Ab-initio electronic structure methods are used to explore potential energy profiles pertinent to the fragmentations of gas-phase radicals thought to be formed in the new negative-ion mode EDD mass spectroscopic studies of peptides. Barriers to fragmentation as well as the associated overall energy differences are computed for the observed C-alpha-C backbone bond cleavage as well as for side-chain loss for a variety of side chains (valine, arginine, glutamic acid, and tyrosine). It is found that C-alpha-C bond cleavage is favored over side-chain loss, although loss of a tyrosine side chain may compete with C-alpha-C cleavage because the tyrosine radical formed can delocalize its unpaired electron over its aromatic ring. In addition, it is found that fragmentation of the nitrogen-centered radicals formed in EDD results in cleavage to produce so-called a center dot/x fragments rather than a/x center dot fragments both because producing the former involves a significantly smaller barrier and is nearly thermoneutral, while cleavage to yield a/x center dot is significantly endothermic.