Sustainability of Virulence in a Phage-Bacterial Ecosystem

Virulent phages and their bacterial hosts represent an unusual sort of predator-prey system where each time a prey is eaten, hundreds of new predators are born. It is puzzling how, despite the apparent effectiveness of the phage predators, they manage to avoid driving their bacterial prey to extinction. Here we consider a phage-bacterial ecosystem on a two-dimensional (2-d) surface and show that homogeneous space in itself enhances coexistence. We analyze different behavioral mechanisms that can facilitate coexistence in a spatial environment. For example, we find that when the latent times of the phage are allowed to evolve, selection favors “mediocre killers,” since voracious phage rapidly deplete local resources and go extinct. Our model system thus emphasizes the differences between short-term proliferation and long-term ecosystem sustainability.The replication strategies of phages fall into two major categories: virulent and temperate. A temperate phage has the ability to integrate its DNA into the host chromosome, where it is then replicated along with the bacterial DNA during cell division. This strategy allows the phage to slow down or completely stop exploitation of the bacteria, thus reducing the risk of driving its host to extinction. A virulent phage lacks this ability, and it is not fully understood how they manage to coexist with their bacterial prey (4, 19). Consider, for example, the highly effective T4 phage. For the sake of argument, let us assume a burst size of 100 offspring upon lysis. On average, not more than a single phage out of each burst of 100 should survive to infect another bacterium, or else the phage would rapidly outgrow the bacteria and drive them to extinction. The half-life (t_1/2) of a free T4 phage particle has been measured to be approximately 10 days in LB at 37°C (6). Therefore, on average, at least t_1/2 × log₂(100) ≈ 2 months should pass between infections to prevent runaway phage growth—a time span that seems highly unreasonable for many of the environments where phage and bacteria interact, such as soil or biofilm. Even a more considered calculation, inserting the above half-life measurement into more realistic Lotka-Volterra-like predator-prey models (9) does not change the conclusion that T4 and other virulent phages appear to be far too effective predators for coexistence to be feasible. It is, however, an undisputed fact that virulent phages and bacteria have coexisted for eons and do so still, everywhere around us and inside us. One possible explanation for this puzzle is that bacteria constantly evolve resistance to existing phages and that the phages evolve to attack resistant bacteria in a continuous arms race. This “Red Queen” argument (23) has, however, been criticized on the grounds that the rates of evolution of phages and bacteria are not symmetric (17, 12). Recent measurements support this: in soil, phages appear to be “ahead of the bacteria in the coevolutionary arms race” (24). We therefore wish to explore mechanisms other than bacterial resistance that may promote coexistence between virulent phages and bacteria.Historically, phage-bacterial ecosystem models have ignored the issue of space, utilizing zero-dimensional approaches, such as ordinary differential equations (e.g., see references 1, 5, 13, 14, 15, and 21). However, many real phage-bacterial ecosystems are found in environments with a complex spatial structure, such as soil, biofilms, or wounds in animal and plant tissue. Schrag and Mittler (20) showed that coexistence between virulent phage and bacteria is feasible in a chemostat but not in serial cultures, due to the heterogeneous nature of the environment in the chemostat. Further, experiments done by Brockhurst et al. (3) indicate that reduced phage dispersal can prolong coexistence for virulent phage and bacteria in spatial environments by creating ephemeral refuges for the bacteria. Kerr et al. (10) introduced a simple cellular automaton to model fragmented populations of phage and bacteria in which coexistence was more easily achieved when migration was spatially restricted. Thus, the main extension to the simple predator-prey framework that we examine will be to add a spatial dimension.We construct and compare two phage-bacterial ecosystem models: one model where the phage and bacteria exist in a two-dimensional space, such as the surface of an agar gel (referred to as the “spatial model”), and the other model where the phage and bacteria are repeatedly mixed, mimicking serial cultures or a well-mixed broth (referred to as the “well-mixed model”). We show that space does indeed enhance coexistence. We then move on to explore other mechanisms that phage could incorporate into their behavior to further enhance coexistence. These can broadly be classified as “hardwired” (where every phage follows the same deterministic strategy) versus “adaptive” (where each phage potentially behaves differently, thus allowing the population to explore different options).We have chosen to look at three specific mechanisms as examples of these categories: (i) phage effectiveness would be reduced if they were unable to register whether they were infecting live, infected, or dead bacteria (a hardwired behavior); (ii) phage could prolong their latent time, concurrently increasing burst size, depending on the number of multiple infections (also a hardwired behavior, but a more “active” sort, where each phage senses and responds to information from the environment; T4 is known to use such a lysis inhibition strategy), and (iii) phage offspring could have altered latent times due to mutations in the holin genes (an adaptive behavior). We will compare each of these mechanisms in the spatial and well-mixed models to investigate whether the heterogeneity possible in a spatial environment affects the outcome.