Shaberi Hazlam S Ahmad, Kappassov Aibek, Matas-Gil Antonio, Endres Robert G
Department of Life Sciences, Imperial College, London, SW7 2AZ, UK.
Center for Integrative Systems Biology and Bioinformatics, Imperial College, London, SW7 2AZ, UK.
Sci Rep. 2025 Jan 23;15(1):2948. doi: 10.1038/s41598-025-86854-7.
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.
许多细胞模式都表现出反应扩散成分，这表明图灵不稳定性可能有助于模式形成。然而，生物基因调控途径比简单的图灵激活剂-抑制剂模型更为复杂，并且通常不需要像图灵条件所要求的那样对参数进行微调。为了解决这些问题，我们采用随机矩阵理论来分析具有稳健统计特性的更大网络的雅可比矩阵。我们的分析表明，图灵模式比之前认为的更有可能偶然出现，并且最稳健的图灵网络具有最优规模，仅由少数分子种类组成，从而显著提高了它们在生物系统中的可识别性。广义而言，这种最优规模源于小网络中最高稳定性与大网络中扩散导致的最大不稳定性之间的权衡。此外，我们发现对于多个固定节点，差异扩散对于图灵模式不再重要。我们的研究结果可能为未来的合成生物学方法提供参考，并为弥合与复杂发育途径之间的差距提供见解。
