Dna has a charge associated with it. what functional group that carries a charge is included in dna, and how do we use the charge to our advantage while doing gel electrophoresis? how does this relate to using the phrase "run to the red" while performing gel electrolysis?

DNA is made up of sugar-phosphate backbone and the phosphate in the DNA contains the negative charge, therefore, DNA is a negatively charged molecule present in the nucleus.

This negative charge is very important in separating the DNA according to their charge and size during gel electrophoresis. During gel electrophoresis DNA of different size is run on an agarose gel in the presence of current and DNA fragments move toward positive charge due to negative in nature.  

Small size DNA moves fast through the gel large size DNA moves slow towards negative pole, therefore, separating the DNA according to their size. In gel electrophoresis, red pole is positive pole and the black pole is negative so runs to the red phrase is signifying that the DNA is always run towards the red pole.