Fast Noise-image Registration for Electron Microscopy

1. INTRODUCTION Single particle electron microscopy (EM) has become the most powerful technique in structural biology for studying large macromolecules and their assemblies. At near physiological conditions, the 3D structure of relevant biological complexes can be determined from sub-nanometer to even near atomic resolution (Frank, 2006). Using a small amount of purified sample, researchers process and average the collected 2D EM data into a 3D reconstruction. In the first step, numerous single molecule images are obtained from multiple EM measures. These images correspond to electronic density 2D projections of the molecule in different random orientations. Because such projections are extremely noisy images, they are aligned and classified by similarity to reduce the signal-to-noise ratio (SNR). In fact, single particle 3D reconstruction is an iterative alignment and classification procedure, where strong image averages produced by classification are used as reference images for the subsequent refinement steps. Therefore, the alignment, which ultimately determines the 3D reconstruction quality, is repeated multiple times. Such alignment typically maximizes a cross-correlation function (simple scalar product of the EM electron density values stored in the 2D images) between experimental noisy images and the reference images. Moreover, the computation time for 3D reconstruction increases with the number of images, becoming a bottleneck for high-resolution studies. Approximately 10 6 image projections are needed to target high-resolution. In this context, the complete process can take even days in a multiprocessor cluster. In summary, the alignment is a critical step that largely