Phage and bacteria diversification through a prophage acquisition ratchet

Lysogeny is prevalent in the microbial-dense mammalian gut. This contrasts the classical view of lysogeny as a refuge used by phages under poor host growth conditions. Here we hypothesize that as carrying capacity increases, lysogens escape phage top-down control through superinfection exclusion, overcoming the canonical trade-off between competition and resistance. This hypothesis was tested by developing an ecological model that combined lytic and lysogenic communities and a diversification model that estimated the accumulation of prophages in bacterial genomes. The ecological model sampled phage-bacteria traits stochastically for communities ranging from 1 to 1000 phage-bacteria pairs, and it included a fraction of escaping lysogens proportional to the increase in carrying capacity. The diversification model introduced new prophages at each diversification step and estimated the distribution of prophages per bacteria using combinatorics. The ecological model recovered the range of abundances and sublinear relationship between phage and bacteria observed across eleven ecosystems. The diversification model predicted an increase in the number of prophages per genome as bacterial abundances increased, in agreement with the distribution of prophages on 833 genomes from marine and human-associated bacteria. The study of lysogeny presented here offers a framework to interpret viral and microbial abundances and reconciles the Kill-the-Winner and Piggyback-the-Winner paradigms in viral ecology.

Introduction the sampling section below). The net rate of each species in the community was given by Here, B i denoted each species of sensitive bacterium, and P i each species of lytic phage. The index i 120 identified each species and ranged from 1 to n, leading to 2n coupled equations per lytic community.

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The bacterial net production rate was the balance between the bacterial growth rate and the 122 infection rate. In the bacterial growth term, the intrinsic growth rate r was reduced by a logistic 123 factor that accounted for the total concentration of bacteria in the lytic community, B = P n i=1 B i , times the infection rate) and viral decay (with a decay constant m).

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The coexistence equilibrium concentrations for each agent in the community, B ? i and P ? i , were 136 obtained by solving analytically the steady-state of Eq.

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Coexistence was required for the n species in the community, that is, B ? i > 0 and P ? i > 0. The The index i identified each species and ranged from 1 to n, leading to 2n coupled equations as in the 153 lytic community. The net production rate of lysogens was the balance between the lysogenic growth 154 rate and the spontaneous prophage induction rate. The lysogenic growth was the intrinsic growth 155 rate times a logistic term that accounted for the fraction of the total concentration of lysogens in 156 the community, L = P n i=1 L i , with respect to the carrying capacity in the lysogenic compartment, phages upon spontaneous prophage induction minus the phage decay and the removal of viable 159 viruses due to superinfection exclusion. A value of = 1/2 accounted for a mix of surface defense 160 mechanism with reversible phage-host binding ( = 0 limit) and defense mechanism inactivating 161 phage DNA ( = 1 limit) Jasien 2017. 162 The equilibrium concentrations, L ? i and T ? i , were obtained analytically by solving the algebraic 163 equations that satisfied steady-state, dL i /dt = 0 and dT i /dt = 0, for the coexistence regime, that 164 is, L ? i > 0 and T ? i > 0 for the n species pairs. The stability conditions were obtained analytically 165 using a linear approximation around the equilibrium values (Strogatz 2015). The Jacobian of 166 the dynamical system was obtained at the coexistence equilibrium, and the determinant of the 167 characteristic polynomial was transformed until extracting analytical expressions for all eigenvalues. 168 The derivation is detailed in the Supplementary Information (S.1.2).

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Lytic-lysogenic coupling. The dynamics of the lytic-lysogenic model described in Eqs.
(1) and 170 (2) was studied for single species with additional terms accounting for direct interaction Jasien 171 2017. The superinfection exclusion mechanism led to a dominance of the lysogenic community.
The escaping lysogenic factor, f , was established using physical arguments that led to likely to form in a richer community. This was based on the lysogenic-lytic cycle hypothesis and 190 the associated speciation through prophage integration. This lead to the proportionality term n in 191 the escaping lysogenic factor above. Second, it was assumed that an increase in the concentration The same applied to the total phage concentration:  and The total bacterial concentration, B ? , was determined by the phage properties, that is, phage The total concentration of lysogens was proportional to the carrying capacity in the lysogenic For the reference values given in Table 1, this was T ? ⇠ 2 · 10 2 phage/ml. Thus, the contribution smaller than the bacterial growth rate, < r, which was the case for the empirical values, Table   362 1.

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To facilitate the comparison with empirical data, the estimated phage-bacteria pair richness  (Figures 5b and 5c).

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The accuracy of the model could be improved by adding the molecular mechanisms leading to 511 the formation of new lysogens, which has been modeled at single strain-level but proven hard to   , where the microbial concentration increased due to the opportunistic growth of newly formed lysogens that escaped lytic phage top-down control by the superinfection exclusion mechanism. If the increase of resources is sustained, phages able to top-down control these newly form lysogens will eventually be selected and lead to a new mature viral-microbial community (red). This process increases the number of viral-host pairs (richness) and number of propahges per bacteria.