BDC-Decomposition for Global Influence Analysis

In biochemical networks, the steady-state input-output influence is the sign of the output steady-state variation due to a persistent positive input perturbation; if the sign does not depend on the value of the strictly positive system parameters, the influence is structural. As recently shown for small perturbations, when the linearized system approximation is valid, steady-state input-output influences can be structurally assessed, for biochemical networks with
$m$
unknown parameters, by means of a vertex algorithm with complexity
$2^{m}$
. This letter shows that the structural input-output influence of a biochemical network is a global property, which does not require any small-perturbation assumption. It also shows that, using a new algorithm, the complexity can be reduced down to
$2^{m-n}$
, where
$n$
is the system order, thus drastically reducing the computation time. Finally, when the uncertain parameters belong to known intervals, non-conservative bounds are given for the steady-state ratio between output and input, allowing for sensitivity analysis.