* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download USC3002_2008.Lect5 - Department of Mathematics
Pharmacogenomics wikipedia , lookup
Hybrid (biology) wikipedia , lookup
Polymorphism (biology) wikipedia , lookup
Behavioural genetics wikipedia , lookup
Human genetic variation wikipedia , lookup
Hardy–Weinberg principle wikipedia , lookup
Genetic drift wikipedia , lookup
Gene desert wikipedia , lookup
Genome evolution wikipedia , lookup
Gene therapy of the human retina wikipedia , lookup
Therapeutic gene modulation wikipedia , lookup
Gene expression profiling wikipedia , lookup
Medical genetics wikipedia , lookup
Gene therapy wikipedia , lookup
Public health genomics wikipedia , lookup
Gene expression programming wikipedia , lookup
Gene nomenclature wikipedia , lookup
Vectors in gene therapy wikipedia , lookup
Koinophilia wikipedia , lookup
Nutriepigenomics wikipedia , lookup
The Selfish Gene wikipedia , lookup
Biology and consumer behaviour wikipedia , lookup
Population genetics wikipedia , lookup
Site-specific recombinase technology wikipedia , lookup
Quantitative trait locus wikipedia , lookup
Genetic engineering wikipedia , lookup
History of genetic engineering wikipedia , lookup
Genome (book) wikipedia , lookup
Artificial gene synthesis wikipedia , lookup
Dominance (genetics) wikipedia , lookup
USC3002 Picturing the World Through Mathematics Wayne Lawton Department of Mathematics S14-04-04, 65162749 [email protected] Theme for Semester I, 2008/09 : The Logic of Evolution, Mathematical Models of Adaptation from Darwin to Dawkins Mendel’s Three Laws gene = inheritance factor for a trait alleles = alternative forms of the same gene 1. Law of Dominance : if traits occur in pairs and crossing parents pure for contrasting traits results in offspring having ONLY one [dominant] trait. Phenotype monohybrid-cross Rr x RrRR,Rr,rR,rr ratios are 3:1 2. Law of Segregation : during the formation of gametes (meiosis) the 2 alleles separate and later at fertilization combine to determine the genotype of the offspring 3. Law of Independent Assortment : alleles for different traits are distributed independently, if each trait occurs in a pair with one member of the pair dominant. Phenotype dyhybrid-cross RrGg x RrGg RRGG, RRGg, RrGg,… ratios are 9:3:3:1 http://www.hobart.k12.in.us/jkousen/Biology/mendel.htm Punnett Square http://www.google.com/search?sourceid=navclient&ie=UTF8&rlz=1T4GGLJ_enSG275SG275&q=P%2dSquare+Practice+Page http://www.hobart.k12.in.us/jkousen/Biology/psquare.htm Summary LAW PARENT CROSS OFFSPRING DOMINANCE TT x tt 100% Tt tall x short tall SEGREGATION Tt x Tt INDEPENDENT ASSORTMENT tall x tall RrGg x RrGg round & green x round & green 75% tall 25% short 9/16 round seeds & green pods 3/16 round seeds & yellow pods 3/16 wrinkled seeds & green pods 1/16 wrinkled seeds & yellow pods There you have them, Mendel's huge contributions to the world of science. A very smart cookie. His work has stood the test of time, even as the discovery & understanding of chromosomes & genes has developed in the 140 years after he published his findings. New discoveries have found "exceptions" to Mendel's basic laws, but none of Mendel's things have been proven to be flat-out wrong. Hail to the "Father of Genetics" ! Combinatorics Cyanogenesis in white clover is determined by two pairs of alleles. If the dominant alleles are present (AB) leaves removed from the tree readily release detectable amounts of HCN Gene A Gene B Precursor Substrate HCN If only one gene A is present cyanogenesis is very slow. If A is absent the plant is acyanogenic. Problem: For a cross between plants heterozygous for both alleles, what is the probability that 1. one offspring will be cyanogenic? 2. one of the offspring will be acyanogenic? 3. one of the offspring will show slow cyanogenesis? Combinatoric Answers 1. 9/16 2. ¼ 3. 3/16 Chi-Squared Statistic Experimental results almost always differ from their expected values. Let us quantify this observation. Is the chi-squared statistic d2 with n-1 degrees of freedom e n classes Example: From a cross between Drosophila known to be heterozygous for vestigial wing 100 offspring were obtained; 30 we vestigial winged and 70 normal. Is this a significant deviation from the expected 3:1 ratio? 2 phenotypes observed exp ected d d2 /e 25 5 1 vestigial 30 normal 70 75 5 0.33 NO, a value at least this large with probability about 0.25, at least this small about 0.75, each > 0.05 1.33 2 Pedigree Diagrams A baby died from a fatal recessive disease controlled by a single gene whose frequency in the general population was 1 in 8 million. What was the genotype of his parents? What is the probability that his fathers mother carried the recessive allele? Molecular Genetics 1. Encoding : How is information arranged ? 2. Processing : How is information processed ? 3. Replication : How is the blueprint replicated whenever a cell divides so that each new cell may have a copy ? 4. Mutation : How is the information modified so as to provide new message material ? Definitions Gene: a length of DNA that carries information for the synthesis of a single polypeptide chain (some proteins, such a haemoglobin, can consist of a number of p.c.’s) Genetic Diversity: "The number of genes range from about 1,000 in bacteria and 10,000 in some fungi to 700,000 or more in many flowering plants and a few animals.” http://www.google.com/search?sourceid=navclient&ie=UTF-8&rlz=1T4GGLJ_enSG275SG275&q=genetic+diversity Genetic Code http://img.sparknotes.com/figures/1/132e5720f3b37836571a1aeb9d163ac3/genetic_code.gif Definitions Species: “a group of organisms capable of interbreeding and producing fertile offspring.” “can share a common gene pool” Example: horses and donkeys are not of same species – can breed but produce infertile mules (female horse with male donkey) or hinnys; Great Danes and Chihuahua’s belong to the same species (Canis lupus familiaris) despite the fact that they can not breed but can share same gene pool through Terriers, etc. http://en.wikipedia.org/wiki/Species Sex: “invented some 4 billion years ago by evolving bacteria as a means for shaking up and rearranging a cells instructions for making more cells.” “mutations add new cards to the deck, sex shuffles the deck” Chromosome Linkage http://www.animalgenome.org/edu/genetics/map.html