3-D shape estimation of DNA molecules from stereo cryo-electron micro-graphs using a projection-steerable snake

Stereo-vision three-dimensional reconstruction of curvilinear structures imaged with a TEM

Deriving accurate three-dimensional (3-D) structural information of materials at the nanometre level is often crucial for understanding their properties. Tomography in transmission electron microscopy (TEM) is a powerful technique that provides such information. It is however demanding and sometimes inapplicable, as it requires the acquisition of multiple images within a large tilt arc and hence prolonged exposure to electrons. In some cases, prior knowledge about the structure can tremendously simplify the 3-D reconstruction if incorporated adequately. Here, a novel algorithm is presented that is able to produce a full 3-D reconstruction of curvilinear structures from stereo pair of TEM images acquired within a small tilt range that spans from only a few to tens of degrees. Reliability of the algorithm is demonstrated through reconstruction of a model 3-D object from its simulated projections, and is compared with that of conventional tomography. This method is experimentally demonstrated for the 3-D visualization of dislocation arrangements in a deformed metallic micro-pillar.

Maximum likelihood orientation estimation of 1-D patterns in Laguerre-Gauss subspaces

A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

Bending modes of DNA directly addressed by cryo-electron microscopy of DNA minicircles

We use cryo-electron microscopy (cryo-EM) to study the 3D shapes of 94-bp-long DNA minicircles and address the question of whether cyclization of such short DNA molecules necessitates the formation of sharp, localized kinks in DNA or whether the necessary bending can be redistributed and accomplished within the limits of the elastic, standard model of DNA flexibility. By comparing the shapes of covalently closed, nicked and gapped DNA minicircles, we conclude that 94-bp-long covalently closed and nicked DNA minicircles do not show sharp kinks while gapped DNA molecules, containing very flexible single-stranded regions, do show sharp kinks. We corroborate the results of cryo-EM studies by using Bal31 nuclease to probe for the existence of kinks in 94-bp-long minicircles.

3D reconstruction and comparison of shapes of DNA minicircles observed by cryo-electron microscopy

We use cryo-electron microscopy to compare 3D shapes of 158 bp long DNA minicircles that differ only in the sequence within an 18 bp block containing either a TATA box or a catabolite activator protein binding site. We present a sorting algorithm that correlates the reconstructed shapes and groups them into distinct categories. We conclude that the presence of the TATA box sequence, which is believed to be easily bent, does not significantly affect the observed shapes.