Solving the Secondary Structure Matching Problem in Cryo-EM De Novo Modeling Using a Constrained <formula formulatype="inline"><tex Notation="TeX">$K$</tex></formula>-Shortest Path Graph Algorithm

Abstract

Electron cryomicroscopy is becoming a major experimental technique in solving the structures of large molecular assemblies. More and more three-dimensional images have been obtained at the medium resolutions between 5 and 10 Å. At this resolution range, major α-helices can be detected as cylindrical sticks and β-sheets can be detected as plain-like regions. A critical question in de novo modeling from cryo-EM images is to determine the match between the detected secondary structures from the image and those on the protein sequence. We formulate this matching problem into a constrained graph problem and present an O(Δ(2)N(2)2(N)) algorithm to this NP-Hard problem. The algorithm incorporates the dynamic programming approach into a constrained K-shortest path algorithm. Our method, DP-TOSS, has been tested using α-proteins with maximum 33 helices and α-β proteins up to five helices and 12 β-strands. The correct match was ranked within the top 35 for 19 of the 20 α-proteins and all nine α-β proteins tested. The results demonstrate that DP-TOSS improves accuracy, time and memory space in deriving the topologies of the secondary structure elements for proteins with a large number of secondary structures and a complex skeleton.

Tracing Beta Strands Using StrandTwister from Cryo-EM Density Maps at Medium Resolutions

“…Deriving atomic structures from density maps at medium resolutions will inevitably involve sophisticated modeling of uncertainties. The methodology in de novo modeling from the medium resolution density maps has been improved recently to work with a large number of helices (Al Nasr et al, 2014), to work with complicated skeletons (Al Nasr et al, 2013), and to build the atomic chains in modeling (Baker et al, 2012b;Lindert et al, 2012). However, the work has been tested mostly using the true position of b strands for density maps at medium resolutions.…”

“…The current topology determination method will be extended to both a traces and b traces. We have shown that additional constraints can be added to represent popular b strand pairing during topology determination (Al Nasr et al, 2014). We illustrate an effective method to build a Ca backbone using b traces (Supplemental Experimental Procedures).…”

A Guided Tour of Selected Image Processing and Analysis Methods for Fluorescence and Electron Microscopy

“…Analysis of Volumes in Structural Biology: Finally, we may try to recognize secondary structure elements [87]- [89], we may identify components by constraining the identification with other experimental sources like mass spectroscopy [90] and proteomics and chemical cross-linking [91], we may add a priori knowledge about atomic models that should fit into the 3D reconstruction [92]- [96], or analyze its possible deformation paths [97], [98].…”

Deriving Protein Backbone Using Traces Extracted from Density Maps at Medium Resolutions

“…The de novo modeling combines information from the density map and the amino acid sequence of the protein to derive the topology of secondary structure traces [21,23,[37][38][39]. A topology maps the secondary structure traces from the density map to the amino acid sequence, and therefore determines how the protein chain thread through the traces.…”

“…A topology maps the secondary structure traces from the density map to the amino acid sequence, and therefore determines how the protein chain thread through the traces. We previously showed that using a dynamic programming method combined with the K-shortest path algorithm, it takes Δ 2 time to rank the top K topologies using DP-TOSS [23,38]. Here N is the number of secondary structure traces detected in the density map and M is the number of secondary structure sequence segments, and Δ 1.…”