The twist energy parameter (E-T) that governs the supercoiling free energy, and the linking difference (Delta l) are measured for p30 delta DNA in solutions containing 0-40 w/v % ethylene glycol (EG). A plot of E-T vs -ln a(w), where aw is the water activity, displays the full (reverse) sigmoidal profile of a discrete structural transition. A general theory for the effect of added osmolyte on a cooperative structural transition between two duplex states, 1 reversible arrow 2, is formulated in terms of parameters applicable to individual base-pair subunits. The resulting fraction of base pairs in the 2-state (f(2)(0)) is incorporated into expressions for the effective torsion and bending elastic constants, the effective twist energy parameter (E-T), and the change in intrinsic twist (Delta l). Fitting the expression for E-T(eff) to the measured E-T values yields reasonably unambiguous estimates of E-T1 and E-T2 the midpoint value (ln a(w))(1/2), and the midpoint slope (partial derivative E-T/partial derivative ln a(w))(1/2), but does not yield unambiguous estimates of the equilibrium constant (K-0), the difference in DNA-water preferential interaction coefficient (Delta Gamma), or the inverse cooperativity parameter (J). Fitting a noncooperative model (assumed J = 1.0) to the data yields K-0 = 0.067 and Delta Gamma = -30.0 per base pair (bp). Essentially equivalent fits are provided by models with a wide range of correlated J, Delta Gamma, and K-0 values. Other results favor Delta Gamma in the range - 1.0 to 0, which then requires K-0 >= 0.914, and a cooperativity parameter, 1/J >= 30.0 bp. The measured delta l(0) and circular dichroism (CD) at 272 nm are found to be compatible with curves predicted using the same f(2)(0) values that best-fit the E-T data. At least 7-10% of the base pairs are inferred to exist in the 2-state in 0.1 M NaG in the complete absence of added osmolyte. Compared with the 1-state, the 2-state has a similar to 2.0- to 2.1-fold greater torsion elastic constant, a similar to 0.70-fold smaller bending elastic constant, a similar to 0.91-fold smaller E-T value, a similar to 0.2% lower intrinsic twist, a somewhat lower CD near both 272 and 245 nm, and less water and/or more EG in its neighborhood. However, the relative change in preferential interaction coefficient associated with the transition is likely rather slight.