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1. DNA of a normal cell
This piece of DNA is an exact copy of the DNA from which it came. When the parent cell divided to create two cells, the cell's DNA also divided, creating two identical copies of the original DNA.
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2. Mutation of DNA
Here is the same section of DNA but from another cell. If you can imagine that DNA is a twisted ladder, then each rung of the ladder is a pair of joined molecules, or a base pair. With this section of DNA, one of the base pairs is different from the original. This DNA has suffered a mutation, either through mis-copying (when its parent cell divided), or through the damaging effects of exposure to radiation or a chemical carcinogen.
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3. Genetically altered cell
Body cells replicate through mitosis, they respond to their surrounding cells and replicate only to replace other cells. Sometimes a genetic mutation will cause a cell and its descendants to reproduce even though replacement cells are not needed. The DNA of the cell highlighted above has a mutation that causes the cell to replicate even though this tissue doesn't need replacement cells at this time or at this place.
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4. Spread and second mutation
The genetically altered cells have, over time, reproduced unchecked, crowding out the surrounding normal cells. The growth may contain one million cells and be the size of a pinhead. At this point the cells continue to look the same as the surrounding healthy cells. After about a million divisions, there's a good chance that one of the new cells will have mutated further. This cell, now carrying two mutant genes, could have an altered appearance and be even more prone to reproduce unchecked.
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5. Third mutation
Not all mutations that lead to cancerous cells result in the cells reproducing at a faster, more uncontrolled rate. For example, a mutation may simply cause a cell to keep from self-destructing. All normal cells have surveillance mechanisms that look for damage or for problems with their own control systems. If such problems are found, the cell destroys itself. Over time and after many cell divisions, a third mutation may arise. If the mutation gives the cell some further advantage, that cell will grow more vigorously than its predecessors and thus speed up the growth of the tumour.
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6. Fourth mutation
The new type of cells grow rapidly, allowing for more opportunities for mutations. The next mutation paves the way for the development of an even more aggressive cancer. At this point the tumour is still contained.