Genome Evolution Course 2009-2010

www.yanaiweb.com/genome

Itai Yanai, Technion – Israel Institute of Technology

Exercise Presentation as PP or PDF: Problem Set 4 – Neutral Evolution

Problem Set #4 assigned November 15^th, 2009

To be submitted as hard-copy in English or Hebrew on November 22^nd, 2009 (at the beginning of class, 9:30am).

E-mail submissions will not be accepted.

Problem 1: The forces of molecular evolution. Kimura argued in 1968 that there was not enough time for natural selection to cause the amount of divergence observed and proposed that most of the changes are neutral with regard to their fitness. What evolutionary force fixes a neutral mutation in the population?

Problem 2: A beautiful equation, k=m. Consider two populations of size X and 2X, respectively. The population that is twice as large generates twice as much variation each generation (given the same mutation rate). The bigger population will thus have faster rate of divergence. Explain the error in this argument. In other words, why does the rate of substitution not depend on the population size?

Problem 3: Slightly advantageous mutations. An interesting aspect of the neutral theory is that mutations with small selective fitness (s) will act as though they are neutral. Show that for s = 1/(4N), where N is the population size, the substitution rate (k) is the same as for neutral mutations.

Problem 4: Properties of the genetic code. Choosing one of the 61 codons at random, I change one of the three nucleotides to another nucleotide, thus altering it to another codon. What is the probability that the new codon will be synonymous the original?

Problem 5: Learn by doing. Calculate K_S and K_A for between the human and mouse Mgst3 gene (microsomal glutathione S-transferase 3) according to the Li, Pamilo, and Bianchi presented in class. Make sure to provide the B₀ B₂ B₄ A₀ A₂ A₄ L₀ L₂ and L₄ that were the basis for your calculations.

NM_004528.2      ATGGCTGTCCTCTCTAAGGAATATGGTTTTGTGCTTCTAACTGGTGCTGCCAGCTTTATA 60

NM_025569.1      ATGGCTGTCCTCTCTAAGGAGTATGGATTTGTGCTTCTCACTGGTGCTGCCAGCTTTGTG 60

                 ******************** ***** *********** ****************** *

NM_004528.2      ATGGTGGCCCACCTAGCCATCAATGTTTCCAAGGCCCGCAAGAAGTACAAAGTGGAGTAT 120

NM_025569.1      ATGGTGCTCCACCTAGCCATCAACGTGGGCAAAGCCCGCAAGAAGTACAAGGTAGAGTAC 120

                 ******  *************** **   *** ***************** ** *****

NM_004528.2      CCTATCATGTACAGCACGGACCCTGAAAATGGGCACATCTTCAACTGCATTCAGCGAGCC 180

NM_025569.1      CCTGTCATGTACAGCACAGATCCTGAGAACGGGCATATGTTCAACTGCATTCAGCGCGCC 180

                 *** ************* ** ***** ** ***** ** ***************** ***

NM_004528.2      CACCAGAACACGTTGGAAGTGTATCCTCCCTTCTTATTTTTTCTAGCTGTTGGAGGTGTT 240

NM_025569.1      CACCAGAACACGTTGGAGGTGTACCCTCCCTTCCTGTTTTTCCTAACGGTGGGAGGTGTT 240

                 ***************** ***** ********* * ***** *** * ** *********

NM_004528.2      TACCACCCGCGTATAGCTTCTGGCCTGGGCTTGGCCTGGATTGTTGGACGAGTTCTTTAT 300

NM_025569.1      TACCACCCGCGCATAGCTTCTGGCCTGGGCCTGGCCTGGATTATTGGGCGAGTCCTTTAC 300

                 *********** ****************** *********** **** ***** *****

NM_004528.2      GCTTATGGCTATTACACGGGAGAACCCAGCAAGCGTAGTCGAGGAGCCCTGGGGTCCATC 360

NM_025569.1      GCATATGGCTACTACACAGGAGACCCTAGCAAGCGGTATCGAGGAGCCGTGGGCTCTCTT 360

                 ** ******** ***** ***** ** ********   ********** **** **  *

NM_004528.2      GCCCTCCTGGGCTTGGTGGGCACAACTGTGTGCTCTGCTTTCCAGCATCTTGGTTGGGTT 420

NM_025569.1      GCCCTCTTTGCCCTGATGGGCACCACCGTGTGCTCTGCTTTCCAGCATCTCGGCTGGATC 420

                 ****** * * * ** ******* ** *********************** ** *** *