ABSTRACT
3D electron microsscopy aims at the reconstruction of density volumes corresponding to the electrostatic potential distribution of macro-molecules. There are many factors limiting the resolution achievable when this technique is applied to biological macromolecules: microscope imperfections, molecule flexibility, lack of projections from certain directions, unknown angular distribution, noise, etc. In this communication we explore the quality gain in the reconstruction by including a priori knowledge such as particle symmetry, occupied volume, known surface relief, density nonnegativity and similarity to a known volume in order to improve the quality of the reconstruction. If the reconstruction is represented as a series expansion, such constraints can be expressed by set of equations that the expansion coefficients must satisfy. In this work, these equation sets are specified and combined in a novel way with the ART + blobs reconstruction algorithm. The effect of each one on the reconstruction of a realistic phantom is explored. Finally, the application of these restrictions to 3D reconstructions from experimental data are studied.
ABSTRACT
In this work, a powerful parametric spectral estimation technique, 2D-auto regressive moving average modeling (ARMA), has been applied to contrast transfer function (CTF) detection in electron microscopy. Parametric techniques such as auto regressive (AR) and ARMA models allow a more exact determination of the CTF than traditional methods based only on the Fourier transform of the complete image or parts of it and performing some average (periodogram averaging). Previous works revealed that AR models can be used to improve CTF estimation and the detection of its zeros. ARMA models reduce the model order and the computing time, and more interestingly, achieve increased accuracy. ARMA models are generated from electron microscopy (EM) images, and then a stepwise search algorithm is used to fit all the parameters of a theoretical CTF model in the ARMA model previously calculated. Furthermore, this adjustment is truly two-dimensional, allowing astigmatic images to be properly treated. Finally, an individual CTF can be assigned to every point of the micrograph, by means of an interpolation at the functional level, provided that a CTF has been estimated in each one of a set of local areas. The user need only know a few a priori parameters of the experimental conditions of his micrographs, for turning this technique into an automatic and very powerful tool for CTF determination, prior to CTF correction in 3D-EM. The programs developed for the above tasks have been integrated into the X-Windows-based Microscopy Image Processing Package (Xmipp) software package, and are fully accessible at www.biocomp.cnb.uam.es.
