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The theory of robust sensitivity of feedback controlled biochemical metabolic pathways is extended to the stochastic case where the deterministic parameter uncertainties are replaced by stochastic state-multiplicative ones. As a case study, we consider the well-studied threonine synthesis pathway in  E. coli , leading from Aspartate to the end product Threonine, via a complex five step mechanism. Following the linearisation of each step in the pathway around pre-chosen, biochemical-sound, set point, the original system is assembled as a stochastic linear system where the uncertainties in the enzymes concentrations appear as state-multiplicative stochastic terms in both the dynamical and input matrices. The effect of the three negative feedback loops that regulate the system dynamics is first investigated. Given a disturbance signal, we then study the sensitivity of the system to variations in certain kinetic and thermodynamical variables to assess the possible optimality of the system in theandsenses.

Robust stochastic sensitivity analysis of the threonine synthesis pathway