  Biochemical mechanisms with mass action kinetics are often modeled by systems
of polynomial differential equations (DE). Determining directly if the DE
system has multiple equilibria (multistationarity) is difficult for realistic
systems, since they are large, nonlinear and contain many unknown parameters.
Mass action biochemical mechanisms can be represented by a directed bipartite
graph with species and reaction nodes. Graph-theoretic methods can then be used
to assess the potential of a given biochemical mechanism for multistationarity
by identifying structures in the bipartite graph referred to as critical
fragments. In this article we present a graph-theoretic method for conservative
biochemical mechanisms characterized by bounded species concentrations, which
makes the use of degree theory arguments possible. We illustrate the results
with an example of a MAPK network.
