Identifiability of SDEs for reaction networks

TL;DR

This paper studies when the stochastic differential equations modeling biochemical reaction networks can be uniquely identified from their diffusion approximations, revealing cases of non-identifiability and structural equivalences.

Contribution

It provides new conditions and theorems for assessing the identifiability of SDEs in reaction networks, highlighting structural ambiguities.

Findings

Some reaction networks have non-identifiable reaction rates.

Different network structures can produce the same diffusion law.

Results extend to compare with deterministic and Markov chain models.

Abstract

Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of the stochastic differential equations associated to the reaction network. We derive conditions under which the law of the diffusion approximation is identifiable and provide theorems for verifying identifiability in practice. Notably, our results show that some reaction networks have non-identifiable reaction rates, even when the law of the corresponding stochastic process is completely known. Moreover, we show that reaction networks with distinct graphical structures can generate the same diffusion law under specific choices of reaction rates. Finally, we compare our framework with identifiability results in the deterministic ODE setting and the discrete continuous-time Markov chain models for reaction networks.