Various sequences of single and double stranded DNA can wrap and colloidally stabilize single- walled carbon nanotubes in solution. The binding of divalent ions to these complexes results in a 10 meV emission energy red-shift of the photoluminescence of the nanotube. In this work, this optical modulation is linked to specific secondary structure changes in the adsorbed DNA. Dynamic light scattering is used to rule out aggregation and inter-particle effects. It is observed that the transition can also be induced thermally over the temperature range between 0 and 50 degrees C without ion addition. Interestingly, we find evidence of the dissociation of a DNA duplex at the surface, as confirmed using both selective dialysis and DNA electrophoresis on a 20% PAGE gel. Consistent with several observations is a mechanism that proceeds via a competitive, stepwise process of partial desorption of the DNA along the length of SWNT. A two-state mathematical model quantitatively describes the equilibrium for various divalent ions binding to DNA adsorbed at the nanotube surface.