Final answer:
The missing protein in the in vitro transcription system is the sigma factor, which is essential for the specificity of transcription initiation in bacteria. Bacteria are unlikely to transcribe a gene with a eukaryotic promoter because they require a compatible bacterial promoter.
Step-by-step explanation:
In an in vitro transcription system containing a bacterial gene that initiates transcription from random points, the protein most likely missing from the reaction is the sigma factor (also known as the o-factor). The sigma factor is essential for initiating prokaryotic transcription because it enables the RNA polymerase to recognize the promoter regions, such as the -35 region and the Pribnow box, and begin transcription at the correct site on the DNA.
Without the sigma factor, transcription would start at random locations, leading to the synthesis of RNA that does not correspond to actual genes. In the context of a bacterial gene with a eukaryotic promoter, the bacterium is unlikely to transcribe the gene properly because bacterial RNA polymerase requires a compatible bacterial promoter to initiate transcription.