Final answer:
Microtubules bind to chromosomes during mitosis using a process where spindle microtubules dynamically extend and retract until they bind to the kinetochores on the chromosomes.
Step-by-step explanation:
During mitosis in animal cells, microtubules and chromosomes bind to each other through a process involving the dynamic instability of the spindle microtubules. Specifically, during prometaphase, microtubules extend and retract from the spindle poles through a mechanism known as dynamic instability until they come into contact with and firmly bind to the kinetochores on the chromosomes. Each sister chromatid develops a kinetochore in its centromeric region, which attracts and binds the mitotic spindle microtubules. Once a microtubule attaches to a kinetochore, it aids in orienting the chromosome so that the kinetochores of sister chromatids face opposite poles, eventually allowing all sister chromatids to be attached via their kinetochores to microtubules from opposing poles.