To start out, there are chemical conditions that affect division rate. This ultimately depends on the cells genetic makeup and environmental conditions. Extracellular (outside of the cell) chemicals can act as signals, such as signals from the body or nearby cells. An broad example of these signals can be mitogens, as there are many different types. Mitogens are most often proteins, which signal the cell to begin mitosis. These mitogens enter what is called a signal transduction pathway. Here is where MAPK (mitogen activated protein kinase) is involved, ultimately leading to mitosis.
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I encourage you to read some journal entries, as this is where raw data and insight can be truly found.