AI Insight
This study presents a mathematical model of quorum sensing, where bacterial populations coordinate behavior through chemical signals, focusing on how populations can go extinct despite appearing stable. The researchers found that the scaling parameter r, which controls signal production and removal rates, significantly affects the energy barrier preventing extinction—at r=1, properly accounting for signal fluctuations increases the barrier by 55% compared to simplified models. Their theoretical predictions, validated through stochastic simulations, show that populations can temporarily cross density thresholds without entering irreversible extinction if signal levels remain high.
Why it matters
Understanding extinction barriers in quorum-sensing populations has practical applications for controlling bacterial infections and designing synthetic biological systems. The findings suggest that signal dynamics play a crucial role in population persistence, which could inform strategies to either destabilize harmful bacterial populations or stabilize beneficial engineered microbes.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: We introduce a simple reaction-network model of a quorum-sensing population that couples the cell density $x$ to the signal density $w$. In the four-channel cell-signal network studied here, scaling signal production and removal by the same factor $r$ leaves all deterministic equilibria, and their stability types, unchanged. Nevertheless, we show that $r$ shifts the quasipotential barrier $Delta V(r)$ for rare transitions towards extinction, and thus, under metastable exit assumptions, the mean time to reach a fixed neighbourhood of the extinction state on the exponential scale $e^{NDelta V(r)}$. We compute the barrier by minimization of the path action with the signal retained as a fluctuating coordinate, and we compare it with exact stochastic simulation of population-threshold crossing times regressed in $N$. Over a range of $r$, the minimum-action barriers satisfy $Delta V(r)=Delta V_infty+O(1/r)$, where $Delta V_infty$ is obtained by eliminating the signal first. At $r=1$, the barrier is 55% larger than $Delta V_infty$. The saddle barrier $Delta V(r)$ is also the least action needed to enter the basin of extinction, but the density threshold can be crossed more cheaply: at $r=0.5$ the cheapest crossing costs 7.7% less action, keeps the signal high, and is usually followed by recovery. Simulated arrival times in this neighbourhood, which include failed attempts, grow with slopes within two fitted standard errors of the saddle barrier at every tested rate, and within $0.004$ of it if the logarithmic prefactor term is omitted. Under either regression model they exclude $Delta V_infty$ at $rle2$ by at least $4.4$ fitted standard errors, without using the action solver.
Source: Computing Extinction Barriers in a Quorum-Sensing Reaction Network