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PubMed2002

Protein structure comparison using bipartite graph matching and its application to protein structure classification.

A measure of protein structure similarity is calculated from the matching of pairs of secondary structure elements between two proteins. The interaction of each pair was estimated from their axial line segments and combined with other geometric features to produce an optimal discrimination between intrafamily and interfamily relationships. The matching used a fast bipartite graph-matching algorithm that avoids the computational complexity of searching for the full subgraph isomorphism between the two sets of interactions. The main algorithm used was the "stable marriage" algorithm, which works on the ranked "preferences" of one interaction for another. The method takes 1/10 of a second for a typical comparison making it suitable as a fast pre-filter for slower, more exhaustive approaches. An application to protein structure classification is described.

Algorithms↗
PubMed1980

Early detection of abnormal labor using the Friedman labor graph.

Early recognition and appropriate management of abnormal labor can reduce perinatal mortality and morbidity and lower the cesarean section rate. A simple labor graph devised over 25 years ago and later modified makes labor abnormalities easy to detect; the two main divisions of labor, the latent and active phases, are easily recognized. A prolonged latent phase has no serious effects on mother or fetus, but protraction and arrest disorders of the active phase--eg, protracted cervical dilatation, arrest or failure of descent of the presenting part--may have a deleterious effect. Common causes of a prolonged latent phase include false labor and inappropriate use of analgesia and anesthesia. Fetopelvic disproportion and fetal malposition are common causes of disorders of the active phase.

Adolescent↗
PubMed1993

Structure-activity maps for visualizing the graph variables arising in drug design.

Structure-activity problems are characterized by the topological and topographical character of the structural information determining the activity. Traditional statistical methodology requires that this predictive information be mapped to a vector space. To circumvent this vexing conversion of structural information to vector form, the edge-deletion metric is defined on the space of chemical graphs that defines the topology of the molecules. This paper proposes structure-activity maps and transformation-effect maps for directly visualizing the structure-activity relationships. The maps are illustrated using the hypotensive activities of clonidine analogs and the sweet taste of Perillartine analogs.

Clonidine↗
PubMed2002

Effect heterogeneity by a matching covariate in matched case-control studies: a method for graphs-based representation.

The authors describe a method for assessing and characterizing effect heterogeneity related to a matching covariate in case-control studies, using an example from veterinary medicine. Data are from a case-control study conducted in Texas during 1997-1998 of 498 pairs of horses with colic and their controls. Horses were matched by veterinarian and by month of examination. The number of matched pairs of cases and controls varied by veterinarian. The authors demonstrate that there is effect heterogeneity related to this characteristic (i.e., cluster size of veterinarians) for the association of colic with certain covariates, using a moving average approach to conditional logistic regression and graphs-based methods. The method described in this report can be applied to examining effect heterogeneity (or effect modification) by any ordered categorical or continuous covariates for which cases have been matched with controls. The method described enables one to understand the pattern of variation across ordered categorical or continuous matching covariates and allows for any shape for this pattern. This method applies to effect modification when causality might be reasonably assumed.

Animals↗
PubMed2025

Learning directed acyclic graphs for ligands and receptors based on spatially resolved transcriptomic data of ovarian cancer.

To unravel the mechanism of immune activation and suppression within tumors, a critical step is to identify transcriptional signals governing cell-cell communication between tumor and immune/stromal cells in the tumor microenvironment. Central to this communication are interactions between secreted ligands and cell-surface receptors, creating a highly connected signaling network among cells. Recent advancements in in situ-omics profiling, particularly spatial transcriptomic (ST) technology, provide unique opportunities to directly characterize ligand-receptor signaling networks that power cell-cell communication. In this paper, we propose a novel statistical method, LRnetST, to characterize the ligand-receptor interaction networks between adjacent tumor and immune/stroma cells based on ST data. LRnetST utilizes a directed acyclic graph model with a novel approach to handle the zero-inflated distributions of ST data. It also leverages existing ligand-receptor regulation databases as prior information, and employs a bootstrap aggregation strategy to achieve robust network estimation. Application of LRnetST to ST data of high-grade serous ovarian tumor samples revealed both common and distinct ligand-receptor regulations across different tumors. Some of these interactions were validated through both a MERFISH dataset and a CosMx SMI dataset of independent ovarian tumor samples. These results cast light on biological processes relating to the communication between tumor and immune/stromal cells in ovarian tumors. An open-source R package of LRnetST is available on GitHub at https://github.com/jie108/LRnetST.

Humans↗
PubMed2000

Protein domain decomposition using a graph-theoretic approach.

MOTIVATION: Automatic decomposition of a multi-domain protein into individual domains represents a highly interesting and unsolved problem. As the number of protein structures in PDB is growing at an exponential rate, there is clearly a need for more reliable and efficient methods for protein domain decomposition simply to keep the domain databases up-to-date. RESULTS: We present a new algorithm for solving the domain decomposition problem, using a graph-theoretic approach. We have formulated the problem as a network flow problem, in which each residue of a protein is represented as a node of the network and each residue--residue contact is represented as an edge with a particular capacity, depending on the type of the contact. A two-domain decomposition problem is solved by finding a bottleneck (or a minimum cut) of the network, which minimizes the total cross-edge capacity, using the classical Ford--Fulkerson algorithm. A multi-domain decomposition problem is solved through repeatedly solving a series of two-domain problems. The algorithm has been implemented as a computer program, called DomainParser. We have tested the program on a commonly used test set consisting of 55 proteins. The decomposition results are 78.2% in agreement with the literature on both the number of decomposed domains and the assignments of residues to each domain, which compares favorably to existing programs. On the subset of two-domain proteins (20 in number), the program assigned 96.7% of the residues correctly when we require that the number of decomposed domains is two.

Algorithms↗
PubMed2002

Multiple sequence alignment using partial order graphs.

MOTIVATION: Progressive Multiple Sequence Alignment (MSA) methods depend on reducing an MSA to a linear profile for each alignment step. However, this leads to loss of information needed for accurate alignment, and gap scoring artifacts. RESULTS: We present a graph representation of an MSA that can itself be aligned directly by pairwise dynamic programming, eliminating the need to reduce the MSA to a profile. This enables our algorithm (Partial Order Alignment (POA)) to guarantee that the optimal alignment of each new sequence versus each sequence in the MSA will be considered. Moreover, this algorithm introduces a new edit operator, homologous recombination, important for multidomain sequences. The algorithm has improved speed (linear time complexity) over existing MSA algorithms, enabling construction of massive and complex alignments (e.g. an alignment of 5000 sequences in 4 h on a Pentium II). We demonstrate the utility of this algorithm on a family of multidomain SH2 proteins, and on EST assemblies containing alternative splicing and polymorphism. AVAILABILITY: The partial order alignment program POA is available at http://www.bioinformatics.ucla.edu/poa.

Algorithms↗
PubMed2002

Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees.

MOTIVATION: Gene expression data clustering provides a powerful tool for studying functional relationships of genes in a biological process. Identifying correlated expression patterns of genes represents the basic challenge in this clustering problem. RESULTS: This paper describes a new framework for representing a set of multi-dimensional gene expression data as a Minimum Spanning Tree (MST), a concept from the graph theory. A key property of this representation is that each cluster of the expression data corresponds to one subtree of the MST, which rigorously converts a multi-dimensional clustering problem to a tree partitioning problem. We have demonstrated that though the inter-data relationship is greatly simplified in the MST representation, no essential information is lost for the purpose of clustering. Two key advantages in representing a set of multi-dimensional data as an MST are: (1) the simple structure of a tree facilitates efficient implementations of rigorous clustering algorithms, which otherwise are highly computationally challenging; and (2) as an MST-based clustering does not depend on detailed geometric shape of a cluster, it can overcome many of the problems faced by classical clustering algorithms. Based on the MST representation, we have developed a number of rigorous and efficient clustering algorithms, including two with guaranteed global optimality. We have implemented these algorithms as a computer software EXpression data Clustering Analysis and VisualizATiOn Resource (EXCAVATOR). To demonstrate its effectiveness, we have tested it on three data sets, i.e. expression data from yeast Saccharomyces cerevisiae, expression data in response of human fibroblasts to serum, and Arabidopsis expression data in response to chitin elicitation. The test results are highly encouraging. AVAILABILITY: EXCAVATOR is available on request from the authors.

Algorithms↗
PubMed2002

An automatic block and spot indexing with k-nearest neighbors graph for microarray image analysis.

MOTIVATION: In this paper, we propose a fully automatic block and spot indexing algorithm for microarray image analysis. A microarray is a device which enables a parallel experiment of ten to hundreds of thousands of test genes in order to measure gene expression. Due to this huge size of experimental data, automated image analysis is gaining importance in microarray image processing systems. Currently, most of the automated microarray image processing systems require manual block indexing and, in some cases, spot indexing. If the microarray image is large and contains a lot of noise, it is very troublesome work. In this paper, we show it is possible to locate the addresses of blocks and spots by applying the Nearest Neighbors Graph Model. Also, we propose an analytic model for the feasibility of block addressing. Our analytic model is validated by a large body of experimental results. RESULTS: We demonstrate the features of automatic block detection, automatic spot addressing, and correction of the distortion and skewedness of each microarray image.

Algorithms↗
PubMed2002

ProClust: improved clustering of protein sequences with an extended graph-based approach.

MOTIVATION: The problem of finding remote homologues of a given protein sequence via alignment methods is not fully solved. In fact, the task seems to become more difficult with more data. As the size of the database increases, so does the noise level; the highest alignment scores due to random similarities increase and can be higher than the alignment score between true homologues. Comparing two sequences with an arbitrary alignment method yields a similarity value which may indicate an evolutionary relationship between them. A threshold value is usually chosen to distinguish between true homologue relationships and random similarities. To compensate for the higher probability of spurious hits in larger databases, this threshold is increased. Increasing specificity however leads to decreased sensitivity as a matter of principle. Sensitivity can be recovered by utilizing refined protocols. A number of approaches to this challenge have made use of the fact that proteins are often members of some larger protein family. This can be exploited by using position-specific substitution matrices or profiles, or by making use of transitivity of homology. Transitivity refers to the concept of concluding homology between proteins A and C based on homology between A and a third protein B and between B and C. It has been demonstrated that transitivity can lead to substantial improvement in recognition of remote homologues particularly in cases where the alignment score of A and C is below the noise level. A natural limit to the use of transitivity is imposed by domains. Domains, compact independent sub-units of proteins, are often shared between otherwise distinct proteins, and can cause substantial problems by incorrectly linking otherwise unrelated proteins. RESULTS: We extend a graph-based clustering algorithm which uses an asymmetric distance measure, scaling similarity values based on the length of the protein sequences compared. Additionally, the significance of alignment scores is taken into account and used for a filtering step in the algorithm. Post-processing, to merge further clusters based on profile HMMs is proposed. SCOP sequences and their super-family level classification are used as a test set for a clustering computed with our method for the joint data set containing both SCOP and SWISS-PROT. Note, the joint data set includes all multi-domain proteins, which contain the SCOP domains that are a potential source of incorrect links. Our method compares at high specificities very favorably with PSI-Blast, which is probably the most widely-used tool for finding remote homologues. We demonstrate that using transitivity with as many as twelve intermediate sequences is crucial to achieving this level of performance. Moreover, from analysis of false positives we conclude that our method seems to correctly bound the degree of transitivity used. This analysis also yields explicit guidance in choosing parameters. The heuristics of the asymmetric distance measure used neither solve the multi-domain problem from a theoretical point of view, nor do they avoid all types of problems we have observed in real data. Nevertheless, they do provide a substantial improvement over existing approaches. AVAILABILITY: The complete software source is freely available to all users under the GNU General Public License (GPL) from http://www.bioinformatik.uni-koeln.de/~proclust/download/

Algorithms↗
PubMed1989

An extension of the graph theoretical approach to predict the secondary structure of large RNAs: the complex of 16S and 23S rRNAs from E. coli as a case study.

An algorithm using the graph theoretical approach to predict secondary structures of large nucleic acids is discussed. Reliability of prediction can be improved by incorporating available experimental data and sequence homology information. As a case study, this algorithm is applied to predict the secondary structure of the 16S-23S rRNA complex from E. coli. It was found that several structures of the complex can coexist. The computer program developed to predict the secondary structure of large RNAs can be run on IBM PC/AT compatible systems.

Algorithms↗
PubMed2025

Integration of multi-source gene interaction networks and omics data with graph attention networks to identify novel disease genes.

MOTIVATION: The pathogenesis of diseases is closely associated with genes, and the discovery of disease genes holds significant importance for understanding disease mechanisms and designing targeted therapeutics. However, biological validation of all genes for diseases is expensive and challenging. RESULTS: In this study, we propose DGP-AMIO, a computational method based on graph attention networks, to rank all unknown genes and identify potential novel disease genes by integrating multi-omics and gene interaction networks from multiple data sources. DGP-AMIO outperforms other methods significantly on 20 disease datasets, with an average AUROC and AUPR exceeding 0.9. The superior performance of DGP-AMIO is attributed to the integration of multiomics and gene interaction networks from multiple databases, as well as triGAT, a proposed GAT-based method that enables precise identification of disease genes in directed gene networks. Enrichment analysis conducted on the top 100 genes predicted by DGP-AMIO and literature research revealed that a majority of enriched GO terms, KEGG pathways and top genes were associated with diseases supported by relevant studies. We believe that our method can serve as an effective tool for identifying disease genes and guiding subsequent experimental validation efforts. AVAILABILITY AND IMPLEMENTATION: DGP-AMIO is publicly available at https://github.com/yangkaiyuan1027/DGP-AMIO.

Gene Regulatory Networks↗
PubMed2025

IGCN: integrative graph convolution networks for patient level insights and biomarker discovery in multi-omics integration.

MOTIVATION: Developing computational tools for integrative analysis across multiple types of omics data has been of immense importance in cancer molecular biology and precision medicine research. While recent advancements have yielded integrative prediction solutions for multi-omics data, these methods lack a comprehensive and cohesive understanding of the rationale behind their specific predictions. To shed light on personalized medicine and unravel previously unknown characteristics within integrative analysis of multi-omics data, we introduce a novel integrative neural network approach for cancer molecular subtype and biomedical classification applications, named Integrative Graph Convolutional Networks (IGCN). RESULTS: To demonstrate the superiority of IGCN, we compare its performance with other state-of-the-art approaches across different cancer subtype and biomedical classification tasks. Our experimental results show that our proposed model outperforms the state-of-the-art and baseline methods. IGCN identifies which types of omics data receive more emphasis for each patient when predicting a specific class. Additionally, IGCN has the capability to pinpoint significant biomarkers from a range of omics data types. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/bozdaglab/IGCN.

Humans↗
PubMed2025

Tsbrowse: an interactive browser for ancestral recombination graphs.

SUMMARY: Ancestral recombination graphs (ARGs) represent the interwoven paths of genetic ancestry of a set of recombining sequences. The ability to capture the evolutionary history of samples makes ARGs valuable in a wide range of applications in population and statistical genetics. ARG-based approaches are increasingly becoming a part of genetic data analysis pipelines due to breakthroughs enabling ARG inference at biobank-scale. However, there is a lack of visualization tools, which are crucial for validating inferences and generating hypotheses. We present tsbrowse, an open-source, web-based Python application for the interactive visualization of the fundamental building blocks of ARGs, i.e. nodes, edges and mutations. We demonstrate the application of tsbrowse to various data sources and scenarios, and highlight its key features of browsability along the genome, user interactivity, and scalability to very large sample sizes. AVAILABILITY AND IMPLEMENTATION: Tsbrowse is installed as a Python package from PyPI (https://pypi.org/project/tsbrowse/), while a development version is maintained at https://github.com/tskit-dev/tsbrowse. Documentation is available at https://tskit.dev/tsbrowse/docs/. Source code is archived on Zenodo with DOI, https://doi.org/10.5281/zenodo.15683039.

Software↗
PubMed2026

GBSC: graph-based sequence clustering method for similar short tandem repeats in protein sequences.

MOTIVATION: Short tandem repeats (STRs) are abundant in protein sequences and play important role in determining their structures and functions. Strikingly, the unusual compositional characteristics of tandem repeats break classical sequence analysis tools. RESULTS: Here, we establish the first algorithm to effectively identify and cluster STRs: Graph-Based Sequence Clustering (GBSC) features linear time complexity, and clusters protein sequence fragments based on their STRs, while allowing for insertions and mutations and supporting the analysis of imperfect or cryptic repeats. Due to its computational efficacy, our algorithm can be used to systematically scan for patterns in large datasets. We compare our method both to state-of-the-art methods for identifying STRs in proteins and alternative clustering approaches. Unlike existing STR analysis methods, GBSC clusters repeat patterns rather than raw sequences, operating at the level of structural repeat identity, while tolerating biological variations and preventing erroneous merging of structurally and functionally distinct motifs. Whereas functional annotation is typically only available at the protein level, the functions of individual STRs and sequences of adjacent STRs remain largely unknown. On a challenging use case we here demonstrate and discuss how our method can be used to associate previously unannotated repetitive protein fragments with similar ones, allowing the transfer of annotation by similarity. For the first time, GBSC offers a tool that systematically extends this fundamental bioinformatics principle to low-complexity regions across large datasets. AVAILABILITY AND IMPLEMENTATION: GBSC is available at GitHub https://github.com/patryk-jarnot/GBSC and https://doi.org/10.5281/zenodo.18965247. The data and scripts to reproduce the analysis are available at https://doi.org/10.5281/zenodo.16906653.

Microsatellite Repeats↗
PubMed2026

ARGformer: learning on ancestral recombination graphs with transformers.

MOTIVATION: Recent advances in inference of the ancestral recombination graph (ARG), which describes how segments of chromosomes trace back through recombination and shared lineages, have made it possible to reconstruct genome-wide genealogies for large cohorts, but it remains difficult to summarize and use this information for population genetic analyses. RESULTS: We present ARGformer, an encoder-only transformer that learns context-dependent embeddings with a self-supervised masked objective finetuned with contrastive learning for downstream retrieval tasks. We train ARGformer on genealogies from coalescent simulations and on genealogies inferred from ancient and present-day Homo sapiens genomes. Using only these learned embeddings, without access to genotype matrices, ARGformer captures patterns of global population structure and supports ancestry inference through clustering and nearest-neighbor retrieval. On genealogies that include archaic hominins, ARGformer can highlight Denisovan-derived segments in Oceanian genomes and reveals Oceanian-like ancestry in South American Indigenous populations. AVAILABILITY AND IMPLEMENTATION: ARGformer is available at https://github.com/AI-sandbox/ARGformer.

Humans↗
PubMed2026

Interactive exploration of biobank-scale ancestral recombination graphs with Lorax.

MOTIVATION: Ancestral Recombination Graphs (ARGs) provide a comprehensive representation of genetic ancestry and underpin analyses of natural selection, disease association, and population history. However, existing visualization tools are limited in scalability and interactivity, making ARGs difficult to explore at biobank scale. RESULTS: We introduce Lorax, a GPU-accelerated, web-native platform for real-time visualization of population-scale ARGs. Lorax integrates genomic position, coalescent time, local genealogy, and metadata, enabling interactive exploration of ancestry and variant inheritance in biobank-scale datasets. AVAILABILITY AND IMPLEMENTATION: Lorax is freely available as a live demo at https://lorax.ucsc.edu/ and as a Python package "lorax-arg" on PyPI. The source code and documentation are available on GitHub at https://github.com/pratikkatte/lorax.

Software↗
PubMed2003

Generating consensus sequences from partial order multiple sequence alignment graphs.

MOTIVATION: Consensus sequence generation is important in many kinds of sequence analysis ranging from sequence assembly to profile-based iterative search methods. However, how can a consensus be constructed when its inherent assumption-that the aligned sequences form a single linear consensus-is not true? RESULTS: Partial Order Alignment (POA) enables construction and analysis of multiple sequence alignments as directed acyclic graphs containing complex branching structure. Here we present a dynamic programming algorithm (heaviest_bundle) for generating multiple consensus sequences from such complex alignments. The number and relationships of these consensus sequences reveals the degree of structural complexity of the source alignment. This is a powerful and general approach for analyzing and visualizing complex alignment structures, and can be applied to any alignment. We illustrate its value for analyzing expressed sequence alignments to detect alternative splicing, reconstruct full length mRNA isoform sequences from EST fragments, and separate paralog mixtures that can cause incorrect SNP predictions. AVAILABILITY: The heaviest_bundle source code is available at http://www.bioinformatics.ucla.edu/poa

Algorithms↗