Byzantium had first been reconstructed in the time of Septimius Severus not just as a Roman city, but modelled on Rome itself, on and around seven hills. Later Constantine the Great chose it as his new capital, renaming it Constantinople, and it remained the capital of the eastern part of the Roman empire.
Arcadius (reign AD 395-408)
The story of Constantinople as an independent entity begins during the reign of co-emperors Arcadius (c.AD 378-408) and Honorius (AD 385-423), under whom the two parts of the Roman empire finally went their own ways (Arcadius succeeding Theodosius in Constantinople in AD 395). As Rome fell in AD 410 the burden of sustaining roman civilization alas fell solely to the eastern capital.
The eastern empire, largely by reason of its geographical situation, was bypassed by the ant-like hordes of invaders who befell Rome.
The Parthian threat from the east had also ceased as Parthia had to contend with the Scythian menace on her own eastern frontier.
The independent Arabian tribes, now beginning to be known as the Saracens, might worry Romans and Persians alternately, having their own retreat secured by the wastes of the Arabian desert, but they constituted no real menace to neither of the great powers.