The review by Trifonov provides a timely account of nucleosome positioning [1]. The author has made numerous important contributions, as summarized in his account of 30 years cracking the chromatin code. A recent perspective on nucleosome positioning will help readers identify contributions from others [2].
There are two ideas in Trifonov's review that I wish to expand upon. Both relate to the structure of nucleosomes and chromatin. X-ray crystallography provides a largely static, atomic resolution view of the nucleosome. It is a histone-DNA complex that contains 147 basepairs of double stranded, mostly B-form DNA [3,4]. The DNA is wrapped ∼1.7 left-handed turns around a histone octamer. It has been argued that this octameric state of the nucleosome is an artifact created through experimental peculiarities, environmental conditions, or both [5]. Instead nucleosomes exist as a family of states as categorized in [6]. The family is inclusive so Trifonov's 125 bp nucleosome [1] can likely be adopted. Chromatin in its simplest conceptual form is a segment of double stranded DNA that contains many nucleosomes. By this definition, chromatin must also exist as a family of states. The states of chromatin have long been characterized as either extended or condensed without much regard for the particular state of the nucleosome. Extended chromatin has relatively few nucleosomes spaced far from each other along the DNA. It resembles "beads-on-a-string" where the beads are nucleosomes and the string is linker DNA. Condensed chromatin has many nucleosomes packed tightly together. It is characterized as a more or less regular, continuous fiber. These states of chromatin should also be considered artifactual entities or experimental constructs that are certainly important for our understanding. But, biologically, chromatin possesses an additional linker histone and resides in a molecular soup of proteins, small molecules, various species of ions, and RNA. It is confined to the cell nucleus and may have tethers attached to it. The DNA itself may be damaged, e.g. by radiation, or possess covalently attached chemical modifications. In any case DNA is the common thread both literally and figuratively. The path of DNA is sufficient to build a model of chromatin and the sequence of DNA is sufficient for bioinformatics.
First, the path of DNA. It is true that any continuous 3D space curve with uniform cross-section can also be represented by two internal coordinates: curvature and torsion. For such a space curve the Fuller-Crick formalism is valid. However, one must admit that DNA is not a simple space curve. The chemical composition, material properties and geometric cross-sections of DNA are not well described as continuous, uniform or homogeneous. DNA varies