PMC

Linear increase of colony radii with time. The radii of three colonies of Pseudomonas aeruginosa grown at 21°C are plotted as a function of time. The three sets of data correspond to three different inoculation volumes: 1 µL (red dots), 3 µL (green squares), and 14 µL (blue stars). The solid lines are the least square fits to straight lines. For all three colonies, the radius increased linearly with time and the rate of the increase was approximately independent of the initial size of the colony, as would be the case under high-nutrient conditions. Note that for the largest colony the expansion seems to slow down slightly at the end, possibly because of nutrient depletion. Similar behavior was observed for other colonies of P. aeruginosa and Escherichia coli for all growth conditions studied. The obtained values of the expansion velocities are given in . The inset shows a fluorescent image of a P. aeruginosa colony grown at 21°C; fluorescence from only one of the two alleles is shown.

Neutrality of Pseudomonas aeruginosa strains at 37°C. The gray dots represent individual measurements along the sector boundaries at pixel resolution (one pixel is 50 µm) from 24 colonies (524 sector boundaries) of P. aeruginosa. Positive φ represent boundary bending from cyan toward yellow sectors. Each red dot is the mean position of the gray dots in one of the 10 equidistant bins along the X-axis. The error bars represents 95% confidence intervals of the mean values. The green line is the expected dependence if the strains are neutral, [φ(r)] = 0. Since the expected line passes through all of the error bars, we cannot reject the hypothesis that the strains are neutral. In fact, the largest fitness difference consistent with the data is ~10⁻⁴. This comes from using to find v_⊥/v_‖ and relating v_⊥/v_‖ to the fitness difference, as in and . It is then reasonable to conclude that these strains can be considered equally fit on the timescales of our experiments. The corresponding data for P. aeruginosa strains grown at 21°C are also consistent with the assumption that the strains are equally fit. Escherichia coli strains are also equally fit (see and ).

Dependence of diversity at the expansion front on the initial size of the population in experiments (A), on-lattice simulations (B), and off-lattice simulations (C). The average number of sectors at the end of a range expansion is plotted against the square root of the initial radius of the colony R₀. These coordinates are chosen so that the theoretically predicted dependence (see ) is a straight line (solid lines). The error bars represent 95% confidence intervals. Parameters D_s/v_‖ and D_g/v_‖ can be estimated from the slope of the fit and its intercept with the Y-axis, respectively. A, Escherichia coli (black squares), Pseudomonas aeruginosa at 37°C (red triangles), and P. aeruginosa at 21°C (blue dots). B, Three different island-carrying capacities: N = 3 (black squares), N = 30 (red triangles), and N = 300 (blue dots). Each data point is the average of 40 simulations. Notice that the populations with higher N have more sectors in agreement with because populations with higher densities have lower D_g. In this plot, the error bars are represented by the size of the markers used. C, Because of the discrete nature of these simulations, we use the square root of the number of cells at inoculation as a proxy for the initial radius.

Plots of average spatial heterozygosity as a function of angle during range expansions from well-mixed 1 : 1 populations in our model (A), on-lattice simulations (B), off-lattice simulations (C), and experiments (D). A, Solution of with D_s = 1, D_g = 1, v_‖ = 1, and R₀ = 1 at various times t. Note that there is no significant difference between H(500, ϕ) and H(1000, ϕ) because H(t, ϕ) reaches a nontrivial limit shape as t → ∞. B, H(t, ϕ) from 24 on-lattice simulations with the same parameters as in , except that N = 300. In agreement with A, we see a gradual decrease of H(t, 0) with time. The radius r = v_‖t + R₀ is in direct correspondence with time t. C, H(t, ϕ) at the expansion frontier from 10 off-lattice simulations, as in . Because off-lattice simulations model a monolayer of cells, any spatial point in a colony has a unique genetic state; hence, H(t, 0) = 0. D, Average spatial heterozygosity calculated from eight Escherichia coli colonies inoculated with 3 µL of the bacterial mix of cells. As in B, radius r is directly related to time t because the spatiogenetic pattern is a frozen record of the genetic composition of the front. The dip in H(t, ϕ) widens with time, in agreement with . Similar to C, H(t, 0) = 0 because we assume that f(t, ϕ) is either 0 or 1 at every pixel. This assumption is valid only after the initial fixation time, as discussed in the text.

Genetic demixing in experiments (A), on-lattice simulations (B), and off-lattice simulations (C). Different colors label different alleles, and the initial mixing ratio was 1 : 1. A, The petri dish was inoculated with a drop (bounded by the white circle) of a mixture of Pseudomonas aeruginosa cells labeled with two different fluorescent markers that do not affect the relative fitness of the cells. As the drop dries out and the colony starts to expand (shown by arrows), the population at the front of the expansion demixes (separates) into sectors of different colors. This genetic demixing is due to the loss of local genetic diversity during the expansion (see ; ; ). This plate was incubated at 37°C. B, The habitat was a 1,000 × 1,000 array of islands arranged on a square lattice. Each island could harbor at most N = 30 individuals, consistent with the width of the layer of actively growing cells found in . The simulation was started with a well-mixed population occupying a disk of radius R₀ = 80 lattice spacings in the center of the habitat. C, The simulation was initiated with 1,024 agents placed at random within a circular inoculant in the center of the habitat. The boxed region of the colony is shown in the inset at a higher magnification. We attribute the slightly square shape of the colony to the underlying square grid used to solve the nutrient reaction-diffusion equation.

Chirality and boundary wandering in Escherichia coli colonies. A, Genetic demixing in a chiral E. coli colony. The image, taken from the bottom of the petri dish, shows the fluorescent signal from only one of the two segregating alleles. Bacterial colonies of Pseudomonas aeruginosa at 37°C and 21°C did not exhibit chiral growth. B, Twisting of sector boundaries in E. coli colonies. The gray dots represent individual measurements along the sector boundaries at pixel resolution (one pixel is 50 µm) from 30 colonies (390 sector boundaries). Each red dot is the mean position of the gray dots in one of the 50 equidistant bins along the X-axis. The green line is the least square fit to the red dots. According to , the slope of the green line equals v_⊥/v_‖, which yields v_⊥/v_‖ = 0.32. As shown in A and B, all sector boundaries twist on average in the same direction for chiral growth. In contrast, sector boundaries between nonneutral strains bend in both clockwise and counterclockwise directions because the boundaries around the fitter strains bend outward (). To exclude possible small fitness differences, we also separately analyzed boundaries that would bend in opposite directions if the strains were nonneutral. Nonneutrality would result in different values of v_⊥/v_‖ for these two sets of boundaries. Upon applying equivalent tests to those used in , we confirmed that v_⊥/v_‖ are the same, which supports the previous finding that these strains are neutral (). C, Random walks of sector boundaries. The same data as in B are used to plot the variance of φ(r); gray dots are the individual data points, and red dots are the averages. The green line is the least square fit to the first 25 red dots; the last 25 dots are not used because of large fluctuations due to a smaller sample size at large r. According to , the slope of the green line equals 2D_s/v_‖. The data sets for P. aeruginosa at 37°C and 21°C show similar behavior of the variance of φ(r), but the data set for E. coli fluctuates less partly because of the larger sample size and larger spatial diffusion constant compared with those of the other two experiments.