Final answer:
The centromere is where spindle microtubules attach during mitosis and meiosis, with the attachment facilitated by kinetochores. This attachment is pivotal for the chromosomes to be segregated into daughter cells.
Step-by-step explanation:
The centromere is a key structure in cell division, both during mitosis and meiosis. The centromere acts as the attachment point for spindle microtubules, which are essential for the segregation of chromosomes into daughter cells. These spindle microtubules form the mitotic spindle, emerging from the centrosomes, which are microtubule-organizing centers located at opposite poles of the cell. Each centrosome comprises a pair of centrioles.
During the late phase of prophase, known as prometaphase, the nuclear membrane breaks down, allowing spindle microtubules to attach to the kinetochores located on the centromeres of sister chromatids. This is followed by metaphase, where chromosomes align at the cell's equator and are securely attached to the spindle microtubules from both poles, ensuring that each sister chromatid moves to opposite ends of the cell during subsequent cell division phases.