Moment-based metrics for molecules computable from cryogenic electron microscopy images.

Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution three-dimensional (3D) structure of biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3D reconstruction, known as Kam's method, relies on the moments of the two-dimensional (2D) images. Inspired by Kam's method, we introduce a rotationally invariant metric between two molecular structures, which does not require 3D alignment. Further, we introduce a metric between a stack of projection images and a molecular structure, which is invariant to rotations and reflections and does not require performing 3D reconstruction. Additionally, the latter metric does not assume a uniform distribution of viewing angles. We demonstrate the uses of the new metrics on synthetic and experimental datasets, highlighting their ability to measure structural similarity.

Fast principal component analysis for cryo-electron microscopy images.

Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-EM projection images affected by radial point spread functions that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For N images of size L × L, our method has time complexity O(NL3 + L4) and space complexity O(NL2 + L3). In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude.

A FAST SIMPLE ALGORITHM FOR COMPUTING THE POTENTIAL OF CHARGES ON A LINE.

We present a fast method for evaluating expressions of the form u j = ∑ i = 1 , i ≠ j n α i x i - x j , for j = 1 , … , n , where αi are real numbers, and xi are points in a compact interval of R . This expression can be viewed as representing the electrostatic potential generated by charges on a line in R 3 . While fast algorithms for computing the electrostatic potential of general distributions of charges in R 3 exist, in a number of situations in computational physics it is useful to have a simple and extremely fast method for evaluating the potential of charges on a line; we present such a method in this paper, and report numerical results for several examples.

CTD phosphatase: role in RNA polymerase II cycling and the regulation of transcript elongation.

The repetitive C-terminal domain (CTD) of the largest RNA polymerase II subunit plays a critical role in the regulation of gene expression. The activity of the CTD is dependent on its state of phosphorylation. A variety of CTD kinases act on RNA polymerase II at specific steps in the transcription cycle and preferentially phosphorylate distinct positions within the CTD consensus repeat. A single CTD phosphatase has been identified and characterized that in concert with CTD kinases establishes the level of CTD phosphorylation. The involvement of CTD phosphatase in controlling the progression of RNAP II around the transcription cycle, the mobilization of stored RNAP IIO, and the regulation of transcript elongation and RNA processing is discussed.

Dephosphorylation of RNA polymerase II by CTD-phosphatase FCP1 is inhibited by phospho-CTD associating proteins.

Reversible phosphorylation of the repetitive C-terminal domain (CTD) of the largest RNA polymerase (RNAP) II subunit plays a key role in the progression of RNAP through the transcription cycle. The level of CTD phosphorylation is determined by multiple CTD kinases and a CTD phosphatase, FCP1. The phosphorylated CTD binds to a variety of proteins including the cis/trans peptidyl-prolyl isomerase (PPIase) Pin1 and enzymes involved in processing of the primary transcript such as the capping enzyme Hce1 and CA150, a nuclear factor implicated in transcription elongation. Results presented here establish that the dephosphorylation of hyperphosphorylated RNAP II (RNAP IIO) by FCP1 is impaired in the presence of Pin1 or Hce1, whereas CA150 has no influence on FCP1 activity. The inhibition of dephosphorylation is observed with free RNAP IIO generated by different CTD kinases as well as with RNAP IIO engaged in an elongation complex. These findings support the idea that specific phospho-CTD associating proteins can differentially modulate the dephosphorylation of RNAP IIO by steric hindrance and may play an important role in the regulation of gene expression.