Alexander of Imereti was a son of Bagrat I of Imereti and an unnamed daughter of Qvarqvare II Jakeli, atabeg of Samtskhe. The Jaqelis held the Georgian feudal office of Eristavi. An Eristavi could be "governor of a region" or an "army-commander" , roughly equivalent to the Byzantine strategos and normally translated into English as "duke".
In about 1426, Bagrationi married John IV of Trebizond. He was a son of Emperor Alexios IV of Trebizond and Theodora Kantakouzene. According to Trebizond: The Last Greek Empire of the Byzantine Era (1926) by William Miller, earlier in that same year John had murdered a courtier who allegedly served as the lover of his mother. He had then attempted to assassinate both of his own parents but the palace staff defended the royal couple. John had gone into exile in Georgia. Their marriage was the result of an attempted alliance between John IV and Alexander I.
Failing to secure sufficient support from his father-in-law, John left Georgia in 1427. He headed to Caffa, a Genoese colony in the Crimea. By 1429, John was able to charter a large galley and its crew. He led them to an invasion of Trebizond. Alexios IV prepared to face his son in the battlefield. He was assassinated during the night by supporters of his son. John proceeded to succeed his father with Bagrationi as his Empress. He executed the assassins of his father in order to deny any connection with them.
Their daughter Theodora Komnene married Uzun Hassan of Ak Koyunlu. Her maternity has been questioned because of marrying a non-Christian monarch, a practice previously followed by illegitimate daughters of Emperors such as Maria Despina Palaiologina. "Dell'Imperadori Constantinopolitani", a manuscript held in the Vatican Library. The document is also known as the "Massarelli manuscript" because it was found in the papers of Angelo Massarelli (1510 - 1566). Masarelli is better known as the general secretary of the Council of Trent, who recorded the daily occurings of the council.
An account by Caterino Zeno dated to 1574 names another daughter, Eudokia-Valenza of Trebizond. This Valenza was a reported wife of Niccolò Crispo, Lord of Syros. However she is reported as having a daughter who married in 1429. John IV and Bagrationi are unlikely to have been the grandparents of a married woman only three years following their own marriage. Valenza is considered likely to have been a sister of John IV, instead of a daughter. Niccolò Crispo had eleven children. According to his own correspondence, Niccolò was also a son-in-law of Jacopo of Lesbos. His children could be from either of his two marriages. They included (among others) Francesco II Crispo, Duke of the Archipelago and Fiorenza Crispo, mother of Catherine Cornaro.
According to the Europäische Stammtafeln: Stammtafeln zur Geschichte der Europäischen Staaten (1978) by Detlev Schwennicke, Bagrationi was dead by 1438. John IV went on to marry an unnamed Turkish lady. The "Europäische Stammtafeln" considers this second wife to have been a daughter of Dawlat Berdi. Dawlat rivaled Olugh Mokhammad of Kazan for leadership of the Golden Horde from 1419 to 1422. Both were defeated and succeeded by Baraq.