Barrier Trees for Metabolic Adjustment Landscapes

We construct and analyze a discrete fitness landscape called metabolic adjustment landscape, from sub-networks covered by different productive flux distributions of a metabolic network. The topological structure of this landscape, i.e., the local minima and saddle points, can be compactly represented as a hierarchical structure called barrier tree. The switching from one local optimal flux pattern to another one is accompanied by adjustment costs, since genes have to be turned on or off. This phenomenon gives raise to saddle points in the metabolic adjustment landscape. Our approach allows calculating the minimal cost pathway that connects any two local minima in the landscape. Furthermore, our method yields a detailed ordering which reactions have to be (de-)activated to switch from one flux distribution to another one with minimal adjustment costs. Such a mechanistic hypothesis can guide experimental verification. We apply our approaches to a network describing the central carbon metabolism of E. coli.