原始细胞进化的PDE模型和多级选择下的染色体起源
A PDE Model for Protocell Evolution and the Origin of Chromosomes via Multilevel Selection
摘要：
复杂的细胞生命的进化涉及两个主要的转变：自我复制的遗传实体封装成细胞单位和单个基因聚集成集体复制的基因组。在本文中，我们制定了一个最小模型的原始细胞内的原始染色体的进化。我们模拟了一个简单的原始细胞，由两种类型的基因组成：一个“快基因”具有基因水平自我复制的优势，一个“慢基因”在基因水平上复制得更慢，但它赋予了原始细胞水平繁殖的优势。原细胞水平的复制能力取决于细胞的快基因和慢基因的组成。我们使用偏微分方程来描述原始细胞内的基因组成如何在细胞内和细胞间竞争下随时间演变。我们发现，快速复制子的基因水平优势对原始细胞进化的多层次动力学投下了长长的阴影：当原始细胞水平繁殖同样需要两个基因时，原始细胞之间的竞争水平无法产生快速和慢速复制子的共存。通过引入一个“二聚体复制子”组成的一个连接对的慢和快的基因，我们分析表明，两个基因之间的共存可以促进快速和二聚体复制子之间的成对多层次竞争，并提供了数量证据的共存快，慢，和二聚体复制子之间的三态竞争。我们的研究结果表明，二聚化，或形成一个简单的染色体样二聚体复制子，可以帮助克服低水平选择的阴影，并与确定性的多级选择合作，使两个基因的共存，这两个基因在原细胞水平上是互补的，但在单个基因水平复制的水平上竞争。
英文摘要：
The evolution of complex cellular life involved two major transitions: the encapsulation of self-replicating genetic entities into cellular units and the aggregation of individual genes into a collectively replicating genome. In this paper, we formulate a minimal model of the evolution of proto-chromosomes within protocells. We model a simple protocell composed of two types of genes: a "fast gene" with an advantage for gene-level self-replication and a "slow gene" that replicates more slowly at the gene level, but which confers an advantage for protocell-level reproduction. Protocell-level replication capacity depends on cellular composition of fast and slow genes. We use a partial differential equation to describe how the composition of genes within protocells evolves over time under within-cell and between-cell competition. We find that the gene-level advantage of fast replicators casts a long shadow on the multilevel dynamics of protocell evolution: no level of between-protocell competition can produce coexistence of the fast and slow replicators when the two genes are equally needed for protocell-level reproduction. By introducing a "dimer replicator" consisting of a linked pair of the slow and fast genes, we show analytically that coexistence between the two genes can be promoted in pairwise multilevel competition between fast and dimer replicators, and provide numerical evidence for coexistence in trimorphic competition between fast, slow, and dimer replicators. Our results suggest that dimerization, or the formation of a simple chromosome-like dimer replicator, can help to overcome the shadow of lower-level selection and work in concert with deterministic multilevel selection to allow for the coexistence of two genes that are complementary at the protocell-level but compete at the level of individual gene-level replication.
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