One of the key challenges of understanding biological cells is trying to make rigorous and quantitative statements in the face of enormous model uncertainty: While we typically know some things about a cellular process we never know everything, which leaves mathematical models hugely under-determined and makes common modeling approaches unreliable. The focus of our research is thus to study complex systems such as cellular processes, not by ignoring or guessing unknown details, but by deriving testable predictions that are provably independent of them. For example, specifying some features of a system while leaving everything else unspecified allows us to establish physical performance bounds for classes of intracellular processes such as feedback control. Additionally, we develop theoretical tools to exploit naturally occurring cell-to-cell variability to test specific hypotheses within large reaction networks. For example, the network invariants we derived showed that mRNA-protein fluctuation data in E. coli contradict the majority of published models of stochastic gene expression.