Modeling protein target search in human chromosomes

Several processes in the cell, such as gene regulation, start when key proteins recognise and bind to short DNA sequences. However, these sequences can be hundreds of million times shorter than genome, they are hard find by simple diffusion: diffusion-limited association rates may underestimate $in~vitro$ measurements up several orders magnitude. Moreover, increase if is coiled rather straight. Here we model how this works $in~vivo$ mammalian cells. We use chromatin-chromatin contact data from state-of-the-art Hi-C experiments map protein target-search onto a network problem. The nodes represent segment weight links proportional measured probabilities. then put forward master equation for density searching that allows us calculate across genome analytically. For segments where high, enriched with active genes have high RNA expression levels. This paper suggests DNA's 3D conformation important search offers method interpret protein-binding profiles eukaryotes cannot explained sequence itself.