An exact theory of histone-DNA adsorption and wrapping

– We find exact solutions to a one-dimensional (1D) interacting particle theory and apply the results to the adsorption and wrapping of polymers (such as DNA) around protein particles (such as histones). Each adsorbed protein is represented by a Tonks gas particle. The length of each particle is a degree of freedom that represents the degree of DNA wrapping around each histone. Thermodynamic quantities are computed as functions of wrapping energy, adsorbed histone density, and bulk histone concentration (or chemical potential); their experimental signatures are also discussed. Histone density is found to undergo a two-stage adsorption process as a function of chemical potential, while the mean coverage by high affinity proteins exhibits a maximum as a function of the chemical potential. However, fluctuations in the coverage are concurrently maximal. Histone-histone correlation functions are also computed and exhibit rich two length scale behavior. Introduction. – Molecular adsorption onto 1D substrates occur in many biological settings such as protein adsorption on DNA/RNA [1, 2] and microtubules [3, 4]. Motivated by the microscopic details of such systems [4], we study histone-polymer binding and wrapping by solving a 1D theory of interacting particles with dynamically varying particle lengths. Histones are a class of hockey-puck shaped oligomer proteins about 10nm in diameter that wrap DNA. As shown in Fig. 1a, DNA can wrap around the edge of each histone protein complex at most 1.7 times, about 146 base pairs (bp) [5, 6]. DNA-histone complexes (nucleosomes) play vital roles in compacting DNA and regulating nucleic acid processing by mediating the accessibility by other regulatory proteins [1, 7, 8]. Acetylation levels of specific subgroups on the histone protein can affect their binding affinity, thereby providing a control mechanism for association and dissociation. When DNA needs to be processed (e.g. replicated), histones must move out of the way to allow other processing proteins access. Proposed mechanisms for histone dynamics include detachment/reattachment and sliding [7, 8]. Modeling the qualitative aspects of the histone binding isotherm on a one-dimensional substrate can potentially aid our understanding of DNA-histone and histone-histone interactions and their association/dissociation processes in biology. We present a first attempt at describing histone isotherms using an exact statistical mechanical theory. The system depicted in Fig. 1 is mapped onto a generalized Tonks-Takahashi gas [9,10] of one dimensional particles of dynamically varying length. Base pairs that come into contact with each histone protein defines a footprint which we associate with particle lengths. We consider the collective behavior of the particles mediated only by the mutual exclusion of their footprints along a tensionless DNA substrate. We also neglect the non-nearest-neighbor c © EDP Sciences 754 EUROPHYSICS LETTERS