Applications of the gröbner fan to gene network reconstruction (abstract only)
Elena Dimitrova, Brandilyn Stigler, Abdul Salam Jarrah, Reinhard Laubenbacher · ACM communications in computer algebra · 2008
Gröbner fans have gained popularity in computational commutative algebra and algebraic geometry with applications ranging from Gröbner basis conversion to the emerging field of tropical mathematics. Recently Gröbner fans have been employed for the selection of minimal models that fit measurement data from gene regulatory networks. The model space is described as the sum of an interpolating polynomial function f and the set of all polynomials that vanish on the data, that is, the ideal of data points. A minimal model can be chosen by computing the reduction of f with respect to a fixed Gröbner basis, which is dependent on the choice of term order. As Gröbner fans partition the set of Gröbner bases into equivalence classes, they can be thought of as parametrizations of the model space. This characterization permits exploration of the model space and discovery of "most likely" models. In this poster we show how Gröbner fans are used to two reconstruct gene regulatory networks: lactose metabolism in the bacterium E. coli and tissue development in the roundworm C. elegans.