Previous experimental studies of the effects of changes in sequence on the elastic constants and other properties of DNAs are analyzed using the recently parametrized two-state cooperative transition model. With appropriate assumptions regarding the relative preference of particular subsequences for the b and a states, the model gives an approximately quantitative account of the surprisingly large observed effects of replacing 25 bp of natural sequence near the middle of an similar to 1100 bp DNA by 16 bp of alternating (CG)(8) sequence on the fraction f(b) of base-pairs in the b-state and on the torsion elastic constant. This demonstrates the effect of the strong cooperativity of the transition to significantly influence the state of the DNA over surprisingly large domains of the flanking DNA. With appropriate assumptions regarding the disposition of nonrelaxing (permanent) and slowly relaxing bends between the a and b states, the two-state model resolves the discrepancy between experimental estimates of the magnitude of the nonrelaxing bends obtained from studies of synthetic straight and natural DNA sequences by cryo-electron microscopy on the one hand and by j-factors inferred from the kinetics of ligase cyclization of small similar to 200 bp circular DNAs on the other. Approximately quantitative agreement with the experiments is again obtained.