Within the nucleus of each cell lies DNA - an unfathomably long, twisted, and intricately coiled molecule - segments of which make up the genes that provide the instructions that a cell needs to operate. As we near the 60(th) anniversary of the discovery of the DNA double helix, crucial questions remain about how the physical arrangement of the DNA in cells affects how genes work. For example, how a cell stores the genetic information inside the nucleus is complicated by the necessity of maintaining accessibility to DNA for genetic processing. In order to gain insight into the roles played by various proteins in reading and compacting the genome, we have developed new methodologies to simulate the dynamic, three-dimensional structures of long, fluctuating, protein-decorated strands of DNA. Our a priori approach to the problem allows us to determine the effects of individual proteins and their chemical modifications on overall DNA structure and function. Here we present our recent treatment of the communication between regulatory proteins attached to precisely constructed stretches of chromatin. Our simulations account for the enhancement in communication detected experimentally on chromatin compared to protein-free DNA of the same chain length as well as the critical roles played by the cationic 'tails' of the histone proteins in this signaling. The states of chromatin captured in the simulations offer new insights into the ways that the DNA, histones, and regulatory proteins contribute to long-range communication along the genome.