535 research outputs found
3D ab initio modeling in cryo-EM by autocorrelation analysis
Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-EM) is
the task of estimating the 3D structure of a molecule from a set of noisy 2D
projections, taken from unknown viewing directions. Many algorithms for SPR
start from an initial reference molecule, and alternate between refining the
estimated viewing angles given the molecule, and refining the molecule given
the viewing angles. This scheme is called iterative refinement. Reliance on an
initial, user-chosen reference introduces model bias, and poor initialization
can lead to slow convergence. Furthermore, since no ground truth is available
for an unsolved molecule, it is difficult to validate the obtained results.
This creates the need for high quality ab initio models that can be quickly
obtained from experimental data with minimal priors, and which can also be used
for validation. We propose a procedure to obtain such an ab initio model
directly from raw data using Kam's autocorrelation method. Kam's method has
been known since 1980, but it leads to an underdetermined system, with missing
orthogonal matrices. Until now, this system has been solved only for special
cases, such as highly symmetric molecules or molecules for which a homologous
structure was already available. In this paper, we show that knowledge of just
two clean projections is sufficient to guarantee a unique solution to the
system. This system is solved by an optimization-based heuristic. For the first
time, we are then able to obtain a low-resolution ab initio model of an
asymmetric molecule directly from raw data, without 2D class averaging and
without tilting. Numerical results are presented on both synthetic and
experimental data
Unsupervised cryo-EM data clustering through adaptively constrained K-means algorithm
In single-particle cryo-electron microscopy (cryo-EM), K-means clustering
algorithm is widely used in unsupervised 2D classification of projection images
of biological macromolecules. 3D ab initio reconstruction requires accurate
unsupervised classification in order to separate molecular projections of
distinct orientations. Due to background noise in single-particle images and
uncertainty of molecular orientations, traditional K-means clustering algorithm
may classify images into wrong classes and produce classes with a large
variation in membership. Overcoming these limitations requires further
development on clustering algorithms for cryo-EM data analysis. We propose a
novel unsupervised data clustering method building upon the traditional K-means
algorithm. By introducing an adaptive constraint term in the objective
function, our algorithm not only avoids a large variation in class sizes but
also produces more accurate data clustering. Applications of this approach to
both simulated and experimental cryo-EM data demonstrate that our algorithm is
a significantly improved alterative to the traditional K-means algorithm in
single-particle cryo-EM analysis.Comment: 35 pages, 14 figure
Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM
We introduce a new rotationally invariant viewing angle classification method
for identifying, among a large number of Cryo-EM projection images, similar
views without prior knowledge of the molecule. Our rotationally invariant
features are based on the bispectrum. Each image is denoised and compressed
using steerable principal component analysis (PCA) such that rotating an image
is equivalent to phase shifting the expansion coefficients. Thus we are able to
extend the theory of bispectrum of 1D periodic signals to 2D images. The
randomized PCA algorithm is then used to efficiently reduce the dimensionality
of the bispectrum coefficients, enabling fast computation of the similarity
between any pair of images. The nearest neighbors provide an initial
classification of similar viewing angles. In this way, rotational alignment is
only performed for images with their nearest neighbors. The initial nearest
neighbor classification and alignment are further improved by a new
classification method called vector diffusion maps. Our pipeline for viewing
angle classification and alignment is experimentally shown to be faster and
more accurate than reference-free alignment with rotationally invariant K-means
clustering, MSA/MRA 2D classification, and their modern approximations
Toward single particle reconstruction without particle picking: Breaking the detection limit
Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray
crystallography and NMR spectroscopy as a high-resolution structural method for
biological macromolecules. In a cryo-EM experiment, the microscope produces
images called micrographs. Projections of the molecule of interest are embedded
in the micrographs at unknown locations, and under unknown viewing directions.
Standard imaging techniques first locate these projections (detection) and then
reconstruct the 3-D structure from them. Unfortunately, high noise levels
hinder detection. When reliable detection is rendered impossible, the standard
techniques fail. This is a problem especially for small molecules, which can be
particularly hard to detect. In this paper, we propose a radically different
approach: we contend that the structure could, in principle, be reconstructed
directly from the micrographs, without intermediate detection. As a result,
even small molecules should be within reach for cryo-EM. To support this claim,
we setup a simplified mathematical model and demonstrate how our
autocorrelation analysis technique allows to go directly from the micrographs
to the sought signals. This involves only one pass over the micrographs, which
is desirable for large experiments. We show numerical results and discuss
challenges that lay ahead to turn this proof-of-concept into a competitive
alternative to state-of-the-art algorithms
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