Microbial Range Expansions on Liquid Substrates

Despite the importance of fluid flow for transporting and organizing populations, few laboratory systems exist to systematically investigate the impact of advection on their spatial evolutionary dynamics. To address this problem, we study the morphology and genetic spatial structure of microbial colonies growing on the surface of a nutrient-laden fluid ${10}^4$ to ${10}^5$ times more viscous than water in Petri dishes; the extreme but finite viscosity inhibits undesired thermal convection and allows populations to effectively live at the air-liquid interface due to capillary forces. We discover that S. cerevisiae (baker’s yeast) growing on a viscous liquid behave like “active matter”: They metabolically generate fluid flows many times larger than their unperturbed colony expansion speed, and that flow, in turn, can dramatically impact their colony morphology and spatial population genetics. We show that yeast cells generate fluid flows by consuming surrounding nutrients and decreasing the local substrate density, leading to misaligned fluid pressure and density contours, which ultimately generates vorticity via a thresholdless baroclinic instability. Numerical simulations with experimentally measured parameters demonstrate that an intense vortex ring is produced below the colony’s edge. As the viscosity of the substrate is lowered and the self-induced flow intensifies, we observe three distinct morphologies: At the highest viscosity, cell proliferation and movement produces compact circular colonies with, however, a stretched regime of exponential expansion; intermediate viscosities give rise to compact colonies with “fingers” that are usually monoclonal and then break into smaller cell clusters; at the lowest viscosity, the expanding colony fractures into many genetically diverse, mutually repelling, islandlike fragments that can colonize an entire 94-mm-diameter Petri dish within 36 hours. We propose a simple phenomenological model that predicts the early colony dynamics. Our results provide rich opportunities to study the interplay between fluid flow and spatial population genetics for future investigations.

Popular Summary

Fluid motion plays a vital role in the transport and organization of a wide variety of biological systems. Hydrodynamic flows shape and reorganize microbial populations across all scales, affecting growth and strongly influencing population genetics. Experimental model systems can play an essential role in studying the surprising and complex behavior of living systems in fluid environments. We present an example of such a laboratory system that, combined with theory, uncovers a novel coupling between the metabolism of cell colonies and self-generated fluid flows.

In contrast to prior investigations that focused on microbial populations growing on hard agar plates, we introduce a novel experiment that probes microbial expansion on the surface of nutrient-rich liquid substrates that are 100 000 times more viscous than water. This experimental system allows us to investigate how flows impact the spatial structure of a population and its evolution.

We discover that nonmobile microbial colonies growing on these substrates create a vortex ring within the liquid by locally reducing the fluid density. The flow from the vortex, driven by unstable density variations caused by the metabolism of the cells, pushes back on the colony. This interaction can lead to remarkable fingerlike protrusions at the colony frontier, as well as entirely fragmented colonies that spread radially many times faster than their expansion velocity in the absence of a flow.

The rich diversity of observed behaviors suggests that microbial expansion on viscous fluids possess strikingly different growth dynamics from well-studied experiments on a hard agar substrate, providing a novel framework to examine the interplay between fluid flow and spatial population dynamics.

Figure 1

Selected yeast colony morphologies on (a) a hard agar plate after 72 h of growth and on the surface of the viscous substrate with decreasing viscosities: (b) for $\eta =600\pm 90\mathrm{Pa}\mathrm{s}$ after 72 h of growth, (c) $\eta =450\pm 70\mathrm{Pa}\mathrm{s}$ after 84 h of growth, (d) $\eta =300\pm 45\mathrm{Pa}\mathrm{s}$ after 36 h of growth, and (e) magnification of a single representative finger from regime (c). Qualitatively similar morphologies are observed in the range of viscosities indicated in (b)–(d). The figure shows merged bright-field and fluorescent images White, transmitted bright field; red, YFP strains; cyan, mCherry strains. The scale bars in (a) and b) correspond to 5 mm, the scale bars in (c) and (d) to 10 mm, and to 2 mm in (e).

Figure 2

(a) Azimuthally averaged yeast colony radius $R(t)$ during the first 24 h of growth on hard agar (blue circles) and on a liquid substrate with viscosity $\eta =600\pm 90\mathrm{Pa}\mathrm{s}$ (green squares). (b) The corresponding colony front velocity is extracted from $R(t)$. The colony exhibits two growth regimes on the liquid substrate: a superlinear regime for $t<t^{*}$ and a slowly decaying phase for $t>t^{*}$. We find that the colony front velocity approaches $v(t)=0.5\pm 0.05\mathrm{mm}/\mathrm{day}$ at long times ($t\gg t^{*}$) which is less than the velocity of yeast colonies growing on 2% hard agar plates. (c) Consecutive front spatial positions at equal 40-min intervals during the first 24 h of growth on liquid substrate with the same viscosity as (a) and (b), overlayed on top of a fluorescent (top) and a bright-field (bottom) image of the colony. Note that genetic demixing begins at the edge of the colony after the front slows down. The scale bar corresponds to 1 mm.

Figure 3

Experimental flow field at the viscous substrate’s surface over the first 48 h for compact yeast colony growth at a substrate viscosity of $\eta =600\pm 90\mathrm{Pa}\mathrm{s}$ for $t<t^{*}$ (a), $t>t^{*}$ (b), and $t\gg t^{*}$ (c). Each represented velocity field is averaged over 3 h. The central gray region delineated by red dashed lines indicates the growing colony’s radius position masking the fluorescent beads; we cannot directly measure the velocity below the colony with this experimental setup. The color map represents the flow velocity amplitude. The azimuthal average of the velocity radial profile is plotted every 10 min for $t<t^{*}$ (d) and every 20 min for $t>t^{*}$ (e) and $t\gg t^{*}$ (f). The lines’ intensity increases chronologically with times.

Figure 4

Experimental setup for a yeast colony growing on a thin layer of agar in a sealed container filled with the viscous liquid; no liquid-air interfaces are present, removing the possibility of Marangoni flows. (a) The colony is anchored to the top or bottom walls of a Petri dish and (b) on the side wall of a culture flask. Gravity points downward, and the fluid is seeded with fluorescent PIV beads to track fluid motion. (c) Fluid flow streamlines near the yeast colony (the dark circular patch) in the same configuration as (b) during a time interval of $\mathrm{\Delta }t\approx 6\mathrm{h}$ obtained via maximum intensity projection. The scale bar corresponds to 5 mm.

Figure 5

Baroclinic vorticity generation rate $\partial \mathbf{\omega }/\partial t\approx (1/{\rho }^2)(\mathbf{\nabla }\rho \times \mathbf{\nabla }p)$ normal to a radial cross section before flow is initiated by a yeast colony fixed at the surface of the viscous fluid in a radially symmetric Petri dish. The colony position is indicated by the brown bar, the pressure isobars in blue, and the density contours in gray. The isobars are near horizontal due to small density differences originating from nutrient depletion (in this simulation, $\mathrm{\Delta }{\rho }_{\max }\sim -0.003\mathrm{g}/\mathrm{mL}$). Whenever the pressure and density contours cross at an angle, vorticity is generated via the baroclinic term in Eq. (2).

Figure 6

(a) Snapshot of the simulated flow field below the yeast colony (brown bar) after flow is initiated, for $t\gg t^{*}$. The simulated flow field qualitatively matches our experiments with a vortex ring produced around the colony. (b) Azimuthal average of the numerical flow field using the measured parameters in Table 2 plotted every 12 h at the substrate fluid surface. The black circles correspond to the experimental flow radial profile measured for similar flow parameters after 24 h of growth and an initial $\eta =600\pm 90\mathrm{Pa}\mathrm{s}$. (c) Simulated and experimental peak radial velocity determined from PIV measurements 48 h after inoculation as a function of fluid height below the colony. The blue line with circles corresponds to the simulated values using the parameters in Table 2, the black shaded region is the standard deviation of the simulated points, and the black circles correspond to experimental data.

Figure 7

Morphologies of yeast colonies growing on a liquid media substrate over time at a variety of viscosities. Quoted substrate viscosities are accurate to about 10% (see Table 1). The figure shows merged bright-field and fluorescent images. White, transmitted bright field; red, YFP strains; cyan, mCherry strains. All images have the same scale, and the scale bar at the lower right corresponds to 10 mm. The left column is an enlargement of the colonies after 12 h of growth, and its scale bar corresponds to 5 mm.

Figure 8

(a) Magnification of experimental demixing patterns formed by two different yeast strains growing on a substrate with a viscosity $\eta =600\pm 90\mathrm{Pa}\mathrm{s}$ at different time points. The first three images have the same scale represented by the white bar on the upper right of the images; the scale bar corresponds to $100\mu \mathrm{m}$. The final picture at the bottom shows the same feature at the larger colony scale; the scale bar now corresponds to $500\mu \mathrm{m}$. (b) Snapshot of the simulated flow field below the yeast colony (brown bar) after flow is initiated. The simulated flow field is very similar to the one displayed in Fig. 6 except with a free boundary condition beneath the yeast colony. (c) Azimuthal average of the numerical flow field using the measured parameters in Table 2 plotted every 12 h at the substrate fluid surface with free boundary condition beneath the yeast colony.

Figure 9

Numerical solution of Eq. (11) for $h(\mathbf{r},t)/h_0$ at different values of $\mu -\alpha$ and equal time intervals. The radial coordinate $r$ is measured in units of $\sqrt{D_h/\mu }$, the width of the Fisher wave in the absence of a dilational flow. The colored dots correspond to the prediction of $h$ as a function of time from Eq. (16) and show good agreement between the theoretical prediction and simulation. (a) For $\alpha =0$, the colony height increases to $h/h_0=1$, and the front propagates radially with a constant velocity $v_F=2\sqrt{D_h\mu }$ with $\mu =1$. (b) When $\alpha <\mu$, the colony front propagation velocity increases exponentially with time, and the colony height decreases to $h^{*}=h_0(1-\alpha /\mu )<h_0$. (c) When $\alpha =\mu$, the dilational flow is strong enough to decrease the colony height below one cell size and $h(t)$ goes to zero logarithmically with radius. (d) For $\alpha >\mu$, the colony thins exponentially fast, potentially signaling that holes open during its early exponential growth; these holes may be responsible for the highly fragmented colonies at later times.

Figure 10

(a) Colony radius as a function of time during the first day of growth for two different viscosities: blue circles, $\eta =600\pm 90\mathrm{Pa}\mathrm{s}$; green squares, $\eta =300\pm 45\mathrm{Pa}\mathrm{s}$; black line, exponential fit realized for $t<t^{*}$. The short-time behavior is consistent with an exponential growth of the colony radius in both cases, but the growth is much faster at lower viscosity. (b) Same as in (a) with experiments realized for colonies growing on a 1-mm-thin substrate liquid film on the top of a nutrient-rich gel layer. We find that the exponential fit realized for $t<t^{*}$ exhibits a similar expansion rate for both viscosities.

Figure 11

Low-viscosity ($\eta =300\pm 45\mathrm{Pa}\mathrm{s}$) range expansion on a liquid substrate in the fragmentation regime. This image is taken for $t\gg t^{*}$ in a single experiment under conditions similar to those in Fig. 1, except that the substrate fluid height is $H=4\mathrm{mm}$ instead of 7 mm. The more isolated cell fragments clearly collect on the midplanes separating the larger “continents,” consistent with the downwellings associated with a vortex ring underneath each continent, as suggested by the sketch on the top. The scale bar corresponds to 10 mm.

Figure 12

Upon deposition on the highly viscous substrate fluid, yeast cells first spread uniformly in the circular inoculant region usually called the “homeland” [7] and then clump together via a coarsening process. (a) Distribution of cells 20 min after inoculation on the viscous substrate and (b) enlarged view immediately after inoculation (left) and after 20 min (right). The initially uniform distribution of yeast segregates into large clumps in a phase-separation process, suggestive of attractive interactions. The bottom scale bar corresponds to $100\mu \mathrm{m}$.

Figure 13

(a) Shear viscosity and (b) corresponding shear stress for different polymer concentrations measured via steady-state flow tests. The fluid is weakly shear thinning for $\dot{\gamma }\lesssim {10}^{-1}{\mathrm{s}}^{-1}$ and reaches a Newtonian plateau at less than or equal to 2% polymer. For other concentrations, a power law of $\tau =m{\dot{\gamma }}^n$ describes the shear stress for shear rates of $\dot{\gamma }\lesssim {10}^{-1}{\mathrm{s}}^{-1}$. (c) and (d) plot $m$ and $n$ as a function of polymer concentration; the fluid becomes more non-Newtonian (shear thinning) as more polymer is added.

Figure 14

Fit to the fluorescein diffusion constant $D$ in our viscous fluid. The blue line corresponds to the measured initial radial profile, and the green line is measured the final profile. Black dotted line represents the profile predicted by Eq. (d1) with the best-fit value of $D$

Figure 15

Simulated average flow velocity as a function of mass flux rate $j_{\text{colony}}=a{c}_1$ into a submerged yeast colony in rich nutrient conditions. The velocity field is determined above the center of the colony in the rising plume of fluid from the bottom to the top of the domain.

Figure 16

Radially symmetric simulation of the concentration field $c/c_1$ below a yeast colony (the thick brown bar) on the surface of our viscous liquid after 48 h and at $\eta =400\pm 50\mathrm{Pa}\mathrm{s}$. Equally spaced contours of constant concentration are shown.

Figure 17

A polyhedral dual mesh (blue cells) and corresponding height field $h$ used by the forcedThinFilmFoam program [52].

Figure 18

Total number of nutrient molecules absorbed by the yeast relative to the original number of nutrient molecules in the fluid $N/N_0$ as the fluid viscosity is varied. The height of the fluid is $H=7\mathrm{mm}$ and the rest of the simulation parameters are set using the values in Table 2. The Rayleigh number $\mathrm{Ra}=(H^3\beta c_{1}g)/(D\nu )$ varies from 0 to approximately $10^4$ due to the changing viscosity $\nu$, and the mass flux number $G=(Ha)/({\rho }_0\beta D)\equiv H/\ell$ is fixed at $G\approx 4.4$. Note that the stronger advection of the substrate fluid at lower viscosities leads to an enhanced uptake of nutrient molecules.