Under acidic conditions (less than pH 6.5)
The global triplex unfolding proceeds in a monophasic triplex-to-coil collapse
(3.16)
and the equilibrium constant, KT, can be written as
(3.17)
where SWSCSH represents the Watson–Crick–Hoogsteen triplex; ΔHT and ΔST are the van't Hoff enthalpy and entropy of triplex formation, respectively; αT is the molar fraction of the coiled strands in the structured triplex form; and CT is the total species concentration. At the maximum temperature of the derivative absorbance versus temperature curves (dA/dT vs. T), RT should be equal to ∼0.63 [16]; therefore, the van't Hoff equation can be written as
(3.18)
Under near physiological conditions (pH 7.0–7.5)
The global triplex unfolding proceeds in a biphasic triplex-to-duplex-to-single transition and can be deconvoluted into two coupled subtransitions, a Hoogsteen transition and a Watson–Crick transition,
and the corresponding equilibrium constants, KH and KWC, can be given by, respectively
(3.19)
(3.20)
where SWSC represents the Watson–Crick duplex; ΔHH, ΔSH, ΔHWC, and ΔSWC are the van't Hoff enthalpies and entropies for the Hoogsteen transition, respectively; αH is the molar fraction of the Hoogsteen strand in the structured triplex state for the Hoogsteen transition; and αWC is the molar fraction of the Watson–Crick duplex in the corresponding coiled state for the Watson–Crick transition. Although the two transitions may overlap each other in a certain range, this cross-effect can be nearly neglected at the melting temperatures, and the values of αWC and αH at which the derivative absorbance vs. temperature curves reach their maxima should be ∼0.42 and ∼0.50, respectively [17]. Thus, the van't Hoff equations can be simplified by
(3.21)
(3.22)
Under alkaline conditions (more than pH 8.0)
The triplex strand is not formed, and the complex unfolding merely includes a monophasic duplex-to-coil transition. That is,
and the equilibrium constant, KD, can be given by
(3.23)