Spatiotemporal establishment of dense bacterial colonies growing on hard agar

  1. Mya R Warren
  2. Hui Sun
  3. Yue Yan
  4. Jonas Cremer
  5. Bo Li  Is a corresponding author
  6. Terence Hwa  Is a corresponding author
  1. University of California, San Diego, United States
  2. California State University, Long Beach, United States
  3. Fudan University, China
22 figures and 1 additional file


Figure 1 with 1 supplement
Experimental observations of the growth and morphology of a bacterial colony.

(A–E) Confocal images of an E. coli colony harboring GFP expression growing on 1.5% agar (glucose minimal medium) taken at various time after seeding (t=0). The center of the colony is indicated by the red dot. Single- and multi-layer regions are distinguished by red circles based on fluorescence intensity; see 'Experimental Methods'. (F) The radius of the first (red) and second layer (orange) of the colony, as well as their difference (green), versus time. (G) The cross-sectional profile of the growing bacterial colony at indicated time after single-cell inoculation. (H) After the buckling at around t=13 h, the colony radius (red symbols) increased at a constant speed VR=45.2 μm/h (red line), while the colony height (blue symbols) increased linearly with speed VH=12.4 μm/h (blue line). The latter slowed down some time after t=24 h. (I) The dependence of the radial speed VR (red symbols) and the vertical speed VH (blue symbols) on cell growth rate (x-axis), for colonies grown in minimal medium with 8 different carbon sources (Supplementary file 1-Table S1): glucose (O); arabinose (□); mannitol (); maltose (◇); fructose (); melibiose (); sorbitol (); mannose (☆). The lines are best linear fit of the data.
Figure 1—source data 1

Experimental data for the temporal development of colony profiles and velocities.
Figure 1—figure supplement 1
Data for five repeats of E.coli EQ59 grown on 1.5% (w/v) agar in minimal medium with 0.2% glucose (11 mM), and incubated, covered, at 37°C for up to 3 days; cf. 'Experimental Methods'.

Their radii and heights were periodically monitored using a confocal microscope. To monitor the colony growth over long periods of time, we started with identical colonies at seed time separated by several hours. Growth curves extending over a period of multiple days were obtained by 'stitching together' the radii and height data at times where they overlapped; cf. section on Experimental Methods. The recorded radii data (A)-(E) and height data (G)-(K) clearly showed linear regimes. The data were fitted by straight lines over the linear regimes to obtain the speed of radial expansion VR (F) and that of the height increasing VH (L) for these five repeated experiments. VR has an average of 42.84 μm/h and standard deviation of 2.42 μm/h. VH has an average of 12.18 μm/h and standard deviation of 0.56 μm/h. Similar analyses were done for colonies grown in other carbon sources described in Figure 1I.
Figure 1—figure supplement 1—source data 1

Repetitions for the temporal development of colony height and radius.
Schematics of cell-cell, cell-agar, cell-fluid, and surface tension forces investigated in this study.

Green area indicates the colony (with cells in yellow). Blue area indicates the agar.
Figure 3 with 1 supplement
The simulated growth and morphology of a bacterial colony.

(A) A semi-log plot of number of cells vs. time showing the exponential growth of the population starting from a single cell at t=0. Red line shows exponential growth rate of 0.96 h-1. (B) Cross sections of the growing colony at various times after seeding of a single cell. (C) Plots of the radius (red) and height (blue) vs. time up to t=20 h, showing that, after an initial transient period of ~10 h, the growing colony increases linearly at the radial speed VR18 μm/h (red line) and vertical speed VH6.0 μm/h. The blue arrow at t=6 h indicates the time when the colony height starts to increase. (D) The radius of the first (red) and second (orange) layer of the colony as well as their difference (green) vs. time. (E–M) Top view of the colony at various time. Cells in the bottom layer (blue) and upper layers (yellow) are fitted into red circles. The time evolution of buckling phenomenon is captured in detail in (J–M).
Figure 3—figure supplement 1
The spatially varying cell density ρ (per unit volume of colony) is related to the spatially varying cell volume fraction ϕ by ρ=ϕρcell, where the volume fraction ϕ is defined as the volume of all cells in a unit volume of the colony and ρcell is the constant mass density of a typical mature cell; cf. Appendix 1.2 on nutrient update.

(A) and (B): The volume fraction ϕ in the xz cross section of the colony, calculated with the mean m and standard deviation σ, with (AλS=1.0 h-1, m = 0.678, and σ=0.030; and (BλS=0.5 h-1, m=0.680, and σ=0.034. (C) and (D): The effect of coarse-graining size to the volume fraction ϕ. The average of ϕ (C) and the standard deviation of ϕ (D) in the coarse-graining with different sizes.
Figure 4 with 2 supplements
The cross-sectional anatomy of a simulated colony.

(A) Snapshot of cross-sectional view of the colony at t=20 h. Cyan represents horizontally oriented cells (45o with z-axis); Yellow represents vertically oriented cells (45o with z-axis). (B) Fraction of vertically oriented cells averaged over z vs radius. (C) A side view of the azimuthally averaged director field, indicating the orientation of the rod-like cells. (D) A side view of the azimuthally averaged velocity field. (E) Vertical component of velocity, Vz, at various values of z along the center of the colony. Increase in vertical speed is seen only for the bottom 10 µm (F) A cross-sectional view of the colony, color representing the time since last division. Purple and blue represent cells that have not divided for the past 10 h, and red represents the actively dividing cells. (G) A cross-sectional view of the local growth rate in the colony, with the color bar showing the values of local growth rate. A disc-shaped 'growth zone' is revealed by the red color at the bottom of the colony.
Figure 4—figure supplement 1
A few top layers of cells in the colony visualized using simulation data.

(A) and experimental data (B). In (A), a cell is colored green (resp. red) if its angle with the vertical z-axis is less (resp. greater) than 45.
Figure 4—figure supplement 2
Fraction of verticalized cells increase for large colonies.

(A) The bottom view of a simulated colony at t=7h, with the cells outlined by the black curves. Overlapping cells are of different layers. (B)-(D) show the fraction of vertically oriented cells (cells with an angle <45o with z axis) plotted versus the radius of the colony (B), the height of the colony up to 80 µm (C), and the height of the colony up to 10 µm (D).
Figure 5 with 2 supplements
Vertical penetration of nutrients.

(A) The profiles of nutrient concentration Cctr(z)=C(0,0,z) along the z-axis at different times. (B) The profile Cctr(z) in the uniform scale vs. that in the rescaled z-axis, zλS. (C) The numerical results for the height velocity VH vs. the batch culture growth rate λS with a fixed cell division length ldiv (open circles) and variable ldiv (asterisk), respectively. The square root fit for the open circles (solid line) is given by the expression VH=5.5λS+0.6; the linear fit for circles with λS0.5 h-1 (dashed line) is given by the expression VH=3.2λS+2.9.
Figure 5—figure supplement 1
Semi-log plot of the steady-state nutrient profile Cctr(z) = C(0, 0, z) : reconstructed from 3D simulations (green *); and the numerical solution to the 1D model (cf. Appendix 2.3 on nutrient penetration) with discretization Δz=4 μm (green circles) and Δz=0.1 μm (black line), respectively.

The linear part below the line of the Monod constant KS=0.02 mM (dashed blue line) indicates the exponential decay of the concentration. Shown in the window is the quadratic curve Cctr(z)= 0.0663z-0.4332+0.016 (red dotted line), fitting the numerical solution to the 1D model with Δz=0.1 μm for the concentration value above the Monod constant.
Figure 5—figure supplement 2
Profiles of nutrient concentration Cctrz=C(0,0,z) versus z for various values of the batch culture growth rate λS.

These nutrient profiles were reconstructed from 3D simulations. A larger value of the batch culture growth rate λS leads to a lower nutrient concentration, indicating a faster consumption of nutrients by cells.
Coarse-grained view of director, velocity and pressure fields in the bottom layer of colony.

(A) The bottom view of a simulated colony. Color scheme is the same as in Figure 4A. (B) Bars show the planar component of the coarse-grained director field at the bottom layer. (C) Arrows show the planar component of the coarse-grained velocity field at the bottom layer. Colors in (B) and (C) indicate the local pressure; see scale bar on the far right. The pressure is expressed in unit of P0=γsurf/w0 where γsurf is the surface tension, the main force underlying pressure build-up in our model.
Spatiotemporal nutrient profiles.

(A) The xz cross sectional view of the nutrient concentration inside the colony and in the agar, at time t=20 h. (B) The nutrient profile at the agar surface for different times. The nutrient concentration vs. time at the center (C) and at the periphery (D) of the colony at the agar surface.
Figure 8 with 2 supplements
Physical characteristics near the outer periphery of the colony.

(A) The azimuthally averaged local speed of radial expansion Vr vs. the signed distance Δr from the edge of the colony (cf. Equations (A1.5.1) in Appendix 1) at various times. (B) The azimuthally averaged local height H vs. Δr at various times. (C) The azimuthally averaged local speed of vertical expansion Vz vs.Δr, averaging over t= 12, 16, 20 hr. (D) The azimuthally averaged local pressure P vs. Δr at time t= 20 h. As in Figure 6, pressure is expressed in unit of P0=γsurf/w0. (E) The azimuthally averaged height H vs. Δr at growth rate λS= 0.5 h-1 and 1.0 h-1. (F) The simulated colony horizontal expansion speed VR vs. the batch culture growth rate λS with a fixed ldiv(red open circles) and a growth-rate dependent ldiv (red closed circles) using dynamic friction. The dashed line that fits the open circles is given by VR=16.9λS+0.8; the solid line that fits the closed circles for λS0.5 h-1 is VR=5.7λSldiv-0.2; the dash dotted line fits the closed circles with VR= 22.1λS- 5.2. In these expressions, the speeds are in unit of μm/h and growth rate in  h-1. For comparison, we also include simulated VR vs. λS with a growth-rate dependent ldiv, for a model with static friction alone (see Equations (A1.4.6) of Appendix 1) between cell and agar (blue triangles).
Figure 8—figure supplement 1
The azimuthally averaged and rescaled local growth rate λ/λS as function of the signed distance Δr to the colony rim with various values of the batch culture growth rate λS.

Precise definition of this signed distance Δr is given in Equations (A1.5.1) in Appendix 1.5 on coarse-grained variables. At the rim Δr=0, the nutrient concentration C is close to Cs, the constant concentration value in the boundary condition, and λ/λS is close to Cs/(Cs+KS), which is 0.96 with our choice of parameters Cs=0.5 mM and KS=0.02 mM. (A) The average is taken over the entire colony, where the variation of the (rescaled) local growth rate is within 6%. (B) The average is taken over 1/3 of the colony near the rim, where the variation of the (rescaled) local growth rate is within 2%.
Figure 8—figure supplement 2
A zoomed in view of the periphery of the colony shown in Figure 4A, overlaid with coarse-grained velocity field (zoomed in view of the same periphery region in Figure 4D).

Δr is the signed distance from the edge of the colony. Wb is the buckling width.
Parameter dependence of colony growth characteristics.

Simulation results using the full model with 2x increase in glucose concentration (panel A) and 4x decrease in all frictional parameters (panel B) for VR (red bars) and VH (blue bars). Specifically, in panel (A) we fix the friction at a high level (with μca=0.8, μcc=0.1, γcc,t=10000 μm1h1, and hran=0.1 μm), and use Cs=0.5 mM as the lower glucose concentration, Cs=1.0 mM as the higher glucose concentration. In panel (B), we fix the glucose concentration at the lower level (Cs=0.5 mM), and vary the friction, from the higher value of μca=0.8, μcc=0.1, γcc,t=10000 μm-1h-1hran=0.1 μm used in (A) to the lower value of μca=0.2, μcc=0.025, γcc,t=2500 μm-1h-1hran=0.025 μm. The corresponding experimental results are shown in panels C and D: In (C), glucose concentration was varied with agar density fixed at 1.5%. In (D), agar density was varied with glucose fixed at 0.2% (w/v). The data for VH in panel C is consistent with a square root dependence on nutrient concentration (blue line) expected from the basic analysis in Figure 5.
Figure 9—source data 1

Experimental data on the horizontal and vertical colony expansion speeds at various glucose and agar concentrations.
A schematic summary of key mechanisms in the growth of an E.coli colony.

After an initial, exponential monolayer growth, buckling occurs at the center of the colony. Cells then grow actively only in the bottom layers (red vertical arrows) whose thickness (HS) is determined by the nutrient penetration level (dashed blue line). Cells lying above them are passively pushed up. Throughout this yellow triangular region, cells are oriented vertically. Near the colony edge (cyan region), the cells are oriented planarly and grow outward (horizontal red arrow) continuously in a spread mode to expand the colony in the radial direction. The width of this annulus (Wb) is determined by mechanical effects arising from the surface tension which pulls the thin layer of cells into the agar, and cell-agar friction which builds up the pressure from the outer edge of the layer, eventually causing buckling at an inner radius where cells transition to the vertical orientation (the green region). These two characteristic parameters, HS and Wb, set the speeds of radial and vertical expansions, VR and VH, respectively, as shown in red. The growth rate dependence of these parameters is shown in blue.
Schematic of the computational box and different regions in the model of simulation.

The computational box is Ω=(L, L)×(L, L)×(a, b), where all L, a, and b are positive numbers in the units of length. This box is divided into the air region Ω0, colony region Ω1, and agar region Ω2=(L, L)×(L, L)×(a, 0), respectively. See Supplementary file 1-Table S5 for typical values of L, a, and b used in our simulations. The colony surface or colony-air interface Γ01 separates the colony from air. The plane z = 0 in the computational box is divided into two parts. One is the interface that separates the colony from agar, and is denoted by Γ12. The remaining part, denoted Γ02, separates the air from agar. Note that, since the bacterial colony grows with time t, all the air region Ω0, the colony region Ω1, the colony-air interface Γ01, and the colony-agar interface Γ02 depend on time t.
Schematic view of cell growth and division.

(A) A sphero-cylinder model of an E.coli cell. Here, w0 is the diameter of each of the hemispheres, p and q are the centers of these hemispheres, l=|pq| is the cylindrical length of the cell, n=(pq)/l is the unit vector along the cylindrical axis of the cell, and rc is the center of the cell. (B) Cell division. Once the cylindrical length of a cell reaches a critical value ldiv, the cell divides into two daughter cells. The two centers of hemispheres of the mother cell become the centers of hemispheres of the daughter cells. Each of these two daughter cells has the cylindrical length l0 with fluctuations, where l0 is a constant cylindrical length for any new born cell and any initial cell in the simulation. Fluctuations of angular velocities are also introduced for the daughter cells; cf. Appendix 1.3.
Schematic view of cell-cell and cell-agar interactions.

(A) Cell-cell interaction. Two cells, centered at rc and rc', respectively, are in contact with each other. The shortest distance between the central cylindrical lines of the two cells is d=aa' with a and a' two points on the cylindrical central lines of these two cells, respectively. The amount of the overlap of these two cells is δcc=w0-d. We shall denote by rcc the center of the line segment connecting a and a'. The total interaction force, exerted at center rcc, is the sum of the normal force Fcc,n in the normal direction ncc=(a-a')/d and the tangential force Fcc,t in a direction orthogonal to ncc that is determined by the relative velocities of these two cells; see the details in Appendix 1.4 on force calculations. (B) Cell-agar interaction. A cell, centered at rc, touches the agar surface that has the mean position at z=0 and the roughness hran (the maximum fluctuation around the mean), with δca the amount of the overlap of the cell and agar. If the center of the hemispherical cap of the cell corresponding to the end that dips into the agar is p=xa, ya, za, then δca=w0/2 za. Denote rca=(xa, ya, za-w0/2), which is the midpoint of the line segment along the vertical line passing through the point p between z=0 and z=-δca. The total cell-agar interaction force Fca, exerted at the center rca, is the superposition of a normal force Fca,n in the vertical direction and the tangential force Fca,t in a direction along the xy plane that is determined by the velocity of the cell; cf. Appendix 1.4.
Schematic view of surface tension acting on cells at the colony boundary.

(A) a snapshot of part of a growing colony from a typical computer simulation. The red curve defines the macroscopic colony-air interface which is used in updating the nutrient profile; cf. Γ01 in Figure 11 and Appendix 1.1. Cells on the top of the colony are held down by the surface tension force. (B) A sequence of configurations of colony during the early stage of growth. Top: Initial cells grow exponentially and form a monolayer. All cells in this layer are held down by the surface tension force. Middle: As more cells are born in the monolayer, the frictions between these cells and the rough agar surface increase. The competition between such frictions and the surface tension force that pulls down cells leads to an accumulation of the lateral pressure in the cells. The monolayer buckles up once that the surface tension can no longer hold down all the cells in the monolayer. Such buckling occurs at certain radial distance from the center of colony; cf. Figure 8D. Bottom: Once the monolayer buckles, the colony starts to grow vertically. In the meantime, the buckling region moves outward as the colony expands radially. (C) The parameters used in the definition of surface tension force. The parameter hcell is the height of a cell that sticks out of the macroscopic colony surface; it is measured from the mean height of the agar surface z=0 to the 'tallest point' in the cell. The blue and red lines describe the macroscopic water level (indicated by hw) and colony height (indicated by h), respectively. The parameter δh is used to control how tightly the surface tension holds back those cells on the top of the colony. See more details in Appendix 1.4c.
Appendix 1—figure 1
Schematic view of a nested finite difference grid for the agar region Ω2.
Appendix 1—figure 2
The standard (A) and modified (B) model for friction between two objects, as a function of tangential relative velocity between the two objects, where μs and μd are the static and dynamic friction constants, respectively.
Appendix 1—figure 3
Schematic of the derivation of the surface tension force.
Appendix 2—figure 1
Experimental measurement on VR and VH with various batch culture growth rates.

Data are fitted with the stright line VR=51.27λS7.96 and the squre root curve VH=12.7λS for the redial and vertical speeds of expansion VR and VH respectively. (B) Simulation results on VR and VH with various batch culture growth rates and with a variable diviting length ldiv. data are fitted for λS0.5h1 using the straight line VR=22.1λS5.24 the squre-root curve VH=6.12λS, respectively.
Appendix 2—figure 2
Statistics of cells undergoing growth transition.

(A) The histogram of the number of generations of the cells that experienced high-to-low growth rate transition.(B) Curves of growth rates vs. shifted time for 100 cells randomly selected from those 80% cells.
Author response image 1
Lack of verticalization for thin colonies.

(A) Reproduction of Figure 2A from (Su et al., 2012). (B) Bottom view of a simulated colony at t=7h. (C) The fraction of vertically oriented cells (defined by the angle with the z-axis less than 45 degrees) vs. height from the simulation.
Author response image 2
Experimental results on the confocal images of a bacterial colony at different positions, from the center to the edge.

The bacterial strain and the growth medium are the same as described in “Experimental Methods” in the main text, except that the thickness of agar dish is ~0.3mm. The picture was taken at roughly 24 hours after the initial inoculation.
Author response image 3
The dynamic and static friction models distinguished by the growth-rate dependence of radial expansion speed.

(A) From main text Figure 1F. Experimental results on the radial speed VR and the vertical speed VH with respect to various batch culture growth rates. (B) From Figure 8F in the main text (new version). Simulation results of radial speed VR of the colony, where both static and dynamic frictions are included in simulations. (C) New simulation results of radial speed VR of the colony, where only the static friction is included.

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  1. Mya R Warren
  2. Hui Sun
  3. Yue Yan
  4. Jonas Cremer
  5. Bo Li
  6. Terence Hwa
Spatiotemporal establishment of dense bacterial colonies growing on hard agar
eLife 8:e41093.