b-cells proliferate when an antigen is encountered by the immune system. the b-cells that are capable of producing antibodies against this specific antigen are produced in greater numbers, along with memory cells (for quicker response in case of another infection).
cytotoxic t-cells proliferate when there is a disease like cancer which results in abnormal self-cells, or when a cell starts producing viral proteins (as a result of a viral infection). proliferation of helper t-cells occurs when the helper t-cells encounter antigens presented by the APC in the lymph nodes.
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