Fourier Shell Correlation, FSC
Fourier Shell Correlation
Fourier Shell Correlation (FSC) is a measure of reliability of the three-dimensional (3D) structures of biological macromolecules obtained by “single particle analysis”. FSC is expressed as a function of spatial frequency by the following equation (normalized cross correlation).
Here, F1(k) and F2(k)are 3D Fourier transforms of the two structures reconstructed from arbitrary two independent sets of TEM images obtained. F2(k)* is a complex conjugate of F2(k), and Σk,ΔkF(k) means summing up F(k) over a small range Δk around k.
FSC (k) takes a value between +1 and –1 for every spatial frequency k. The value of FSC (k) close to +1 means that the two reconstructed structures agree well, indicating a high degree of reliability of the obtained structure. If FSC does not decrease monotonically with spatial frequency k at high frequencies, the reliability of the FSC function is considered to be low.
The following example shows the FSC and spatial resolution for mouse apoferritin.
First, a data set of TEM images acquired for single particle analysis is randomly divided into two groups, and two independent 3D structures are obtained by image-processing analysis for each group. FSC is calculated using the two obtained 3D structures.
Fig. 1(a) shows a 3D density map of apoferritin reconstructed from 120,295 particles extracted from 840 cryo-TEM images. Fig. 1(b) is the FSC calculated for this 3D density map. The values of FSC at low frequencies are close to +1 and damped with increasing frequency monotonically towards 0. This behavior confirms high reliability of the FSC function.
In single particle analysis, it is common to define the spatial resolution of the obtained structure to be the reciprocal of the spatial frequency at which FSC = 0.143. (The value “0.143” is a value adopted based on statistical discussion about the correlation of random noise and on referring the resolution defined for X-ray crystallography.) The resolution for apoferritin was determined to be 0.153 nm from a spatial frequency of 6.5 nm-1 at which FSC takes a value of 0.143.
(Proofread by Specially Appointed Professor Keichi Namba, Osaka University)
Here, F1(k) and F2(k)are 3D Fourier transforms of the two structures reconstructed from arbitrary two independent sets of TEM images obtained. F2(k)* is a complex conjugate of F2(k), and Σk,ΔkF(k) means summing up F(k) over a small range Δk around k.
FSC (k) takes a value between +1 and –1 for every spatial frequency k. The value of FSC (k) close to +1 means that the two reconstructed structures agree well, indicating a high degree of reliability of the obtained structure. If FSC does not decrease monotonically with spatial frequency k at high frequencies, the reliability of the FSC function is considered to be low.
The following example shows the FSC and spatial resolution for mouse apoferritin.
First, a data set of TEM images acquired for single particle analysis is randomly divided into two groups, and two independent 3D structures are obtained by image-processing analysis for each group. FSC is calculated using the two obtained 3D structures.
Fig. 1(a) shows a 3D density map of apoferritin reconstructed from 120,295 particles extracted from 840 cryo-TEM images. Fig. 1(b) is the FSC calculated for this 3D density map. The values of FSC at low frequencies are close to +1 and damped with increasing frequency monotonically towards 0. This behavior confirms high reliability of the FSC function.
In single particle analysis, it is common to define the spatial resolution of the obtained structure to be the reciprocal of the spatial frequency at which FSC = 0.143. (The value “0.143” is a value adopted based on statistical discussion about the correlation of random noise and on referring the resolution defined for X-ray crystallography.) The resolution for apoferritin was determined to be 0.153 nm from a spatial frequency of 6.5 nm-1 at which FSC takes a value of 0.143.
(Proofread by Specially Appointed Professor Keichi Namba, Osaka University)
Fig. 1
3D density map of mouse apoferritin obtained by single particle analysis and its FSC. (a) 3D density map. (b) An FSC function calculated from the two 3D density maps. The resolution was determined to be 0.153 nm from a spatial frequency of 6.5 nm-1 at which FSC = 0.143.
Term(s) with "Fourier Shell Correlation" in the description
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