Final answer:
In prophase, the first phase of mitosis, the nuclear envelope breaks down into vesicles, and other cellular structures undergo changes in preparation for chromosome segregation.
Step-by-step explanation:
The phase during which the nuclear envelope starts to break down is known as prophase, which is the first phase of mitosis. During prophase, not only does the nuclear envelope dissociate into small vesicles, but various other cellular structures also undergo significant changes. The Golgi apparatus and endoplasmic reticulum fragment and disperse toward the cell periphery, the nucleolus disappears, and centrosomes begin moving to opposite poles of the cell. Concurrently, microtubules start extending between the centrosomes, pushing them farther apart, and the process of mitotic spindle formation begins. The sister chromatids condense and become visible under a light microscope, indicating that the cell is preparing for chromosome segregation.