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Template-free detection of macromolecular complexes in cryo electron tomograms.

Xu M, Beck M, Alber F - Bioinformatics (2011)

Bottom Line: Cryo electron tomography (CryoET) produces 3D density maps of biological specimen in its near native states.Applied to small cells, cryoET produces 3D snapshots of the cellular distributions of large complexes.However, so far only a small fraction of all protein complexes have been structurally resolved.

View Article: PubMed Central - PubMed

Affiliation: Program in Molecular and Computational Biology, University of Southern California, Los Angeles, CA 90089, USA.

ABSTRACT

Motivation: Cryo electron tomography (CryoET) produces 3D density maps of biological specimen in its near native states. Applied to small cells, cryoET produces 3D snapshots of the cellular distributions of large complexes. However, retrieving this information is non-trivial due to the low resolution and low signal-to-noise ratio in tomograms. Current pattern recognition methods identify complexes by matching known structures to the cryo electron tomogram. However, so far only a small fraction of all protein complexes have been structurally resolved. It is, therefore, of great importance to develop template-free methods for the discovery of previously unknown protein complexes in cryo electron tomograms.

Results: Here, we have developed an inference method for the template-free discovery of frequently occurring protein complexes in cryo electron tomograms. We provide a first proof-of-principle of the approach and assess its applicability using realistically simulated tomograms, allowing for the inclusion of noise and distortions due to missing wedge and electron optical factors. Our method is a step toward the template-free discovery of the shapes, abundance and spatial distributions of previously unknown macromolecular complexes in whole cell tomograms.

Contact: alber@usc.edu

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Related in: MedlinePlus

Neighborhood volumes defined as a series of concentric shells around voxel location xi for voxel i∈𝒯. Schematic view of a 2D grid with individual voxels shown as dark grey dots. Concentric shells are constructed that are centered at xi. The largest radius is defined as R. All radii are defined as rj=jR/M, with M as the maximal number of shells. A neighborhood volume Vj(xi)={k∈𝒯:rj−1</xk−xi/≤rj} is defined as all voxels that fall into a concentric shell defined by two radii, rj−1 and rj with rj−1<rj. As an example, the neighborhood shell V10(xi) is shown in light grey, defined as the set of voxels located between radii r9 and r10.
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Figure 2: Neighborhood volumes defined as a series of concentric shells around voxel location xi for voxel i∈𝒯. Schematic view of a 2D grid with individual voxels shown as dark grey dots. Concentric shells are constructed that are centered at xi. The largest radius is defined as R. All radii are defined as rj=jR/M, with M as the maximal number of shells. A neighborhood volume Vj(xi)={k∈𝒯:rj−1</xk−xi/≤rj} is defined as all voxels that fall into a concentric shell defined by two radii, rj−1 and rj with rj−1<rj. As an example, the neighborhood shell V10(xi) is shown in light grey, defined as the set of voxels located between radii r9 and r10.

Mentions: Rotation-invariant feature vectors p(xi) describe the intensity distribution of the tomogram in the neighborhood of a voxel located at xi. To construct a feature vector at the voxel location xi, we divide the neighborhood of the voxel xi into M concentric shells (Fig. 2)(4)where Vj(xi) is defined as the set of voxels that fall into the concentric shell centered at xi and is defined by the two radii rj−1 and rj, where with rj=jR/M and R is the largest chosen radius. If a concentric shell Vj(xi) is thin (i.e. rj+1−rj≈ voxel length), then the voxel intensities f(xk) with k∈Vj(xi) can be approximated by a spherical function g that is defined on the surface of a sphere in spherical coordinates.(5)where , and θ, ϕ are the colatitude and longitude angles, respectively. g can then be approximated by a sum of its spherical harmonics (Hobson, 1931):(6)where L is a given bandwidth, and alm is a coefficient associated with the complex spherical harmonics function Ylm, which is independent to g.Fig. 2.


Template-free detection of macromolecular complexes in cryo electron tomograms.

Xu M, Beck M, Alber F - Bioinformatics (2011)

Neighborhood volumes defined as a series of concentric shells around voxel location xi for voxel i∈𝒯. Schematic view of a 2D grid with individual voxels shown as dark grey dots. Concentric shells are constructed that are centered at xi. The largest radius is defined as R. All radii are defined as rj=jR/M, with M as the maximal number of shells. A neighborhood volume Vj(xi)={k∈𝒯:rj−1</xk−xi/≤rj} is defined as all voxels that fall into a concentric shell defined by two radii, rj−1 and rj with rj−1<rj. As an example, the neighborhood shell V10(xi) is shown in light grey, defined as the set of voxels located between radii r9 and r10.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3117359&req=5

Figure 2: Neighborhood volumes defined as a series of concentric shells around voxel location xi for voxel i∈𝒯. Schematic view of a 2D grid with individual voxels shown as dark grey dots. Concentric shells are constructed that are centered at xi. The largest radius is defined as R. All radii are defined as rj=jR/M, with M as the maximal number of shells. A neighborhood volume Vj(xi)={k∈𝒯:rj−1</xk−xi/≤rj} is defined as all voxels that fall into a concentric shell defined by two radii, rj−1 and rj with rj−1<rj. As an example, the neighborhood shell V10(xi) is shown in light grey, defined as the set of voxels located between radii r9 and r10.
Mentions: Rotation-invariant feature vectors p(xi) describe the intensity distribution of the tomogram in the neighborhood of a voxel located at xi. To construct a feature vector at the voxel location xi, we divide the neighborhood of the voxel xi into M concentric shells (Fig. 2)(4)where Vj(xi) is defined as the set of voxels that fall into the concentric shell centered at xi and is defined by the two radii rj−1 and rj, where with rj=jR/M and R is the largest chosen radius. If a concentric shell Vj(xi) is thin (i.e. rj+1−rj≈ voxel length), then the voxel intensities f(xk) with k∈Vj(xi) can be approximated by a spherical function g that is defined on the surface of a sphere in spherical coordinates.(5)where , and θ, ϕ are the colatitude and longitude angles, respectively. g can then be approximated by a sum of its spherical harmonics (Hobson, 1931):(6)where L is a given bandwidth, and alm is a coefficient associated with the complex spherical harmonics function Ylm, which is independent to g.Fig. 2.

Bottom Line: Cryo electron tomography (CryoET) produces 3D density maps of biological specimen in its near native states.Applied to small cells, cryoET produces 3D snapshots of the cellular distributions of large complexes.However, so far only a small fraction of all protein complexes have been structurally resolved.

View Article: PubMed Central - PubMed

Affiliation: Program in Molecular and Computational Biology, University of Southern California, Los Angeles, CA 90089, USA.

ABSTRACT

Motivation: Cryo electron tomography (CryoET) produces 3D density maps of biological specimen in its near native states. Applied to small cells, cryoET produces 3D snapshots of the cellular distributions of large complexes. However, retrieving this information is non-trivial due to the low resolution and low signal-to-noise ratio in tomograms. Current pattern recognition methods identify complexes by matching known structures to the cryo electron tomogram. However, so far only a small fraction of all protein complexes have been structurally resolved. It is, therefore, of great importance to develop template-free methods for the discovery of previously unknown protein complexes in cryo electron tomograms.

Results: Here, we have developed an inference method for the template-free discovery of frequently occurring protein complexes in cryo electron tomograms. We provide a first proof-of-principle of the approach and assess its applicability using realistically simulated tomograms, allowing for the inclusion of noise and distortions due to missing wedge and electron optical factors. Our method is a step toward the template-free discovery of the shapes, abundance and spatial distributions of previously unknown macromolecular complexes in whole cell tomograms.

Contact: alber@usc.edu

Show MeSH
Related in: MedlinePlus