Universality and predictability in molecular …

1 COGEDE-1039; NO. OF PAGES 10 Please cite this article in press as: Nourmohammad A, et al.: Universality and predictability in molecular quantitative genetics, Curr Opin Genet Dev (2013), and predictability in molecular quantitative geneticsArmita Nourmohammad1,3, Torsten Held2,3and Michael La ssig2 molecular traits, such as gene expression levels or proteinbinding affinities, are increasingly accessible to quantitativemeasurement by modern high-throughput techniques. Suchtraits measure molecular functions and, from an evolutionarypoint of view, are important as targets of natural selection. Wereview recent developments in evolutionary theory andexperiments that are expected to become building blocks of aquantitative genetics of molecular traits.

2 We focus on universalevolutionary characteristics: these are largely independent of atrait s genetic basis, which is often at least partially show that universal measurements can be used to inferselection on a quantitative trait, which determines itsevolutionary mode of conservation or adaptation. Furthermore, Universality is closely linked to predictability of trait evolutionacross lineages. We argue that universal trait statistics extendsover a range of cellular scales and opens new avenues ofquantitative evolutionary systems Laboratories of Physics and Lewis-Sigler Institute forIntegrative Genomics, Princeton University, Princeton, NJ 08544, UnitedStates2 Institut fu r Theoretische Physik, Universita t zu Ko ln, Zu lpicherstr.

3 77,50937, Ko ln, GermanyCorresponding author: La ssig, Michael authors contributed equally to this Opinion in Genetics & Development 2013, 23:xx yyThis review comes from a themed issue on Genetics of systembiologyEdited by Shamil Sunyaev and Fritz Roth0959-437X/$ see front matter, Published by Elsevier traits are important links between geno-types, organismic functions, and fitness. For some mol-ecular traits, recent sequence data and high-throughputtrait measurements have produced quantitative geno-type phenotype maps. Examples include thesequence-dependent binding of transcription factorsand histones to DNA, and the formation of RNA second-ary structures.

4 For the vast majority of complex traits,however, quantitative genotype phenotype maps are outof reach. Even comparatively simple molecular traits,such as gene expression levels, depend on a mosaic ofcis-acting and trans-acting sequence loci. We do not knowtheir precise numbers, positions and trait amplitudes, norrelevant evolutionary rates such as the amount of recom-bination between these loci [1]. This lack of knowledgebegs an obvious question: Which evolutionary propertiesof a quantitative trait are universal, that is, independent ofthese molecular details? In particular, can we formulatenatural selection on quantitative traits and their resultingmodes of evolution independently of their genetic basis?

5 This article is on Universality in molecular evolution. Weintroduce Universality as an emerging statistical propertyof complex traits, which are encoded by multiple genomicloci. We give examples of experimentally observableuniversal trait characteristics, and we argue that univers-ality is a key concept for a new quantitative genetics ofmolecular traits. Three aspects of this concept are dis-cussed in detail. First, universal statistics governs evol-utionary modes of conservation and adaptation forquantitative traits, which can be used to infer naturalselection that determines these modes. Furthermore,there is a close link between Universality and predict-ability of evolutionary processes.

6 Finally, universalityextends to the evolution of higher-level units such asmetabolic and regulatory networks, which provides a linkbetween quantitive genetics and systems in molecular evolutionIn a broad sense, Universality means that properties of alarge system can become independent of details of itsconstituent parts. This term has been coined in statisticalphysics, where it refers to macroscopic properties of largesystems that are independent of details at the molecularscale [2]. For example, the amount of fluid running througha tube per unit time depends only on the viscosity of thefluid, the diameter of the tube, and the pressure gradient,but not on the detailed chemical composition of the , rather different fluids have the same flux propertiesas long as their viscosity is the same.

7 This a strong,experimentally testable statement. It is not always true:if the tube narrows at some point into a nozzle, the fluidbecomes turbulent and other things besides viscosity mat-ter. This tells another upfront message: Universality isusually not a mathematical identity, but an approximationthat is accurate in some cases but not in also arises in evolutionary biology. As inphysics, it is a property of systems with a large numberof components, and it has strong consequences for exper-iment and data analysis. In the following, we will discuss anumber of examples, and we will pinpoint these com-ponents and experimental consequences in each population genetics, Kimura s celebrated diffusionmodel for the evolution of allele frequencies is a universalAvailable online at Current Opinion in Genetics & Development 2013, 23:1 10description [3].

8 The Kimura model predicts that thefrequency distribution of mutant alleles in a large popu-lation depends only on the size of the population and theselection coefficients of the alleles, but not on the detailsof the reproductive process of individuals. Many moredetailed models of reproduction, including the Wright Fisher process [4], the Moran process [5], and branchingprocesses [6], have a common diffusion limit in largepopulations. Importantly, the universal frequency spectraof the Kimura model are statistical quantities; observingsuch spectra requires frequency data from a large numberof segregating alleles in a population. Hence, the uni-versal spectrum most frequently observed in genomicdata is the famous inverse-frequency form for synon-ymous alleles, which evolve near neutrality.

9 For allelesunder selection, Universality is often confounded by theheterogeneity of selection coefficients at different geno-mic may arise even in Darwinian evolution understrong selection, for example, in rapidly adapting asexualpopulations. Due to the lack of recombination, compe-tition between simultaneously spreading beneficialmutations leads to complex patterns of rise and fall intheir population frequencies. However, if an adaptiveprocess is carried by a large number of segregating alleles,it can be described in a simpler way by a so-calledtraveling fitness wave [7 12,13 ,14 ,15,16 ]. The speedof this wave, which is also referred to as fitness flux [17],becomes a universal quantity: it depends primarily on rateand average effect of beneficial mutations, but not on thedetailed distribution of their selection coefficients[10,12,14 ,16 ].

10 In other words, the fitness flux decouplesfrom details of the underlying genomic evolution. Moregenerally, the distribution of fixed mutations becomesinsensitive to the details of genomic fitness effects andcan be characterized by only a few effective parameters[10,14 ,16 ]. This feature has also been observed in amicrobial evolution experiment under strong selectionpressure [18]. Another striking universal feature emergesfor passenger mutations carried to fixation by hitchhik-ing with linked beneficial alleles: their substitution ratebecomes independent of their selection coefficients andclose to the neutral mutation rate [19,14 ,15]. This effectincreases the substitution rate of deleterious mutations,which may have significant impact on the adaptivedynamics of pathogens [20] and on cancer progression[21].