Final answer:
The nuclear envelope breaks down during the prometaphase stage of mitosis when lamins filaments are phosphorylated, allowing spindle fibers to attach to kinetochores on sister chromatids.
Step-by-step explanation:
During mitosis, the nuclear envelope breaks down when lamins filaments are phosphorylated. This event occurs specifically during the prometaphase stage of mitosis. Prometaphase is marked by the disintegration of the nuclear membrane which allows the mitotic spindle fibers to attach to the kinetochores on sister chromatids.
In Prometaphase II, the nuclear envelopes are completely broken down, leading to the formation of a fully-fledged spindle. Each sister chromatid features an individual kinetochore, which then attaches to microtubules emanating from opposite poles. The disassembly of the nuclear envelope is facilitated by the phosphorylation of proteins that compose its structure, notably the nuclear lamins. This phosphorylation causes the lamins to dissociate from each other, which in turn leads to the fragmentation and disintegration of the nuclear envelope.
Such a mechanism ensures that the sister chromatids are correctly attached to the spindle apparatus, which is essential for their proper segregation into the two new daughter cells during the later stages of mitosis, particularly anaphase. After mitosis concludes in telophase and the chromatids have reached opposite poles, new nuclear envelopes reform around the separated chromatids, signaling the end of mitotic events and the restoration of the nuclei in the daughter cells.