Evolutionary Advantage of Diversity-Generating Retroelements in Switching Environments

TL;DR

A two-timescale framework is introduced separating fast VR diversification from slow TR evolution, allowing the dynamics of DGR-controlled loci to be analytically understood from the TR design point of view and clarifies when constitutive DGR activation is evolutionarily favored.

Abstract

Diversity-Generating Retroelements (DGRs) create rapid, targeted variation within specific genomic regions in phages and bacteria. They operate through stochastic retro-transcription of a template region (TR) into a variable region (VR), which typically encodes ligand-binding proteins. Despite their prevalence, the evolutionary conditions that maintain such hypermutating systems remain unclear. Here we introduce a two-timescale framework separating fast VR diversification from slow TR evolution, allowing the dynamics of DGR-controlled loci to be analytically understood from the TR design point of view. We quantity the fitness gain provided by the diversification mechanism of DGR in the presence of environmental switching with respect to standard mutagenesis. Our framework accounts for observed patterns of DGR activity in human-gut \textit{Bacteroides} and clarifies when constitutive DGR activation is evolutionarily favored.

Figures (3)

• Figure 1: Illustration of the DGR system.(a) The main components of a DGR are shown. The template region (TR, blue) is copied into the variable region (VR, orange) at rate $\nu$, with mutations introduced specifically at adenine (A) positions. The TR mutates at rate $\mu$. The fitness of an individual---defined by its (TR, VR) pair---depends solely on its VR sequence. (b) Sketch of a fluctuating environment. Every interval $\tau$, the environment switches to favor a different target (VR) sequence. The population frequency $f(t)$ of the fittest sequence (with fitness $S_e$) then adapts to these shifts.
• Figure 2: VR selection. (a) Effective growth rate as a function of the switching rate $\nu$ for $L=1$. (b) Same as (a) for length $L=10$. Takeover times for the DGR system estimated from simulations (more than 99.5% of the population) (c) and from Eq. \ref{['takeover']}(d) vs. diversification rate $\nu$ for $L=1$. Parameter values: $Q=4$, $s=1$, population size $=10^{8}$, $\mu=10^{-5}$.
• Figure 3: TR selection.(a) to (c). Fraction $f_{not~A}$ of sequences in the $\bf TR$ population carrying non-adenine nculeotides. (a)$\nu\tau\gg 1$ ($\tau=200$, $\mu=10^{-7}$, $10^{-6}$, and $10^{-5}$); (b)$\nu\tau= 1$ ($\nu=1/\tau=10^{-2}$, $5\cdot 10^{-2}$ and $10^{-1}$); (c)$\nu\tau\ll 1$ ($\mu=10^{-6}$, $10^{-5}$ and $10^{-4}$ and $\tau=5$). Increasing values of $\nu$ or $\mu$ are shown in blue, orange and green successively. Dashed lines correspond to the expressions of Eq. \ref{['eq:exp_nu_tau']} in the respective regimes. (d) Probability $P_{A~lost}$ that the fraction of $\bf TR$ with an $A$ (initially, equal to 1) is lower than $1/Q=1/4$ as a function of $\nu \tau_0$ where $\tau_0$ is the typical duration of an environment. Dashed line corresponds to $\left( \nu \tau_0 \right)^\beta$. We take $\mu=10^{-4}$, $\beta=1/2$ and $\nu=10^{-3}$, $10^{-2}$ and $10^{-1}$. (e) Phase diagram in the $(L,\tau)$ plane. Dashed lines show the theoretical prediction for $\tau_c$ in Eq. \ref{['eq:tau_c']} Blue points are determined by solving the dynamics for infinite population size. Parameters are $\mu=10^{-6}$ and $\nu=10^{-2}$.