Population Dynamics of Phage and Bacteria in Spatially Structured Habitats Using Phage λ and Escherichia coli

Abstract

Bacteria living in physically structured habitats are exposed heterogeneously to both resources and different types of phages. While there have been numerous experimental approaches to examine spatially distributed bacteria exposed to phages, there is little theory to guide the design of these experiments, interpret their results, or expand the inferences drawn to a broader ecological and evolutionary context. Plaque formation provides a window into understanding phage-bacterium interactions in physically structured populations, including surfaces, semisolids, and biofilms. We develop models to address the plaque dynamics for a temperate phage and its virulent mutants. The models are compared with phage λ-Escherichia coli system to quantify their applicability. We found that temperate phages gave an increasing number of gradually smaller colonies as the distance increased from the plaque center. For low-lysogen frequency this resulted in plaques with most of the visible colonies at an intermediate distance between the center and periphery. Using spot inoculation, where phages in excess of bacteria were inoculated in a circular area, we measured the frequency and spatial distribution of lysogens. The spot morphology of cII-negative (cII(-)) and cIII(-) mutants of phage λ displays concentric rings of high-density lysogenic colonies. The simplest of these ring morphologies was reproduced by including multiplicity of infection (MOI) sensitivity in lysis-lysogeny decisions, but its failure to explain the occasional observation of multiple rings in cIII(-) mutant phages highlights unknown features of this phage. Our findings demonstrated advantages of temperate phages over virulent phages in exploiting limited resources in spatially distributed microbial populations.

Importance: Phages are the most abundant organisms on earth, and yet little is known about how phages and bacterial hosts are influencing each other in density and evolution. Phages can be either virulent or temperate, a difference that is highlighted when a spatially structured bacterial population is infected. Phage λ is a temperate phage, with a capacity for dormancy that can be modified by single gene knockouts. The stochastic bias in the lysis-lysogeny decision's probability is reflected in plaque morphologies on bacterial lawns. We present a model for plaque morphology of both virulent and temperate phages, taking into account the underlying survival of bacterial microcolonies. It reproduces known plaque morphologies and speaks to advantages of temperate phages in a spatially structured environment.

FIG 1

Plaque morphology caused by a single initial phage. The progeny spread on a bacterial lawn with a relatively low initial density of bacteria. The four panels reflect the final patterns obtained about 12 h after an initial infection of a wild-type λ and mutants that lack one of the central factors in the lysis-lysogeny decision circuit (29, 59–62). wt is wild-type λ phage displaying a classical turbid plaque, whereas the cI⁻ mutant gives a clear plaque. The two mutants shown in the lower panels give weaker turbid plaques, with additional spatial features. Scale bar, 1 mm. For the influence of mutants on the λ phage regulatory network see, e.g., the work of Avlund et al. and Trusina et al. (56, 63).

FIG 2

Simulation of plaque dynamics caused by a single virulent phage. (a) The development of the bacterial density with the default parameter set and initial bacterial density B₀ = 1/(320 μm²). The gray region shows the final number of bacteria per microcolony as a function of the distance from the infection center r. We define the plaque radius, r_half, as a position at which the bacterial concentration is half of that at large distances. (b) The development of the plaque radius, r_half, from the simulation shown in panel a. The bottom panels show the final plaque radius (c to e), the plaque expansion speed dr_half/dt (f to h), and the plaque appearance delay time (time at which r_half start to increase from zero) (i to k) as a function of phage/bacterial parameters. For each plot, all parameter but the varied parameter are kept at their default values. The filled circles are the data with B₀ = 1/(320μm²), and the open circles are those with B₀ = 1/(36 μm²). For the dependence on phage diffusion rate D_p (c and f), we also show dashed lines that are proportional to $\sqrt{D_p}$.

FIG 3

Simulations of plaques formed by a single temperate phage infection. Default parameters were used for a lawn with initial density B₀ = 1/(320 μm²), here shown after 10 h of incubation. The width of the shown area is 3 mm. Scale bar, 1 mm. (a) Simulation with no MOI dependence and α = 0.1. The microcolonies dominated by sensitive bacteria are shown as blue, lysogens are red, and gray marks cells in latency. The same color code applies to panels b to d. (b) Simulation with MOI dependence and α = 0.1. (c) Simulation with no MOI dependence and α = 0.005. (d) Simulation with MOI dependence and α = 0.005. (e) Simulation with no MOI dependence and α = 0.005 as in panel c, where the colonies smaller than 10 μm in radius are displayed in a lighter shade of gray in proportion to their radius. (f) Simulation with MOI dependence and α = 0.005 The visualization method is the same as that in panel e. (g) Profiles of lysogens, sensitive cells, infected cells, and the number of cells that directly took the lysogen decision (cumulative sum over time) for the simulations with no MOI dependence and α = 0.005. (h) Profiles as described for panel g but for the simulations with MOI dependence and α = 0.005.

FIG 4

Morphology of spots obtained by spot assay. The plaques are formed by initial addition of a droplet of water with phages, progeny of which spread on the growing bacterial lawn. The bottom agar was supplemented with maltose. The rightmost panels show part of the plaque at higher magnification and with red beads that mark the initial distribution of phages. The estimated initial conditions represent bacterial density B₀ = 1/(36 μm²) and phage density P₀ = 1/(18 μm²). Thus, API within the droplet is 3 for the wt and 2 for the cIII⁻ and cII⁻ mutants. Scale bar, 1 mm.

FIG 5

Quantification of the spot assay. (a) Morphology from the spot experiments with the API under the spot at 30 for the wt and 20 for the cIII⁻ and cII⁻ mutants. The bottom agar was supplemented with maltose. We use an initial bacterial density of B₀ = 1/(320 μm²), which is a lower B₀ than that used in the experiment shown in Fig. 4, to minimize colony overlaps for counting. Scale bar, 1 mm. (b) Lysogen frequency is evaluated from (microcolony count in the middle)/B₀ for different API (average phage input) values. (c) Average microcolony volume in the middle, evaluated from the diameter of the colony in the image, assuming that each microcolony is spherical. The error bar for the data in panel b is from the square root of the colony count, and for panel c it shows the standard deviation. (d) Testing lysogenic state in spots. Samples were picked from either the rings or the central region, as shown in the image. Colonies purified from the samples were tested for immunity to λ phage. The results are tabulated to the right, as (number of λ-immune colonies)/(number of tested colonies). In experiment 2 (exp2), the bottom agar was supplemented with maltose.

FIG 6

Simulations of spots formed by spot assay. Initial bacterial density is B₀ = 1/(36 μm²), and images were taken after 10 h of incubation. The area shown has a width of 4 mm, with the middle of the spot being the left bottom corner. The colonies smaller than 10 μm in radius are displayed in a lighter shade of gray in proportion to their radii. The initial spot size is circular, with a radius of 2 mm. For all simulations, α = 0.01 was used. (a) Simulation with no MOI dependence and API of 2. (b) Simulation with no MOI dependence and API of 20. (c) Simulation with MOI dependence and API of 2. (d) Simulation with MOI dependence and API of 20. (e) Profiles of lysogens, sensitive cells, infected cells, and number of cells that directly took the lysogen decision (cumulative sum over time) for the simulations with MOI dependence and API of 2. (f) Profiles as described for panel e but for the simulations with MOI dependence and API of 20.