Equal impact of diffusion and DNA binding rates on the potential spatial distribution of nuclear factor κB transcription factor inside the nucleus

Abstract

There are two physical processes that influence the spatial distribution of transcription factor molecules entering the nucleus of a eukaryotic cell, the binding to genomic DNA and the diffusion throughout the nuclear volume. Comparison of the DNA-protein association rate constant and the protein diffusion constant may determine which one is the limiting factor. If the process is diffusion-limited, transcription factor molecules are captured by DNA before their even distribution in the nuclear volume. Otherwise, if the reaction rate is limiting, these molecules diffuse evenly and then find their binding sites. Using well-studied human NF-κB dimer as an example, we calculated its diffusion constant using the Debye-Smoluchowski equation. The value of diffusion constant was about 10⁻¹⁵ cm³/s, and it was comparable to the NF-κB association rate constant for DNA binding known from previous studies. Thus, both diffusion and DNA binding play an equally important role in NF-κB spatial distribution. The importance of genome 3D-structure in gene expression regulation and possible dependence of gene expression on the local concentration of open chromatin can be hypothesized from our theoretical estimate.