Morphogenesis of bacterial colonies in liquid crystalline environments

TL;DR

This work demonstrates that bacterial colonies proliferating in nematic liquid crystals form aligned, single-cell-wide chains whose subsequent buckling is driven by a competition between growth-induced viscous compression and the LC’s elastic resistance. By combining experiments with a continuum slender-filament model, the authors show that LC elasticity enforces end-to-end alignment, while distributed growth-induced stresses along the chain lead to highly localized buckles, distinct from classical Euler buckling. The theory identifies four key dimensionless parameters—the aspect ratio $\Lambda$, the viscosity-anisotropy ratio $\chi$, the anchoring strength $w$, and the Ericksen number $Er$—and predicts a scaling $\Lambda^* \sim Er^{-1/2}$ for the buckling threshold, with $L^*$ decreasing as LC rigidity increases and anchoring strengthens. Quantitative agreement between measured buckling lengths and theory yields plausible anchoring strengths and validates the mechanism by which LC elasticity sculpts proliferating colonies. Overall, the work reveals a mechanistic pathway by which anisotropic, elastic environments can control living matter morphogenesis and points to broader implications for bacteria in natural LC-like media and for designing programmable living materials.

Abstract

Natural bacterial habitats are often complex fluids with viscoelastic and anisotropic responses to stress; for example, they can take the form of liquid crystals (LCs), with elongated microscopic constituents that collectively align while still retaining the ability to flow. However, laboratory studies typically focus on cells in simple liquids or complex fluids with randomly-oriented constituents. Here, we show how interactions with LCs shape bacterial proliferation in multicellular colonies. Using experiments, we find that in a nematic LC, cells generically form aligned single-cell-wide "chains" as they reproduce. As these chains lengthen, they eventually buckle in a highly localized manner. By combining our measurements with a continuum mechanical theory, we demonstrate that this distinctive morphogenetic program emerges because cells are kept in alignment due to the LC's elasticity; as each chain lengthens, growth-induced viscous stresses along its contour eventually overcome the elasticity of the surrounding nematic, leading to buckling. Our work thus reveals and provides mechanistic insight into the previously-overlooked role of LCs in sculpting bacterial life in complex environments.

Figures (9)

• Figure 1: Proliferating nonmotile bacteria form chain-like colonies in liquid crystalline environments.(a) Fluorescent confocal microscopy time sequence of nonmotile E. coli proliferating in nutrient-rich LC-free fluid; cells form an isotropic dispersion as they grow, divide, and diffuse apart. (b) Same as in a, but in nematic DSCG solution (15w/w%); cells instead remain aligned end-to-end, forming a single-cell-wide chain that eventually buckles. (c) Same as in b with crossed-polarizer imaging overlaid (directions indicated by A and P), revealing local reorientation of the LC director field $\boldsymbol{n}$ accompanying chain buckling (bright regions). The overall far-field orientation imposed on the director by the underlying substrate is shown by the double-headed arrow. (d) Three-dimensional confocal reconstruction of a chain-like colony after 520, showing the serpentine, single-cell-wide internal structure. (e) Schematic of the LC director profile around a rod-shaped bacterium with weak tangential anchoring; boojums (topological defects) form at the cell poles where the director field must accommodate the curved cell surface. (f) Fluorescent confocal micrograph with crossed-polarizer imaging overlaid (directions indicated by A and P) of two cells dispersed in nematic DSCG solution. The image shows the local reorientation of the LC director field $\boldsymbol{n}$ around the cell, with the emergence of boojums at the cell poles. The overall far-field orientation imposed on the director by the underlying substrate is shown by the double-headed arrow. Experiments showed are performed using a microfluidic device 25 in height, 25 in width, and 22 in length.
• Figure 2: LC-mediated elastic forces are required for chain formation.(a) Non-proliferating E. coli cells (i) remain randomly dispersed in LC-free fluid but (ii) spontaneously align and form end-to-end aggregates in nematic DSCG (18w/w%). Images show confocal micrographs with crossed-polarizer imaging overlaid in (ii) as in Fig. \ref{['fig:fig_expt_chain']}(c),(f). (b) Time sequence showing chain disintegration after LC removal; LC-free solvent is introduced at $t = 0$. Cells remain in smaller side-by-side aggregates after LC removal, likely due to residual surface adhesin interactions chekli2023escherichianwoko2021bacteria that persist after cells are brought together by LC-induced elastic forces. See Movie S\ref{['vid:dilution video']} for full field of view and dynamics.
• Figure 3: Characterization of chain buckling.(a) Successive centerline configurations of a buckling chain in 18w/w% DSCG, with colors indicating time. The chain initially grows straight before developing highly localized, sharply curved buckles. (b) Tortuosity (contour length divided by end-to-end distance) as a function of contour length for the chain in a; the sharp increase marks the onset of buckling at the critical length $L^*$. (c) Measured buckling lengths for chains in 15w/w% (light blue, $n=13$) and 18w/w% (light orange, $n=38$) DSCG. Horizontal lines indicate means; the critical buckling length decreases with increasing LC concentration ( ** indicates $p \leq 0.01$, two-sample $t$-test).
• Figure 4: Continuum model of a growing bacterial chain in a nematic LC. The chain is treated as a slender filament of fixed radius $a$ and growing length $L(t)$. The transverse ($\hat{\bm{y}}$) displacement $u(s,t)$ is parameterized by the arclength $s$. Growth generates internal compression $T(s,t)$ along the chain contour due to viscous drag from the surrounding LC, while chain deflections are resisted by the elastic restoring force from the deformed nematic director field (wavy lines, bottom).
• Figure 5: Theoretical predictions for the critical buckling length.(a) Dimensionless critical buckling length $\Lambda^*\equiv L^*/(2a)$ as a function of the Ericksen number $\hbox{Er}\equiv a^2\zeta_\parallel\alpha /(2\pi K)$ for different values of the dimensionless anchoring strength $w\equiv aW/K$. Solid curves show numerical solutions of the linear stability analysis [Eq. \ref{['eq:eigen']}]; dashed curves show the analytical approximation [Eq. \ref{['eq:fittedmixed']}]. The scaling $\Lambda^*\sim\hbox{Er}^{-1/2}$ reflects the balance between growth-induced viscous compression and LC elastic restoring forces. (b)$\Lambda^*$ as a function of $w$ for different values of $\hbox{Er}$. For weak anchoring ($w\ll1$), the director can slip relative to the bacterial cell surface, reducing the effective elastic coupling and allowing buckling at shorter chain lengths; for strong anchoring ($w\gg1$), the coupling saturates and $\Lambda^*$ becomes independent of $w$. Both panels show predictions for the free-free boundary conditions and $\chi\approx5$ [Methods]. Symbols show experimentally measured buckling lengths at 15 w/w% (filled circle) and 18 w/w% (open circle) DSCG, plotted at their corresponding $\hbox{Er}$ values; comparison with theory yields inferred anchoring strengths $w\approx0.01$, corresponding to $W\approx 2.6\times 10^{-7}\,\J/m^2$.