Even in the SERIALIZABLE isolation level, multiple selects can be made in parallel. If you want to put a lock on the row on the select clause, use select ... for update
.
References:
http://dev.mysql.com/doc/refman/5.1/en/select.html :
If you use FOR UPDATE with a storage engine that uses page or row locks, rows examined by the query are write-locked until the end of the current transaction. Using LOCK IN SHARE MODE sets a shared lock that permits other transactions to read the examined rows but not to update or delete them.
http://dev.mysql.com/doc/refman/5.1/en/set-transaction.html#isolevel_serializable :
SERIALIZABLE
This level is like REPEATABLE READ, but InnoDB implicitly converts all plain SELECT statements to SELECT ... LOCK IN SHARE MODE if autocommit is disabled.