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Section: New Results

FFT-accelerated methods for fitting molecular structures into Cryo-EM maps

Participants : Alexandre Hoffmann, Sergei Grudinin.

We have developed a set of new methods for fitting molecular structures into Cryo-EM maps. The problem can be formally written as follows, We are given two proteins 𝒫1 and 𝒫2, and we also have d1:3, the electron density of 𝒫1 and (Yk)k=0Natoms-1, the starting positions of the atoms of 𝒫2. Assuming we can generate an artificial electron density d2:3 from (Yk)k=0Natoms-1, our problem is to find a transformation of the atoms T:33 that minimize the L2 distance between d1 and d2.

In image processing this problem is usually solved using the optimal transport theory, but this method assumes that both of the densities have the same L2 norm which is not necessarily the case for the fitting problem. To solve this problem, one instead starts by splitting T into a rigid transformation Trigid (which is a combination of translation and rotation) and a flexible transformation Tflexible. Two classes of methods have been developed to find Trigid :

The NANO-D team has already developed some algorithms based on the FFT to find Trigid and we have been developing an efficient extension of these to find Tflexible.