Optimal network sizes for most robust Turing patterns
Abstract Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor models and generally do not require fine-tuning of para...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-025-86854-7 |
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| author | Hazlam S. Ahmad Shaberi Aibek Kappassov Antonio Matas-Gil Robert G. Endres |
| author_facet | Hazlam S. Ahmad Shaberi Aibek Kappassov Antonio Matas-Gil Robert G. Endres |
| author_sort | Hazlam S. Ahmad Shaberi |
| collection | DOAJ |
| description | Abstract Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor models and generally do not require fine-tuning of parameters as dictated by the Turing conditions. To address these issues, we employ random matrix theory to analyze the Jacobian matrices of larger networks with robust statistical properties. Our analysis reveals that Turing patterns are more likely to occur by chance than previously thought and that the most robust Turing networks have an optimal size, consisting of only a handful of molecular species, thus significantly increasing their identifiability in biological systems. Broadly speaking, this optimal size emerges from a trade-off between the highest stability in small networks and the greatest instability with diffusion in large networks. Furthermore, we find that with multiple immobile nodes, differential diffusion ceases to be important for Turing patterns. Our findings may inform future synthetic biology approaches and provide insights into bridging the gap to complex developmental pathways. |
| format | Article |
| id | doaj-art-2df97353a89546eaab944d7de7d01c95 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-2df97353a89546eaab944d7de7d01c952025-01-26T12:24:04ZengNature PortfolioScientific Reports2045-23222025-01-0115111310.1038/s41598-025-86854-7Optimal network sizes for most robust Turing patternsHazlam S. Ahmad Shaberi0Aibek Kappassov1Antonio Matas-Gil2Robert G. Endres3Department of Life Sciences, Imperial CollegeDepartment of Life Sciences, Imperial CollegeDepartment of Life Sciences, Imperial CollegeDepartment of Life Sciences, Imperial CollegeAbstract Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor models and generally do not require fine-tuning of parameters as dictated by the Turing conditions. To address these issues, we employ random matrix theory to analyze the Jacobian matrices of larger networks with robust statistical properties. Our analysis reveals that Turing patterns are more likely to occur by chance than previously thought and that the most robust Turing networks have an optimal size, consisting of only a handful of molecular species, thus significantly increasing their identifiability in biological systems. Broadly speaking, this optimal size emerges from a trade-off between the highest stability in small networks and the greatest instability with diffusion in large networks. Furthermore, we find that with multiple immobile nodes, differential diffusion ceases to be important for Turing patterns. Our findings may inform future synthetic biology approaches and provide insights into bridging the gap to complex developmental pathways.https://doi.org/10.1038/s41598-025-86854-7 |
| spellingShingle | Hazlam S. Ahmad Shaberi Aibek Kappassov Antonio Matas-Gil Robert G. Endres Optimal network sizes for most robust Turing patterns Scientific Reports |
| title | Optimal network sizes for most robust Turing patterns |
| title_full | Optimal network sizes for most robust Turing patterns |
| title_fullStr | Optimal network sizes for most robust Turing patterns |
| title_full_unstemmed | Optimal network sizes for most robust Turing patterns |
| title_short | Optimal network sizes for most robust Turing patterns |
| title_sort | optimal network sizes for most robust turing patterns |
| url | https://doi.org/10.1038/s41598-025-86854-7 |
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