Neutral theory 3: Rates and patterns of molecular evolution Predictions of the neutral theory 1. Within species variation is correlated with divergence between species. 2. Evolutionary rate is inversely related functional constraint. 2. Base composition at neutral sites reflects mutational equilibrium. 4. A molecular clock. Neutral theory is “the” rigid null hypothesis for molecular evolution 1
1. Polymorphism and divergence are correlated Neutral theory is a bridge between microevolution and macroevolution Neutral population polymorphism within species is correlated with neutral divergence between species 1. Variation within and among species: polymorphism & divergence This is one place where the genetic code is relevant: 1. Synonymous (S) 2. Non-synonymous (NS) Neutrality and selection have different impacts on polymorphism: 1. Neutrality: NS residence times determined by N e 2. Selection: NS residence times reduced by natural selection Let’s look at the ratio NS:S [ratio of counts] 2
1. Variation within and among species: polymorphism & divergence Comparison of the ratio of synonymous and nonsynonymous polymorphism within species to divergence between species. Neutral theory suggests that the fraction of variation that is nonsynonymous within species should be the same as between species. Species 1 Species 2 Species 3 6:2 10:3 12:4 Polymorphism within a Genealogies within species populations 17:6 14:5 19:6 Substitutions between species Species level phylogenies Synonymous (S) Non-synonymous (NS) S:NS Polymorphic 28 9 3.1 Fixed 50 17 2.9 Data are hypothetical. Ratios are tested by using a G-test on the counts of S and NS. These hypothetical data are not significant. If positive selection were acting, residence times for NS would be lower within species and polymorphic S:NS > fixed S:NS. 2. Rate of evolution is inversely related to functional constraint Rate variation is well known: • Fast genes (D-loop) verses slow genes (Histones) • Introns verses exons • Synonymous verse nonsynonymous sites Neutral theory is consistent with such rate variation - Asserts only that polymorphism is selectively equivalent - Frequency of such polymorphism can change among genes, sites etc. 3
Note: two ways it is commonly measured 10 20 30 40 50 60 ....|....| ....|....| ....|....| ....|....| ....|....| ....|....| Mus2.FAS MTTPALLPLS -----GRRIP PLNL--GPP- ----SFPHHR ATLRLSEKFI LLLILSAFIT Human_GIA ---------- ---------- ---------- -----MNSNF ITFDLKMSLL PSNLFSAFIT Human_GIB MTTPALLPLS -----GRRIP PLNL--GPP- ----SFPHHR ATLRLSEKFI LLLILSAFIT Mus_GIA MPVGGLLPLF SSPGGGGLGS GLGGGLGGG- ----RKGSGP AAFRLTEKFV LLLVFSAFIT Rabbit_GIA ---------- ---------- ---------- ---------- ---------- ---------- Sus_GIA MPVGGLLPLF SSPAGGGLGG GLGGGLGGGG GGGGRKGSGP SAFRLTEKFV LLLVFSAFIT 70 80 90 100 110 120 ....|....| ....|....| ....|....| ....|....| ....|....| ....|....| Mus2.FAS LCFGAFFFLP DSSKHKRFDL G-LEDVLIPH VDAGKG---- AKNPGVFLIH GPDEHRHREE Human_GIA LCFGAIFFLP DSSKLLSGVL FHSSPALQPA ADHKPGPGAR AEDAAEGRAR RREEGAPGDP Human_GIB LCFGAFFFLP DSSKHKRFDL G-LEDVLIPH VDAGKG---- AKNPGVFLIH GPDEHRHREE Mus_GIA LCFGAIFFLP DSSKLLSGVL FHSNPALQPP AEHKPGLGAR AEDAAEGRVR HREEGAPGDP Cebus Rabbit_GIA ---------- ---------- ---------- ---------- AEDAADGRAR PGEEGAPGDP Saimiri Sus_GIA LCFGAIFFLP DSSKLLSGVL FHSSPALQPA ADHKPGPGAR AEDAADGRAR PGEEGAPGDP Aotus Callithrix Lagothrix Brachyteles Alouatta Ateles Pan Homo Pongo Macaca Hylobates Tarsius Galago Otolemur Cheirogaleus 0.01 Eulemur Ave of all pairwise distances Tree length 2. Rate of evolution is inversely related to functional constraint Mean number of substitution per site at the three codon positions of the epsilon-globin gene of primates. Two measures are presented: (i) the average over all pair wise comparisons between genes; and (ii) the sum of the branch lengths of the epsilon globin gene tree. Mean number of substitutions/site Cebus Saimiri Aotus 0.15 0.8 Callithrix subst/site as a sum pairwise subst/site Lagothrix 0.6 0.1 Brachyteles over tree Alouatta 0.4 Ateles 0.05 Pan 0.2 Homo 0 0 Pongo Macaca 1 2 3 Hylobates Codon position Tarsius Galago mean pairwise subst rate Otolemur Subst rate as a sum of branch lengths Cheirogaleus 0.01 Eulemur Under both measures of substitution rate, 3rd codon positions evolve faster than 1 st and 2 nd positions. Gene tree for primate epsilon globins Note: mean number of substitutions per site were computed in all cases by using the Jukes and Cantor (1969) correction. 4
2. Rate of evolution is inversely related to functional constraint Neutral Model Beneficial: rare and frequency quickly goes to zero Deleterious: frequency = f D f 0 = 1 - f D Neutral: frequency = f 0 Kimura, 1968: The neutral mutation rate per site is: µ 0 = µ T f 0 The neutral substitution rate per site is: k = µ T f 0 2. Rate of evolution is inversely related to functional constraint The rate of evolution depends on the “size ( f 0 ) of the selective sieve” New mutations New mutations Fixation in a “fast gene” Fixation in a “slow gene” Kimura’s f 0 is the fraction of mutations that passes through the “sieve”. 5
2. Rate of evolution is inversely related to functional constraint Example: 3 rd codon positions verses synonymous sites Some changes at 3 rd codon positions are NOT synonymous Prediction: f 0 for 3 rd codon positions < f 0 for synonymous sites 1. rate 3 rd codon positions < rate for synonymous sites 2. 2. Rate of evolution is inversely related to functional constraint The average substitution rate between primates and rodents is higher for synonymous sites as compared with third codon positions. The results are based on a sample of 82 nuclear genes. 45 Mean at 3 rd positions: 0.40 Primate Rodent 40 gene gene Mean at synonymous sites: 0.61 35 number of proteins 30 25 20 t 1 15 t 0 10 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 More substitutions / site / 2x80 million years Ancestral gene 3rd codon postions Synonymous sites Mean number of substitutions per site This result is consistent with neutral theory given that between primates and rodents is t = t 0 + f 0 is smaller for 3 rd codon positions because some t 1 . The unit of time is 2 × 80my; the time mutations at such site will be nonsynonymous. since primates and rodents shared a common ancestor. Data from Bielawski, Dunn and Yang (2000) Genetics. 156:1299-1308. 6
2. Rate of evolution is inversely related to functional constraint We can put sites into a wide variety of categories: • 5’ and 3’ flanking regions • 5’ and 3’ untranslated regions • Introns • Exons • 3 rd positions of 4-fold degenerate codons • Nonsynonymous sites of a codon • Functional domains • Pseudogenes 2. Rate of evolution is inversely related to functional constraint Comparison of mean substitution rates in different parts of genes and pseudo-genes. Data is from Li et al. (1985). Substitution rate is the mean number of substitutions per site per 10 9 years. Rates are an average over 3000 mammalian genes. 5 Substitutions per site per 10 9 years 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 Introns 5' flanking region 5' untranslated region Non-synonymous sites Syonymous sites 3' untranslated region 3' flanking region Pseudogenes 7
2. Rate of evolution is inversely related to functional constraint Sites subject to selection will have variable f 0 depending on the level of functional constraints acting on that site: 1. Nonsynonsymous sites 2. Functional domains 3. Etc. 2. Rate of evolution is inversely related to functional constraint Multiple sequence alignment of four vertebrate beta-globin genes representing 450 million years of evolution. Amino acids shaded in green represent sites that appear conserved for over those 450millin years. Note: many of the shaded sites are located in the heme pocket or at the interfaces between globins subunits, consistent with the notion that sites most critical to protein function evolve at the slowest rates. 8
2. Rate of evolution is inversely related to functional constraint Substitution rate differs in different polypeptide domains of preproinsulin. C chain : 1.1 × 10 -9 / site / year 5 fold higher rate in C chain A&B chains : 0.2 × 10 -9 / site / year Note that c-chain rate is still lower than in many other proteins, and at synonymous sites, so its amino acid sequence must still has considerable functional importance to the protein, probably in folding to lowest free energy so that disulfide bonds can be formed. 2. Rate of evolution: differences among genes Let’s estimate the width of the selective sieve: Under neutral theory: • The synonymous substitution rate ( k S ) is equal to the neutral mutation rate. • The nonsynonymous substitution rate ( k N ) measures the substitution rate for neutral amino acid changes. • Thus the ratio of these rates ( k N / k S ) represents the fraction of amino acid mutations that are neutral: this is f 0 for amino acids • The fraction of amino acid mutations that are deleterious ( f D ) must be 1 - ( k N / k S ). Let’s take the Neuroleukin gene of primates as an example: k N = 0.016 k S = 0.300 The fraction of amino acid changes that are neutral is 0.016/0.300 = 0.053, a small amount. Hence the fraction of amino acid changes that are deleterious is 1 - 0.053 = 0.95! 9
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