Network based models for biological applications

This paper analyses the adequacy of different types of networks in biological process modeling. The assumptions are sustained by two case studies. The first one is a lattice-based computer model to simulate the growth of nonvascular tumors with nutrient consumption constraints. The modeling solution is able to reproduce the classic three-layer structure familiar from multicellular spheroids: cell proliferation, quiescent and necrosis. The accuracy of this model is tested by comparing it to a fractal morphometric technique of two patterns, one of them obtained by simulation, the other developed in vitro. The second application is the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. This is a new preferential attachment scheme, different from those specific for the construction of scale-free graphs, because its new nodes prefer to attach to existing nodes with lower degree. We relate this mechanism to a simple food-web model studied by simulations.