随机反应网络中从单条件轨迹推断参数响应的极限

中文摘要 AI 辅助

即使精确知道马尔可夫生成元在一个环境条件下的形式，也不能确定该生成元如何随环境变化，除非提供额外的反应结构信息。我们针对由化学恒化器物种驱动的质量作用反应网络建立了这种不可辨识性。不同的化学嵌入可以在参考浓度u0处共享相同的生成元和路径定律，但在恒化器如何进入各个反应通道方面存在差异。改变整数化学恒化器反应物分子数并重新缩放相应的动力学常数，可在u0处保持所有倾向函数不变。这种模糊性已经出现在低分子数的基元反应中：一个单物种出生-死亡例子在参考条件下具有相同的路径测度，但无量纲稳态敏感性分别为一和零。因此，单条件数据可以确定在u0处观测到的马尔可夫动力学，但无法确定其参数响应。作为先前化学结构互补作用的例证，我们还表明，一个已知的化学计量积分坐标在线性噪声近似内施加了一个条件零频率恒等式。

英文摘要

Even exact knowledge of the Markov generator at one environmental condition does not determine how that generator changes with the environment unless additional reaction-structure information is supplied. We establish this non-identifiability for mass-action reaction networks driven by a chemostatted species. Distinct chemical embeddings can share the same generator and path law at a reference concentration u0 while differing in how the chemostat enters individual reaction channels. Changing integer chemostat reactant molecularities and rescaling the corresponding kinetic constants preserves all propensities at u0 . This ambiguity already occurs for low-molecularity elementary reactions: a one-species birth--death example has identical path measures at the reference condition but dimensionless stationary sensitivities one and zero. Single-condition data can therefore determine the observed Markov dynamics at u0 without determining their parametric response. As an illustration of the complementary role of prior chemical structure, we also show that a known stoichiometric integral coordinate imposes a conditional zero-frequency identity within the linear-noise approximation.

发表机构

• CRCLille--Cancer Research Center of Lille, Universit\'e de Lille, UMR 9020 CNRS, Inserm U1366, CHU de Lille, France

机构由 AI 辅助整理，请以论文原文为准。