  Discrete dynamic models are a powerful tool for the understanding and
modeling of large biological networks. Although a lot of progress has been made
in developing analysis tools for these models, there is still a need to find
approaches that can directly relate the network structure to its dynamics. Of
special interest is identifying the stable patterns of activity, i.e., the
attractors of the system. This is a problem for large networks, because the
state space of the system increases exponentially with network size. In this
work we present a novel network reduction approach that is based on finding
network motifs that stabilize in a fixed state. Notably, we use a topological
criterion to identify these motifs. Specifically, we find certain types of
strongly connected components in a suitably expanded representation of the
network. To test our method we apply it to a dynamic network model for a type
of cytotoxic T cell cancer and to an ensemble of random Boolean networks of
size up to 200. Our results show that our method goes beyond reducing the
network and in most cases can actually predict the dynamical repertoire of the
nodes (fixed states or oscillations) in the attractors of the system.
