Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities.

Area of Science:

• Structural Biology
• Computational Biology
• Biophysics

Background:

• Cryo-electron microscopy (cryo-EM) has revolutionized molecular structure elucidation.
• Significant hardware and data processing advancements have driven cryo-EM progress.
• Cryo-EM was recognized as Nature Methods' Method of the Year 2015 and Nobel Prize in Chemistry 2017.

Purpose of the Study:

• To introduce the computational challenges in 3-D molecular structure reconstruction using cryo-EM.
• To highlight the interdisciplinary nature of cryo-EM computational tasks.
• To present statistical models for abstracting cryo-EM complexities.

Main Methods:

• Utilizing computational tools from signal processing, statistics, optimization, and machine learning.
• Adapting algorithms for noisy, incomplete, and large-scale cryo-EM datasets.
• Developing and applying statistical models like multi-reference alignment and multi-target detection.

Main Results:

• Identification of diverse computational tasks essential for cryo-EM.
• Demonstration of the need for robust algorithms to handle extreme data conditions.
• Exploration of mathematical theories including group, invariant, and information theory in cryo-EM.

Conclusions:

• Cryo-EM structure determination relies heavily on sophisticated computational approaches.
• Mathematical frameworks provide valuable insights into cryo-EM data analysis.
• Continued development in computational methods will further advance cryo-EM capabilities.