In higher organisms, all cells share the same genome, but every cell expresses only a limited and specific set of genes that defines the cell type. During cell division, not only the genome, but also the cell type is inherited by the daughter cells. This intriguing phenomenon is achieved by a variety of processes that have been collectively termed epigenetics: the stable and inheritable changes in gene expression patterns. This article reviews the extremely rich and exquisitely multi-scale physical mechanisms that govern the biological processes behind the initiation, spreading and inheritance of epigenetic states. These include not only the changes in the molecular properties associated with the chemical modifications of DNA and histone proteins, such as methylation and acetylation, but also less conventional changes, typically in the the physics that governs the three-dimensional organization of the genome in cell nuclei. Strikingly, to achieve stability and heritability of epigenetic states, cells take advantage of many different physical principles, such as the universal behavior of polymers and copolymers, the general features of dynamical systems, and the electrostatic and mechanical properties related to chemical modifications of DNA and histones. By putting the complex biological literature under this new light, the emerging picture is that a limited set of general physical rules play a key role in initiating, shaping and transmitting this crucial "epigenetic landscape". This new perspective not only allows to rationalize the normal cellular functions, but also helps to understand the emergence of pathological states, in which the epigenetic landscape becomes dysfunctional.

The biologically important problem of DNA braiding was studied in the past by means of dual-DNA magnetic tweezer experiments. In such experiments, two DNA molecules are braided about each other using an externally imposed force and torque. Here we develop a theoretical model of molecular braiding that includes interactions between molecules, thermal fluctuations, and the elastic response of molecules, all in a consistent manner. This is useful to study the chiral effects of helix-dependent electrostatic interactions on the braid's equilibrium geometrical and mechanical properties. When helixdependent forces are weak, our model yields a reasonably accurate reproduction of previously measured extension-rotation curves, where only very slight chirality has been observed. On the other hand, when helix-specific electrostatic forces are strong, the model predicts several new features of the extension-rotation curves. These are: (a) a distinct asymmetry between left-handed and right-handed DNA braiding; (b) the emergence, under a critical pulling force, of coexistence regions of tightly and loosely wound DNA; (c) spontaneous formation of left-handed DNA braids at zero external torque (zero bead rotations). Strong chiral forces are expected for braiding experiments conducted in solutions in which there are counter-ions that bind specifically in the DNA grooves.

Homologous pairing and braiding (supercoiling) have crucial effects on genome organization, maintenance, and evolution. Generally, the pairing and braiding processes are discussed in different contexts, independently of each other. However, analysis of electrostatic interactions between DNA double helices suggests that in some situations these processes may be related. Here we present a theory of DNA braiding that accounts for the elastic energy of DNA double helices as well as for the chiral nature of the discrete helical patterns of DNA charges. This theory shows that DNA braiding may be affected, stabilized, or even driven by chiral electrostatic interactions. For example, electrostatically driven braiding may explain the surprising recent observation of stable pairing of homologous double-stranded DNA in solutions containing only monovalent salt. Electrostatic stabilization of left-handed braids may stand behind the chiral selectivity of type II topoisomerases and positive plasmid supercoiling in hyperthermophilic bacteria and archea.