In the year 1744 Leonard Euler gave the first modern formulation for the energetics underlying the bending of elastica, thin elastic strips. This theory is of great importance for the understanding of the behavior of DNA inside the chromatin complex, the DNA-protein complex that fills the nuclei of plant and animal cells. After introducing the history of Euler elastica, I shall present the following applications and extensions of Euler's theory:
(1) Twisting DNA under tension: I demonstrate that this leads typically to the formation of multiple plectonemes that turn some of the local twist into global conformational changes. Our theory agrees perfectly with experimental data from several labs.
(2) Nucleosomes: breathing and force-induced unwrapping: Our theoretical analysis indicates a mechanism through which the nucleosomal two-DNA-turn design allows to combine stability of the nucleosome and accessibility of DNA binding proteins to their binding sites inside the wrapped portion.
(3) Chromatin fiber geometry: a packing problem: It is demonstrated that the 33 and 44nm diameters observed in experiments correspond to superdense fibers where the wedge-shaped nucleosomes are tightly stacked. We further show how the linker DNA energetics determines which of the 2 diameters is chosen for a given linker length.