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Proteins are the workhorses that underlie the vast majority of function in living organisms. Many proteins operate as molecular machines, meaning that they perform their task by mechanical means. For instance, a ratcheting motion of the ribosome advances incoming genetic code as it works to translate RNA into new proteins. Because of this, discovering a 3D structure (also called a conformation) of a protein, and understanding how these conformations change, is an important part of understanding how proteins work. Cryo-electron microscopy (cryo-EM) is a laboratory technique used to discover 3D structures of proteins. Cryo-EM experiments take a sample containing many copies of a protein and produce a large number of very noisy 2D images that can be used recover a 3D model. An important advantage of cryo-EM is that it does not require the sample to be crystallized, as with X-ray crystallography. This can be a very difficult task, and we are not able to crystallize many important biological molecules that we would like to study. The primary difficulty encountered in cryo-EM experiments is the large amount of noise in the 2D images that are produced. When the sample only contains a single conformation of the protein, information from many images can be combined to overcome noise and produce a high quality 3D reconstruction. These methods can also be applied if the sample contains a handful of sharply distinguished conformations. However, this approach fails if the sample contains proteins with continuous conformational changes, such as the ratcheting motion of the ribosome. In this talk, we will first give an overview of how cryo-EM works and why current algorithms struggle with continuous conformations. Then we will present a proposed new algorithm for cryo-EM, due to Dashti et al., that uses ideas from differential geometry to attempt to reconstruct not just a single 3D structure, but the entire range of conformational changes present in a sample.

Please let Mariel (mariel@math.ucdavis.edu) know if you want to meet with the speaker or join the dinner after the talk.