受体信号网络中的幽灵动力学：竞争型癌症抑制模型的快慢自适应扩展

中文摘要 AI 辅助

受体占有率模型用于量化癌症信号的抑制作用，通常将靶标占有率作为下游活性的替代指标。尽管这种简化能得到低维模型，但无法体现细胞内网络产生的延迟通路关闭、瞬时耐药性或非单调活力响应。我们构建了一个快慢框架，将药物-靶标占有率与下游信号活性区分开：快变量X代表占有率，活性变量A代表促存活信号，慢变量B代表包括磷酸酶诱导、应激适应或信号重编程在内的自适应反馈。快速占有率弛豫允许准稳态约化，而弱反馈保证全局收敛到唯一平衡点；更强的反馈可能使冻结的活性子系统接近鞍结折叠，产生幽灵 regime，即轨迹在消失的高活性平衡点的残余附近徘徊。我们确定慢自适应通道何时保持反平方根幽灵定律，或在横向交叉下产生动态延迟尺度O(ε^(-1/3))。将活性与活力耦合可将这些延迟转化为剂量-响应曲线中的肩峰，而自适应滞后可能在无特设强迫的情况下产生早期超调。对时间分辨活力数据的概念验证拟合再现了不同测量浓度和观测时间的模式，并揭示了实际可识别性限制。该框架还预测了表观效力的暴露时间依赖性偏移，包括IC₅₀(t)，因为活力整合的是随时间变化的信号活性，而非仅受体占有率。

英文摘要

Receptor occupancy models quantify inhibition of cancer signalling, often treating target occupancy as a proxy for downstream activity. Although this simplification yields low-dimensional models, it cannot represent delayed pathway shutdown, transient resistance, or non-monotone viability responses generated by intracellular networks. We formulate a fast--slow framework that distinguishes drug--target occupancy from downstream signalling activity. The fast variable $X$ represents occupancy, the activity variable $A$ represents pro-survival signalling, and the slow variable $B$ represents adaptive feedback including phosphatase induction, stress adaptation, or signalling rewiring. Rapid occupancy relaxation permits a quasi-steady reduction, while weak feedback guarantees global convergence to a unique equilibrium. Stronger feedback may bring the frozen activity subsystem near a saddle-node fold, producing a ghost regime in which trajectories linger near the remnant of a vanished high-activity equilibrium. We determine when slow adaptive passage preserves the inverse-square-root ghost law or, under transverse crossing, produces the dynamic delay scale $O(\varepsilon^{-1/3})$. Coupling activity to viability translates these delays into shoulders in dose--response curves, while adaptive lag may generate early-time overshoot without ad hoc forcing. A proof-of-concept fit to time-resolved viability data reproduces patterns across measured concentrations and observation times and reveals practical identifiability limitations. The framework also predicts exposure-time-dependent shifts in apparent potency, including $IC_{50}(t)$, because viability integrates signalling activity over time rather than receptor occupancy alone.

发表机构

• Department of Mathematics and Applied Mathematics, University of Pretoria（比勒陀利亚大学数学与应用数学系）

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