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Biophysics of interface formation We first confirmed that swarming E. coli cells form macroscopically visible interfaces if and only if complementary adhesins are present in adjacent cell populations (Fig. 2a, Supplementary Fig. S11). We seeded a pair of colonies with complementary adhesins that cytoplasmically express red and yellow fluorescent proteins (Ag2-RFP|Nb2-YFP) (Fig. 2a left). We fitted a generalized Hill function to the resulting fluorescence profiles (Methods Equation 1) and determined the width of a transition region for adhesive cell pairings to be 500 ± 10μm (mean ± STD, n = 3 replicates throughout if not stated otherwise), which was significantly narrower than 1290 ± 20μm (p < 0.001, Tukey’s HSD) for non-adhesive pairings (Ag2-RFP|Ag2-YFP) (Fig. 2a left/right). As the interface remains much wider than the size of a single cell (∼ 2μm), the narrowing of the transition region suggests that cells are intermixed with incomplete blocking. Additionally, the total cell density is characteristically increased at the interface with cell density reductions on either side. Without adhesion, both strains combine to a nearly homogeneous distribution (Fig. 2a right). Hence, these adhesins mediate a novel type of emergent density patterning distinct from previously established mechanisms relying on signalling and motility [29] or inter-strain competition [30]. To quantitatively capture this interface-forming behavior and larger scale patterning, we introduced adhesion into a minimal continuum model of bacterial swarming [30] (Fig. 2b, Supplementary Text S1). Each strain i is described by a spatio-temporal density ρi(r,t) (r position, t time), which grows to saturation ρmax at rate gi, spreads with effective diffusion constant Di, and interacts with a complementary adhesive strain j to form a new phase ρij via adhesion of strength K. In accordance with our previous results [10], the adhesion is considered irreversible. Using initial conditions of two spatially localized strains, the model recapitulates the outgrowing wavefronts, as well as the characteristic peak and troughs at the interface, which are absent without the adhesins (Fig. 2c, Supplementary Video S4). Matching simulation and experiment yielded biologically reasonable estimates for all model parameters (D = 47 ± 8μm2s−1, g = 14 ± 6h−1, K = 130 ± 50h−1), (Fig. 2c). This model predicts that tuning seeding conditions enables quantitative control over various geometric interface prop- erties, which we confirmed experimentally (Figs. 2d-i, Supplementary Text S1): Decreasing adhesion binding rate K should widen the interface (Fig. 2d), which we confirmed by adding a small peptide competitive inhibitor (EPEA) against Nb2 [10] to quantitatively titrate adhesin levels; varying inducer concentration produced equivalent results (Supplemen- tary Fig. S12). Delaying the expansion of one colony by varying relative initial seeding concentrations (Supplementary Fig. S13) should produce interfaces angled and shifted towards the delayed colony (Figs. 2e vs. 2f), which we confirmed over a wide range of seeding ratios (Fig. 2i). Differences in expansion rate D1 vs. D2 should lead to interfaces curved towards the slower-growing colony - even engulfing them (Fig. 2g, Supplementary Video S5), which we confirmed by using a slow-growing Nb3 variant, Nb3-1 [10]. The Nb3, Ag3, Ag2 and Nb2 lines all have comparable expansion rates (Supplementary Fig. S14). Non-point source seeding should behave like a summation of many point sources, which we confirmed by seeding one strain in a line, producing the expected parabola (Fig. 2h, Supplementary Fig. S15). For extensions to the model, see Supplementary Texts S1.6, S1.7, Video S6. Swarming adhesion mechanism