In this work, we examine how volume exclusion caused by regions of high chromatin density might influence the time required for proteins to find specific DNA binding sites. The spatial variation of chromatin density within mouse olfactory sensory neurons is determined from soft X-ray tomography reconstructions of five nuclei. We show that there is a division of the nuclear space into regions of low-density euchromatin and high-density heterochromatin. Volume exclusion experienced by a diffusing protein caused by this varying density of chromatin is modeled by a repulsive potential. The value of the potential at a given point in space is chosen to be proportional to the density of chromatin at that location. The constant of proportionality, called the volume exclusivity, provides a model parameter that determines the strength of volume exclusion. Numerical simulations demonstrate that the mean time for a protein to locate a binding site localized in euchromatin is minimized for a finite, nonzero volume exclusivity. For binding sites in heterochromatin, the mean time is minimized when the volume exclusivity is zero (the protein experiences no volume exclusion). An analytical theory is developed to explain these results. The theory suggests that for binding sites in euchromatin there is an optimal level of volume exclusivity that balances a reduction in the volume searched in finding the binding site, with the height of effective potential barriers the protein must cross during the search process.

We can learn much about cell function by imaging and quantifying sub-cellular structures, especially if this is done non-destructively without altering said structures. Soft X-ray tomography (SXT) is a high-resolution imaging technique for visualizing cells and their interior structure in 3D. A tomogram of the cell, reconstructed from a series of 2D projection images, can be easily segmented and analyzed. SXT has a very high specimen throughput compared to other high-resolution structure imaging modalities; for example, tomographic data for reconstructing an entire eukaryotic cell is acquired in a matter of minutes. SXT visualizes cells without the need for chemical fixation, dehydration, or staining of the specimen. As a result, the SXT reconstructions are close representations of cells in their native state. SXT is applicable to most cell types. The deep penetration of soft X-rays allows cells, even mammalian cells, to be imaged without being sectioned. Image contrast in SXT is generated by the differential attenuation soft X-ray illumination as it passes through the specimen. Accordingly, each voxel in the tomographic reconstruction has a measured linear absorption coefficient (LAC) value. LAC values are quantitative and give rise to each sub-cellular component having a characteristic LAC profile, allowing organelles to be identified and segmented from the milieu of other cell contents. In this chapter, we describe the fundamentals of SXT imaging and how this technique can answer real world questions in the study of the nucleus. We also describe the development of correlative methods for the localization of specific molecules in a SXT reconstruction. The combination of fluorescence and SXT data acquired from the same specimen produces composite 3D images, rich with detailed information on the inner workings of cells.

For a chemical signal to propagate across a cell, it must navigate a tortuous environment involving a variety of organelle barriers. In this work we study mathematical models for a basic chemical signal, the arrival times at the nuclear membrane of proteins that are activated at the cell membrane and diffuse throughout the cytosol. Organelle surfaces within human B cells are reconstructed from soft X-ray tomographic images, and modeled as reflecting barriers to the molecules' diffusion. We show that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane. Inactivation can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers, leading to arrival times at the nuclear membrane that are comparable to models in which the cytosol is treated as an open, empty region. In the limit of strong signal inactivation this is achieved by filtering out molecules that traverse non-geodesic paths.