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 and , and we also have , the electron density of and , the starting positions of the atoms of . Assuming we can generate an artificial electron density from , our problem is to find a transformation of the atoms that minimize the distance between and .
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 norm which is not necessarily the case for the fitting problem. To solve this problem, one instead starts by splitting into a rigid transformation (which is a combination of translation and rotation) and a flexible transformation . Two classes of methods have been developed to find :
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the first one uses optimization techniques such as gradient descent, and
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the second one uses Fast Fourier Transform (FFT) to compute the Cross Correlation Function (CCF) of and .
The NANO-D team has already developed some algorithms based on the FFT to find and we have been developing an efficient extension of these to find .