发表机构
School of Mathematics and Statistics, Hefei Normal University（合肥师范学院数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对具有非线性空间位阻的广义核糖体流动模型，推导了夹带增益的相关准则，发现经典模型不存在的维度诱导增益机制，高维链可实现正二阶夹带增益。
AI 中文摘要
核糖体流动模型（RFM）是用于描述沿mRNA链单向运输的非线性 compartmental 模型。我们研究了一种广义RFM，其中经典的线性自由空间因子被单调非线性空间位阻响应取代。在回顾分析所需的全局平衡和周期性夹带特性后，我们推导了夹带增益（GOE）的精确加权边耗散恒等式，这通过非线性位阻定律的曲率给出了全局无GOE准则。特别地，二次位阻模型在任意维度和任意周期性驱动振幅下均无正GOE，仅当所有速率共享共同的乘性调制时等式成立。在一维情况下，我们获得了基于凸性的清晰分类，并在相关凸性失效时构造了正GOE示例。在更高维度中，二阶变分由对称雅可比矩阵控制，其对角项编码局部曲率，非对角项表示最近邻运输耦合。这导出了精确的Riccati准则、异质链的维度一致条件以及同质情况下的闭式临界维度。我们还展示了一种非线性位阻，其中低维链无正二阶GOE，而高维链存在可实现的正GOE。这些结果揭示了经典RFM中不存在的维度诱导增益机制。
英文摘要
The ribosome flow model (RFM) is a nonlinear compartmental model for unidirectional transport along an mRNA chain. We study a generalized RFM in which the classical linear free-space factor is replaced by a monotone nonlinear steric-hindrance response. After recalling the global equilibrium and periodic entrainment properties needed for the analysis, we derive an exact weighted edge-dissipation identity for the gain of entrainment (GOE). This yields a global no-GOE criterion formulated through the curvature of the nonlinear hindrance law. In particular, the quadratic hindrance model admits no positive GOE in any dimension and for arbitrary periodic forcing amplitudes, with equality only when all rates share a common multiplicative modulation. In one dimension, we obtain a sharp convexity-based classification and construct positive-GOE examples when the relevant convexity fails. In higher dimensions, the second variation is governed by a symmetric Jacobi matrix whose diagonal terms encode local curvature and whose off-diagonal entries represent nearest-neighbor transport coupling. This leads to an exact Riccati criterion, a dimension-uniform condition for heterogeneous chains, and a closed-form critical dimension in the homogeneous case. We also exhibit a nonlinear hindrance for which low-dimensional chains have no positive second-order GOE, while a higher-dimensional chain admits a realizable positive GOE. These results reveal a dimension-induced gain mechanism that is absent from the classical RFM.
Comments28 pages, 1 figure
