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Regulated CRISPR Modules Exploit a Dual Defense Strategy of Restriction and Abortive Infection in a Model of Prokaryote-Phage Coevolution

Fig 1

Bifurcation analysis of a simple model of a prokaryotic immune system with regulated autoimmunity side effect.

(A) p, q and v denote densities of uninfected, infected cells, and phage respectively. q undergoes autoimmunity at a rate of γqϕ, while p undergoes autoimmunity at a suppressed rate determined by δγpϕ. The second figure shows the bifurcation behavior of the free cell densities with respect to the control parameter δ, beyond a certain critical value of which one of the steady states vanishes. (B,C) Two-parameter bifurcation diagram revealing coexistence (C) and host extinction (E). Each plot instance is denoted by a tuple <AB> where A and B can indicate low (L) or high (H) values or extinction (E) of prokaryote (free—solid, infected—dotted) and phage (dashed) respectively. GPϕ and GQϕ denote the rescaled free cell autoimmunity rate and infected cell autoimmunity (abortive infection) rates respectively. High values of GQϕ lead to complete phage evasion. Parameter values αp = 1 hr−1, Φ = 108 cells ml−1, γv = 5 hr−1, αv = 50, αq = 5×10−9 ml phage−1hr−1.

Fig 1