Invariant recognition of molecular projections in vitreous ice preparations

Abstract

Multivariate statistical analysis (MSA) techniques are beautiful tools in the study of large complex data sets. They have been successfully applied to study the structures of different biological macromolecules based on large numbers of electron microscopical images of the particles. However, prerequisite for the application of such eigenvector eigenvalue analysis techniques to large image data sets is that the images in the set are aligned relative to each other. Alignment is a difficult issue: it is hardly possible to attain alignment of a complex and noisy data set without introducing bias in the data set. We have recently proposed the application of the rotation, translation and mirror-invariant double auto-correlation function (DACF) to avoid reference image bias of the data set. The DACF is derived from the auto-correlation function (ACF) of an image by calculating secondary ACFs along concentric rings (i.e., in polar coordinates) of the first ACF. Here, we introduce in detail the double self-correlation function (DSCF), which has some advantages as compared to the DACF. Loss of image information is the price we pay for the invariance properties of DSCF (and DACF). Nevertheless, we show here, using the giant hemoglobins of the common earthworm as an example, that the DSCF technique can successfully be applied to study a real-life noisy data set of randomly oriented biological macromolecules embedded in vitreous ice.