Fundamental limits to transcriptional regulatory control

Gene expression is typically regulated by gene regulatory proteins that bind to the DNA. Experiments have shown that these proteins find their DNA target site via a combination of 3D diffusion in the cytoplasm and 1D diffusion along the DNA. This stochastic transport sets a fundamental limit on the precision of gene regulation. We derive this limit analytically and show by particle-based GFRD simulations that our expression is highly accurate under biologically relevant conditions.