Walking along chromosomes with super-resolution imaging, contact maps, and integrative modeling.

Chromosome organization is crucial for genome function. Here, we present a method for visualizing chromosomal DNA at super-resolution and then integrating Hi-C data to produce three-dimensional models of chromosome organization. Using the super-resolution microscopy methods of OligoSTORM and OligoDNA-PAINT, we trace 8 megabases of human chromosome 19, visualizing structures ranging in size from a few kilobases to over a megabase.

Sample drift correction in 3D fluorescence photoactivation localization microscopy.

The recent development of diffraction-unlimited far-field fluorescence microscopy has overcome the classical resolution limit of ~250 nm of conventional light microscopy by about a factor of ten. The improved resolution, however, reveals not only biological structures at an unprecedented resolution, but is also susceptible to sample drift on a much finer scale than previously relevant. Without correction, sample drift leads to smeared images with decreased resolution, and in the worst case to misinterpretation of the imaged structures.

Revisiting histograms and isosurface statistics.

Recent results have shown a link between geometric properties of isosurfaces and statistical properties of the underlying sampled data. However, this has two defects: not all of the properties described converge to the same solution, and the statistics computed are not always invariant under isosurface-preserving transformations. We apply Federer's Coarea Formula from geometric measure theory to explain these discrepancies.