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      A mathematical model of endothelial nitric oxide synthase activation with time delay exhibiting Hopf bifurcation and oscillations

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      Mathematical Biosciences
      Elsevier BV

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          Abstract

          <p class="first" id="P2">Nitric Oxide (NO) is a gaseous compound that serves as a signaling molecule in cellular interactions. In the vasculature, NO is synthesized from endogenous agents by endothelial nitric oxide synthase (eNOS) where it plays key roles in several functions related to homeostasis, adaptation, and development. Recent experimental studies have revealed cycles of increasing and decreasing NO production when eNOS is stimulated by factors such as glucose or insulin. We offer a mathematical model of a generic amino acid receptor site on eNOS wherein this species is subject to activation/deactivation by a pair of interactive kinase and phosphatase species. The enzyme kinetic model is presented as a system of ordinary differential equations including time delay to allow for various intermediate, unspecified complexes. We show that under conditions on the model parameters, varying the delay time may give rise to a Hopf bifurcation. Properties of the bifurcating solutions are explored via a center manifold reduction, and a numerical illustration is provided. </p>

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          Author and article information

          Journal
          Mathematical Biosciences
          Mathematical Biosciences
          Elsevier BV
          00255564
          November 2016
          November 2016
          : 281
          : 62-73
          Article
          10.1016/j.mbs.2016.09.003
          5067240
          27614021
          79fb13b3-9d20-47ff-8017-aff2da346444
          © 2016

          https://www.elsevier.com/tdm/userlicense/1.0/

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