Final answer:
Phosphorylation is an example of how a regulatory transcription factor is activated, as it can alter the protein's function and enable it to regulate gene expression.
Step-by-step explanation:
Regulatory Transcription Factor Activation
Among the options provided for how a regulatory transcription factor is activated, d) Phosphorylation is a correct example. Phosphorylation is a process that can modify proteins, including transcription factors, by adding a phosphate group, which can alter the protein's function, location, or interaction with other molecules. This modification can activate the transcription factor, allowing it to bind DNA at specific sites and regulate gene expression.
Methylation of DNA (a) usually acts epigenetically rather than directly activating transcription factors. Binding to a repressor protein (b) typically inhibits a transcription factor, preventing gene expression. Inhibition by a microRNA (c) is a post-transcriptional mechanism that does not activate transcription factors but rather decreases the stability of mRNA transcripts.