During the Rule of Diocletian, in 285-306, the Roman Empire had grown so large that it was not possible to control under one ruler. So Diocletian split the empire in half, through Rome was still very much a pagan civilization. In 313, Constantine (emperor of the west) and Licinius (emperor the east) agreed to end the ban on Christianity. Historically, Constantine defeated Licinius to become the emperor of the east also. When Constantine became emperor, Constantinople was founded in 330 as the Christian city and the new capital of the Roman Empire. Constantinople was now the center of the Empire, and Christianity was a legal religion.
After the death of Constantine, other emperors rules over his land, further refining the capitol that he had founded. Christianity was recognized as state religion in 391, and pagans were persecuted as once the Christians were. The fall of Rome to the Goths in around 475 left the west in waste, but Rome still had the east, founded of different principles, to carry on the legacy of the long-standing empire. But Constantinople was almost nothing like Rome.
Constantinople had aspects of the Roman empire, flavored with the beliefs of Christianity, and the fine quality of the Persian Empire. As means of fortification, seven layers of walls were built around the empire to make it a touch fortress, and a fairly safe place to live for its people. The educated were won over by the literature of Christian fathers such as Jerome and Augustine; manuscripts were illuminated with drawings surrounding the writing. The classical myths were still used in stories and in art, though they no longer were such an important part of the empire. But the classical values of art were given over to the symbolic realism of Christian art, and classical form was modified for the convenience of Christian purposes all the way down to architecture. In terms of architecture, the Roman Basilicas were adapted to be used as churches.
They did try to cling to the ways of the West with their emperors and law, but the Byzantine in its entirety could not resist their Arab and Muslim foes for long, finally submitting to them in 687. However, Constantinople hung strong thanks to it's fortified walls. However, the Turks were able to defeat the walls of Constantinople during the Renaissance by the use of cannons. By firing at the same spot over and over, they were able to collapse the walls one by one and take the city.