bioRxiv Science⌕ Search
Home/Archive/bioRxiv

bioRxiv · 10.1101/2022.07.08.499368

Directed Shortest Walk on Temporal Graphs

Khodaverdian, A.·Yosef, N.
View original source ↗Export metadata ↓

Abstract

BackgroundThe use of graphs as a way of abstracting and representing biological systems has provided a powerful analysis paradigm. Specifically, graph optimization algorithms are routinely used to address various connectivity queries, such as finding paths between proteins in a protein-protein interaction network, while maximizing objectives such as parsimony. While present studies in this field mostly concern static graphs, new types of data now motivate the need to account for changes that might occur to the elements (nodes) that are represented by the graph on the relationships (edges) between them. Results and DiscussionWe define the notion of Directed Temporal Graphs as a series of directed subgraphs of an underlying graph, ordered by time, where only a subset of vertices and edges are present. We then build up towards the Time Conditioned Shortest Walk problem on Directed Temporal Graphs: given a series of time ordered directed graphs, find the shortest walk from any given source node at time point 1 to a target node at time T [≥] 1, such that the walk is consistent (monotonically increasing) with the timing of nodes and edges. We show, contrary to the Directed Shortest Walk problem which can be solved in polynomial time, that the Time Conditioned Shortest Walk (TCSW) problem is NP-Hard, and is hard to approximate to factor [Formula] for T [≥] 3 and{varepsilon} > 0. Lastly, we develop an integer linear program to solve a generalized version of TCSW, and demonstrate its ability to reach optimality with instances of the human protein interaction network. ConclusionWe demonstrate that when extending the shortest walk problem in computational biology to account for multiple ordered conditions, the problem not only becomes hard to solve, but hard to approximate, a limitation which we address via a new solver. From this narrow definition of TCSW, we relax the constraint of time consistency within the shortest walk, deriving a direct relationship between hardness of approximation and the allowable step size in our walk between time conditioned networks. Lastly we briefly explore a variety of alternative formulations for this problem, providing insight into both tractable and intractable variants. AvailabilityOur solver for the general k-Time Condition Shortest Walk problem is available at https://github.com/YosefLab/temporal_condition_shortest_walk

Explore related subjects

bioinformaticsPreprint

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Khodaverdian, A., Yosef, N.. 2022-07-10. Directed Shortest Walk on Temporal Graphs. https://doi.org/10.1101/2022.07.08.499368

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

spatialMET: an open and scalable framework for spatial metabolomics analysis

Mass spectrometry imaging (MSI) enables spatially resolved metabolomics in intact tissue sections, but analysis remains challenging at scale. Existing MSI workflows often require users to combine multiple software tools, while others rely on proprietary vendor software that limits interoperability and reproducibility. To address these challenges, we developed spatialMET, an open-source framework that provides an end-to-end workflow for MSI analysis. spatialMET provides a unified platform for preprocessing, spatial domain detection, and visualization. Downstream analyses include differential abundance testing, spatial autocorrelation and gradient analysis, dimensionality reduction, and correlation network analysis. Spatial domain detection uses hcdist, a C-based hierarchical clustering implementation that substantially reduces runtime and memory use relative to existing R-based approaches. spatialMET can be run through an interactive R Shiny application or as a standalone command-line workflow for larger datasets or high-performance computing environments. Applied to mouse small cell lung cancer MALDI-MSI data containing 284,673 pixels, spatialMET identified tumor-associated, stromal, and adjacent lung spatial domains that aligned with matched histology. Differential abundance analysis identified 117 m/z features that differed between tumor and stromal regions, while spatial autocorrelation analyses revealed spatially structured abundance patterns. Applying spatialMET to mouse lung adenocarcinoma data from an entire lung lobe containing 338,477 pixels further demonstrated scalability and captured spatial heterogeneity across tumor and surrounding lung tissue. In summary, spatialMET provides a scalable, open-source framework for end-to-end spatial metabolomics analysis, and it is distributed as a Docker container for reproducible deployment. Source code and installation instructions are available at https://github.com/biodatalab/spatialMET.

bioinformatics↗
bioRxiv2026

Probing the transcriptome response to shivering in skeletal muscle using a multilayered bioinformatics approach

Cold acclimation holds therapeutic potential for improving metabolic health. We previously demonstrated that repeated cold-induced shivering enhances insulin sensitivity in humans. However, the molecular pathways that underlie the skeletal muscle shivering response, and how these relate to beneficial physiological effects, remain poorly understood. In this study, we combined complementary bioinformatics approaches to allow in-depth analysis of the transcriptomic response of human skeletal muscle to repeated shivering. We identified a robust transcriptional signature and show a sex-specific component in the shivering skeletal muscle response, which seemed to diminish following cold adaptation. Our findings provide mechanistic insights into cold-induced muscle adaptations, shed light on potential interesting molecular targets for further investigation, and emphasize the importance of including both sexes in future cold acclimation studies.

bioinformatics↗
bioRxiv2026

An Information Geometry approach to model topological trajectories and Gene Expression Radius from UMAP geometry.

Understanding the relationship between gene expression dynamics and cellular identity remains a central challenge in single cell biology. Here, we introduce a novel computational and mathematical framework that integrates information geometry, fuzzy topology, and UMAP analysis to model gene expression landscapes derived from single cell RNA sequencing data. We formalize gene expression data as a fuzzy topological space, where interactions between expression points are governed by probabilistic distributions inspired by manifold learning approaches such as UMAP. Within this framework, we define an information geometric structure through a Fisher metric induced by these distributions, enabling the computation of geodesic trajectories that capture cellular differentiation processes. A key contribution of this work is the derivation of analytical conditions, expressed as expression radius formulas, that characterize local neighborhoods in gene expression space. These conditions allow for the identification of genes associated with stem cell states and predictions in transitional cell types in future work. Application of the proposed framework to single cell datasets reveals biologically meaningful gene sets enriched in key regulatory pathways and transcription factors, demonstrating the capacity of our approach to uncover latent structure in complex gene expression data. Our results suggest that integrating differential geometry with statistical learning theory offers a powerful paradigm for modeling genotype and phenotype relationships and cellular state transitions, with potential implications for precision medicine and systems biology.

bioinformatics↗