Optimization problems in electron microscopy of single particles

Abstract

Electron Microscopy is a valuable tool for the elucidation of the three-dimensional structure of macromolecular complexes. Knowledge about the macromolecular structure provides important information about its function and how it is carried out. This work addresses the issue of three-dimensional reconstruction of biological macromolecules from electron microscopy images. In particular, it focuses on a methodology known as "single-particles" and makes a thorough review of all those steps that can be expressed as an optimization problem. In spite of important advances in recent years, there are still unresolved challenges in the field that offer an excellent testbed for new and more powerful optimization techniques.

PyTom: A python-based toolbox for localization of macromolecules in cryo-electron tomograms and subtomogram analysis

“…The initially unknown parameters t i and r i in Eq. (1) are often referred to as 'hidden variables' (Sorzano et al, 2006). The best estimate of A can be calculated by optimizing S, which requires determination of the hidden parameters h -a process known as alignment.…”

Fast multiscale reconstruction for Cryo-EM

“…Yet the importance of a robust first estimation cannot be overstated. Several works have indeed demonstrated that the nature of this initial structure can considerably affect the final reconstruction ( Henderson et al, 2012 , Sorzano et al, 2006 ).…”

“…The presence of heavy noise on nearly identical projections, their low contrast, the conformational heterogeneity of molecular complexes, the unknown projection directions, the finite number of measurements, and the incomplete knowledge of the imaging process all cause the determination of the 3D structure to be a highly ill-posed inverse problem that may also suffer from overfitting. Moreover, the convergence of the global process depends heavily on the quality of the initial reconstruction ( Sorzano et al, 2006 , Henderson et al, 2012 ).…”

Advances in image processing for single-particle analysis by electron cryomicroscopy and challenges ahead

“…The whole 3D reconstruction process is commonly managed starting with an initial model estimation, which can be seen as an estimation of the start-ing point in the solution landscape, followed by a refinement to move along the whole landscape, improving the reconstructed model in every step. The refinement algorithms easily get stuck in local minima of the solution landscape [90]. Therefore, a good design of the initial volume estimation and refinement algorithms is key in the accuracy of the final 3D model generated.…”