What chemicals regulate the cell cycle how do they work?

Cyclins are the proteins that regulate the cell cycle through cyclin depedent kinases (Cdks).

Explanation:

Cyclins are the proteins that control the activity of cyclin dependent kinases. The levels of various cyclins fluctuates throughout the cell cycle. The active cyclin-dependent kinases (Cdks) regulate the cell cycle by phosphorylating the enzymes and other proteins that are needed during specific phase of the cell cycle.  

Example: M-cdks are the Cdks of M phase and activated cyclin--M-Cdk complex phosphorylate the protein to make the cell proceed through mitosis.

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the unequal cytoplasmic division that  results  in  one egg  and three polar bodies ensures that a fertilized  egg has  ample nutrients  forits journey  to  the uterus.