Cryo-EM map interpretation and protein model-building using iterative map segmentation.

A procedure for building protein chains into maps produced by single-particle electron cryo-microscopy (cryo-EM) is described. The procedure is similar to the way an experienced structural biologist might analyze a map, focusing first on secondary structure elements such as helices and sheets, then varying the contour level to identify connections between these elements. Since the high density in a map typically follows the main-chain of the protein, the main-chain connection between secondary structure elements can often be identified as the unbranched path between them with the highest minimum value along the path. This chain-tracing procedure is then combined with finding side-chain positions based on the presence of density extending away from the main path of the chain, allowing generation of a Cα model. The Cα model is converted to an all-atom model and is refined against the map. We show that this procedure is as effective as other existing methods for interpretation of cryo-EM maps and that it is considerably faster and produces models with fewer chain breaks than our previous methods that were based on approaches developed for crystallographic maps

The Universal Askey-Wilson Algebra

In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension $\Delta$ of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call $\Delta$ the {\it universal Askey-Wilson algebra}. We give a faithful action of the modular group ${\rm {PSL}}_2({\mathbb Z})$ on $\Delta$ as a group of automorphisms. We give a linear basis for $\Delta$. We describe the center of $\Delta$ and the 2-sided ideal $\Delta[\Delta,\Delta]\Delta$. We discuss how $\Delta$ is related to the $q$-Onsager algebra.Comment: 24 page