A component of the CLASSICAL COMPLEMENT PATHWAY. C2 is cleaved by activated complement c1s into complement c2b and complement c2a. C2a, the COOH-terminal fragment containing a serine PROTEASE, combines with complement c4b to form C4b2a (CLASSICAL PATHWAY C3 CONVERTASE) and subsequent C4b2a3b (CLASSICAL PATHWAY C5 CONVERTASE).