Active Density Pattern Formation in Bacterial Binary Mixtures

Microbial communities often exhibit complex spatial structures that are important for their functioning, ecology, and evolution. While the role of biochemical interactions is extensively studied, how physical interactions contribute to structuring typically multispecies and phenotypically diverse bacterial communities is unclear. Here, we examined how motility, a major bacterial trait, affects the organization of model binary mixtures of motile and nonmotile Escherichia coli bacteria, revealing a novel type of active self-organization. Motile bacteria induce large-scale, fluctuating density patterns in nonmotile bacteria across a wide range of physiologically relevant cell densities. Combining experiments and quantitative modeling, we demonstrate that this pattern formation solely results from physical interactions and relies on two key ingredients: By swimming in circles at surfaces, the motile bacteria generate recirculating hydrodynamic flows that advect nonmotile cells, and the breaking of vertical symmetry by gravity permits local density accumulation. The density patterns fluctuate as the advection landscape slowly rearrange with motile cells configurations on the surfaces. This new nonequilibrium mechanism for pattern formation in bacteria belongs to a different class compared to previous models for self-organization in self-propelled systems, which rely on localized traffic jamming in two dimensions. It is instead similar to fluctuation-dominated phase ordering in active nematics. The behavior also drives the formation of large scale and highly structured aggregates of nonmotile cells that express adhesins in the mixture, and it showcases how motile species activity can shape the spatial organization of complex microbial communities.

Figure 1

Nonequilibrium density patterns in bacterial binary mixtures. (a) Scheme of the binary mixture experiment, featuring differently tagged motile and nonmotile E. coli strains mixed in various proportions after separate growth. (b) Microscopy images of mNeonGreen-tagged nonmotile E. coli strain in a bacterial mixtures with a motile E. coli strain (motile cells volume fraction ${\varphi }_M=0.18\%$, nonmotile ${\varphi }_{\text{NM}}=5.3\%$), measured $8\mu \mathrm{m}$ above the bottom of the $50\mu \mathrm{m}$ high experimental chamber. (c) Microscopy images of the mCherry-tagged motile E. coli strain in the same conditions as (b). (d) Microscopy images of the control where two differently tagged nonmotile strains of E. coli were mixed at the same volume fractions in the same conditions. (e) Phase diagram of the density heterogeneities of the nonmotile strain in binary mixtures with a motile one as a function of the volume fraction of both strains. The color scale represents the heterogeneity level. Each point represents the geometric mean of at least three biological replicates. (f) Aggregation of adhesive nonmotile cells alone (${\varphi }_M=0\%$) or in mixture with ${\varphi }_M=0.2\%$ motile cells. Images are taken 80 min after sample preparation.

Figure 2

Tumbling affects the density heterogeneities through the persistence of surface swimming. (a) Microscopy image of E. coli mixtures of a motile nontumbling strain ($\mathrm{\Delta }cheY$ mCherry, ${\varphi }_M=0.18\%$) and a nonmotile strain (mNeonGreen, ${\varphi }_{\text{NM}}=5.3\%$), at $8\mu \mathrm{m}$ above the bottom of the chamber, featuring heterogeneous patterns of nonmotile cell density. (b) Phase diagram of the density fluctuations in mixtures of a nontumbling motile strain ($\mathrm{\Delta }cheY$) (volume fraction in abscissa) with a nonmotile strain (volume fraction in ordinate). The color scale representing the heterogeneity level is the same as that in Fig. 1. (c) Heterogeneity levels of the nonmotile cells in a binary mixture with indicated motile strains, as a function of their volume fraction. The volume fraction of the nonmotile strain is kept constant (${\varphi }_{\text{NM}}=5.3\%$). (b),(c) Each point represents the geometric mean of three replicates. (c) Error bars indicate the standard deviation. (d) Trajectories of the different strains used as the motile strain in the binary mixtures, which were tracked at the bottom of the experimental chamber. (e) Probability density distribution of the radii of curvature of individual circular swimming trajectories of WT and $\mathrm{\Delta }cheY$ motile cells. Lines represent kernel density estimates. (f) Scatter plot of the persistence time $\tau$ of the same trajectories as (e), as a function of the radius of curvature of the trajectory, and probability density distribution of $\tau$ (right side). (e),(f) The data set comprises 4137 ($\mathrm{\Delta }cheY$) and 4475 (WT) individual swimming trajectories in eight biological replicates.

Figure 3

Dynamics of the nonmotile cells within the density patterns. (a) Instantaneous velocity field of the nonmotile strain at ${\varphi }_{\text{NM}}=5.3\%$ in a mixture with the motile strain $\mathrm{\Delta }cheY$ at ${\varphi }_M=0.53\%$, in the motility buffer (buoyancy $\mathrm{\Delta }\rho g=1$). (b) Flow structure factor $E\left(q\right)$ of the flow field of the nonmotile strain mixed with the indicated motile strains at indicated cell densities and buoyancies. (c) Temporal autocorrelation of the nonmotile cell velocity $C_v(t;q)$ as a function of the lag time $t$ for the Fourier component of the velocity $v(q,t)$ that corresponds to the peak of $E\left(q\right)$, $q=0.06\mu {\mathrm{m}}^{-1}$, in the indicated conditions. The velocity is measured on a shorter (0.2 s) time window than (a),(b) (2 s) to increase temporal resolution. (b),(c) The nonmotile cell density is ${\varphi }_{\text{NM}}=5.3\%$. Points indicate the mean, and error bars indicate the standard error of the mean on two biological replicates. (d) Example of the three-dimensional tracking of nonmotile cells close to a hole, performed in the mixture ${\varphi }_{\text{NM}}=5.3\%$, $\mathrm{\Delta }cheY{\varphi }_M=0.53\%$ in the motility buffer (buoyancy $\mathrm{\Delta }\rho g=1$). The white star represents the mean position of the hole center over the whole recording time, and the colored points represent the $XY$ projection of the 3D trajectories of the tracers (tagged nonmotile cells). (e) Average vertical velocity of the tracers $\langle V_z\rangle$ (black circles) and their density (green circles) as a function of their distance $r$ to a hole. (f) Average radial velocity of the tracers $\langle V_r\rangle$ (black circles) and horizontal speed $|V_{2\text{D}}|=\langle \sqrt{V_x^2+V_y^2\phantom{{}^1}}\rangle$ (inset) as a function of the distance $r$ to a hole. (e),(f) The velocities were quantified from 639 individual 3D trajectories situated less than $60\mu \mathrm{m}$ away from a hole center. Each data point represents the binned mean, and the vertical error bars represent the standard error of the mean. The continuous lines are simulated flows generated by circular swimmers ($R=10\mu \mathrm{m}$, $a^S{v}_0=70\mu {\mathrm{m}}^2$/s). The blue line (d) sums the vertical flow speed from the circular trajectories ($V_{Z,\text{simu}}$) and the sedimentation speed ($V_{\text{sed}}=0.05\mu \mathrm{m}/\mathrm{s}$). The yellow line (e) is the radial diffusive speed ($V_{\text{Diff}}$), while the green line (e) sums $V_{\text{Diff}}$ and the radial flow speed from the circular trajectories ($V_{r,\text{simu}}$).

Figure 4

Sedimentation controls the density heterogeneities. (a) Confocal images of the vertical distribution of nonmotile cells at the two extreme buoyancies $\mathrm{\Delta }\rho g=1$ (motility buffer) and $\mathrm{\Delta }\rho g=0$ (density-matched medium). (b) Phase diagram of the density fluctuations in a mixture of $\mathrm{\Delta }cheY$ motile strain (volume fraction in abscissa) with a nonmotile strain (volume fraction in ordinate) in density-matched suspending media ($\mathrm{\Delta }\rho g=0$). The color scale representing the heterogeneity level is the same as that in Fig. 1. (c),(d) Dose-dependence effect of buoyancy on the sedimentation (c) and the density fluctuations (d) of the most heterogeneous binary mixture (${\varphi }_M=0.18\%$, ${\varphi }_{\text{NM}}=5.3\%$, motile strain $\mathrm{\Delta }cheY$). (c) Nonmotile cell fraction (abscissa), measured by cell counting in confocal microscopy, as a function of the vertical position ($z$) in a channel of $50\mu \mathrm{m}$ height (ordinate), for suspensions at different buoyancies, normalized to motility buffer ($\mathrm{\Delta }\rho g$). The gray lines are exponential fits of the cell fraction as a function of $z$. (d) Density fluctuations of the nonmotile strain as a function (main figure) of the inverse of the exponential decay length ${\lambda }_{\text{sed}}$ of the sedimentation profile and (inset) of the normalized buoyancy $\mathrm{\Delta }\rho g$. (a)–(d) Each point represents the geometric mean of three replicates. Error areas (c) and bars (d) indicate the standard deviation.

Figure 5

Recirculation flows lead to heterogeneities of nonmotile cells in simulations of circular swimmers at surfaces. (a) Map of the axisymmetric mean flow field generated by a circularly swimming force dipole. The flow field is computed between two no-slip walls spaced by $H=40\mu \mathrm{m}$, and the dipole circulates $z_M=0.7\mu \mathrm{m}$ (about one cell body) above the bottom wall. Shown are the flow speed normalized to dipole force $a^S{v}_0$ (color), the velocity vectors (arrows), and streamlines in the ($r,z$) plane (solid lines), featuring a recirculation around a fixed point close to the circle radius. (b) Normalized recirculation flux, ${max}_{\left\{r\right\}}\mathrm{\Phi }\left(r\right)/a^S{v}_0$ [Eq. (A13), in $\mu \mathrm{m}$] as a function of the recirculation radius. The solid line indicates $1/R$ dependence. Inset: Scheme of the flow field generation. (c) Mean and maximum of the flow speed inside the circle as a function of the position of the fixed point (recirculation radius). Solid lines indicate power-law dependences. (d) Example of mean flow field generated by a population of circular surface swimming dipoles (density ${\varphi }_{Mc}=0.2\%$, $n_{Mc}=5\times {10}^3$ circles, for which experimental heterogeneity is maximal) for the distribution of circle radii of Fig. 2. Trajectory centers are evenly distributed at both surfaces and independent from each other. The vertical ($v_z$) and horizontal ($|v_{2\text{D}}|=\sqrt{v_x^2+v_y^2\phantom{{}^1}}$) components are shown in the ($x,y$) plane, $z=8\mu \mathrm{m}$ above the bottom wall. Color scales indicate $v/a^S{v}_0$ in $\mu {\mathrm{m}}^{-1}$. (e) Reconstructed microscopy image of negatively buoyant diffusive tracers ($v_{\text{sed}}=0.05\mu \mathrm{m}$/s, $D=0.3\mu {\mathrm{m}}^2$/s) that followed the mean circular swimmers flow field for 100 s, for the same conditions as (d). (f) Heterogeneity level of the nonmotile tracers, computed in simulations as a function of the volume fraction of motile circular swimmers ${\varphi }_{Mc}$ for nonmotile cells (NM) with volume fraction ${\varphi }_{\text{NM}}=0.4\%$, for a persistence time $\tau =60$ s. Control: homogeneous distribution; $\mathrm{\Delta }\rho g=1$: sedimenting NM; $\mathrm{\Delta }\rho g=0$: nonsedimenting NM; Long: elongated motile cells; Exp: experimental data for nontumbling motile cells, $\mathrm{\Delta }\rho g=1$ and ${\varphi }_{\text{NM}}=0.53\%$. Error bars for simulated data indicate standard error of the mean over six repeats. Experimental data encompass three biological replicates, and the error bar is standard deviation.