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== Citation ==

Esteve-Yagüe, Carlos / Diepeveen, Willem / Öktem, Ozan / Schönlieb, Carola-Bibiane
Spectral decomposition of atomic structures in heterogeneous cryo-EM.
2023. Inverse Problems, Vol. 39, p. 034003

== Abstract ==

We consider the problem of recovering the three-dimensional atomic structure of a
exible macromolecule from a heterogeneous cryo-EM dataset. The dataset contains noisy tomographic
projections of the electrostatic potential of the macromolecule, taken from dierent
viewing directions, and in the heterogeneous case, each image corresponds to a dierent 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 exible structures from noisy tomographic projections.

== Keywords ==

== Links ==

https://iopscience.iop.org/article/10.1088/1361-6420/acb2ba/meta

== Related software ==

== Related methods ==

== Comments ==

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WikiSysop: Created page with "== Citation == Esteve-Yagüe, Carlos / Diepeveen, Willem / Öktem, Ozan / Schönlieb, Carola-Bibiane Spectral decomposition of atomic structures in heterogeneous cryo-EM. 2..."