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Next we discuss the electronic properties of \(\hbox MP_4\) (\(\hbox M = \hbox Cr\), Mo, W) compounds. Figure 3 represents the calculated electronic band structures along the high symmetry directions of the BZ using HSE06 functional60 and the fermi energy (\(E_F\)) is set to zero. For \(\hbox CrP_4\) as shown in Fig. 3a, the conduction band minimum (CBM) is located along H-Z direction and valence band maximum (VBM) is located along F-H direction, showing a semiconducting behavior with an indirect band gap of 0.47 eV, which is smaller than the reported direct band gap of 0.63 eV58. For \(\hbox MoP_4\) as shown in Fig. 3b, the lowest conduction band and highest valence band are degenerate at \(\Gamma\) point near the \(E_F\), indicating that \(\hbox MoP_4\) is a Dirac semimetal with a four-fold degenerate Dirac point at the \(\Gamma\) point61. Moreover, our calculations show that the valence and conduction bands of \(\hbox WP_4\) exhibit linear dispersion near the \(E_F\) and cross along the \(\Gamma\)-X high symmetry direction (Fig. 3c) due to the band inversion mechanism39,40. To further explore the topological electronic properties, we establish a tight binding (TB) model using the maximally localized Wannier functions (MLWFs)62,63 to search the nodal points in the 3D BZ. We find that the nodal points (or band crossing points) of valence and conduction bands in \(\hbox WP_4\) form a continuous nodal ring in the full BZ (see Fig. 3d), thus, \(\hbox WP_4\) can be termed as a topological nodal line semimetal with a closed nodal ring protected by PT symmetry34,35,41.
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The Systems Biology Markup Language (SBML) [48] is the most commonly used standard for representing biochemical reactions, or gene-regulatory networks, and databases like BioModels [49] provide a huge variety of subcellular models for download. Specifically models for the Tan et al. [46] and Van Leeuwen et al. [30] are available in SBML (See Supplementary Files 1 and 2 respectively). SBML allows the specification of reactions independently of the method used to simulate them and allows differing simulation methods and tools to be compared.
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