无标度拓扑对遗传调控网络鲁棒性和可进化性的影响
The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks
摘要：
我们研究了无标度（SF）和Erdos-Renyi（ER）拓扑结构如何影响布尔阈值动力学模型基因调控网络的可进化性和鲁棒性之间的相互作用。与Oikonomou和Cluzel（2006）的观点一致，我们发现具有SFin拓扑的网络，即传入节点的SF拓扑和传出节点的ER拓扑，比传入和传出节点都具有ER拓扑的网络更容易向特定的振荡目标进化。对于具有SFboth和SFout拓扑的网络，也发现了类似的结果。SFout拓扑结构的功能最接近于生物基因网络的结构（Babu等人，2004）通过扩展到具有振荡或非振荡性质的多个目标输出，进一步详细地与ER拓扑进行比较。对于相同长度的多个振荡目标，SFout和ER网络之间的差异增强，但对于非振荡目标，这两种类型的网络表现出相当相似的演化。我们发现SF网络比ER网络更容易产生振荡，这可以解释为什么SF网络比ER网络更容易演化为振荡表型。尽管他们更大的进化，我们发现，SFout拓扑结构的网络也更强大的突变比ER网络。此外，SFout拓扑对初始条件的变化更鲁棒（环境鲁棒性）。对于这两种拓扑结构，我们发现，一旦人口的网络已经达到目标状态，进一步的中性进化可以导致增加的突变鲁棒性和环境鲁棒性的初始条件的变化。
英文摘要：
We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SFin topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SFboth and SFout topologies. The functionality of the SFout topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SFout and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SFout topologies are also more robust to mutations than ER networks. Furthermore, the SFout topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.
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