计算群体感应反应网络中的灭绝势垒
Computing Extinction Barriers in a Quorum-Sensing Reaction Network
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中文总结 AI 辅助
本文研究群体感应反应网络中灭绝势垒的计算，发现信号缩放因子r改变准势垒，通过最小作用路径方法计算势垒并与随机模拟验证，揭示低r下更廉价的穿越路径。
中文摘要 AI 辅助
我们引入了一个简单的群体感应种群反应网络模型，该模型将细胞密度$x$与信号密度$w$耦合。在我们研究的四通道细胞-信号网络中，将信号产生和去除按相同因子$r$缩放，会使得所有确定性平衡点及其稳定性类型保持不变。然而，我们证明$r$会改变稀有灭绝转变的准势垒$\u0394V(r)$，因此在亚稳态逃逸假设下，平均到达灭绝状态固定邻域的时间按指数尺度$e^{N\u0394V(r)}$变化。我们通过最小化路径作用来计算势垒，其中信号作为波动坐标保留，并将其与在$N$上回归的种群阈值穿越时间的精确随机模拟进行比较。在$r$的一个范围内，最小作用势垒满足$\u0394V(r)=\u0394V_\infty+O(1/r)$，其中$\u0394V_\infty$通过先消除信号获得。在$r=1$时，势垒比$\u0394V_\infty$大55%。鞍点势垒$\u0394V(r)$也是进入灭绝盆所需的最小作用，但密度阈值可以更便宜地穿越：在$r=0.5$时，最便宜的穿越花费的作用少7.7%，保持信号高，并且通常随后恢复。该邻域内的模拟到达时间（包括失败尝试）的斜率在每个测试速率下都在鞍点势垒的两个拟合标准误差内，如果省略对数前因子项，则在其0.004以内。在两种回归模型下，它们在$r\le2$时至少排除$\u0394V_\infty$达4.4个拟合标准误差，且不使用作用求解器。
英文摘要
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 $ΔV(r)$ 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 $e^{NΔV(r)}$. 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 $ΔV(r)=ΔV_\infty+O(1/r)$, where $ΔV_\infty$ is obtained by eliminating the signal first. At $r=1$, the barrier is 55% larger than $ΔV_\infty$. The saddle barrier $ΔV(r)$ 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 $ΔV_\infty$ at $r\le2$ by at least $4.4$ fitted standard errors, without using the action solver.
发表机构
- School of Computation, Information and Technology, Technische Universität München（计算、信息与技术学院，慕尼黑工业大学）
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