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PreprintCited by 6Protein Structure and DynamicsMachine Learning in BioinformaticsEnzyme Structure and Function

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Structure-Aware Annotation of Leucine-rich Repeat Domains

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Xu, Boyan, Cerbu, Alois, Lim, Daven, Tralie, Christopher J, Krasileva, Ksenia·2023·PLoS Computational Biology
DOI 10.1101/2023.10.27.562987PMC PMC11567593

Preprint — published as 10.1371/journal.pcbi.1012526

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Abstract

Protein domain annotation is typically done by predictive models such as HMMs trained on sequence motifs. However, sequence-based annotation methods are prone to error, particularly in calling domain boundaries and motifs within them. These methods are limited by a lack of structural information accessible to the model. With the advent of deep learning-based protein structure prediction, existing sequenced-based domain annotation methods can be improved by taking into account the geometry of protein structures. We develop dimensionality reduction methods to annotate repeat units of the Leucine Rich Repeat solenoid domain. The methods are able to correct mistakes made by existing machine learning-based annotation tools and enable the automated detection of hairpin loops and structural anomalies in the solenoid. The methods are applied to 127 predicted structures of LRR-containing intracellular innate immune proteins in the model plant Arabidopsis thaliana and validated against a benchmark dataset of 172 manually-annotated LRR domains. Author summary: In immune receptors across various organisms, repeating protein structures play a crucial role in recognizing and responding to pathogen threats. These structures resemble the coils of a slinky toy, allowing these receptors to adapt and change over time. One particularly vital but challenging structure to study is the Leucine Rich Repeat (LRR). Traditional methods that rely just on analyzing the sequence of these proteins can miss subtle changes due to rapid evolution. With the introduction of protein structure prediction tools like AlphaFold 2, annotation methods can study the coarser geometric properties of the structure. In this study, we visualize LRR proteins in three dimensions and use a mathematical approach to ‘flatten’ them into two dimensions, so that the coils form circles. We then used a mathematical concept called winding number to determine the number of repeats and where they are in a protein sequence. This process helps reveal their repeating patterns with enhanced clarity. When we applied this method to immune receptors from a model plant organism, we found that our approach could accurately identify coiling patterns. Furthermore, we detected errors made by previous methods and highlighted unique structural variations. Our research offers a fresh perspective on understanding immune receptors, potentially influencing studies on their evolution and function.

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Figures

Fig 1 Embedding of protein backbone curve into normal bundle followed by projection onto an orthonormal frame yields a 2D curve containing a flattened slinky shown in lower right. The cumulative winding number, computed using the classic formula from calculus, is computed from the projection. Sloped linear segments of the winding number curve indicate coiling. Protein shown is A. thaliana NLR with TAIR [1] ID AT3G44400.2.
Fig 1 Embedding of protein backbone curve into normal bundle followed by projection onto an orthonormal frame yields a 2D curve containing a flattened slinky shown in lower right. The cumulative winding number, computed using the classic formula from calculus, is computed from the projection. Sloped linear segments of the winding number curve indicate coiling. Protein shown is A. thaliana NLR with TAIR [1] ID AT3G44400.2.CC BY · PubMed Central
Fig 2 A discontinuous clipped ReLU function is regressed on the graph of the winding number function for A. thaliana NLR with TAIR [1] ID AT3G44400.2. The breakpoints of the regression yields the start and end positions of the LRR domain, highlighted in green. InterPro [19] domain annotations are shown below regression plot.
Fig 2 A discontinuous clipped ReLU function is regressed on the graph of the winding number function for A. thaliana NLR with TAIR [1] ID AT3G44400.2. The breakpoints of the regression yields the start and end positions of the LRR domain, highlighted in green. InterPro [19] domain annotations are shown below regression plot.CC BY · PubMed Central
Fig 3 We determine when to redo the regression using 4 breakpoints by examining the RMS of the LRR component of the loss. This term is above our threshold of 1 for 9/127 of the proteins in A. thaliana.
Fig 3 We determine when to redo the regression using 4 breakpoints by examining the RMS of the LRR component of the loss. This term is above our threshold of 1 for 9/127 of the proteins in A. thaliana.CC BY · PubMed Central
Fig 4 Four breakpoint piecewise linear regression enables detection of a non-coiling structure (highlighted in purple at right) which deviates from the usual coiling in the LRR domain. Below regression plot, a heat map shows the pLDDT (predicted local distance difference test), a per-residue confidence measure given by AlphaFold 2 which is elevated in the non-coiling region. Bottom of plot shows HMM-based InterPro domain annotations which fail to detect non-coiling region within LRR domain. TAIR ID is AT1G72840.2.
Fig 4 Four breakpoint piecewise linear regression enables detection of a non-coiling structure (highlighted in purple at right) which deviates from the usual coiling in the LRR domain. Below regression plot, a heat map shows the pLDDT (predicted local distance difference test), a per-residue confidence measure given by AlphaFold 2 which is elevated in the non-coiling region. Bottom of plot shows HMM-based InterPro domain annotations which fail to detect non-coiling region within LRR domain. TAIR ID is AT1G72840.2.CC BY · PubMed Central
Fig 5 Graph Laplacian eigenvectors of mutual nearest neighbor graph on LRR solenoid curve tangent vectors. LRRPredictor residues are shown as blue horizontal lines on eigenmatrix plot. The 0th and 1st eigenvectors have period matching the expected period of the solenoid as determined by LRRPredictor. Leading eigenvectors of graph Laplacian are periodic and are π/4-phase shifted, thereby yielding projections of LRR coil onto a winding around a circle in a 2D-plane. Phase estimation using the formula θ=tan⁻¹(y/x) of LRR coil at bottom taking values between −π and π.
Fig 5 Graph Laplacian eigenvectors of mutual nearest neighbor graph on LRR solenoid curve tangent vectors. LRRPredictor residues are shown as blue horizontal lines on eigenmatrix plot. The 0th and 1st eigenvectors have period matching the expected period of the solenoid as determined by LRRPredictor. Leading eigenvectors of graph Laplacian are periodic and are π/4-phase shifted, thereby yielding projections of LRR coil onto a winding around a circle in a 2D-plane. Phase estimation using the formula θ=tan⁻¹(y/x) of LRR coil at bottom taking values between −π and π.CC BY · PubMed Central
Fig 6 Discrepancies for LRRpredictor outputs on 127 A. thaliana (green and red) NLRs are higher than those for manually-annotated LRR repeat units used as the training set for the LRRpredictor model (blue, orange). Thus, the cumulative winding number computation faithfully recapitulates the periodicity of the LRR coil.
Fig 6 Discrepancies for LRRpredictor outputs on 127 A. thaliana (green and red) NLRs are higher than those for manually-annotated LRR repeat units used as the training set for the LRRpredictor model (blue, orange). Thus, the cumulative winding number computation faithfully recapitulates the periodicity of the LRR coil.CC BY · PubMed Central
Fig 7 LRRPredictor discrepancy computation reveals proteins with erroneously repeated predictions. NLRs with high-discrepancy LRRPredictor outputs tend to carry repetition errors or missing motif annotations. Orange vertical lines overlaid on winding number plot depict LRRPredictor residues, while purple horizontal lines depict the integer-spaced grid which best approximates the winding number graph evaluated at LRRPredictor residues. A repetition error can be seen in the grid representation as a doubled orange line around residue 685. At bottom, LRRPredictor residues are mapped onto graph Laplacian eigenvector phase estimation, revealing an pair of duplicates with adjacent phase.
Fig 7 LRRPredictor discrepancy computation reveals proteins with erroneously repeated predictions. NLRs with high-discrepancy LRRPredictor outputs tend to carry repetition errors or missing motif annotations. Orange vertical lines overlaid on winding number plot depict LRRPredictor residues, while purple horizontal lines depict the integer-spaced grid which best approximates the winding number graph evaluated at LRRPredictor residues. A repetition error can be seen in the grid representation as a doubled orange line around residue 685. At bottom, LRRPredictor residues are mapped onto graph Laplacian eigenvector phase estimation, revealing an pair of duplicates with adjacent phase.CC BY · PubMed Central
Fig 8 Sliding window L2 distance (SWL2D) from winding number to median secant line detects small hairpins/insertions in LRR coil domain. Structure at bottom is colored according to SWL2D where yellow values are higher.
Fig 8 Sliding window L2 distance (SWL2D) from winding number to median secant line detects small hairpins/insertions in LRR coil domain. Structure at bottom is colored according to SWL2D where yellow values are higher.CC BY · PubMed Central

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Metadata

Authors
Xu, B., Cerbu, A., Lim, D., Tralie, C. J., & Krasileva, K.
Affiliations
  • University of California, Berkeley (US)
  • Ursinus College (US)
Corresponding author
Krasileva, Ksenia
ORCID
Venue
PLoS Computational Biology
Publisher
openRxiv
Published
2023-11-01
Volume
20
Issue
11
Pages
e1012526-e1012526
ISSN
1553-734X (ISSN-L)
DOI
10.1101/2023.10.27.562987
PMC
PMC11567593
OpenAlex
W4404056798
Cited by
6
References
1
Citations by year
2026: 2 · 2025: 4
FWCI
0.82
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • PLoS Computational Biology (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • eScholarship (California Digital Library) (submittedVersion, cc-by)
  • PubMed Central (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
Funders
  • Foundation for the National Institutes of Health (DP2AT011967)
  • U.S. Department of Energy (DESC0020347)
  • Gordon and Betty Moore Foundation
  • Innovative Genomics Institute
  • National Institutes of Health (4dp2at011967-02)
  • National Center for Complementary and Integrative Health (DP2 AT011967)
  • Krell Institute (DE-SC0020347)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Machine Learning in Bioinformatics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Structural Biology › Enzyme Structure and Function
Keywords
leucine-rich repeat domain, protein domain annotation, dimensionality reduction, structural anomalies, Arabidopsis thaliana, protein structure prediction

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CoChat. (2026). Citation check: Structure-Aware Annotation of Leucine-rich Repeat Domains. https://app.cochat.ai/papers/10.1101/2023.10.27.562987
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Xu, B., Cerbu, A., Lim, D., Tralie, C. J., & Krasileva, K. (2023). Structure-Aware Annotation of Leucine-rich Repeat Domains. PLoS Computational Biology. https://doi.org/10.1101/2023.10.27.562987