Slow killing cells survive better in small spaces when stochastically seeded from different planktonic abundances.

A. The final relative abundance of slow killer cells, , is shown as a function of the relative abundance in the planktonic suspension and the relative killing rate pi,S, κr, for Nmax = 9 cell simulations with stochastic seeding. B. The final relative abundance of slow killer cells, , is shown as a function of the deterministically set initial relative abundance of slow killing cells and κr, for Nmax = 9 cell simulations with stochastic seeding. C. The final relative abundance of slow killer cells, , is shown for stochastically seeded Nmax = 1025 cell simulations, again as a function of pi,S and κr. In all panels, the yellow trend lines show where . Slow killer cells survive in a much wider range of scenarios in Nmax = 9 cell simulations than in Nmax = 1025 cell simulations, similarly they also survive in more conditions when seeding is stochastic than when seeding is deterministic.</p

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Fig A: Finite size effects are independent of κF. Fig B: Stochastic Seeding is a major factor in all starting conditions. Fig C: 64 generations leads to semi stable frequencies. Fig D: 64 generations leads to consistent final frequencies. Fig E: Finite size effects are independent of cell growth being limited by low pressure threshold. Fig F: Finite size effects are independent of cell growth being limited by medium pressure threshold. Fig G: Finite size effects are independent of cell growth being limited by high pressure threshold. Fig H: Finite size effects are independent of cell growth being limited by packing fraction. Fig I: Finite size effects are independent of cell growth choice being limited by carrying capacity. Fig J: Killing events prevent jamming in large systems. Fig K: Low Pressure Threshold growth leads to low inter-strain contact. (PDF)</p

Slow killing cells in small systems survive in more starting conditions.

A. This heat map shows how the final relative abundance of the slow killing cells, , depends on its initial relative abundance, Si, and its relative killing rate, κr, in Nmax = 9 cell competitions. Each data point is the result of 1000 simulations. The yellow trend line shows where . B. This heat map shows the standard deviation of from simulations in A. The standard deviations are often quite large as competition in Nmax = 9 cell systems typically ends with one strain being eliminated. C. This heat map shows how the final relative abundance of the slow killing cells, , depends on its initial relative abundance, Si, and its relative killing rate, κr, in Nmax = 1025 cell competitions. In contrast to the Nmax = 9 cell system outcomes, for Nmax = 1025 cell systems, is non-zero for a smaller range of Si and κr. Each of the Nmax = 1025 cell data points is the result of 49 simulations. The red trend line shows where . D. This heat map shows the standard deviation of from simulations in C. The standard deviations here are small compared to the Nmax = 9 cell simulations.</p

Sampling fluctuations of initial conditions in small systems favor the slow killing strain.

The probability distribution of the initial relative abundance of slow killing cells, Si, is shown for Nmax = 9 cell and Nmax = 1025 cell systems (A and C, respectively) with on standard deviation outlined for each (yellow for small systems and red for large). The distribution of Si is of course much broader for the Nmax = 9 cell system than for the 1000 cell system. B, D. These heat maps show the relative impact of each Si for determining , as a function of κr. This calculation is done by weighing the values of for different Si from Fig 3A and 3C by the probability that a particular value of Si occurs (from panels A and C in this figure). This number (w) is then normalized across each row, for ease of viewing. In effect, this quantity () represents how much each Si contributed to the results seen in Fig 2A. The first standard deviation for panels A and C are shown in B and D for each respective environment.</p

Slow killing cells are more robust against invasion when drastically disadvantaged.

A, B. These heat maps plot the final relative abundance of slow killing cells divided by the initial relative abundance of slow killing cells in the planktonic suspension, i.e, , as a function of the relative abundance of slow killers in planktonic suspension and the relative killing rate, κr, for Nmax = 9 cell simulations and Nmax = 1025 cell simulations (A and B, respectively). The black trend lines show where . indicates the slow killing strain increases its relative abundance. C. This heat map shows the difference between for the 9 and Nmax = 1025 cell simulations, i.e., it shows the results from A minus the results from B. Red indicates conditions in which the slow killing strain performs better in the Nmax = 9 cell environment, and blue indicates conditions in which the slow killing strain performs better in the Nmax = 1025 cell environment. White space indicates there is no difference between the two environments. The black contour line shows where the difference is equal to 0 indicating there is no difference between the large and small space.</p

Slow killing strains survive better in small spaces with equal starting abundance.

A. The fractional mean relative abundance of slow killing cells, , after 64 generations of simulation is plotted against the relative killing rate of the slow killer, κr, for different size simulations. Each line consists of 20 evenly spaced data points. Each data point is the mean of many simulations; for the Nmax = 9, 26, 68, 106, 1025, and 10,686 cell simulations we average across 750, 750, 500, 100, 50 and 20 simulations, respectively. For 106, 1025, and 10,686 cell simulations decreases rapidly with decreasing κr. Conversely, for Nmax = 9 cell and 26 cell simulations decreases linearly with κr. The standard error in from the simulations are shown along each trend. B. , the final proportion of the slow killing strain, is plotted against κr. Stochastic seeding means that the initial abundance of the slow killing strain was randomly selected from a binomial distribution with equal chance of either strain and the total cell count = 9 (), thus modeling random attachment events from planktonic suspension. All simulations in A. are seeded in this manner. Deterministic seeding with an equal proportion is impossible for 9 total cells, so we averaged the trends where the initial abundance of the slow killing strain is deterministically set at 4 and 5 cells out of 9 (). There are 20 data points in this trend line; each point is the average of 1000 simulations. These two lines describe simulated “small colony” sizes. The 1025 cell simulations are also stochastically seeded; the initial proportion is expected to be 0.5 +- 0.016. There are 20 data points in this trend line, and each is the average of 50 simulations. This line describes a simulated “large colony” (). The error bars represent standard error. C. γ, the “Seeding Effect” is the difference between the stochastic and deterministic small colony seeding trends divided by the difference between the stochastic, small colony and the large colony trends. This quantifies how much of the “total finite size effect,” i.e., the difference between large and small simulations, is a result of stochastic seeding. Here, γ is plotted against κr, showing that if κr γ > 0.5.</p

Experiments validate that small spaces decrease fitness difference across different abundances.

A. Two mutual killing strains of V. cholerae were grown for 8 hours in colonies ∼1mm in diameter on bare agar and in 7.5μm square holes in TEM grids with different starting abundances (pi,S). The means reported are the results of 3,3,6,5 experiments for the open space and 4,3,3,3 for the small grid. Error bars indicate standard error. B. ΔSf, the difference in between the small grids and bare agar, is plotted against Pi,S. These results recapitulate two effects predicted by our simulations. First, for smaller Pi,S values where the slow killing strain loses, the slow killing strain performs better in the small system than in the large system (i.e., ΔSf > 0). Second, for larger Pi,S values where the slow killing strain wins, the slow killing strain performs worse in the small system than in the large system (i.e., ΔSf < 0). Error bars indicate standard error.</p

Microbial communities in nature are often size constrained.

Microbial colonies studied in the lab are often large, such as these V. cholerae colonies grown on agar (B.). However, colonies in nature are often much smaller. For example, biofilms on grains of sand (A, adapted from [23]) are significantly smaller than those studied in the lab; we show simulations of Nmax = 9 cell systems and a Nmax = 1000 cell simulation with approximate scaling for context. The image in A was used under the Creative Commons Attribution 4.0 International License. C. In our simulations we confine two mutually antagonistic strains (shown in red and blue) to systems of different sizes but with similar cell densities; the shown sizes have ≈ 10, 000 cells, ≈ 1, 000 cells, and ≈ 100 cells respectively after 40 generations of growth. The circles show the extent of the soft intercellular interaction potential.</p

Experiments validate that slow killing strains perform better in small environments.

A. Two mutual killing strains of V. cholerae were grown for 6 hours in large colonies (∼ 1mm in diameter) on bare agar. The strain displayed in yellow is the slow killer and the blue strain is the fast killer. B. The same strains were grown for 6 hours confined to 60μm square holes in TEM grids. The final fraction of the slow killing strain is not significantly different than that of the bare agar. C. The same strains were also confined to TEM grids with 7.5μm holes. The final fraction of slow killing cells is significantly larger in these small grids than in either the large grids or bare agar. The mean frequency of the yellow strain is displayed under each panel (N = 5) where subscript show significance groups and connected panels show significant difference (p < 0.05).</p