A three-dimensional analytical pathway to smoothly connect successive nucleosomes along DNA

Most DNA in the human genome is wrapped on nucleosomes. The nucleosome is an assembly of eight proteins and about 150 base pairs of DNA. Understanding the biological processing of DNA requires knowledge of how the nucleosomes are arranged in space. We have developed a new analytical model to describe the three-dimensional pathways of long stretches of nucleosome-bound DNA. Given the positions and orientations of a set of nucleosomes, we can find a smooth connector that joins the ends of successive nucleosomes along the DNA. Our studies show that the simplest equation which can smoothly connect any two nucleosomes is a quadric function which is uniquely determined by the position and orientation of each pair of successive nucleosomes. Since the equation for the connector only depends on the boundary conditions, our method can be used to connect either theoretical curves describing the nucleosomal pathway or the protein-bound DNA in known high-resolution structures. This treatment makes it possible to study the effect of elastic and electrostatic energies of the connectors on the stable structure of the nucleosomal arrays and to examine the influence of nucleosomal pathways, such as the length of bound DNA, on the global folding of the arrays.