Target Search for Transcription Factors on DNA Chains

Among many structures in the cells of living beings, there are proteins called transcription factors (TF) that are responsible to inhibit or promote the transcription of the DNA. To accomplish their function, the transcription factors perform aleatory searches around the cytoplasm (for prokaryotic cells) and along the DNA chain as well for specific targets located in the DNA. Its movement fits into the class of anomalous Brownian. The efficiency in TFs search has implications in the cellular copy and in protection against viruses, hence the knowledge of the mechanism is of great interest. In the present work, we study the searching process of the TFs by simulating the anomalous Brownian motion through the cytoplasm and DNA chain by means of Levy flights through a lattice model and through a  free grid model. The final distribution of positions of the TF are obtained. The search efficiency is investigated in terms of the model parameters.