Uncertain interactions affect degree distribution of biological networks

Biological interactions are often uncertain events, that may or may not take place under different scenarios. Existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can have misleading results. Here, we address this problem and develop sound mathematical basis to analyze degree distribution of biological networks in the presence of uncertain interactions. We present a comparative study of node degree distributions in two types of biological networks: the classical deterministic networks and the more flexible probabilistic networks. We extend this comparison to joint degree distributions of nodes connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical apparatus we develop allows us to compute these degree distributions quickly even for entire protein protein interaction networks. It also helps us find an adequate mathematical model using maximum likelihood estimation. ^l Our results confirm that power law and log-normal models best describe degree distributions for both probabilistic and deterministic networks. Moreover, the inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected.