  This paper (parts I and II) provides an expository introduction to monotone
and near-monotone dynamical systems associated to biochemical networks, those
whose graphs are consistent or near-consistent. Many conclusions can be drawn
from signed network structure, associated to purely stoichiometric information
and ignoring fluxes. In particular, monotone systems respond in a predictable
fashion to perturbations and have robust and ordered dynamical characteristics,
making them reliable components of larger networks. Interconnections of
monotone systems may be fruitfully analyzed using tools from control theory, by
viewing larger systems as interconnections of monotone subsystems. This allows
one to obtain precise bifurcation diagrams without appeal to explicit knowledge
of fluxes or of kinetic constants and other parameters, using merely
"input/output characteristics" (steady-state responses or DC gains). The
procedure may be viewed as a "model reduction" approach in which monotone
subsystems are viewed as essentially one-dimensional objects. The possibility
of performing a decomposition into a small number of monotone components is
closely tied to the question of how "near" a system is to being monotone. We
argue that systems that are "near monotone" may be more biologically more
desirable than systems that are far from being monotone. Indeed, there are
indications that biological networks may be much closer to being monotone than
random networks that have the same numbers of vertices and of positive and
negative edges.
