Protonation-induced transitions in a DNA brush

We present a mean-field theory of a single-stranded DNA brush neutralized by counterions and by protons. We show that by varying the pH and the ion concentration, one can induce a transition from an expanded ion-neutralized state to a collapsed protonated state of the brush. In a poor solvent regime for the protonated brush, the transition to the protonated state becomes discontinuous and takes place at a proton concentration that may be much smaller than that of the counterions.