发表机构
Universidad Viña del Mar; Embry-Riddle Aeronautical University; Institute for Integrative Systems Biology (I2SysBio), CSIC-Universitat de València; The Santa Fe Institute; Facultad de Ingeniería, Universidad San Sebastián; Centre de Recerca Matemàtica (CRM)（维尼亚德尔马大学; 埃姆布里-里德尔航空大学; 综合系统生物学研究所（I2SysBio），西班牙瓦伦西亚大学与西班牙国家研究委员会; 圣菲研究所; 圣塞巴斯蒂安大学工程学院; 数学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过延迟微分方程模型扩展准种理论，揭示延迟聚合酶可用性可重组吸引盆导致灭绝（τ-倾覆），并证明该机制在突变体自主复制和互补模型中的鲁棒性，提出病毒学预测与实验策略。
AI 中文摘要
准种理论描述了突变和选择如何塑造高度可变的RNA病毒种群，但大多数模型既未明确考虑RNA依赖性RNA聚合酶，也未考虑与其合成和功能激活相关的延迟。最近的一个最小模型表明，延迟的聚合酶可用性可通过重组吸引盆来诱导灭绝，这一机制被称为τ-倾覆。在此，我们将该框架扩展到一个延迟微分方程模型，其中主序列和突变体基因组编码不同的功能性聚合酶。我们刻画了其平衡态和分岔结构，识别出由跨临界分岔和鞍结分岔控制的主序列-突变体共存、仅突变体持续存在（错误灾难）以及完全灭绝。尽管延迟不改变平衡态，但它们重组了吸引盆，并可将原本在固定突变和复制参数下持续存在的种群引向灭绝，从而将τ-倾覆扩展到具有自主突变体复制的系统。我们还恢复了先前研究的互补模型作为极限情况，其中缺陷基因组依赖于主序列来源的聚合酶，从而对分岔结构进行了全面分析。比较这两个模型表明，突变体基因组编码功能性聚合酶的能力决定了主序列丢失是导致突变体替代还是完全种群灭绝。延迟诱导的灭绝在两种设置中的出现证明了τ-倾覆的鲁棒性，并将细胞内复制动力学、互补和准种灭绝联系起来。最后，我们将这一机制转化为具体的病毒学预测，并提出实验策略来测试复制酶时序、RNA降解和功能性互补对病毒持续存在的影响。
英文摘要
Quasispecies theory describes how mutation and selection shape highly variable RNA virus populations, but most models explicitly consider neither RNA-dependent RNA polymerases nor the delays associated with their synthesis and functional activation. A recent minimal model showed that delayed polymerase availability can induce extinction by reorganizing basins of attraction, a mechanism termed τ-tipping. Here, we extend this framework to a delay differential equation model in which master and mutant genomes encode distinct functional polymerases. We characterize its equilibrium and bifurcation structure, identifying master-mutant coexistence, mutant-only persistence (error catastrophe), and complete extinction governed by transcritical and saddle-node bifurcations. Although delays leave the equilibria unchanged, they reorganize their basins of attraction and can redirect populations that would otherwise persist at fixed mutation and replication parameters toward extinction, thereby extending τ-tipping to systems with autonomous mutant replication. We also recover the previously studied complementation model as a limiting case in which defective genomes depend on master-derived polymerase, providing a comprehensive analysis of the bifurcation structure. Comparing the two models shows that the ability of mutant genomes to encode functional polymerases determines whether loss of the master sequence results in mutant replacement or complete population extinction. The occurrence of delay-induced extinction in both settings demonstrates the robustness of τ-tipping and connects intracellular replication kinetics, complementation, and quasispecies extinction. Finally, we translate this mechanism into concrete virological predictions and propose experimental strategies to test the effects of replicase timing, RNA degradation, and functional complementation on viral persistence.
Comments27 pages, 8 figures, 1 table
