Why Do Phage Play Dice?

Abstract

Phage lambda is among the simplest organisms that make a developmental decision. An infected bacterium goes either into the lytic state, where the phage particles rapidly replicate and eventually lyse the cell, or into a lysogenic state, where the phage goes dormant and replicates along with the cell. Experimental observations by P. Kourilsky are consistent with a single phage infection deterministically choosing lysis and double infection resulting in a stochastic choice. We argue that the phage are playing a "game" of minimizing the chance of extinction and that the shift from determinism to stochasticity is due to a shift from a single-player to a multiplayer game. Crucial to the argument is the clonal identity of the phage.Organisms typically use information from the environment to suitably modify their behavior. Some of these can be considered "strategic" decisions for maximizing the chances of success of the population. For example, many organisms are able to adjust their reproductive strategies according to environmental conditions. A typical signal that often triggers changes in the reproductive strategy is population density (1, 6). Temperate bacteriophages are among the simplest organisms that are able to sense population density and choose their reproductive strategy accordingly. In general, temperate phage choose to stay dormant and replicate along with the host (lysogeny) rather than making many virions and killing the host (lysis) when larger numbers of phage attack a bacterial population (4, 7, 10). Phage lambda's choice between lysis and lysogeny has become a paradigm for developmental decisions (12). For this lysis-lysogeny decision, we use game theory to understand under what conditions different strategies might be optimal. In particular, we focus on the determinism versus the stochasticity of the strategy. We show that deterministic strategies are best when the phage has minimal information and must consider itself as the only "player" in the game. In contrast, having multiple identical players can make a stochastic strategy the best.We consider the phage to be playing a game whose purpose is to minimize the chance of extinction. For singleplayer games of this kind, where the player has several options but limited information, the optimal strategies are typically deterministic (13). And it is indeed the case that the lysislysogeny decision is often deterministic. This statement is somewhat at odds with the general perception that stochasticity plays an important role in the decision, a view initiated by reference 2, which invoked stochasticity to explain Kourilsky's measurements (7) of the frequency of lysogenization in lambda. However, our analysis of Kourilsky's data (7, 8) ( Fig. 1; see also Materials and Methods) shows that (i) when a single phage infects a bacterium (i.e., when the multiplicity of infection [MOI] is 1), it invariably goes lytic and (ii) when the MOI is 2, the decision is stochastic, with a slight preference toward lysogeny (this preference increases as the MOI increases...

Population dynamics of decision making in temperate bacteriophages

“…Another important parameter influencing the lyse/lysogenize decision is the number of genetically identical phages coinfecting the same bacterium (24; 25). Based on experimental data for phage (24), it was estimated that the probability to be lysogenized can be as low as 1% for bacteria infected by a single phage, but close to 100% when coinfected by three or more phages (26), the exact values being dependent on the experimental conditions (25; 27; 28). Similar results were obtained for other temperate phages and bacterial hosts (29; 30), indicating that the ability of temperate phages to respond to multiple coinfections plays an important role in their ecology and could represent an evolved trait.…”

Evolutionary stability of the lysis‐lysogeny decision: why be virulent?

“…Stewart and Levin demonstrated broad conditions under which temperate and lytic phages could coexist, and offered two likely explanations for the prevalence of lysogeny: (i) in spatially structured environments, lysogenic colonies are resistant to diffusing phage, and (ii) if the host cell population oscillates, lysogeny is favored when the host population drops below the minimum density required to support a lytic phage population. Lysogeny can also be favored as a bet-hedging strategy in the face of harsh environmental conditions that would eliminate free phage while leaving viable host cells (Avlund et al 2009;Maslov and Sneppen 2015), or when susceptible hosts are completely exhausted by the phage (Sinha et al 2017). Recent experimental and theoretical work has demonstrated that lysis (virulence) is favored when susceptible hosts are abundant, while lysogeny is favored when transmission is limited by available host cells or by spatial structure (Berngruber et al 2013(Berngruber et al , 2015.…”

Solitons and collapse in theλ−repressor protein

“…We find that the last four solitons form as the pairs (4,5) and (6,7). At the putative location of the third soliton, we also observe the formation of a soliton-soliton pair.…”

“…It is described in numerous molecular biology textbooks and review articles [1]- [7]. The interplay between the lysogeny maintaining λ-repressor (CI) protein and the CRO regulator protein that controls the transition to the lytic state is a simple model for more complex regulatory networks, including those that can lead to cancer in humans.…”