Acid base Chenistry Homework help!?

Question

Histidine was electrophoresed in polyacrylamide at pH 6.0 with alanine (pI=6.0) and arginine (pka's 2.2, 9.0, and 12.5). At the end of the experiment, arginine had migrated toward the cathode 6.0 cm, alanine was still at the origin, and histidine was present at 3.0 toward cathode. No histine was present at 0.0 or 6.0 cm. Explain how is it possible that the histidine molecules behaved as though they had a fraction of one electronic charge, when they actually have either +1 or 0 charge.
Jane Protein thinks this result is bogus (histidine should be present only at 0.0 and 6.0 cm) and so this result shows a major experimental error but John Biochem says this result is exactly what any student who understands acid-base equilibrium would predict. Decide whether you agree with Jane or John and explain why.

My comment:
Well, I think that the side chain, on histidine can both donate and accept protons. The imidazole side chain has two nitrogens with different properties: One is bound to hydrogen and donates its lone pair to the aromatic ring and as such is slighty acidic, whereas the other one donates only one electron pair to the ring so it has a free lone pair and is basic. Is this true for PH=6?