  The relationship between components of biochemical network and the resulting
dynamics of the overall system is a key focus of computational biology.
However, as these networks and resulting mathematical models are inherently
complex and non-linear, the understanding of this relationship becomes
challenging. Among many approaches, model reduction methods provide an avenue
to extract components responsible for the key dynamical features of the system.
Unfortunately, these approaches often require intuition to apply. In this
manuscript we propose a practical algorithm for the reduction of biochemical
reaction systems using fast-slow asymptotics. This method allows the ranking of
system variables according to how quickly they approach their momentary steady
state, thus selecting the fastest for a steady state approximation. We applied
this method to derive models of the Nuclear Factor kappa B network, a key
regulator of the immune response that exhibits oscillatory dynamics. Analyses
with respect to two specific solutions, which corresponded to different
experimental conditions identified different components of the system that were
responsible for the respective dynamics. This is an important demonstration of
how reduction methods that provide approximations around a specific steady
state, could be utilised in order to gain a better understanding of network
topology in a broader context.
