  In Systems Biology there is a growing interest in the question, whether or
not a given mathematical model can admit more than one steady state. As
parameter values are often unknown or subject to a very high uncertainty, one
is often interested in the question, whether or not a given mathematical model
can, for some conceivable parameter vector, exhibit multistationarity at all. A
partial answer to this question is given in Feinberg's deficiency one
algorithm. This algorithm can decide about multistationarity by analyzing
systems of linear inequalities that are independent of parameter values.
However, the deficiency one algorithm is limited to what its author calls
regular deficiency one networks. Many realistic networks have a deficiency
higher than one, thus the algorithm cannot be applied directly. In a previous
publication it was suggested to analyze certain well defined subnetworks that
are guaranteed to be of deficiency one. Realistic reaction networks, however,
often lead to subnetworks that are irregular, especially if metabolic networks
are considered. Here the special structure of the subnetworks is used to derive
conditions for multistationarity. These conditions are independent of the
regularity conditions required by the deficiency one algorithm. Thus, in
particular, these conditions are applicable to irregular subnetworks.
