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In this work we examine how volume exclusion caused by regions of highchromatin density might influence the time required for proteins to findspecific DNA binding sites. The spatial variation of chromatin density withinmouse olfactory sensory neurons is determined from soft X-ray tomographyreconstructions of five nuclei. We show that there is a division of the nuclearspace into regions of low-density euchromatin and high-density heterochromatin.Volume exclusion experienced by a diffusing protein caused by this varyingdensity of chromatin is modeled by a repulsive potential. The value of thepotential at a given point in space is chosen to be proportional to the densityof chromatin at that location. The constant of proportionality, called thevolume exclusivity, provides a model parameter that determines the strength ofvolume exclusion. Numerical simulations demonstrate that the mean time for aprotein to locate a binding site localized in euchromatin is minimized for afinite, non-zero volume exclusivity. For binding sites in heterochromatin, themean time is minimized when the volume exclusivity is zero (the proteinexperiences no volume exclusion). An analytical theory is developed to explainthese results. The theory suggests that for binding sites in euchromatin thereis an optimal level of volume exclusivity that balances a reduction in thevolume searched in finding the binding site, with the height of effectivepotential barriers the protein must cross during the search process.

The Influence of Spatial Variation in Chromatin Density Determined by X-ray Tomograms on the Time to Find DNA Binding Sites