We study the dynamics of nucleosomes, DNA-wrapped proteins, along a DNA chain. First we show that a single nucleosome makes a simple symmetric random walk with respect to the DNA sequence. To...Show moreWe study the dynamics of nucleosomes, DNA-wrapped proteins, along a DNA chain. First we show that a single nucleosome makes a simple symmetric random walk with respect to the DNA sequence. To obtain an estimate for the diffusion coefficient, we study a specific random walk in the quarter plane, absorbed by its boundary. There are exact results in two limiting cases, and in general we derive a continuum approximation. Then we show that a DNA chain filled with multiple nucleosomes cannot be transcribed by RNA polymerase if there is only hard-core interaction between the polymerase and the nucleosome. In the end, we suggest an alternative interaction between RNA polymerase and nucleosomes which allows the DNA to be transcribed without the help of other proteins.Show less
