  Mathematical models of stem cell differentiation are commonly based upon the
concept of subsequent cell fate decisions, each controlled by a gene regulatory
network. These networks exhibit a multistable behavior and cause the system to
switch between qualitatively distinct stable steady states. However, the
network structure of such a switching module is often uncertain, and there is
lack of knowledge about the exact reaction kinetics. In this paper, we
therefore perform an elementary study of small networks consisting of three
interacting transcriptional regulators responsible for cell differentiation: We
investigate which network structures can reproduce a certain multistable
behavior, and how robustly this behavior is realized by each network. In order
to approach these questions, we use a modeling framework which only uses
qualitative information about the network, yet allows model discrimination as
well as to evaluate the robustness of the desired multistability properties. We
reveal structural network properties which are necessary and sufficient to
realize distinct steady state patterns required for cell differentiation. Our
results also show that structural and robustness properties of the networks are
related to each other.
