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the first thing that happens is that
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this T-cell becomes activated and it starts reproducing,
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making more copies of itself.
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So, reproduction, proliferation, cell growth happens and
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then those cells become more differentiated.
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They become more mature and they mature into, in this case,
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they mature into cytotoxic cells,
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and they mature into cytotoxic means
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'cyto' - cell, '
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toxic' - killing,
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they mature into cells
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that are capable of killing other cells.