The distribution of fitness effects of adaptive mutations remains poorly understood, both empirically and theoretically. We study this distribution using a version of Fisher's geometrical model without pleiotropy, such that each mutation affects only a single trait. We are motivated by the notion of an organism's chemotype, the set of biochemical reaction constants that govern its molecular constituents. From physical considerations, we expect the chemotype to be of high dimension and to exhibit very little pleiotropy. Our model generically predicts striking cusps in the distribution of the fitness effects of arising and fixed mutations. It further predicts that a single element of the chemotype should comprise all mutations at the high-fitness ends of these distributions. Using extreme value theory, we show that the two cusps with the highest fitnesses are typically well-separated, even when the chemotype possesses thousands of elements; this suggests a means to observe these cusps experimentally. More broadly, our work demonstrates that new insights into evolution can arise from the chemotype perspective, a perspective between the genotype and the phenotype.
Deep Dive into Adaptive mutation of biochemical reaction constants: Fishers geometrical model without pleiotropy.
The distribution of fitness effects of adaptive mutations remains poorly understood, both empirically and theoretically. We study this distribution using a version of Fisher’s geometrical model without pleiotropy, such that each mutation affects only a single trait. We are motivated by the notion of an organism’s chemotype, the set of biochemical reaction constants that govern its molecular constituents. From physical considerations, we expect the chemotype to be of high dimension and to exhibit very little pleiotropy. Our model generically predicts striking cusps in the distribution of the fitness effects of arising and fixed mutations. It further predicts that a single element of the chemotype should comprise all mutations at the high-fitness ends of these distributions. Using extreme value theory, we show that the two cusps with the highest fitnesses are typically well-separated, even when the chemotype possesses thousands of elements; this suggests a means to observe these cusps ex
Adaptive mutation is fundamental to the evolutionary process, and it is medically important to the emergence of drug resistance in microbes [1] and tumors [2]. Given the selective advantage of a mutation, the probability that it fixes in a population (i.e., rises to frequency 1) and the mean time to do so are well-known [3]. Comparatively little is known, however, about the distribution of selective advantages among new mutations. This distribution can be experimentally measured by confronting genetically identical populations with a novel environment such a new food source and measuring the fitness of newly arising mutations [4]. Such measurements are difficult, because adaptive mutations are rare; thus theoretical analysis can offer important insights [5].
A popular predictive framework for studying adaptive evolution is R. A. Fisher’s geometrical model, which considers adaptation in phenotypic “trait” space [6]. Mutations are characterized by the phenotypic changes they induce, which correspond to moves in trait space. Fisher used this model to argue that evolution is primarily driven by the accumulation of many mutations that each have only a small effect [6]. This argument was influential until Motoo Kimura pointed out that mutations with larger effects are more likely to fix, so most adaptive mutations that fix have intermediate effect [7].
Recent studies have applied Fisher’s model to a gamut of questions in evolutionary biology and population genetics; these include the distribution of mutation fitness effects near an optimum [8], sequential adaptation [9,10], and the load of deleterious mutations carried by finite populations [11,12]. Of particular note, predictions from the model regarding epistasis compare favorably with data [13]. The model predicts a roughly exponential distribution of fitness effects for new mutations [14], similar to mutational landscape models of adaptive evolution [15]. This prediction is consistent with experiments in viruses [16] and bacteria [17], although more recent experiments by Rokyta et al. point toward a truncated distribution [18]. Here we consider a geometrical model without pleiotropy, a model in which each mutation affects only a single trait. We are motivated by considering the phenotype at a finer scale than is typical.
One can view the information specifying an organism through a variety of scales [19]. On the largest scale, the phenotype of the entire organism, a single mutation often affects multiple traits, implying substantial pleiotropy. On the finest scale, the genotype, a single mutation often affects only one amino acid codon or one regulatory binding site, implying no pleiotropy. Systems biology is often modeled at the intermediate scale of biochemical reaction constants; multiple codons combine to determine a single biochemical reaction constant and multiple constants combine to determine a single phenotypic trait. Motivated by this useful intermediate level of description, we introduced the word “chemotype” [19] to refer to the set of biochem-ical reaction constants determining the rates of molecular reactions in an organism. Other authors have considered specific biochemical reaction constants to be aspects of the phenotype, for example Hartl, Dykhuizen and Dean [20]. We find it useful to distinguish the chemotype, because it differs in important ways from the large-scale phenotype typically considered.
The chemotype differs from the large-scale phenotype in both dimensionality and pleiotropy. The number of independent high-level phenotypic traits for even a complex organism may be modest [21,22]. The number of independent elements of a chemotype, however, is comparable to the number of an organism’s genes. Each gene codes for a protein or RNA with its own biochemical reaction constants, so each gene contributes at least one element to the chemotype. The chemotype is additionally distinguished by very low pleiotropy, the degree to which single mutations affect multiple traits. Recent experiments on mouse skeletal traits have demonstrated that this system possess a moderate degree of pleiotropy; a given mutation typically affects around five traits [23]. By contrast, a single mutation is expected to affect only one or a few elements of the chemotype. This is because single-nucleotide mutations are dominant in short-term and laboratory evolution [24,25], and they typically change only a single protein residue or a single DNA binding site. Such a change will in turn impact only one or a few biochemical reaction constants, implying very low pleiotropy in chemotype space.
Other authors have considered zero pleiotropy geometric models in the study of drift load [26,12]. We focus here on the distributions of fitness effects of adaptive mutations that arise and that subsequently fix in a population. A general argument shows that these distributions possess sharp cusps, one for each element of the chemotype. Given the high dimensionality of chemotyp
…(Full text truncated)…
This content is AI-processed based on ArXiv data.
