arXiv subjects

Aaditya V. Rangan

Publications and source records attributed to Aaditya V. Rangan.

4 recordsLinked to original sources

arXiv2024

Estimating the tails of the spectrum of the Hessian of the log-likelihood for \textit{ab-initio} single-particle reconstruction in electron cryomicroscopy

Electron cryomicroscopy (cryo-EM) is a technique in structural biology used to reconstruct accurate volumetric maps of molecules. One step of the cryo-EM pipeline involves solving an inverse-problem. This inverse-problem, referred to as \textit{ab-initio} single-particle reconstruction, takes as input a collection of 2d-images -- each a projection of a molecule from an unknown viewing-angle -- and attempts to reconstruct the 3d-volume representing the underlying molecular density. Most methods for solving this inverse-problem search for a solution which optimizes a posterior likelihood of generating the observed image-data, given the reconstructed volume. Within this framework, it is natural to study the Hessian of the log-likelihood: the eigenvectors and eigenvalues of the Hessian determine how the likelihood changes with respect to perturbations in the solution, and can give insight into the sensitivity of the solution to aspects of the input. In this paper we describe a simple strategy for estimating the smallest eigenvalues and eigenvectors (i.e., the `softest modes') of the Hessian of the log-likelihood for the \textit{ab-initio} single-particle reconstruction problem. This strategy involves rewriting the log-likelihood as a 3d-integral. This interpretation holds in the low-noise limit, as well as in many practical scenarios which allow for noise-marginalization. Once we have estimated the softest modes, we can use them to perform many kinds of sensitivity analysis. For example, we can determine which parts of the reconstructed volume are trustworthy, and which are unreliable, and how this unreliability might depend on the data-set and the imaging parameters. We believe that this kind of analysis can be used alongside more traditional strategies for sensitivity analysis, as well as in other applications, such as free-energy estimation.

q-bio.QM↗

arXiv2024

Heterogeneity analysis provides evidence for a genetically homogeneous subtype of bipolar-disorder

Bipolar Disorder (BD) is a complex disease. It is heterogeneous, both at the phenotypic and genetic level, although the extent and impact of this heterogeneity is not fully understood. In this paper, we leverage recent advances in heterogeneity analysis to look for genetically-driven subgroups (i.e., biclusters) within the broad phenotype of Bipolar Disorder. We first apply this covariate-corrected biclustering algorithm to a cohort of 2524 BD cases and 4106 controls from the Bipolar Disease Research Network (BDRN) within the Psychiatric Genomics Consortium (PGC). We find evidence of genetic heterogeneity delineating a statistically significant bicluster comprising a subset of BD cases which exhibits a disease-specific pattern of differential-expression across a subset of SNPs. This disease-specific genetic pattern (i.e., 'genetic subgroup') replicates across the remaining data-sets collected by the PGC containing 5781/8289, 3581/7591, and 6825/9752 cases/controls, respectively. This genetic subgroup (discovered without using any BD subtype information) was more prevalent in Bipolar type-I than in Bipolar type-II. Our methodology has successfully identified a replicable homogeneous genetic subgroup of bipolar disorder. This subgroup may represent a collection of correlated genetic risk-factors for BDI. By investigating the subgroup's bicluster-informed polygenic-risk-scoring (PRS), we find that the disease-specific pattern highlighted by the bicluster can be leveraged to eliminate noise from our GWAS analyses and improve risk prediction. This improvement is particularly notable when using only a relatively small subset of the available SNPs, implying improved SNP replication. Though our primary focus is only the analysis of disease-related signal, we also identify replicable control-related heterogeneity.

q-bio.GN↗

arXiv2023

Robust ab initio solution of the cryo-EM reconstruction problem at low resolution with small data sets

Single particle cryo-electron microscopy has become a critical tool in structural biology over the last decade, able to achieve atomic scale resolution in three dimensional models from hundreds of thousands of (noisy) two-dimensional projection views of particles frozen at unknown orientations. This is accomplished by using a suite of software tools to (i) identify particles in large micrographs, (ii) obtain low-resolution reconstructions, (iii) refine those low-resolution structures, and (iv) finally match the obtained electron scattering density to the constituent atoms that make up the macromolecule or macromolecular complex of interest. Here, we focus on the second stage of the reconstruction pipeline: obtaining a low resolution model from picked particle images. Our goal is to create an algorithm that is capable of ab initio reconstruction from small data sets (on the order of a few thousand selected particles). More precisely, we propose an algorithm that is robust, automatic, and fast enough that it can potentially be used to assist in the assessment of particle quality as the data is being generated during the microscopy experiment.

math.NA↗

arXiv2022

Radial-recombination for rigid rotational alignment of images and volumes

A common task in single particle electron cryomicroscopy (cryo-EM) is the rigid alignment of images and/or volumes. In the context of images, a rigid alignment involves estimating the inner-product between one image of $N\times N$ pixels and another image that has been translated by some displacement and rotated by some angle $γ$. In many situations the number of rotations $γ$ considered is large (e.g., $\mathcal{O}(N)$), while the number of translations considered is much smaller (e.g., $\mathcal{O}(1)$). In these scenarios a naive algorithm requires $\mathcal{O}(N^{3})$ operations to calculate the array of inner-products for each image-pair. This computation can be accelerated by using a fourier-bessel basis and the fast-fourier-transform (FFT), requiring only $\mathcal{O}(N^2)$ operations per image-pair. We propose a simple data-driven compression algorithm to further accelerate this computation, which we refer to as the `radial-SVD'. Our approach involves linearly-recombining the different rings of the original images (expressed in polar-coordinates), taking advantage of the singular-value-decomposition (SVD) to choose a low-rank combination which both compresses the images and optimizes a certain measure of angular discriminability. When aligning multiple images to multiple targets, the complexity of our approach is $\mathcal{O}(N(\log(N)+H))$ per image-pair, where $H$ is the rank of the SVD used in the compression above. The advantage gained by this approach depends on the ratio between $H$ and $N$; the smaller $H$ is the better. In many applications $H$ can be quite a bit smaller than $N$ while still maintaining accuracy. We present numerical results in a cryo-EM application demonstrating that the radial- and degree-SVD can help save a factor of $5$--$10$ for both image- and volume-alignment.

math.NA↗