Limits of Inferring Parametric Response from Single-Condition Trajectories inStochastic Reaction Networks

RESUMO

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.