Final answer:
The kinetochore is the specialized DNA sequence that connects chromosomes to spindle microtubules, facilitating their segregation during the M phase of cell division.
Step-by-step explanation:
The specialized DNA sequence that attaches to microtubules and allows duplicated eukaryotic chromosomes to be separated during the M phase is called the kinetochore. This protein structure is located in the centromeric region of each sister chromatid. During prometaphase and anaphase, the kinetochores attach to mitotic spindle microtubules, ensuring that the sister chromatids are oriented correctly with their kinetochores facing opposite poles. The spindle checkpoint, also known as the M checkpoint, ensures that this attachment is secure before allowing the cell cycle to proceed to the next stage where the separation of sister chromatids occurs, which is an irreversible step.