论文标题
有限异步生物系统模型中的吸引子稳定性
Attractor Stability in Finite Asynchronous Biological System Models
论文作者
论文摘要
我们介绍了数学技术，用于详尽研究异步生物系统模型的长期动力学。具体而言，我们扩展了用于图形动力学系统开发的$κ$等值的概念，以支持对所有可能的吸引子配置的系统分析，这些配置在改变异步更新顺序时可以生成（Macauley and Mortveit（2009））。我们扩展了Veliz-Cuba和Stigler（2011），Goles等人的早期工作。 （2014年），以及其他人通过将长期动力学与拓扑结合进行比较：我们只比较吸引子的确切状态及其过渡，而仅比较吸引子结构。通常，获取此信息在计算上是棘手的。在这里，我们适应动态系统的组合理论来开发大大降低该计算成本的计算方法。我们提供了一种详细的算法，并将其应用于（$ i $）的Escherichia大肠杆菌模型，由Veliz-Cuba和Stigler（2011）提出的Escherichia Coli，以及（$ ii $）的调节网络，涉及控制Caenorhabhabditis elegrans elegrans fileans exkelelans fileans exkeleans fyva equigransor compulsor compulsor fys ulva equigans fys equiners ulva equiners ulva fy。 （2015）。在这两种情况下，我们在顺序更新下发现了这些网络的所有可能限制周期结构。具体来说，对于LAC操纵子模型，而不是检查所有$ 10！ > 3.6 \ cdot 10^6 $顺序更新订单，我们证明，考虑$ 344 $代表性更新订单是足够的，更值得注意的是，这些$ 344 $代表会产生$ 4 $ $ $ $的吸引者结构。对秀丽隐杆线虫模型进行的类似分析表明，它具有$ 125 $不同的吸引子结构。我们以观察模型吸引子结构的多样性和分布的观察，并利用结果讨论它们的鲁棒性。
We present mathematical techniques for exhaustive studies of long-term dynamics of asynchronous biological system models. Specifically, we extend the notion of $κ$-equivalence developed for graph dynamical systems to support systematic analysis of all possible attractor configurations that can be generated when varying the asynchronous update order (Macauley and Mortveit (2009)). We extend earlier work by Veliz-Cuba and Stigler (2011), Goles et al. (2014), and others by comparing long-term dynamics up to topological conjugation: rather than comparing the exact states and their transitions on attractors, we only compare the attractor structures. In general, obtaining this information is computationally intractable. Here, we adapt and apply combinatorial theory for dynamical systems to develop computational methods that greatly reduce this computational cost. We give a detailed algorithm and apply it to ($i$) the lac operon model for Escherichia coli proposed by Veliz-Cuba and Stigler (2011), and ($ii$) the regulatory network involved in the control of the cell cycle and cell differentiation in the Caenorhabditis elegans vulva precursor cells proposed by Weinstein et al. (2015). In both cases, we uncover all possible limit cycle structures for these networks under sequential updates. Specifically, for the lac operon model, rather than examining all $10! > 3.6 \cdot 10^6$ sequential update orders, we demonstrate that it is sufficient to consider $344$ representative update orders, and, more notably, that these $344$ representatives give rise to $4$ distinct attractor structures. A similar analysis performed for the C. elegans model demonstrates that it has precisely $125$ distinct attractor structures. We conclude with observations on the variety and distribution of the models' attractor structures and use the results to discuss their robustness.
