Final answer:
The association of a sigma factor with the core enzyme forms the holoenzyme, crucial for transcription initiation in prokaryotic cells by ensuring RNA polymerase's correct binding to DNA promoters.
Step-by-step explanation:
The association of a sigma factor (σ) with the core enzyme forms a complex referred to as the RNA polymerase holoenzyme. In prokaryotic cells, such as E. coli, the core enzyme consists of four subunits: two alpha (α) subunits, one beta (β) subunit, and one beta-prime (β') subunit. This core enzyme is responsible for the elongation phase of transcription. The addition of a sigma factor to the core enzyme creates the holoenzyme which is essential for transcription initiation. The σ subunit confers specificity, ensuring that the polymerase binds to the appropriate promoter sequences in the DNA and starts mRNA synthesis at the correct site. Without the sigma factor, the core enzyme would not initiate transcription properly, leading to the production of non-functional mRNA.