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Spectral decomposition of atomic structures in heterogeneous cryo-EM
Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England..
Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1118-6483
Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England..
2023 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 39, no 3, p. 034003-, article id 034003Article in journal (Refereed) Published
Abstract [en]

We consider the problem of recovering the three-dimensional atomic structure of a flexible macromolecule from a heterogeneous cryogenic electron microscopy (cryo-EM) dataset. The dataset contains noisy tomographic projections of the electrostatic potential of the macromolecule, taken from different viewing directions, and in the heterogeneous case, each cryo-EM image corresponds to a different conformation of the macromolecule. Under the assumption that the macromolecule can be modelled as a chain, or discrete curve (as it is for instance the case for a protein backbone with a single chain of amino-acids), we introduce a method to estimate the deformation of the atomic model with respect to a given conformation, which is assumed to be known a priori. Our method consists on estimating the torsion and bond angles of the atomic model in each conformation as a linear combination of the eigenfunctions of the Laplace operator in the manifold of conformations. These eigenfunctions can be approximated by means of a well-known technique in manifold learning, based on the construction of a graph Laplacian using the cryo-EM dataset. Finally, we test our approach with synthetic datasets, for which we recover the atomic model of two-dimensional and three-dimensional flexible structures from simulated cryo-EM images.

Place, publisher, year, edition, pages
IOP Publishing , 2023. Vol. 39, no 3, p. 034003-, article id 034003
Keywords [en]
heterogeneous cryo-EM, atomic structure decomposition, graph Laplacian, tomographic reconstruction
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-324760DOI: 10.1088/1361-6420/acb2baISI: 000921748100001Scopus ID: 2-s2.0-85147142754OAI: oai:DiVA.org:kth-324760DiVA, id: diva2:1743534
Note

QC 20230315

Available from: 2023-03-15 Created: 2023-03-15 Last updated: 2023-03-15Bibliographically approved

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Öktem, Ozan

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