Biological networks of an organism show how different bio-chemical entities, such as enzymes or genes interact with each other to perform vital functions for that organism. In this talk, we will discuss the computational challenges centered on uncertainty in the topology of biological networks. We will discuss our new mathematical model, which represent probabilistic networks as collections of polynomials. We show that this is a powerful model that enables solving seemingly very tough computational problems on probabilistic networks efficiently and precisely. We will demonstrate the expressive power of this model on the signal reachability problem, which computes whether an extracellular signal reaches from a membrane receptor to a reporter gene.