Spatial vulnerability: bacterial arrangements, microcolonies, and biofilms as responses to low rather than high phage densities

Abstract

The ability of bacteria to survive and propagate can be dramatically reduced upon exposure to lytic bacteriophages. Study of this impact, from a bacterium's perspective, tends to focus on phage-bacterial interactions that are governed by mass action, such as can be observed within continuous flow or similarly planktonic ecosystems. Alternatively, bacterial molecular properties can be examined, such as specific phage‑resistance adaptations. In this study I address instead how limitations on bacterial movement, resulting in the formation of cellular arrangements, microcolonies, or biofilms, could increase the vulnerability of bacteria to phages. Principally: (1) Physically associated clonal groupings of bacteria can represent larger targets for phage adsorption than individual bacteria; and (2), due to a combination of proximity and similar phage susceptibility, individual bacteria should be especially vulnerable to phages infecting within the same clonal, bacterial grouping. Consistent with particle transport theory-the physics of movement within fluids-these considerations are suggestive that formation into arrangements, microcolonies, or biofilms could be either less profitable to bacteria when phage predation pressure is high or require more effective phage-resistance mechanisms than seen among bacteria not living within clonal clusters. I consider these ideas of bacterial 'spatial vulnerability' in part within a phage therapy context.

Keywords: adsorption; bacteriophage; biofilms; cellular arrangements; ecology; microcolonies; particle transport; phage therapy; phages.

Figure 1

Illustration of phage and bacterial contributions to phage adsorption rates. Generally phages are relatively small and bacteria somewhat larger. Since diffusion rates are inversely proportional to particle size, whereas target size is proportional to particle size, the result is that phage diffusion (larger arrows pointing right) is a more important contributor to phage adsorption than is bacterial diffusion (smaller arrows point left) while bacterial target size is more important than phage target size to the likelihood of phage‑bacterial encounter. An approximate doubling of total bacterial size (lower right) consequently affects target size but has little relevant impact on combined diffusion rates. Note that arrow lengths reflect an assumption that phages are one-tenth the diameter of the coccus and one-twentieth the diameter of the diplococcus.

Figure 2

Shading of bacteria by bacteria. Shown is a progression starting with two “free” coccus-shaped bacteria (left) which is followed by a diplococcus displaying some degree of attachment (middle) that in turn is followed by a diplococcus displaying maximal attachment as well as minimized surface-to-volume ratio (right), i.e., existing as a combined-volume sphere of 2^1/3 -fold increased radius over an individual cell (see calculation, below). The left-hand lack of arrangement shows no shading whereas the right-hand arrangement shows an approximation of maximal shading for a combined spherical shape. The middle arrangement displays some intermediate degree of shading and therefore some intermediate overall target size between maximal and minimal (holding cell volumes constant). Note that the volume of a sphere, V₁, is equal to . Twice its volume (V₂) therefore is , which as a sphere is equal to . For , then r₂ = 2^1/3r₁. With such shading, then, diameter increases by only 2^1/3 = 1.26 fold.

Figure 3

Illustration of the tendency of phages to display biases towards acquisition of locally available bacteria. Here shown to the right is phage acquisition of a bacterium (blue) that is found as part of the same arrangement as a lysing bacterium (red with dashed border). The green arrows represent outwardly diffusing phage progeny released upon bacterial lysis while the shorter, gray arrows illustrate the tendency of those phages that are released immediately adjacent to an uninfected bacterium to encounter that bacterium. Contrasting this second bacterium looming large in the vicinity of an adjacent phage burst, even at a high plankton bacterial density of 10⁸ per mL, each free bacterium (left) occupies a total environmental volume of 10⁴ µm³ (1 cm = 10⁴ µm, meaning that 1 mL = 1 cm³ = 10¹² µm³, where 10¹² µm³/10⁸ bacteria = 10⁴ µm³/bacterium). This density in turn implies an average distance between bacteria of about 10^4/3 (i.e., the cube root of 10⁴ µm³), or more than 10 µm, which one may compare with a typical bacterium diameter of about 1 µm. Thus, bacteria in arrangements can be not-unreasonably described as having local densities that should encourage phage adsorption with higher likelihood than that seen among planktonic, individual bacteria.

Figure 4

The model. Parameters include P (density of phages in environment), k (phage adsorption constant), (phage adsorption constant considering reductions due to shading of bacteria by bacteria found within bacterial arrangements), n (number of bacteria found per arrangement), N (bacterial density of overall environment), L (phage latent period, which is the duration of a phage infection), and (number of bacteria per arrangement lost subsequent to phage infection of one cell in the arrangement). Likelihood of phage adsorption of bacterial arrangements is n and density of arrangements within environments is equal to N/n = N₀/n (or indeed n₀ and N₀/n₀, respectively, to reflect that n changes as a function of time in the figure). The inequality t ≥ 2L indicates how phage acquisition of bacteria within a bacterial arrangement, according to this model, involves at least two sequential rounds of phage infection. The absence of cells in the lower right is intentional as too is the reduction in cell number to n_t in the lower left. Both of these reductions in cell number, going from middle to bottom, indicate phage-induced bacterial lysis.