Supported by NIH R01AG024059, P30 AG024978, and P30 AG008017.
SIAM Journal of Mathematical Analysis
Biomathematics, Biology -- Mathematical models, Biological systems -- Mathematical models
We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders and the other on primary decomposition. Both methods are applied to current examples of gene networks.
Austin, D., & Dinwoodie, I. H. (2015). Monomials and Basin Cylinders for Network Dynamics. SIAM Journal on Applied Dynamical Systems, 14(1), 25-42.