Determining the Equivalence of Small Zero-one Reaction Networks
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910006926901248 |
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| author | Jiao, Yue Tang, Xiaoxian |
| author_facet | Jiao, Yue Tang, Xiaoxian |
| contents | Zero-one reaction networks are pivotal to cellular signaling, and establishing the equivalence of such networks represents a foundational computational challenge in the realm of chemical reaction network research. Herein, we propose a high-efficiency approach for identifying the equivalence of zero-one networks. Its efficiency stems from a set of criteria tailored to judge the equivalence of steady-state ideals derived from zero-one networks, which effectively reduces the computational cost associated with Gröbner basis calculations. Experimental results demonstrate that our proposed method can successfully categorize more than three million networks by their equivalence within a feasible timeframe. Also, our computational results for two important classes of quadratic zero-one networks (3-dimensional with 3 species, 6 reactions; 4-dimensional with 4 species, 5 reactions) show that they have no positive steady states for a generic choice of rate constants, implying these small networks generically exhibit neither multistability nor periodic orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determining the Equivalence of Small Zero-one Reaction Networks Jiao, Yue Tang, Xiaoxian Molecular Networks Zero-one reaction networks are pivotal to cellular signaling, and establishing the equivalence of such networks represents a foundational computational challenge in the realm of chemical reaction network research. Herein, we propose a high-efficiency approach for identifying the equivalence of zero-one networks. Its efficiency stems from a set of criteria tailored to judge the equivalence of steady-state ideals derived from zero-one networks, which effectively reduces the computational cost associated with Gröbner basis calculations. Experimental results demonstrate that our proposed method can successfully categorize more than three million networks by their equivalence within a feasible timeframe. Also, our computational results for two important classes of quadratic zero-one networks (3-dimensional with 3 species, 6 reactions; 4-dimensional with 4 species, 5 reactions) show that they have no positive steady states for a generic choice of rate constants, implying these small networks generically exhibit neither multistability nor periodic orbits. |
| title | Determining the Equivalence of Small Zero-one Reaction Networks |
| topic | Molecular Networks |
| url | https://arxiv.org/abs/2503.00008 |