Physical aspects of precision in genetic regulation

The process by which transcription factors (TFs) locate specific DNA binding sites is stochastic and as such, is subject to a considerable level of noise. TFs diffuse in the three-dimensional nuclear space, but can also slide along the DNA. It was proposed that this sliding facilitates the TF molecules arriving to their binding site, by effectively reducing the dimensionality of diffusion. However, the possible implications of DNA sliding on the accuracy by which the nuclear concentration of TFs can be estimated were not examined. Here, we calculate the mean and the variance of the number of TFs that bind to their binding site in reduced and partially reduced diffusion dimensionality regimes. We find that a search process which combines three-dimensional diffusion in the nucleus with one-dimensional sliding along the DNA can reduce the noise in TF binding and in this way enables a better estimation of the TF concentration inside the nucleus.