Probing Structural Perturbation of Biomolecules by Extracting Cryo-EM Data Heterogeneity

Single-particle cryogenic electron microscopy (cryo-EM) has become an indispensable tool to probe high-resolution structural detail of biomolecules. It enables direct visualization of the biomolecules and opens a possibility for averaging molecular images to reconstruct a three-dimensional Coulomb potential density map. Newly developed algorithms for data analysis allow for the extraction of structural heterogeneity from a massive and low signal-to-noise-ratio (SNR) cryo-EM dataset, expanding our understanding of multiple conformational states, or further implications in dynamics, of the target biomolecule. This review provides an overview that briefly describes the workflow of single-particle cryo-EM, including imaging and data processing, and new methods developed for analyzing the data heterogeneity to understand the structural variability of biomolecules.

AdaReg: data adaptive robust estimation in linear regression with application in GTEx gene expressions

The Genotype-Tissue Expression (GTEx) project provides a valuable resource of large-scale gene expressions across multiple tissue types. Under various technical noise and unknown or unmeasured factors, how to robustly estimate the major tissue effect becomes challenging. Moreover, different genes exhibit heterogeneous expressions across different tissue types. Therefore, we need a robust method which adapts to the heterogeneities of gene expressions to improve the estimation for the tissue effect. We followed the approach of the robust estimation based on γ-density-power-weight in the works of Fujisawa, H. and Eguchi, S. (2008). Robust parameter estimation with a small bias against heavy contamination. J. Multivariate Anal. 99: 2053-2081 and Windham, M.P. (1995). Robustifying model fitting. J. Roy. Stat. Soc. B: 599-609, where γ is the exponent of density weight which controls the balance between bias and variance. As far as we know, our work is the first to propose a procedure to tune the parameter γ to balance the bias-variance trade-off under the mixture models. We constructed a robust likelihood criterion based on weighted densities in the mixture model of Gaussian population distribution mixed with unknown outlier distribution, and developed a data-adaptive γ-selection procedure embedded into the robust estimation. We provided a heuristic analysis on the selection criterion and found that our practical selection trend under various γ's in average performance has similar capability to capture minimizer γ as the inestimable mean squared error (MSE) trend from our simulation studies under a series of settings. Our data-adaptive robustifying procedure in the linear regression problem (AdaReg) showed a significant advantage in both simulation studies and real data application in estimating tissue effect of heart samples from the GTEx project, compared to the fixed γ procedure and other robust methods. At the end, the paper discussed some limitations on this method and future work.

Pre-pro is a fast pre-processor for single-particle cryo-EM by enhancing 2D classification

2D classification plays a pivotal role in analyzing single particle cryo-electron microscopy images. Here, we introduce a simple and loss-less pre-processor that incorporates a fast dimension-reduction (2SDR) de-noiser to enhance 2D classification. By implementing this 2SDR pre-processor prior to a representative classification algorithm like RELION and ISAC, we compare the performances with and without the pre-processor. Tests on multiple cryo-EM experimental datasets show the pre-processor can make classification faster, improve yield of good particles and increase the number of class-average images to generate better initial models. Testing on the nanodisc-embedded TRPV1 dataset with high heterogeneity using a 3D reconstruction workflow with an initial model from class-average images highlights the pre-processor improves the final resolution to 2.82 Å, close to 0.9 Nyquist. Those findings and analyses suggest the 2SDR pre-processor, of minimal cost, is widely applicable for boosting 2D classification, while its generalization to accommodate neural network de-noisers is envisioned.

Robust Clustering Method in the Presence of Scattered Observations

Contamination of scattered observations, which are either featureless or unlike the other observations, frequently degrades the performance of standard methods such as K-means and model-based clustering. In this letter, we propose a robust clustering method in the presence of scattered observations called Gamma-clust. Gamma-clust is based on a robust estimation for cluster centers using gamma-divergence. It provides a proper solution for clustering in which the distributions for clustered data are nonnormal, such as t-distributions with different variance-covariance matrices and degrees of freedom. As demonstrated in a simulation study and data analysis, Gamma-clust is more flexible and provides superior results compared to the robustified K-means and model-based clustering.