A researcher introduces a large polar signaling molecule produced by bacteria to eukaryotic cells that she is culturing in the laboratory. Remarkably, she notices that the signaling of the bacteria results in an increase in eukaryotic gene expression. How is this possible?

There are two possibilities:

The signal is similar in structure to a ligand used by eukaryotes. The pathway used by the signal is utilized by both prokaryotes and eukaryotes.

Both of these would explain that the signaling of the bacteria results in an increase in eukaryotic gene expression.