Epistatic pathways in evolvable mechanical networks

Samar Alqatari, Sidney Nagel
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Abstract

An elastic spring network is an example of evolvable matter. It can be pruned to couple separated pairs of nodes so that when a strain is applied to one of them, the other responds either in-phase or out-of-phase. This produces two pruned networks with incompatible functions that are nearly identical but differ from each other by a set of "mutations," each of which removes or adds a single bond in the network. The effect of multiple mutations is epistatic; that is, the effect of a mutation depends on what other mutations have already occurred. We generate ensembles of network pairs that differ by a fixed number, $M$, of discrete mutations and evaluate all $M!$ mutational paths between the in- and out-of phase behaviors up to $M = 14$. With a threshold response for the network to be considered functional, so that non-functional networks are disallowed, only some mutational pathways are viable. We find that there is a surprisingly high critical response threshold above which no evolutionarily viable path exists between the two networks. The few remaining pathways at this critical value dictate much of the behavior along the evolutionary trajectory. In most cases, the mutations break up into two distinct classes. The analysis clarifies how the number of mutations and the position of a mutation along the pathway affect the evolutionary outcome.
可进化机械网络中的外显路径
弹性弹簧网络是可进化物质的一个例子。它可以被修剪成一对分开的节点,这样当对其中一个节点施加应变时,另一个节点就会做出同相或异相反应。这就产生了两个功能互不兼容的网络,它们几乎完全相同,但通过一系列 "突变 "而彼此不同,每个 "突变 "都会移除或增加网络中的一个键。多重突变的效果是表观的;也就是说,一个突变的效果取决于已经发生的其他突变。我们生成了具有固定数量($M$)离散突变的网络对集合,并评估了处于相位和不处于相位行为之间的所有$M!$突变路径,最高可达$M = 14$。由于网络被认为是功能性的有一个阈值响应,因此不允许出现非功能性网络,只有一些突变路径是可行的。我们发现,临界响应阈值出奇地高,超过这个阈值,两个网络之间就不存在进化上可行的路径。在大多数情况下,突变分为两个不同的类别。分析阐明了突变的数量和突变在路径上的位置如何影响进化结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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