Bipartite and tripartite systems and matrices from genetic control research

Discovering the organizational principles of genetic expression has recently become an arena of substantial investigative effort and modeling challenges. Laboratory findings of geneticists can be couched in terms of classes of stoichiometric networks that through stability analysis lead to classes of matrix patterns. In particular, targets, blocks, and decoys are variables in genetic systems with relationships that can be described by bipartite and tripartite graphs. Related dynamical systems will exhibit stability if a mixture of qualitative and quantitative criteria is applied. Analyses of the models suggest limits of total induction rates of blocks and decoys relative to other rates.