Cells, the fundamental units of life, are governed by complex networks of dynamically interacting molecules. In order to predict and control cellular systems, we must understand how biochemical networks underlie the many fascinating behaviours of cells.

Even with state-of-the art experimental techniques in molecular biology, this can be a monumental challenge. First, biochemical networks are complex and sparsely characterized. This makes it difficult to use mathematical modelling to translate data into an underlying process because there are so many possible models that can fit the same data. Second, many methods in molecular biology generate static snapshots, meaning they do not follow the behaviour of cells over time. This makes it difficult to probe cellular dynamics with such methods.

In order to tackle these problems, I present a novel approach: by deriving mathematical bounds on whole classes of sparsely characterized systems, we can make rigorous predictions with only a handful of testable assumptions. Applying this approach on classes of systems modelling a commonly used technique in molecular biology (the ``dual reporter” assay), I show how naturally occurring fluctuations in cells can be exploited to probe biochemical reaction networks from static snapshot data.