This answer by /u/Guckfuchs may partly answer your question:

The important thing to remember here is that the Roman Empire was never officially split into two different states. According to official state ideology and in the minds of its citizens the empire was always a united entity, even if at times it was governed by more than one emperor. The terms ‘Western Roman Empire’ and ‘Eastern Roman Empire’ should be understood as administrative units of a unitary state, because that is how the Romans themselves viewed it. This means that, at least ideally, the different emperors were always meant to work together as a harmonious governing body, even if they were individually responsible for different geographical parts of the empire. This becomes obvious when you look at Late Roman laws. They are usually issued in the name of the entire council of emperors.