Computational Methods for ThreeDimensional Microscopy Reconstruction
Outline:
Biological structure, on the level of molecule or cell, is imaged by electrons or soft Xrays in conditions that preserve native structure as much as possible. Approaches to the computerized recovery of threedimensional information on a biological object, which are oftentimes formulated or implemented initially in an intuitive way, will be discussed based on physical models of the object and the image formation process. Both threedimensional electron microscopy and Xray tomography can be captured in the same mathematical framework, leading to closely related computational approaches, but the methodologies dier in detail and hence pose different challenges.
Administrative:
The course will meet once a week for two hours. Each of these meetings will comprise a twohour presentation by one of the participants, beginning with presentations by the instructor. The presentations will b e based on chapters in a forthcoming book, whose details are given below. The level of presentations should be suitable for understanding by graduate students in computer science or in biology or in physics; assuming no mathematical knowledge b eyond what can be expected to be possessed by such students. There will be no homeworks or exams. The grade will be determined based on the quality of the presentations. For a good grade, the student will be expected to attend all the meetings from beginning to end.
Text for the course
Computational Methods for Threedimensional Microscopy Reconstruction; edited by Gab or T. Herman (City University of New York) and Joachim Frank (Columbia University); to be published by Springer's imprint BirkhĂ¤user Boston.

Introduction

Tryposoma brucei ribosome at 4.9 A resolution  a case study

Classication using manifold embedding

Quantitative analysis in iterative classication schemes for cryoEM applications

Interchanging geometry conventions in 3DEM: Mathematical context for the development of standards

Xray tomography imaging

Reconstruction from microscopic projections with defocusgradient and attenuation effects

Electron tomography of influenza virus by algebraic reconstruction (ART) with optimized blobs

Using component trees to explore relationships between biological structures
Student learning outcomes
After completing this course students will be able to:

Carefully state and present applications of computers in 3D microscopy of biological structures

Understand the nature of computational approaches for solving problems of structural biology

Apply computer concepts (such a classication, reconstruction, tree algorithms) to practical problems