Kleiman Maya, Tannenbaum Emmanuel
Department of Chemistry, Ben-Gurion University of the Negev, Be'er-Sheva, Israel.
Theory Biosci. 2009 Nov;128(4):249-85. doi: 10.1007/s12064-009-0077-9. Epub 2009 Nov 10.
This article develops mathematical models describing the evolutionary dynamics of both asexually and sexually reproducing populations of diploid unicellular organisms. The asexual and sexual life cycles are based on the asexual and sexual life cycles in Saccharomyces cerevisiae, Baker's yeast, which normally reproduces by asexual budding, but switches to sexual reproduction when stressed. The mathematical models consider three reproduction pathways: (1) Asexual reproduction, (2) self-fertilization, and (3) sexual reproduction. We also consider two forms of genome organization. In the first case, we assume that the genome consists of two multi-gene chromosomes, whereas in the second case, we consider the opposite extreme and assume that each gene defines a separate chromosome, which we call the multi-chromosome genome. These two cases are considered to explore the role that recombination has on the mutation-selection balance and the selective advantage of the various reproduction strategies. We assume that the purpose of diploidy is to provide redundancy, so that damage to a gene may be repaired using the other, presumably undamaged copy (a process known as homologous recombination repair). As a result, we assume that the fitness of the organism only depends on the number of homologous gene pairs that contain at least one functional copy of a given gene. If the organism has at least one functional copy of every gene in the genome, we assume a fitness of 1. In general, if the organism has l homologous pairs that lack a functional copy of the given gene, then the fitness of the organism is kappa(l). The kappa(l) are assumed to be monotonically decreasing, so that kappa(0) = 1 > kappa(1) > kappa(2) > cdots, three dots, centered > kappa(infinity) = 0. For nearly all of the reproduction strategies we consider, we find, in the limit of large N, that the mean fitness at mutation-selection balance is max{2e(-mu) - 1,0} where N is the number of genes in the haploid set of the genome, epsilon is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication, and mu = Nepsilon. The only exception is the sexual reproduction pathway for the multi-chromosomed genome. Assuming a multiplicative fitness landscape where kappa(l) = alpha(l) for alpha in (0, 1), this strategy is found to have a mean fitness that exceeds the mean fitness of all the other strategies. Furthermore, while other reproduction strategies experience a total loss of viability due to the steady accumulation of deleterious mutations once mu exceeds [Formula: see text] no such transition occurs in the sexual pathway. Indeed, in the limit as alpha --> 1 for the multiplicative landscape, we can show that the mean fitness for the sexual pathway with the multi-chromosomed genome converges to e(-2mu), which is always positive. We explicitly allow for mitotic recombination in this study, which, in contrast to previous studies using different models, does not have any advantage over other asexual reproduction strategies. The results of this article provide a basis for understanding the selective advantage of the specific meiotic pathway that is employed by sexually reproducing organisms. The results of this article also suggest an explanation for why unicellular organisms such as Saccharomyces cerevisiae (Baker's yeast) switch to a sexual mode of reproduction when stressed. While the results of this article are based on modeling mutation-propagation in unicellular organisms, they nevertheless suggest that, in more complex organisms with significantly larger genomes, sex is necessary to prevent the loss of viability of a population due to genetic drift. Finally, and perhaps most importantly, the results of this article demonstrate a selective advantage for sexual reproduction with fewer and much less restrictive assumptions than those of previous studies.
本文建立了数学模型,描述二倍体单细胞生物无性繁殖和有性繁殖群体的进化动力学。无性和有性生命周期基于酿酒酵母(面包酵母)的无性和有性生命周期,酿酒酵母通常通过无性出芽繁殖,但在受到压力时会转变为有性繁殖。数学模型考虑了三种繁殖途径:(1)无性繁殖,(2)自体受精,以及(3)有性繁殖。我们还考虑了两种基因组组织形式。在第一种情况下,我们假设基因组由两条多基因染色体组成,而在第二种情况下,我们考虑相反的极端情况,假设每个基因定义一条单独的染色体,我们称之为多染色体基因组。考虑这两种情况是为了探究重组在突变 - 选择平衡以及各种繁殖策略的选择优势中所起的作用。我们假设二倍体的目的是提供冗余,以便基因损伤可以利用另一个可能未受损的拷贝进行修复(这一过程称为同源重组修复)。因此,我们假设生物体的适应性仅取决于包含给定基因至少一个功能拷贝的同源基因对的数量。如果生物体基因组中的每个基因都至少有一个功能拷贝,我们假设其适应性为1。一般来说,如果生物体有l对同源基因缺乏给定基因的功能拷贝,那么该生物体的适应性为kappa(l)。假设kappa(l)是单调递减的,所以kappa(0) = 1 > kappa(1) > kappa(2) > ……,三个点,居中 > kappa(无穷大) = 0。对于我们考虑的几乎所有繁殖策略,我们发现在大N的极限情况下,突变 - 选择平衡时的平均适应性为max{2e^(-μ) - 1, 0},其中N是基因组单倍体集合中的基因数量,ε是给定基因的给定DNA模板链在复制过程中产生突变子代的概率,且μ = Nε。唯一的例外是多染色体基因组的有性繁殖途径。假设适应性景观是乘法形式,即kappa(l) = α^l,其中α ∈ (0, 1),发现这种策略的平均适应性超过了所有其他策略的平均适应性。此外,虽然一旦μ超过[公式:见文本],其他繁殖策略会由于有害突变的稳定积累而导致生存能力完全丧失,但在有性途径中不会发生这种转变。实际上,在乘法景观中当α → 1的极限情况下,我们可以证明多染色体基因组有性途径的平均适应性收敛到e^(-2μ),这总是正的。在本研究中,我们明确考虑了有丝分裂重组,与之前使用不同模型的研究相比,它在其他无性繁殖策略方面没有任何优势。本文的结果为理解有性繁殖生物体所采用的特定减数分裂途径的选择优势提供了基础。本文的结果还为诸如酿酒酵母(面包酵母)等单细胞生物在受到压力时转变为有性繁殖模式提供了一种解释。虽然本文的结果基于单细胞生物中突变传播的建模,但它们仍然表明,在基因组明显更大的更复杂生物体中,有性繁殖对于防止种群因遗传漂变而丧失生存能力是必要的。最后,也许最重要的是,本文的结果在比之前研究更少且限制更少的假设下证明了有性繁殖的选择优势。