Probably the size and a.a. composition (pI) of the protein/proteins.

The DNA-protein interaction also will affect the migration in agarose gel

First the Voltage, temperature and percentage of the gel.

Other is the protein molecular weight and of course the buffer (TBE, TGE, TAE).

If you tell us more about your idea , I can give you some tips .

Noe

The molecular weight of the protein and the type of structure formed by DNA.

The binding stoichiometry as well. Higher the cooperative nature lower would be the mobility compared to unbound DNA

The ionic strength of the sample and the buffer.

Though I do not know in what aspect this question has been asked!

Good luck

pH of running buffer and metals may affect as well.