansion occurs in this model, and thus no radial sector boundaries are present for radial alignment. Instead, bacteria with longer phase exhibit increased activity due to reduced friction, leading to active mixing in which the longer bacteria are driven toward the interface40. As the total biomass is preserved in this minimal model, we highlight a distinct collective mechanical mechanism, which induces the taking over of the longer bacterial phase, regardless of any possible number advantage in inoculation.

Takeover rate is set by differences in aspect ratios and the length of the shorter cell
Having established the competitive advantage of a large aspect ratio through experimental observations, cell-based and continuum models, we next turned to investigating the takeover rates. Figure 3A shows the experimentally obtained strength S(r) from the homeland (r=0) to the outer rim of the colonies for the strain combinations and ζ-values that clearly switched within 3 days (i.e., S(r) > 0.85 in Fig. 1C). We defined the takeover rates, ν, as the slope of S(r) and summarised them in Fig. 3B versus the length of the shorter strain (i.e., lS). We also measured the development of S over time by following the front and confirmed that the takeover rate, ν, is consistent with the dynamics (Supplementary Fig. S13). We paralleled this result with the agent-based simulations to measure the time-dependent strength, S(rf(t)) (Fig. 3C) and the associated takeover rate, νsim. This rate was also dependent on the aspect ratio difference lL/lS, as a more significant lL/lS resulted in a stronger alignment along the channels (Supplementary Fig. S14). Hence, the longer bacteria had enhanced access to the colony front. This is in agreement with the experimental observation that ν is larger for WT/AK than WT/AS.

Surprisingly, we found that the takeover rates for the competition between longest and intermediate strains, WT/AS (grey), are significantly slower than for the two other strain combinations (longest versus shortest, WT/AK, and intermediate versus shortest, AS/AK), although the ratios of aspect ratios (Table 1) were similar for WT/AS and AS/AK (∼1.5). Since our results established that the alignment-induced mechanism governs the competition between growing bacteria, we hypothesised that the difference in takeover rates were related to the relative ability of bacteria to form nematic domains. To explain the differences in the takeover rate ν between WT/AS (longest versus intermediate) and AS/AK (intermediate versus shortest) (Fig. 3B), we used the agent-based model to examine the takeover rate for fixed lL/lS ratio (∼1.5), while varying lS from no local alignment (isotropic) to local alignment (nematic). The transition between isotropic and nematic states is set by excluded volume interactions and is dictated by local density and the particle aspect ratio, with corrections predominantly due to polydispersity of the length. As a result, we absorb the width variations of the bacteria strains in the particle aspect ratio41,42. Given our simulation doubling time, the isotropic-nematic transition occurred around length lS = 3.25. The agent-based model showed that the takeover rate dropped when both bacteria strains had local orientation ordering, see Fig. 3D. This explains why the switching speed was slower for WT/AS than for AS/AK: WT and AS both had nematic order, while in the AS/AK strain combination, only the longer AS were nematically aligning. This is also in accordance with the observation that the sector boundaries are more rugged for WT/AS (Supplementary Fig. S5), indicating that AS cells might be weakly aligning. Together, these results further highlight the directed radial alignment (leading to takeover) results from the interplay between nematic and non-nematic bacteria. Specifically, nematic bacteria align at the boundaries formed with isotropic bacteria, and this alignment must be diminished, when neighbouring bacteria are weakly nematic themselves. The reason is that active anchoring becomes weaker, as it scales with the nematic gradient at the interface24. For instance, the radial expansion of isotropic AK patches directs the chain-formation of WT into the nematic arms (Fig. S10). Furthermore, the takeover rate is independent of the length of the shorter bacteria, in this case of an isotropic and nematic-packing species (Fig. 3D). However, if the shortest bacteria species transition from isotropically packed to nematically ordered state, the takeover rate drops. This radial alignment effect disappears in single species colonies (Supplementary Fig. S15 and Fig. S16), as the incompressible radial expansion flow, in the absence of interspecies interfaces, does not induce radial alignment43,44.

Competition strength weakens in 3D
After establishing the significant advantage of elongation for surface-attached cells, we turned to 3D growth. The results so far have established that emergent nematic alignment is a competitive advantage. The local nematic order has been observed in 3D biofilms45, though theoretically, it is expected that the nematic alignment weakens in 3D46,47 and as such we expected that the takeover strength weakens, compared to surface-attached (2D) conditions. We tested our predictions in WT/AK colonies grown from inoculation beads of small volume (0.05 nl) in low-density (0.5%) agar (inset of Supplementary Fig. S17). We defined a strain ratio, ζn, as the ratio of colony-forming units (CFU) of the longer strain versus the shorter (Supplementary Fig. S17), and imaged (with confocal-scanning laser microscopy) the resulting 3D colonies for various ζn, as shown in Fig. 4A. We then sorted the ensemble of colonies into subgroups of either mono-coloured colonies (WT or AK) or colonies with both strains surviving at the surface (grey); distributions are given in Fig. 4B. For comparison, we also calculated (assuming a binomial distribution) the fraction of colonies that initially contained only AK or WT. The probability of a pure WT inoculation was negligibly small in all cases, in contrast to the probability of pure AK. It is, thus, unlikely that all mono-coloured WT colonies arose from pure WT inoculation beads. Instead, the longer strain (WT) had outcompeted the shorter (AK) during range expansion. We also found examples of the inverse, where AK had taken over the colony surface, even though the inoculum had both WT and AK.

To quantify the takeover strength, we segmented and filtered the image stacks to obtain 3D masks reconstituting a connected colony surface with the width of a single voxel, which were assigned one and only one colour (Supplementary Fig. S18 and Supplementary Movie 5). In order to determine the strength, S3(t), at a specific time, t, we quantified the proportion of the WT strain on the colony surface, as found in Fig. 4C. Interestingly, we found that when WT/AK are mixed four to one (i.e., 1/ζn = 0.25) WT occupies >90% of the surface and that S3(t) decreases, as 1/ζn increases. However, the longer (WT) still occupies a significant fraction despite a low initial ratio in the inoculation beads (Supplementary Fig. S18). For instance, when WT is only ∼2% of the inoculations (1/ζn = 47), it still occupies ∼6% of the final colonies’ surfaces. Taken together, our results indicate that the longer cell still wins, but that its competitive strength is weakened. This is in accordance with our expectation based on relaxed nematic alignment in 3D.

Methods
Bacterial strains
We used three subpopulations of the non-motile66 Escherichia coli B strain REL606: the wild-type strain (WT) and the mreB mutants67 REL606mreBA53S(AS) and REL606mreBA53K(AK)68 (Table 2). All strains are kind gifts from the Kevin Foster Lab. The mreB gene in bacteria codes for the filament protein MreB, which is homologous to actin in eukaryotic cells69. Depletion of the mreBCD operon in E. coli leads to spherical, enlarged, and eventually lysed cells70. More specifically, MreB is responsible for maintaining the rod-like cell shape of E. coli cells by promoting cell wall growth in regions of negative cell wall curvature. Therefore, its depletion leads to homogeneous cell wall growth71 by increasing the helical pitch of the filaments, causing shortening and widening of the bacteria’s shape72. All our strains carried a plasmid that constitutively expressed kanamycin resistance and either GFP, pmaxGFP (pmaxCloning-Vector, Lonza), with excitation/emission of 487/509 nm or RFP, pTurboRFP (pmaxCloning-Vector, Lonza), of 553/574 nm19.

Culture media
Throughout this study, we alternated between the following two media: rich Lysogenic broth (LB) and M63 minimal media (M63+glu) supplemented with 30 μg/ml kanamycin sulphate (≥95%, K1377, Sigma-Aldrich) to retain fluorescence, unless otherwise stated. For agar plates, we used either 0.5% or 1.5% BD BactoTM agar (10455513, Fisher Scientific).

M63+glu. The 5X M63 salt solution was composed of 15 g/l anhydrous KH2PO4 (≥98.0%, P9791, Sigma-Aldrich), 35 g/l anhydrous K2HPO4 (≥99.0%, 60353, Sigma-Aldrich), 10 g/l (NH4)2SO4 (≥99.0%, 09978, Sigma-Aldrich), 2.5 ml 20 mM FeSO4 (≥99.5%, 44970, Sigma-Aldrich), 20 mM Na-Citrate (≥99.5%, 71402, Sigma-Aldrich). The M63 minimal media was composed of 20% 5X M63 salt, 1 μg/ml thiamine hydrochloride (≥99%, T4625, Sigma-Aldrich), 2 mM MgSO4 (≥99.5%, 63138, Sigma-Aldrich), 2 mg/ml glucose (≥99.5%, G7528, Sigma-Aldrich), dissolved in Millipore water.

LB. The medium was composed of 10 g/l GibcoTM BactoTM tryptone (16279751, Fisher Scientific), 5 g/l GibcoTM BactoTM yeast extract (16279781, Fisher Scientific) and 5 g/l NaCl (≥99%, S9888, Sigma-Aldrich) dissolved in Millipore water.

Cell culture
For starting the culture, bacteria from frozen glycerol stocks were streaked on LB or M63+glu agar (1.5%) plates to obtain microcolonies after overnight growth at 37 ∘C. A single colony from the streak plates was transferred into 2 ml LB and incubated overnight at 37 ∘C under constant shaking to prevent biofilm formation. The OD600 of the overnight cultures was measured after a 10-fold dilution (IMPLEN NanoPhotometer C40) to control the strain proportions in the resulting suspension.

Imaging
Confocal laser scanning microscopy (CLSM). On a Leica DMI6000 CS SP5 (Leica, Wetzlar, Germany) we used the Ar (488 nm) and HeNe (543 nm) laser lines sequentially to excite GFP (detection: 498–536 nm) and RFP (detection: 568–641 nm), respectively. We alternated between the following magnification objectives: 5 × air objective (Nplan 5× 0.12 PHO, Leica), 20 × air objective (NplaL 20× 0.40 NA, Leica), and 100 × oil immersion objective (100× 0.17/D/HCX/PL/APO, Leica).

Fluorescence microscopy. We used a Nikon ECLIPSE Ti microscope (Nikon, Tokyo, Japan) paired with an Andor Neo camera (Andor, Belfast, UK). GFP and RFP were excited by a Hg lamp using the FITC (FITC Filter Cube Set, Olympus, York, UK) and Texas Red cubes (Texas RedTM Filter Cube Set, Nikon, Tokyo, Japan), respectively. In combination with one of the following objectives: 4 × air immersion objective (Nikon, Plan Fluor, 4x/0.13, ∞/1.2 WD 16.5), 20 × air immersion objective (Nikon, Plan Fluor, 20x/0.50, ∞/0.17 WD 2.10) and 100 × oil immersion objective (Nikon, Plan Apochromat λ, 100x/1.45 Oil, ∞/0.17 WD 0.13).

Growth rate measurements
Starting from overnight cultures (WT+GFP, WT+RFP, AS+GFP, AS+RFP, AK+GFP, AK+RFP) in M63+glu liquid medium, we diluted 100 × in M63+glu to final volumes of 5 ml. The cultures were incubated at 37 ∘C and the OD600 was measured at regular intervals (1.25h–1.75h) for 5–6h, while making sure to dilute appropriately to stay within the optimal range of the spectrometer. In parallel, we collected samples for CFU measurements. We diluted the sample to adjust the CFU count to ∼100/plate, and 100 μl was plated on 3 LB agar (1.5%) plates and incubated overnight before CFU were counted.

Cell aspect ratio
We collected samples (WT+GFP, AS+GFP, AK+GFP) in the stationary phase (i.e., immediately following overnight culture) and the log phase (3h after dilution) for imaging. Single droplets of bacterial cultures were deposited on coverslides (#1.5) and imaged using fluorescence microscopy and the 100 × objective. We measured the length, l, and width, w, of cells using the line tool in Fiji ImageJ to calculate the aspect ratio.

Competition in liquid co-cultures
Overnight cultures (WT+GFP, WT+RFP, AS+GFP, AS+RFP, AK+GFP, AK+RFP) were grown in M63+glu liquid medium. The OD600 of the overnight cultures was measured and the strains were mixed pairwise (GFP+RFP) in equal proportions (ζ=1) and diluted 100 × in M63+glu. Cultures were incubated at 37 ∘C and cell counts (50000 counts per sample) were measured right after mixing and again after 8 h of incubation, using a BD FACSJazz Cell Sorter (BD Biosciences, cat. no. 655490). In parallel, we measured the OD600 to confirm that the overall growth rates of the co-cultures were the same as for the individual cultures. Data were processed using the Flowkit package73 with a logicle transformation, and clustered with the hdbscan algorithm74. The fraction of double negative events is 6%. After clustering, we extracted the counts of the two main clusters (GFP and RFP) and defined the frequencies of the two populations as the ratio of cell counts of one population (GFP or RFP) over the cell counts of both (GFP+RFP). At t=0, we measured the number ratio of shorter bacteria (mean ± SD) to be (29 ± 1)% for AK+WT, (38 ± 0)% for AK+AS, and (44 ± 1)% for AS+WT, when averaging over the colour combinations (N=2). For the AK+WT case, this means that longer cells are ∼2.4 more in numbers (compared to ∼2.2 from CFU counts).

Relative fitness. The relative fitness, Wij, of strain i in respect to strain j is estimated here as the ratio of the number of doublings of the two competitors (i.e., identical to the ratio of their Malthusian parameters)55:

Wij = ln(N(t)/N(0))i / ln(N(t)/N(0))j, (1)

where N(t)/N(0)i and N(t)/N(0)j are the ratios of number of cells at time t in respect to starting point of strain i and j, respectively. These ratios are obtained from multiplying the ratio of frequencies (i.e., at t=8h in respect to t=0) with the fold-change in total OD600, which in our case was 100.

Cell density measurements
For each strain (WT+GFP, WT+RFP, AK+GFP, AK+RFP) we plated 100 μl of diluted overnight culture on LB plates with agar (1.5%), which were incubated overnight (37 ∘C), before CFU were counted. We found similar results for the two colours and measured the (combined) conversion at OD600 = 1 to be 1.6 · 10^9 CFU and 0.7 · 10^9 CFU, for WT and AK, respectively. Therefore, the cell number ratio between the WT and AK strains in stationary phase (same OD600) was measured to be ∼2.2.

2D competition
Sample preparation and imaging. Starting from overnight cultures, we adjusted the ratios (based on OD600) of the longer cells (WT or AS) versus the shorter (AS or AK) to ζ ∈ {1, 0.1, 0.01, 0.001} and diluted to a final (and combined) OD600 of 0.3. The diluted cell culture was inoculated in 0.5 μl droplets on M63+glu plates with agar (1.5%). After either 20h or 3 days of incubation (37 ∘C), we imaged the colonies using the CLSM and the 5 × objective. A vertical range of 100 μm was scanned and the resulting 3D images had voxel sizes of (x,y,z)=(6.07, 6.07, 10) μm.

Pre-processing. In many cases, colonies had outgrown the field of view (3.1 mm × 3.1 mm), so we stitched 4 images together using the Pairwise Stitching plugin in Fiji ImageJ75. We made a maximum intensity pixel projection of each stack to get a flattened (x,y)-image of pixel size (x,y)=(6.07, 6.07) μm.

Intensity adjustment of colour channels. To boost the contrast between the two channels, we divided channels (GFP and RFP) with each other to amplify the pixel value range of the two channels. Thus, for each pixel, we calculated a new intensity value, p(x,y)0, using a re-scaling value of 100 (8-bit image), such that:

p(x,y)0 = (pGFP(x,y)+100) / (pRFP(x,y)+100), (2)

where pGFP and pRFP are the pixel values from the GFP and RFP channels, respectively. We found this method to be particularly useful in image areas with significant intensity variations (e.g., around the homeland) and for background removal76.

Pixel classification. For further analysis, we wanted all pixels to be classified as either GFP or RFP (never both). Therefore, we used the rescaled pixel intensities, p(x,y)0, distribution of the image and – consistently – found two peaks corresponding to GFP and RFP, and using Otsu’s method, we estimated the threshold value to classify the pixels.

Competition strength as a function of the radial vector in 2D. Colonies had clearly detectable regions and we defined the homeland as the well-mixed centre region, which roughly corresponded to where the original inoculation droplet was deposited. The boundary of this region was found by manual fitting of a circle and we identified the centre of this circle as the starting point of the radial vector r(t)0, and the homeland boundary r(t=0) (after which clear sectors first appear). To account for variations in drop size, we defined the translated radial distance as

r(t) = |r(t)0| - |r(t=0)|. (3)

We defined the ensemble-averaged strength of N colonies to be the re-scaled occupancy of the GFP-expressing (and longer) bacteria at a given radial length r(t) as the sum over the following fraction:

S(r) = (2/N) * sum(CGFP(n)(r(t)) / C(n)(r(t))) - 1, (4)

where C(n)(r(t)) is the total number of pixels of the circle of the n-th colony at radial distance r(t) and CGFP(n)(r(t)) is the number of pixels occupied by GFP-expressing bacteria, such that C(n)(r(t)) = CGFP(n)(r(t)) + CRFP(n)(r(t)). Defined like this, S had the value of 1 (-1) when the GFP-expressing (RFP-expressing) cells had taken over the complete perimeter at a specific radial distance. To compare the S at a specific time, we defined t1 = 1.5 days as halfway from the homeland border to the front of a colony after 3 days of incubation.

Competition strength as a function of time in 2D. Starting from overnight cultures, we adjusted the ratios (based on OD600) of the longer cells (WT) versus the shorter ones (AK) to ζ = 0.001 and diluted to a final (and combined) OD600 of 0.3. The diluted cell culture was inoculated in 0.5 μl droplets on M63+glu plates with agar (1.5%). After 11h of incubation (37 ∘C), fluorescence images were acquired over a period of 10h using our fluorescence microscope and the 4 × objective. Then, following pre-processing, intensity adjustment, and pixel classification, we measured the time-dependent strength of a colony as the sum over the following fraction:

S(t) = 2 * (CGFP(t) / C(t)) - 1, (5)

where C(t) is the total number of pixels of the circle fitted to the periphery at time t and CGFP(t) is the number of pixels occupied by GFP-expressing bacteria, such that C(t) = CGFP(t) + CRFP(t). To calculate dS(r)/dr we fitted S(t) for individual colonies and used the r(t) development at the periphery.

Competition in isogenic bacteria. Starting from overnight cultures, we inoculated 1:1 (ζ=1) two subpopulations (expressing GFP or RFP) of the same strain (WT/WT, AS/AS, or AK/AK) with the same fitness and shape at OD600 = 0.3. Plates were incubated for 20h and CLSM imaged. We found patterns of spatially segregated lineages with a constant number of sectors (Supplementary Fig. S15A); well in accordance with earlier findings19,20.

Zoom in on 2D competition isogenic boundaries. Plates were incubated (37 ∘C) for 3 days, before cutting out the colony and the according square of agar and placing it upside down in a glass-bottomed culture well (HBST-5040, WillCo Wells B.V.). The colonies were imaged with sequential z-stacks using CLSM in combination with the 100 × objective and the resulting voxel size in (x,y,z)=(0.30, 0.30, 0.99) μm.

Varying seeding density. We repeated the competition experiment (20h) for WT/AK but for serial dilutions of seeding density. The co-culture of WT and AK mixed 1:1 and OD600 = 0.3 was diluted 10-, 100-, and 1000-fold. We found the mixing of genotypes reduced in the homeland (i.e., patch sizes enlarged), but WT was still able to completely dominate the expansion front (Supplementary Fig. S4). So even though the seeding density regulates patch sizes77,78, the longer cell still wins.

Rate of range expansion in 2D. Starting from overnight cultures (WT+GFP, AS+GFP, AK+GFP) in LB, we inoculated 0.5 μl droplets of single-strain cultures (OD600 = 0.2) on M63+glu agar (1.5%). After 15 h of incubation (37 ∘C), the plates were placed upside down on our inverted fluorescence microscope and imaged with a frame rate of 1.5 h^-1 during 9h using the 4 × objective. We mapped the colony areas by (manual) thresholding and quantified the range expansion by calculating the effective colony radius, r, from the measured surface area using the Measurement function in Fiji.

Cross-sections. Starting from overnight cultures (WT+GFP and AK+RFP) in LB, bacteria were mixed in equal proportions, reaching a final OD600 of 0.3. The diluted cell culture was inoculated in 0.5 μl droplets on LB agar plates (1.5%). The plates were then incubated for 20h (37 ∘C). Fresh agar (55 ∘C) was poured into the dishes to fully embed the bacterial colonies prior to sectioning. The agar was poured onto the original agar substrate, between the colonies, to avoid immediate direct contact with the colonies. Dishes were left to solidify at the bench (1h). Approximately 1 cm^3 was cut out around the colony, placed on a glass-bottomed dish and cut in half with a scalpel along the diameter of the colony. The halves were then rotated to image the cross-sections. These were imaged at 4 × magnification using the fluorescence microscope, as well as 20 × and 100 × using the CLSM.

Monolayer fronts. Starting from overnight cultures (WT+GFP and AK+RFP) in LB, bacteria were mixed 10:1 in favour of AK (ζ=0.1), before 10-fold dilution, and inoculation on M63+glu agar (1.5%) plates. Following the inoculation, a rectangular piece of agar was cut out, flipped, and transferred upside down into glass-bottomed culture well (HBST-5040, WillCo Wells B.V.) and sealed with Parafilm®. The colonies were incubated (37 ∘C) for varying incubation times: 7.5 h, 9.5 h, and 10 h. Images were taken of the colony edges with two sequential z-stacks (RFP then GFP) using CLSM and the 100 × objective. The z-stacks were taken over vertical ranges of 6 μm to 18 μm, to compensate for slight horizontal tilts of the agar plates. The resulting 3D images had voxel sizes of (x,y,z)=(0.30, 0.30, 0.20) μm.

Single-cell resolution time-lapses
Sample preparation. One colony of each WT and AK was transferred separately into 3 ml LB medium and incubated overnight (37 ∘C) under constant shaking. The OD600 of the overnight cultures were measured and they were mixed in equal proportions (ζ=1), before 10-fold dilution and inoculation on M63+glu agar (1.5%) plates. Shortly following the inoculation, a rectangular piece of agar was cut out, flipped, and transferred upside down into glass-bottomed culture well (HBST-5040, WillCo Wells B.V.) and sealed with Parafilm®.

Single-cell resolution time-lapses. The colonies were imaged in our inverted fluorescence microscope using the 100 × objective. Fluorescence images were acquired with a frame rate of 2/h during 12h. In addition, z-stacks were collected over a total range of 2 μm (0.5 μm spacing) for each time frame to cope with the relative roughness of the agar substrate surface at high magnification.

Data analysis. The z-stacks were high-pass filtered and summed into a single image using a custom-made MATLAB procedure, thereby collapsing all the sharpest regions into a single plane. Bacteria were segmented by thresholding each time frame multiple times (twice for AK, thrice for WT) to consider variations in intensity and saturation within a single time frame. The binary images resulting from different thresholds (of the same time frame) were summed to collect as many bacteria as possible, despite non-uniform contrasts, see Supplementary Movies 6, 7 for examples. Bacteria were detected using the Regionprops function in MATLAB (Image Processing Toolbox version 11.7). The function returned the (x,y)-coordinates and the orientation of each bacterium (major axis of the ellipse that has the same second-moments as the bacterium pixels region).

The local nematic order parameter q for a bacterium n, is calculated by locating the Nn = 8 nearest neighbours ni of the same strain and then using the definition:

q = (1/Nn) * sum(cos(2θi)), (6)

with θi the orientation of the neighbouring bacteria orientation. To calculate the probability density function, PDF, all n are radially grouped and the front region was defined as the portion for which WT cells form a continuous layer. The intermediate (middle) region corresponds to the AK-rich region of strong segregation behind the front, and the homeland to the disorganized portion further inward. When such regions have not yet formed, the three regions were defined as equidistant radial bands.

3D competition
Encapsulating bacteria in inoculation beads. We produced four batches of 2.5% agarose inoculation beads containing different ratios of WT+GFP and AK+RFP following the procedure outlined in Ref. 21, excepting the following modifications: i) Cell densities in the beads were either OD600 = 0.65 or OD600 = 1.45 (OD600 = 4 or OD600 = 8.6 in the cell mix) for 1/ζn ∈ {0.25, 12, 16} and 1/ζn = 47, respectively. The latter was obtained by up-concentration through centrifugation of the overnight cultures. Varying the densities ensured reasonable numbers of (WT+GFP), despite low ratios (high 1/ζn). We ii) filtered the PBS-bead suspensions through strainers with mesh sizes of 70, 50, and 40 μm and let at least 10 ml additional PBS flow through the strainers to wash off the remaining silicone oil. We collected the beads in the 40 μm strainer (diameters of 40–50 μm) by turning it upside down and flushing with 6–9 ml LB. More details can be found in the associated protocol79.

Mono-strain 3D colonies. As a control, we also prepared beads with two colours of the same strain. We followed the exact same procedure but with a different bacteria mixture: Overnight cultures were mixed 1:1 by adjusting the OD600 (WT+GFP/WT+RFP, AK+GFP/AK+RFP, AS+GFP/AS+RFP) and diluted in LB to a final (overall) OD600 = 0.07 (0.4 in the cell mix).

Bead concentration measurements. To measure the strain ratios and number of cells within the inoculation beads, we did serial dilutions (10^-7 - 10^-5) of the spare cell mixture from the encapsulation process. We plated 100 μl of the dilution on LB agar (1.5%) plates and incubated overnight. From the number and colour of CFU, we deduce i) the ratio of WT to AK cells (1/ζn) and ii) the overall cell concentration of the mixture. Based on these results, we estimated the number of cells encapsulated within a bead by modelling the beads as perfect spheres with a radius of 45 μm. The strain ratios were estimated from counting 1606, 2900, 3918, and 3472 CFU for 1/ζn ∈ {0.25, 12, 16, 47}, respectively.

As the small size limited the number of cells per bead and as the strains had different cell volumes (Table 1 in the main text), we defined a strain ratio, ζn, as the ratio of CFU of the longer strain versus the shorter (measured before encapsulation in the beads). We found 1/ζn ∈ {0.25, 12, 16} with OD600 = 0.65 and 1/ζn = 47 with OD600 = 1.45; the higher density for the latter ensured WT cells in most beads at this extreme ratio.

Embedment of inoculation beads in 0.5% agar. To investigate competition in 3D, we embedded the inoculation beads within a 0.5% agar growth medium. We followed the protocol outlined in ref. 21, excepting the following adaptions: i) Frozen bead stocks were diluted with LB (based on the measured concentration of beads per 1 ml frozen stock) aiming for 10 beads per well. Specifically, we diluted {650, 970, 130, 85} μl of frozen bead stock in 1 ml LB for 1/ζn ∈ {0.25, 12, 16, 47}, respectively. We counted on average 10.9 ± 3.3 beads per well and ii) we incubated all colonies for 10h.

3D colony imaging. After incubation, wells were preserved at 4 ∘C until imaging (<24h) using the CLSM and the 20 × objective (discarding colonies that had reached the agar-glass or the agar-air interface). For bi-coloured colonies, we recorded two sequential (RFP then GFP) z-stacks with a resulting voxel volume of (x,y,z)=(1.51, 1.51, 1.33) μm. For each strain ratio (1/ζn), we collected images from 4-5 different wells (>40 colonies in total). As a control, we also mixed 1:1 (i.e., ζn = 1) two subpopulations (expressing GFP or RFP) of the same strains and found that surface coverage was similar for both strains (Supplementary Fig. S21). In the case of WT/WT, this is well in accordance with earlier findings21.

Segmentation of 3D images. The 3D colony images were processed, segmented, and filtered for the surface using BiofilmQ80 and Fiji/ImageJ81. Only colonies expressing both strains were segmented, following the exact process described in ref. 21.

Competition strength as a function of time in 3D. We defined the ensemble-averaged strength of GFP-expressing bacteria (WT) on the colony surface as the re-scaled sum over the area fraction:

S3(t) = (2/N) * sum(AGFP(n)(t) / A(n)(t)) - 1, (7)

where AGFP(n)(t) is the area of GFP-expressing bacteria and A(n)(t) is the total surface area of the n-th colony at time t, such that A(n)(t) = AGFP(n)(t) + ARFP(n)(t). In contrast to the 2D case, S3 is a function of t (instead of r(t)) as it refers to the surface at a given t, with varying r(t). For colonies whose visible surface only expressed one of the two strains, we assigned AGFP(n) = 1 (GFP-mono-coloured) or AGFP(n) = 0 (RFP-mono-coloured). We also calculated the expectation value of the subset of N originating from pure RFP-expressing cells from estimated number of cells per bead (CFU/Vbead), the total number of colonies (N), and the WT/AK ratio (ζn); assuming a binomial distribution.

Rate of range expansion in 3D. Starting from overnight cultures (WT+GFP, AS+GFP, AK+GFP) in LB, cells were embedded at low concentration ( ∼ 10/well) in M63+glu agar (0.5%) matrix following the protocol described in ref. 11. After 6h of incubation (37 ∘C) the monoclonal colonies were imaged using our fluorescence microscope with a frame rate of 3/2h during 16h with a 20 × objective. Similar to the 2D case, we quantified the range expansion by manual thresholding and calculated the effective colony radius, r, from the (maximum-intensity) z-projected cross-sectional area using the Measurement function in Fiji.

Statistics. All mean values are given as mean plus/minus the standard deviation (SD) or the standard error of the mean (SEM), when this is stated and only when data are tested against the null hypothesis that it is normally distributed. The normal distributions of S were assessed with Shapiro-Wilk tests. Their distributions were compared between the WT and AK strains with Mann-Whitney U Tests. The significance of the differences in ν were evaluated with a Student t-test.

Computational models
Particle model. The particle-based model is based on the SPR model presented and described in 8. A single bacteria is described as a rod, α, consisting of a rigid chain of a number of Yukawa segments, nα, separated by length, lα, with segments of different rods repelling one another with a Coulomb-like point potential with potential strength, U0 = 250 (previous work has shown that results are independent on U0 provided it is large enough82), resulting in a total potential, U. The Yukawa screening length, λ, is taken as the width of the particle with the aspect ratio of the rod: L = nαlα/λ. Other particle potentials are used in the literature (Bsim 2.083), but our results are robust independently of this choice.

Bacterial growth is done stochastic. So, for every timestep, Δt, we draw a random number randn (taken from the absolute value of a normal distribution with mean 0 and standard deviation 1). This random number is multiplied by the current particle length and the growth rate γ and then added to the particle length. The choice of distribution and the resulting length polydispersity does not matter. As long as an uncorrelated distribution is chosen, the method in the continuum limit gives the most basic ODE growth solver (Gro84):

∂L/∂t = γL (8)

and polydispersity affect the isotropic nematic transition only as a correction. When the rod has reached the division length l, the particle is split into two. The timescales given in the manuscript are normalised by the generation time, which is purely set by γ.

We use overdamped equations of motion to then update the particle position and orientations8:

f_r * ∂r_α/∂t = - ∂U/∂r_α (9)

f_t * ∂θ_α/∂t = - ∂U/∂θ_α, (10)

where rα and θα are the centre and orientation of rod α, respectively and fr, ft being the drag coefficients. This gives local force propagation even in the non-equilibrium state of an expanding colony, which retains the importance of mechanical interactions that are the highlight of our manuscript. This is in contrast to other bacterial solvers (e.g., Gro84 and BSim 2.083) which use instantaneous global force minimisation to update the bacteria’s positions and orientations.

At time zero (t=0), 40 rods are initialised in a small area with 10 rods having division aspect ratio, lL, and random aspect ratios (uniform distribution) between lL/2 and lL and 30 rods having division aspect ratio, lS, and random aspect (uniform distribution) ratios between lS/2 and lS, such that ζ = 0.25.

Competition strength in the particle model. To determine the competition strength Sf(t) at the interface at it evolves over time, we count all particles that exist in the front. We do this by dividing the colony into 10 slices (with centre at the centre of mass of the colony), determine the particle that is furthest from the centre of the colony and then take into account all particles that inhabit up to 5 decay lengths λ into the colony.

The takeover rate, νsim, in the simulations is calculated from the Sf(t) curve of 10 different trajectories. The νsim is the linear fit from generation time 5.5 to time 7.5.

Continuum model. To describe the bacterial colony on a course-grained level, we study the evolution of the nematic order parameter Q=2q(nbnb - I), where q and nb show the magnitude and orientation of the order, respectively, and I represent the identity tensor30. In line with other dry active nematic studies85,43, we use the dynamics of the Q-tensor is described by the Beris-Edwards equation

DQij/Dt = χEij + ΓHij, (11)

with respect to a symmetric gradients E (shear tensor) and anti-symmetric ω (vorticity tensor) of a velocity field u. We use the convected co-rotational time derivative DQij/Dt = (∂t + uk∂k) Qij - ωikQkj + Qikωkj.

In Eq. (11), χ is the aligning parameter (taken as 0.8) and Γ=0.1 is the rotational diffusivity which along with Hij, the molecular field, describes the relaxation of the Q-tensor toward the minimum of a free energy described by:

F = A/2 * (Q:Q)^2 + K/2 * |∇Q|^2. (12)

The free energy includes the nematic alignment term (with coefficient A = 0.01) and an elastic term K which penalises gradients in the Q tensor. Velocity is taken in the overdamped limit

fu = -ξ∂Q + η∇^2(∂Q), (13)

where ξ is the activity coefficient related to force dipoles generated from division events (positive to correspond to the extensile limit), which is balanced by frictional dissipation into the surface f and a small viscous dissipation with viscosity η=0.01. The outer edge of the colony is taken by assuming high friction f = 400 outside a radius R > 30. In the interior, we take f = 4.

To distinguish the two bacterial concentrations, we introduce a phase-field binary order parameter ϕ, which evolves according to a Cahn-Hillard model

∂tϕ + ∇(uϕ) = Γϕ∇^2μ, (14)

where μ = δF/δϕ - ∇(δF/δ∇ϕ) is the chemical potential with Γϕ = 0.3 a mobility coefficient. We add to the free energy F a single well potential fDW = Aϕ/2 * ϕ^2 and an interfacial term fI = Kϕ/2 * (∇ϕ)^2 with Aϕ = 0.002 and Kϕ = 0.02 such that all bacterial phase-separation comes from activity dependence. We take ϕ < 0 as the shorter bacteria and ϕ > 0 as the longer bacteria. This is imposed by taking the phenomenological parameters ξ and K to be dependent on the local ϕ as:

ξ = 0.2 (ϕ > 0) / 0.1 (ϕ < 0) (15)

K = 0.09 (ϕ > 0) / 0.05 (ϕ < 0) (16)

since it is well established that both orientational elasticity K and extensile activity due to division ξ are higher for higher aspect ratios38,39. All equations are solved using a finite-difference method, and we initialise our system by taking ϕ = 0.01 for radius R < 25, between R=25 and R=30 ϕ = -0.01 and ϕ = 0 for R > 30 in a system of size 80 by 80.

We emphasize that the purpose of the continuum model is to demonstrate how the longer bacteria, through an active anchoring mechanism, can compete at the interface. The model does not capture the initial radial expansion and, as a result, does not produce radially aligned sectors. Instead, the increased activity of the active material enables mixing between species. The phase corresponding to the longer bacteria can advect toward the front, where they align with the interface. This alignment allows them to once again dominate the outer region.

This advective, active mixing mechanism bypasses the need for biomass deposition, which is why the longer bacteria overtake the front in both experiments and particle-based simulations. Recent work on active mixing in particle-based models, driven by reduced friction, shows behaviour consistent with our continuum model, as no radial interfaces are observed40.

Neglecting the biomass increase is a limitation of the current biphasic continuum model. However, including the biomass effects in the continuum model would require extension to a ternary field to allow for an expanding front. Such an extension could capture the impacts of radial expansion together with active anchoring effects between the two expanding species in the bulk.

Radial induced alignment due to growth. The alignment mechanism at the interface between two species can be understood in terms of active stresses, expressed as ∇(ξQ). At an interface characterized by a unit normal vector m, the dominant contribution to the force density arises from ξ(∇S(m*nb)nb - 1/2m), where ∇S represents gradients in the nematic order. For simplicity, we neglect gradients in ξ; their inclusion would only amplify this effect. Importantly, this interfacial force vanishes only when the director field nb is either tangential or parallel to the interface. Otherwise, the resulting force generates a flow that reorients nb, tangentially in extensile clusters or normally in contractile ones24. We emphasize that at the front of the colony, this active force will force the longer bacteria to become parallel aligned with this front, which allows the longer bacteria to spread along the interface.

For single-species colonies, we observe no global radial alignment, consistent with earlier observations (Supplementary Fig. S15 and Fig. S16)43,44. In radial expanding colonies without perturbations, the outward flow generated by growth alone does not produce sufficient strain or vorticity to drive large-scale radial alignment. Instead, we find that local patches of nematic order emerge spontaneously, but these domains remain uncorrelated with each other and with the overall growth direction. Previous work44 demonstrated that deliberately breaking radial flow symmetry (i.e., through voids) can facilitate global radial alignment. Our findings suggest that gradients in the local nematic order itself are enough to break symmetry, reinforcing nematic alignment within the ordered regions and allowing for localized self-organization without requiring external perturbations.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the authors present an experimental and simulation study, where they investigate the effect of differences in cell length on the segregation of and competition between two bacterial strains, using E. coli mutants as a model system, as they grow over an agar plate. The main claims of the authors are that:\n(1) The longer WT cells win the competition while spreading via growth on the agar, which is well supported by the results.\n(2) This advantage of longer cells comes from the nematic alignment of the longer cells with each other which allows a rapid directional spreading towards the edge of the colony, where fresh nutrients are available that allow them to outgrow the shorter cells at the edge and take over the propagation front. Here, major concerns can be raised. Indeed, although this mechanism is in principle plausible, over several previous rounds of revisions in which I participated, the relative consensus between the reviewers was that the evidence was not solid enough to rule out alternative mechanisms.\nIn particular, there appears to be more elongated than short cells at the edge of the colony from the start, which the reviewers interpreted as a possible coffee-ring-like effect that would enrich longer cells from the start. I did not find the authors’ response on the coffee-ring effect fully satisfactory: If the balance of physical parameters that allows coffee-ring suppression and exclusion from the edge for long colloids in the PS system of Yunker et al was the same in bacteria, one would expect no coffee ring for rod-shaped bacteria. This is not the case, even when the cells are non-motile, as evidenced by many papers including the ones cited by the authors.\nIn the previous rounds of revision, I suggested to follow the cell ratio over time at the edge of the colony from the time of inoculation onward. The authors provided Fig. S10, which shows a gradual takeover of the longer cells over time and strengthens the case of the authors. However the record is shown only 11h after the initial spot inoculation. This hides the early dynamics, and prevents us from understanding whether an initial coffee ring effect is present. Moreover, it was done for a very small fraction of longer cells. I would like to see the early dynamics and the initial ratio of longer cells at the edge, also for higher fraction of longer cells. This would resolve whether a coffee-ring effect can be considered as an alternative explanation.\nRegarding the concerns raised by the other referee about the possibility of nematic ordering and then its role in the takeover, be it the main driver or an action in synergy with a coffee-ring effect, I think the best way to resolve the matter is experimentally. Figure 2D suggests that long cells align towards the edge in the middle of the colony and along the edge at the front, which would support a role of nematic alignment for gaining the front faster and then to block the other cells there.\nUnfortunately, this is only one time point and a single condition, as well as apparently the characterization of a single replicate. I thus suggest to carry a full and exhaustive characterization of the distribution of orientations at these different positions across the colony, for all conditions (WT/AK, WT/AS, and AK/AS), several time points as the colony develops, and averaged over several replicates. This would undoubtedly greatly help confirm (or infirm) the authors’ proposed mechanism.\nI also note that the distribution of theta runs from -80 to 80 for the simulations (Fig2B), but from -100 to 100 for the experiments (Fig 2D). What is the unit of theta? And if it is degrees, why does it not run from -90 to +90 as one would expect?\nOther minor points:\nThe legend of Movie 4 still does not indicate the initial ratio, which should be zeta=1 from the previous round of revision\nOn the Malthusian ratio, I still find the new wording (“fold-change” alone) slightly confusing, I would recommend using “fold-change in total OD” for better clarity\nIn discussion, about the sentence “However, our results suggest that in other natural habitats such as on surfaces, in soils, and animal tissue, … the advantageous morphology is the rod shape”. In soil and tissue, the upper surface of the colony is often not exposed to air, as is the case on surfaces and in the experiments here, but rather to a potentially nutritious milieu. The data of Smith et al. suggest that in these cases nutrient supply from the top might change the behavior radically. Please nuance.\nIn sum, if the authors can revise their manuscript appropriately and address the raised major points thoroughly, they would have in my opinion a good case for publication in Nature communications."}, "author_response": ""}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors present an experimental and simulation study, where they investigate the effect of differences in cell length on the segregation of and competition between two bacterial strains, using E. coli mutants as a model system, as they grow over an agar plate. The main claims of the authors are that:\n(1) The longer WT cells win the competition while spreading via growth on the agar, which is well supported by the results.\n(2) This advantage of longer cells comes from the nematic alignment of the longer cells with each other which allows a rapid directional spreading of the WT towards the edge of the colony, where fresh nutrients are available that allow WT to outgrow the shorter cells at the edge and take over the propagation front.\n(3) The nematic alignment seems to happen because of pinning of the nematicity of the longer cells along the long cells/short cells boundary regions.\nConsidering the response of the authors to both referees’ comments, I think there are a few points that need further clarification before the paper can be considered for publication:\nI also note that the distribution of theta runs from -80 to 80 for the simulations (Fig2B), but from -100 to 100 for the experiments (Fig 2D). What is the unit of theta? And if it is degrees, why does it not run from -90 to +90 as one would expect?\n- The role of biomass increase, which they argue without showing would be too slow to explain the alignment. Including simulations of the continuous model that include it, as previously suggested, would be a great way to show this. Also, why would the bacteria orient first radially and then perpendicularly to the edge, if biomass increase and thus colony expansion do not play a role, as the authors seem to argue?\n- The mechanism of nematic alignment of long cells to the long/short domain boundaries is not demonstrated in this system. Is there an increased ordering/nematicity next to boundaries compared to within the domain in the experiments and/or simulations? Does the ordering propagate from the edges to the center of long cell cluster?\nMinor:\nThe abstract and introduction need to be reformated\nFig 4: why present 1/zeta instead of zeta just for this figure? It is confusing when reading\nRef 33 of supplementary in Fig S17 do not show what the authors claim: this reference considers only the growth of single cells inside an agar gel.\nFig S10 seems to be mislabeled as Fig S8 in the Supplementary text, model part."}, "author_response": "We thank the reviewer for giving us the possibility to strengthen the relation between nematic ordering and radial alignment. In the present version of our manuscript, we have re-analyzed our data and added new to emphasize the connection and strengthen our proposed mechanism.\nIn the original manuscript, we showed how the nematic alignment of the wild-type (WT) and the shortest mutant (AK) changes within the first hours of colony-formation (Fig. 2E and S10B), going from similar distributions of the order parameter to high local alignment of WT – considerably less for AK, in accordance with prior studies [doi:10.1103/PhysRevX.8.031065]. We also showed that when the density is high enough, the patches of local nematic order have an overall direction (Fig. 2B+D), dependent on their distance to the periphery (front versus middle).\nWe are limited by our raw data. The analysis of alignments requires single-cell resolution time-lapse, and we only have recorded single-cell resolution time-lapses for the WT/AK case. In addition, time is a parameter that cannot be compared from dataset to dataset because of huge density variations in the “coffee stain” pattern (Fig. 2 versus Fig. S10). Instead, we analyzed an additional dataset, which we have not presented before, that within the time-range and region-of-interest forms the nematic channels and the outer rim (in contrast to fig. S10 and movies 3+4). We show how the nematic ordering, q, and angle to the front, theta, changes from low density conditions (5.5h) to high density conditions (full confluency at 22h), where a more static characteristic pattern is formed.\n[...]\nThese new analyses are in full accordance with Fig. 2D in the manuscript and provide additional example of WT takeover, despite fluctuating initial conditions. We added a reference to this in the main text (l. 108):\n“...once the cell monolayer becomes confluent (Supplementary Fig. S11). ”\nFurthermore, we added the AK directions of the dataset in Fig. 2 for comparison as Supplementary Fig. S8 and a reference to this figure in the caption of Fig. 2.\n[...]\nAlso, we inserted the number of segmented cells (N) for all regions in all cases, and added a more detailed description of the (front, middle, homeland)-binning in Single-cell resolution time-lapses/Data analysis of the Supplementary Information. Therefore, our new analysis and figures support our previous claim on the importance of the nematic ordering and strong directionality in the WT takeover process.\nI also note that the distribution of theta runs from -80 to 80 for the simulations (Fig2B), but from -100 to 100 for the experiments (Fig 2D). What is the unit of theta? And if it is degrees, why does it not run from -90 to +90 as one would expect?\nWe thank the reviewer for noticing this. It has been fixed and specified that these are degrees and not radians.\n- The role of biomass increase, which they argue without showing would be too slow to explain the alignment. Including simulations of the continuous model that include it, as previously suggested, would be a great way to show this. Also, why would the bacteria orient first radially and then perpendicularly to the edge, if biomass increase and thus colony expansion do not play a role, as the authors seem to argue?\nAs suggested by the referee, we address this point by more carefully articulating the hypotheses in the revised manuscript, because extending the continuum model to include biomass increase would require significant modification of the model to extend it from binary fields to at least three-phase fields, allowing for an expanding interface.\nWe now clearly describe the key mechanisms that lead to the longer bacteria eventually overtaking the smaller ones at the front.\n● Biomass expansion leads to the formation of radial interfaces between the smaller and larger bacteria.\n● The larger bacteria align at any interface (either with the agar surrounding or the shorter, less nematically aligned bacteria), through a process called active anchoring,. (https://doi.org/10.1039/C7SM00325K, https://doi.org/10.1103/PhysRevE.102.020601, https://doi.org/10.1073/pnas.2106038118, https://doi.org/10.1103/PhysRevE.74.030904). This arises from gradients in nematic ordering at interfaces where the active agents generate forces, either through self-motility or cell division.\n● Due to this alignment, larger bacteria tend to deposit more at the colony front through the channels formed along these radial interfaces. This is why in both the particle simulation and experiments we see small regions of longer bacteria starting to form regions at the colony front . These bumps eventually subside as the longer bacteria reorient themselves at the interface, allowing them to overtake the entire front of the colony (Similar behaviour in bacteria where species have different division rates https://doi.org/10.1038/s41559-018-0734-9 and https://doi.org/10.1073/pnas.1809587115).\n[...]\n- The mechanism of nematic alignment of long cells to the long/short domain boundaries is not demonstrated in this system. Is there an increased ordering/nematicity next to boundaries compared to within the domain in the experiments and/or simulations? Does the ordering propagate from the edges to the center of long cell cluster?\nIndeed, as the referee correctly points out, in addition to the interface at the front of the colony, a secondary interface forms between the long and short bacterial domains within the bulk. At this internal interface, the active anchoring mechanism aligns the longer bacteria along the boundary. As shown in the manuscript (Fig. 3D), this alignment enables the longer bacteria to overtake the shorter ones, particularly when the latter exhibit weaker nematic order.\nWe emphasize that active anchoring is a well-established mechanism (https://doi.org/10.1039/C7SM00325K, https://doi.org/10.1103/PhysRevE.102.020601, https://doi.org/10.1073/pnas.2106038118, https://doi.org/10.1103/PhysRevE.74.030904) and it can be understood by decomposing the active forces into components parallel and perpendicular to the interface with normal m and tangent vector t between nematic and isotropic regions with gradients of the nematic order |∇𝑞| and nematic orientation n.\n[...]\nMinor:\nThe abstract and introduction need to be reformated\nThis has been done primarily by rearranging and adding a few sentences, to keep the short format.\nFig 4: why present 1/zeta instead of zeta just for this figure? It is confusing when reading\nWe are aware that this can cause confusion, however, we have decided to keep this nomenclature to i) emphasize this is a somewhat different measure (zeta versus zeta_0) and ii) in favor of the scaling of Fig. 4.\nRef 33 of supplementary in Fig S17 do not show what the authors claim: this reference considers only the growth of single cells inside an agar gel.\nThis inconsistency has now been corrected by removing the reference and inserting two others.\nFig S10 seems to be mislabeled as Fig S8 in the Supplementary text, model part.\nWe thank the reviewer for noticing this. This error has been corrected in the present SI manuscript."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have addressed my comments satisfactorily. I notably appreciate the characterization of the dynamics of establishment, which strengthens the points of the authors in my opinion. I believe the paper can be accepted for publication, although I did note a small number of minor points for the author’s consideration:\nl. 80 I am not sure what the purpose of the reference to Fig 2C at the end of the first sentence of the paragraph is, especially because 2A and 2B are not introduced yet. Was it intended to be 1C?\nl.103 It would be good to refer the reader to the specific images that illustrate the boundary alignment in the simulations, in Fig. 2 and the corresponding movie (time stamps 4 and 6 generations).\nMovies: Including timestamps in the movies could be a good idea\nTable 1: there might be some typos in the standard deviations of the aspect ratios l/w – they seem quite small compared to the ones of l and w\nL113 & 115 “90° to r” “along r”. In the new version of the text, the radial vector r is no longer defined.\nL125-141 In this paragraph, when describing the behavior of the continuum phase model, the authors sometimes talk about “longer/shorter bacteria” when they are talking about the two phases (especially starting from l.134). This creates a bit of confusion, especially because they compare the model to the experiments in the same paragraph. I think they should carefully distinguish continuous model and experiments by systematically talking about “short/long bacterial phases” or something similar for the former.\nl. 163 “this transition”: please remind that this is the nematic/isotropic, because the intercalated sentence of previous revisions slightly broke the flow of text.\nl. 169 – 171 “Specifically, … at the interface (20).” I think it should be clearer that the first sentence is a deduction from the literature (ref 20) rather than a direct observation. I suggest changing “this alignment is diminished,” into “this alignment must be diminished”.\nL 172 I think the authors might have meant Fig. S10 and not S8.\nL 172 – 173 “The takeover rate … phase).” This sentence was slightly confusing. I assume the authors refer to Fig 3D, where the takeover rate for a given aspect ratio only depends on whether the smaller bacteria are nematic or isotropic, but not on their length for a given orientational order? Pointing to the figure might help clarify the message.", "reviewer_2": "The authors have revised their manuscript according to our comments. Since we have already gone through multiple rounds of revision, I will only focus on the last points.\nThe addition of a time series of the ratio of cells at the edge is welcome, and strengthens the case of the authors, by showing a gradual takeover dynamics at the front. I however regret that it only starts 11 h after inoculation, which hides the early dynamics and the initial ratio. The dynamics at several initial inoculation ratios would also have been nice.\nOn the coffee-ring-like effect, I do not quite buy the authors argument. If the balance of physical parameters that allows coffee-ring suppression and exclusion from the edge for long colloids in the PS system of Yunker et al was the same in bacteria, one would expect no coffee ring for rod-shaped bacteria. This is not the case, even when the cells are non-motile, as evidenced by many papers including the ones cited by the authors. And we are not even accounting for the drop drying on an agar gel here vs glass slides in the cited papers.\nHowever, this question is secondary, and resolving it would require a study probably beyond the scope of this paper, since the data provided by the authors in Fig S10 contribute to alleviate the primary concern more solidly than any hand-waved argument could.\nThe legend of Movie 4 still does not indicate the initial ratio, which should be zeta=1 from the authors reply\nOn the Malthusian ratio, I was indeed confused by the wording. I think that “fold-change” alone might still be confusing, I would recommend using “fold-change in total OD” for clarity\nAbout the sentence “However, our results suggest that in other natural habitats such as on surfaces, in soils, and animal tissue, … the advantageous morphology is the rod shape”. In soil and tissue, the upper surface of the colony is often not exposed to air, as is the case on surfaces and in the experiments here, but rather to a potentially nutritious milieu. The data of Smith et al. suggest that in these cases nutrient supply from the top might change the behavior radically. Please nuance.\nIn sum, I consider that the proposed mechanism of overtake on surfaces is likely to be correct and supported by a reasonable amount of evidence. I would have preferred a more thorough investigation of the dynamics at the front, which would be more in line with the standard of publication in Nature physics, but overall I am not opposed to publication at this stage.", "reviewer_4": "My view of the manuscript has not been changed by the authors’ response because it does not address my questions directly; see my detailed response below. And the theoretical derivation (the font is messed up in the response letter completely, so I followed the corresponding section in the SI) is exactly opposite to the experimental observation in the cited paper (Dell’Arciprete et al., Nat. Commun., 2018, doi: 10.1038/s41467-018-06370-3). Again, I agree that the phenomenon reported in the paper is conceptually interesting and novel, but the quality of both the experimental data and the theoretical analysis has not reached the level required to substantiate the novelty or other manuscripts in Nat. Phys.\nMajor:\n1. Regarding the coffee-ring effect: The authors claimed that the coffee-ring effect, if significant, should favor isotropic particles accumulating at the edge rather than anisotropic particles. However, the paper cited (Yunker et al., Nature, 2011, doi: 10.1038/nature10344) deals with hydrophobic polystyrene particles, which differ fundamentally from the hydrophilic E. coli cells decorated with LPS. The long-range interactions between particles and clustering at the air-water interface for these two systems can be quite distinct, making a direct analogy between them questionable. More importantly, Yunker et al. pointed out that coffee-ring effect of anisotropic particles is restored by adding surfactant to the suspension, which can be abundant in culturing media or secreted by bacteria. Therefore, this citation does not fully address my concern, raised upon viewing Movie S2, that long cells appear more prevalent at the front compared to the ratio inferred from OD. What I think would really be helpful is to quantify the number and distribution of cells near the edge of the homeland immediately after the initial droplet dries. This would clarify whether the perceived prevalence of long cells at the front in Movie S2 at the initial time point is significant.\n2. Regarding radial alignment of the nematic arms: The authors seem to have misunderstood the model and conclusions of Dell’Arciprete et al. (2018). While the equations they provide recapitulate the model in 1D and in 2D, the crucial point they omit in the 2D case is that the sign of in the key equation (in the third-to-last line of the new section in the SI, page 8; Dell’Arciprete et al. denote this by ) plays a critical role in determining the steady-state. If the growth-induced flow is compressible, then and there is a stable steady-state at . However, what Dell’Arciprete et al. found in their data is that the flow is incompressible, , and there is no radial alignment. Instead, Dell’Arciprete et al. found that their bacterial colonies feature only nematically ordered “microdomains” whose length scale roughly corresponds to the cell length. As I described in my last review, the conditions that give rise to radial alignment are not trivial: they critically depend on the nature of the growth-induced flow. For instance, Nijjer et al. (doi: 10.1038/s41467-021-26869-6) showed that verticalization in the core of growing biofilms—which affects the in-plane growth-induced flow experienced by cells in the basal layer by introducing a “growth void” in the core—causes radial alignment in the periphery; without this perturbation to the growth-induced flow, radial alignment does not occur. As such, the explanations that the authors provide here are incorrect.\nMinor:\n3. Regarding the continuum model: While I understand the authors’ point that removing injection of biomass due to growth from the continuum model is useful for “highlight[ing] a distinct collective mechanical mechanism” (lines 118–119 in the new manuscript), I believe the model-based analysis is incomplete without a model that actually tries to explain the data. If cells are growing at the front (which they clearly are), then such growth should be included in at least one version of the model. Moreover, the authors suggest that the model was formulated without growth to illustrate that the proposed takeover mechanism is independent of “any possible number advantage in inoculation,” but imposing equal growth rates to the two species would not necessarily introduce a number advantage to either, and should not be conflated with the issue with a number advantage at the front due to, e.g., the coffee-ring effect. The authors’ illustration of a growth-independent mechanical mechanism is interesting, but I believe that, without consideration of a version of the model with growth, this analysis is incomplete."}, "author_response": "We are happy that the reviewer recommends publication and we are grateful for the time spent to make us aware of the following set of minor points:\nl. 80 I am not sure what the purpose of the reference to Fig 2C at the end of the first sentence of the paragraph is, especially because 2A and 2B are not introduced yet. Was it intended to be 1C?\nWe thank the reviewer for noticing this and as references to fig 1 are redundant at this point in the text, we decided to remove the reference.\nl.103 It would be good to refer the reader to the specific images that illustrate the boundary alignment in the simulations, in Fig. 2 and the corresponding movie (time stamps 4 and 6 generations).\nIndeed, this specific reference has now been inserted.\nMovies: Including timestamps in the movies could be a good idea\nWe thank the reviewer for this comment, however, as all frame rates are specified in the captions, we have decided to keep the 7 movies as they are.\nTable 1: there might be some typos in the standard deviations of the aspect ratios l/w – they seem quite small compared to the ones of l and w\nWe thank the reviewer for pointing this out and, as we found the table caption was ambiguous, we have corrected this.\nL113 & 115 “90° to r” “along r”. In the new version of the text, the radial vector r is no longer defined.\nWe are grateful that the reviewer noticed that this definition (unintendedly) was removed during the last iteration. This has now been reinserted.\nL125-141 In this paragraph, when describing the behavior of the continuum phase model, the authors sometimes talk about “longer/shorter bacteria” when they are talking about the two phases (especially starting from l.134). This creates a bit of confusion, especially because they compare the model to the experiments in the same paragraph. I think they should carefully distinguish continuous model and experiments by systematically talking about “short/long bacterial phases” or something similar for the former.\nWe agree and have now clarified this according to the suggestion of the reviewer.\nl. 163 “this transition”: please remind that this is the nematic/isotropic, because the intercalated sentence of previous revisions slightly broke the flow of text.\nThis has now been corrected.\nl. 169 – 171 “Specifically, … at the interface (20).” I think it should be clearer that the first sentence is a deduction from the literature (ref 20) rather than a direct observation. I suggest changing “this alignment is diminished,” into “this alignment must be diminished”.\nThis has been clarified, as suggested.\nL 172 I think the authors might have meant Fig. S10 and not S8.\nWe thank the reviewer for making us aware of this, and this has been corrected.\nL 172 – 173 “The takeover rate … phase).” This sentence was slightly confusing. I assume the authors refer to Fig 3D, where the takeover rate for a given aspect ratio only depends on whether the smaller bacteria are nematic or isotropic, but not on their length for a given orientational order? Pointing to the figure might help clarify the message.\nIndeed, the message of this paragraph has been clarified in the present version of the manuscript."}]

Decision letter