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. Focusing on chromosomal regions that contribute to compartments, we discover distinct structures that, in spite of considerable variability, can predict whether such regions correspond to active (A-type) or inactive (B-type) compartments. Imaging through the depths of entire nuclei, we capture pairs of homologous regions in diploid cells, obtaining evidence that maternal and paternal homologous regions can be differentially organized. Finally, using restraint-based modeling to integrate imaging and Hi-C data, we implement a method-integrative modeling of genomic regions (IMGR)-to increase the genomic resolution of our traces to 10 kb.

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. This poses a problem especially for techniques such as Fluorescence Photoactivation Localization Microscopy (FPALM/PALM) or Stochastic Optical Reconstruction Microscopy (STORM), which often require minutes recording time. Here we discuss an approach that corrects for three-dimensional (3D) drift in images of fixed samples without the requirement for fiduciary markers or instrument modifications. Drift is determined by calculating the spatial cross-correlation function between subsets of localized particles imaged at different times. Correction down to ~5 nm precision is achieved despite the fact that different molecules are imaged in each frame. We demonstrate the performance of our drift correction algorithm with different simulated structures and analyze its dependence on particle density and localization precision. By imaging mitochondria with Biplane FPALM we show our algorithm's feasibility in a practical application.

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. We describe an improved substitute for histograms based on weighting with the inverse gradient magnitude, develop a statistical model that is invariant under isosurface-preserving transformations, and argue that this provides a consistent method for algorithm evaluation across multiple datasets based on histogram equalization. We use our corrected formulation to reevaluate recent results on average isosurface complexity, and show evidence that noise is one cause of the discrepancy between the expected figure and the observed one.