Final answer:
Spindle fibers attach to kinetochores during mitosis, meiosis I, and meiosis II, particularly during the prometaphase stage. Mitotic spindle fibers play a pivotal role in the accurate segregation of chromosomes during cell division.
Step-by-step explanation:
Spindle fibers attach to kinetochores during various stages of cell division. In the context of your question, spindle fibers attach to kinetochores during mitosis and both meiosis I and meiosis II, ensuring that chromosomes are accurately segregated into daughter cells. However, if we focus on the attachment of spindle fibers specifically to kinetochores, this occurs during prometaphase in mitosis, as well as in prometaphase I in meiosis I and during meiosis II.
The connection of the mitotic spindle fibers to the kinetochores starts during prophase in mitosis, with the actual attachment occurring in prometaphase. During metaphase I of meiosis, spindle fibers attach to the paired homologous chromosomes. Similarly, in metaphase of mitosis and meiosis II, it is sister chromatids that line up along the equator of the cell, each attached to spindle fibers.
The mitotic spindles arise from the centrosome, while the component of the spindle fibers that attaches to the kinetochore is known as the kinetochore microtubules. Proper attachment of mitotic spindle fibers to kinetochores is crucial for accurate and complete DNA replication and segregation during cell division.