[cryoEM] Introduction to FSC, Fourier shell correlation

Fourier Shell Correlation

Fourier Shell Correlation (FSC) It is the reliability measurement index of three-dimensional structure of biological macromolecules obtained by single particle analysis of freeze electron microscope .FSC From the following formula （ normalized cross correlation ） Expressed as a function of spatial frequency .

here $F_1(k)$、$F_2(k)$ Is any two groups of independent TEM Three dimensional Fourier transform of two structures of image reconstruction .$F_2(k{)}^{\ast }$ Is complex conjugate ,${\sum }_{K,△k}F(k)$ It means that k A small area nearby ($△k$) Li Qiuhe $F(k)$.
FSC(k) For each spatial frequency k The value is +1~-1 Between , near 1 It shows that the consistency of the two reconstructed structures is good , It shows that the obtained structure has high reliability . If FSC At high frequency, it does not change with spatial frequency k Monotonic decrease , Think FSC Function reliability is low .
The following example shows FSC And spatial resolution of mouse deoxyprotein . First , Use a set of... For single particle analysis TEM The images were randomly divided into two groups , Perform image processing and analysis for each group , Get two independent three-dimensional structures , Using the two three-dimensional structures obtained FSC.
In single particle analysis, the spatial resolution of the obtained structure is usually defined as FSC=0.143 The reciprocal of the spatial frequency of time .（0.143 It is a statistical discussion and reference based on the correlation of random noise x The resolution defined by X-ray crystallography is ） stay 6.5 nm-1 At the spatial frequency of , The resolution of ferritin is 0.153 nm, and FSC The value of is 0.143.


chart 1(a) Shows 840 Extracted from the low temperature transmission electron microscope image 120,295 Three dimensional density map of desferritin reconstructed by particles . chart 1(b) This is it 3D Calculated by density diagram FSC. Under low frequency FSC The value of is close to +1, And monotonously with the increase of frequency 0 attenuation . This confirms FSC High reliability of functions .