Classically, theoretical studies focusing on biological systems are based on toric networks, which does not seem to be coherent with the biological reality. We think that the dynamics of biological networks is also regulated by fixed boundaries, illustrated for instance by external magnetic fields, chemical potentials or environmental constraints. The aim of this paper is to go further in the study of the impact of fixed boundary conditions by showing that they significantly affect the relative size of certain basins of attraction. We argue that this is a critical point in real biological networks by giving an example of boundary influence in the genetic regulatory network of the flower’s morphogenesis of the plant Arabidopsis thaliana.