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<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JDMSC-2781</article-id>
      <title-group>
        <article-title>Spatial omics-informed graph neural networks for metabolic flux estimation in microbial communities</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Kumar</surname>
            <given-names>V. Uday</given-names>
          </name>
          <aff>Department of Data Science, Gokaraju Rangaraju Institute of Engineering and Technology, Hyderabad, Telangana, 500090, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Manikandan</surname>
            <given-names>N. K.</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Vel Tech Rangarajan Dr. Sagunthala R&amp;D Institute of Science and Technology, Avadi, Chennai, Tamil Nadu, 600062, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Kaushik</surname>
            <given-names>C.</given-names>
          </name>
          <aff>Department of Electronics and Communication Engineering, VNR Vignana Jyothi Institute of Engineering &amp; Technology, Hyderabad, Telangana, 500118, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Anusha</surname>
            <given-names>P.</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Ramachandra College of Engineering, Eluru, Andhra Pradesh, 534007, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Goud</surname>
            <given-names>Parameshwari M.</given-names>
          </name>
          <aff>Department of Mathematics, Vardhaman College of Engineering, Hyderabad, Telangana, 501218, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Pallavi</surname>
            <given-names>L.</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, B. V. Raju Institute of Technology, Telangana, Hyderabad, 502313, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Saranya</surname>
            <given-names>K.</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Andhra Pradesh, 522302, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Malempati</surname>
            <given-names>Sreelatha</given-names>
          </name>
          <aff>Department of Computer Science &amp; Engineering, R. V. R &amp; J. C. College of Engineering, Guntur, Andhra Pradesh, 522019, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>9-B</issue>
      <fpage>3533</fpage>
      <lpage>3542</lpage>
      <pub-date date-type="pub">
        <day>30</day>
        <month>09</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>This research showed a spatial omics integrated Graph Neural Network (GNN) framework for high, resolution metabolic flux estimation across heterogeneous microbial communities using spatially resolved transcriptomic, proteomic, and metabolomic signals combined with microenvironmental interaction graphs. The research is geared towards creating a computational method that can predict cell, specific metabolic fluxes accurately while reflecting metabolic heterogeneity, microbial interactions, and spatially constrained biochemical dynamics. The method creates multi, layer spatial graphs of which nodes are microbial taxa or single cells, edges depict spatial proximity and biochemical interaction strength, and node features incorporate multi, omics signals normalized through spatial, aware preprocessing. A physics, guided flux inference component directs the GNN by stoichiometric and thermodynamic feasibility constraints taken from microbial metabolic models. Full training running spatiotemporal mini, batching as a tool to optimize allows the model to capture non, linear relationships between the local omics states and the emergent flux distributions under nutrient gradients, stress conditions, and community, level cross, feeding. The performance evaluation is based on accuracy, F1, MAE of flux magnitudes, training dynamics, latency profiling, and model stability illustrate that spatial, omics guided GNNs outperform non, spatial baselines by 1832% and at the same time allow sub, second flux inference which is perfect for real, time microbial ecosystem monitoring.</p>
      </abstract>
      <kwd-group>
        <kwd>Spatial omics</kwd>
        <kwd>Graph neural networks (GNNs)</kwd>
        <kwd>Metabolic flux estimation</kwd>
        <kwd>Microbial interactions</kwd>
        <kwd>Genome</kwd>
        <kwd>Scale metabolic models (GEMs)</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
