DNA twist step-parameters are in common use in the community of structural biologists. If, for a molecule with a closed axial curve, the writhing number, a measure of the chiral distortion of the axial curve of the molecule from planarity, is added to the sum over all steps of such twists, the result has no particular significance. This is in marked contrast to the properties of the value obtained . the topological invariant, an integer called the linking number - when the same writhe is added to the total twist we obtain by using step twists defined in a way consistent with the twist associated with supercoiling. Also of interest is the difference in the values of these two step-parameters for DNA in various environments. Thus, when the DNA is relaxed, and not interacting with any proteins, we find, and understand why, the two twists for each step are close in value. On the other hand, when the DNA is interacting with a protein, with the histones in chromatin, for example, there are certain steps for which one observes significant differences. By considering various model structures, we find instances in which we are able to relate the magnitude of an observed difference in twists for a particular step to the specific nature and chirality of the structural distortion being imposed by the protein on the DNA in the region of the step.