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Date Created: 09/18/15
MAPPING FUNCTION 12709 As you learned in class as the map distance between two linked genes increases the probability of multiple crossovers between them increases too Thus the observed frequency of crossover recombination between the two genes will underestimate the true map distance between them if the two genes are quite far apart To correct for these underestimateserrors the great geneticist JBS Haldane developed a mapping function ie an equation to correct for these underestimates due to multiple crossovers His mapping function relies on the Poisson equation so you should refer back to the Poisson web handout available at our course web site Once again the Poisson equation is X Px m39e m X where m is the mean number of events for a defined unit of space or time eg crossovers per meiosis x is the number of successes e g specific number of actual crossovers and e is the natural base 2717271727 We are interested in the special case of having x 0 or no crossovers Plugging x 0 into the above equation reduces it to P 0 m0 01 e e If 6quot refers to the probability of having no crossover then 1 7 6quot is the probability of having one or more crossovers Haldane noted that this probability is the one that underlies the frequency of recombination RF That is one or more crossovers contribute to the recombination frequency He formalized this in his following equation RF 05 1 am The 05 is for the fact that any crossover affects only two of the four chromatids of a tetrad as we noted in class As an example let s say that the observed recombination frequency is 275 0275 Then plugging this into Haldane s equation we get 0275 05 1 e39m Rearranging this equation we can solve for 6quot em 1 2 x 0275 045 We can now take logg In or the natural log of both sides of this equation and then solve for m In this way m 08 Thus on average there are 08 crossovers per meiosis for this chromosomal region Again because any crossover affects only two of four chromatids of a tetrad for every 08 crossovers 04 chromatids will be affected Thus the expected frequency of recombinants in a test cross will be 04 We can now convert this recombination frequency into map units or centimorgans resulting in a corrected map distance of 04 cM Note that the observed recombination frequency was originally 0275 In contrast the Haldane corrected recombination frequency is 04 This is a fairly substantial increase implying that considerable multiple crossovers are expected and were likely overlookednot counted by the original observed recombination frequency 12709 B COMPLETE LINKAGE no crossover cis dihybrid Fruit ies e es w1n s pr red vg full pr 7 purple Vg 7 vestigial Pro en eno es Abbreviated geno pes Pheno pes 050 pr pr vg vg 05011715r ngr 050 red full 050 prpr vg Vg 050 pr Vg 050 purple vestigial C COMPLETE LINKAGE no crossover trans dihybrid Pro en eno es Abbreviated geno pes Pheno pes 050 pr pr Vg vg 050 pr vg 050 red vestigial 050 prpr vg vg 050 pr vg 050 purple full LINKAGE AND CROSSING OVER XO Variation is bene cial a species best bet for adaptation in an everchanging unpredictable environment Independent assortment maximizes variation eg four test cross phenotypes each at equal frequency Linkage minimizes variation ie two test cross phenotypes only with complete linkage XO restores some of the variation lost by linkage ie four test cross phenotypes but at unequal frequencies Why linkage For gene organization easier to organize 24 human chromosomes than 30000 genes mgapmr D INCOMPLETE LINKAGE crossover cis dihybrid Abbreviated geno pes Number relative 11 Parental or recombinant 1 pf Vg 1339 047 Parental red full 2 pr Vg 1195 042 Parental purple vestigial 3 pr Vg 151 005 Recombinant red vestigial 4 pr vg 154 005 Recombinant purple full Total 2839 100 CHISQUARE TEST OF LINKAGE H0 Two genes unlinked so independent assortment and eXpectation of 11 1 1 phenotypic ratio in test cross H1 Two genes linked so no independent assortment or eXpectation of 111 1 phenotypic ratio in test cross Pheno pesgeno pes Observed Expected 10 7 Ef E pr vg 1339 025 2839 70975 1339 7 709252 70975 5592 pr vg 1195 025 2839 70975 1195 7 709752 70975 3318 pr vg 151 025 2839 70975 1517 709752 70975 4399 pr vg 154 025 2839 70975 154 7 709752 70975 4352 Totals 2839 2839 x2 67989 df4713oc005 gt As P x2 67989 ltlt on see Table 22 reject H0 in favor H1 two genes are most likely linked RECOMBINATION CROSSOVER AND MAPPING Recombination frequency RF Proportion of recombinant chromosomes or offspring phenotypes 1 RF 1 map unit 1 centiMorgan cM A single crossover affects only two of the four chromatids of a tetrad in prophase I meiosis Female Drosophila crossover male Drosophila don t cM map distances can be used to predict the progeny of genetic crosses The positive relationship between crossover frequency and map distance can be easily eXplained khwa MAP DISTANCES AND GENETIC CROSSES Problem 7 These 2 genes linked to same autosome by map distance of 20 cM Predict progeny phenotype frequencies from test cross with trans dihybrid individual Fruit ies body color wings e gray cu straight e 7 ebony cu curly THREE POINT GENE TEST CROSS Fruit ies e es wing veins wing edges V red cv crossveins ct straight V 7 vermillion CV 7 crossveinless ct 7 cut Test cross TC V V CV CV ct ct X V V CV CV ct ct Progeny offspring XO class gamete l V CV CH 94 2 V CV Ct 3 3 V CV CH 45 4 V CV CH 580 5 V CV Ct 40 6 V CV Ct 89 7 V CV Ct 592 8 V CV CH 5 Total 1448 gt DETERMINING GENE ORDER lVIIDDLE GENE 2 X0 class Closest 0 X0 class Displaced gene 2 X0 class 2 V Cv Ct 4 V cv Ct Ct 8 V CV CH 7 V CV Ct Ct gt CALCULATING CM DISTANCES 1 X0 classes m Closest 0 X0 class Displaced gene 1 X0 class 1 V CV CH 94 4 V CV Ct v 3 V CV CH 45 4 V cv Ct CV 5 V CV Ct 40 7 v CV Ct cv 6 V CV Ct 89 7 v CV Ct V DOES FIRST X0 INFLUENCE A SECOND gt Coefficient of coincidence CC observed double XO eXpected double XO gt Interference I l 7 CC CC 0 1 gt1 I 1 0 lt0 Positive interference 2 crossovers independent Negative interference rst inhibits second rst stimulates second GENETIC MARKERS A Polymorphic variable DNA sequences used to distinguish among alleles genes individuals andor populations B These polymorphic sequences can differ by one base single nucleotide polymorphisms SNPs or can correspond to allele differences at a reference gene C Often their map positions are known thereby making them particularly powerful for positional cloning POSITIONAL CLONING Association of trait to known genetic marker thereby greatly facilitating search for its gene A Hypothetical species 211 4 1 025 D d C c 2 025 D d c c 3 025 ddC c 4 025 d d c 0 independent assortment B Same species same test cross but different disease Neurodegenerative disease D disease d healthy 1 025Dde 1 050DdAa 2 025Ddbb 2 050ddaa 3 025 ddB b 4 025 ddb b linked but far apart Tightly linked Ie test cross of same heterozygote from above left who is also a Z 2 heterozygote 1 05022Cc 1 025Zsz 1 025Z2Aa 2 050chc 2 025Z2bb 2 025Z2aa 3 0252231 3 02522Aa 4 02522171 4 02522616 Progeny Genotype f Muscular disease Z disease 2 healthy Progeny Genotype f PROBLEMS Chapter 5 problems 4 5 9 10 15 18 20 24 1608 1 Theory Hypothesis that has withstood critical testing to the point where it is as close to truth as possible in science 2 Law of equal segregation Factors alleles come in pairs that separate segregate into different gametes during meiosis 3 Multiplication rule Probability of two or more independent events occurring together is the product of their separate probabilities 4 Addition sum rule Probability that any one of two or more mutually exclusive events occurring is the sum of their separate probabilities 5 Independent assortment Factors alleles for different traits unlinked genes are shuf ed into gametes independently randomly by chance of each other 6 Recombination Generation of new progeny genotypesphenotypes from those of their parent s by segregationindependent assortment unlinked genes and crossover for linked genes GENERAL TERMS that we assume you know Please refer to your tethook as needed chromosome gene allele diploid 2n haploid 11 homologous chromosome homologue nonhomologous chromosome chromosome types genotype phenotype heterozygous homozygous dominant recessive MODEL SPECIES Genome size Viruses Bacteriophage T2 or T4 180 kb kilobases 1000 base pairs or bp Bacteriophage lambda 7L 50 kb Bacteria Escherichia 001139 E coll 46 mb megabases 1 million bp Eukaryotes Fungi Saccharomyces cerevisiae yeast 121 mb Neurospora crassa bread mold 40 mb Plants Arabidopsis thaliana mustard weed 125 mb Oryza sativa rice 420 mb Pisum sativum peas Animals Caenorhabditis elegans nematode worm 97 mb Drosophila melanogaster fruit y 180 mb Mus domesticus mouse 3 gb gigabases 1 billion bp Homo sapiens human 32 g General characteristics gt Practical easy to raise and cross short generation times lot of progeny wellstudied gt Tradeoff between simple to study versus compleX relevant to humans gt Each brings something special or unique to the study of genetics VERY BRIEF IHSTORY OF GENETICS 500 BC Greeks gemmules Aristotle to 1639h century Male provides form and instructions female provides substance for offspring 1739h century Homunculus 1839h to 1939h centuries Blending and particles Gregor Mendel 18221884 Experiments in Plant Hybridization 1866 1868 Meischer nuclein nucleic acids discovered 1900 Rediscovery of Mendel s work 1902 Chromosome theory of inheritance 1953 Watson and Crick the double heliX 1990 Gene therapy rst clinical trials 2001 Completion of the draft 90 done human genome HHWWSQMWNB D IO39 Practical Peas easy to growcross short generation times with many progeny focused on distinct discontinuous traits GREGOR MENDEL 2 Excellent experimental scientist adhered to the scienti c method 1822 1884 3 Statististics Mathematical analysis of data 4 Lucky 7 traits 7 chromosomes in peas yet no eVidence of linkage see page 133 1 Lots of variation among geneticists and species but we ll try to use the following scheme as much as possible GENETIC 2 Dominant condition 7 Provides singleletter code for gene its allele is capitalized SYMBOLISM Recessive condition 7 Same singleletter code as in 2 above but its allele is lowercase 3 When referring to gene or allele formally italicize name When referring to protein for gene no italics 1809 l Pedigree Family tree or genealogy often used as basis to study the transmission genetics of some specific trait 2 Rare conditiontrait Mutation or outside introduction for that feature occurs only once within the pedigree 3 Propositus Affected individual who draws attention of geneticistphysician to family 4 Probability Relative frequency of an event or outcome 5 Developmental noise Phenotypic variation due to random developmental uctuations in cell number cell movement and the like 6 Epistasis Qualitatively mutant alleles of one gene mask expression of alleles of another gene Quantitatively non additive non independent interactions of two or more genes 1 Generations numbered with Roman numerals from oldest top to youngest bottom HUMAN 2 Within a generation individuals numbered with Arabic numerals from left to right PEDIGREES 3 Within a single family children of the motherfather presented from oldest left to youngest right 4 Autosomal or sex linked If autosomal both sexes affected If sex linked primarily males affected 5 Dominant or recessive If dominant then variable offspring possible when identical parents crossed If recessive only offspring with the same phenotype as two parents will be produced 6 ominant or recessive If dominant then in a family with affected children at least one parent must also be affected RELATION g EXPLANATION GENETIC Monozygotic twins 100 From same fertilized egg RELATEDNESS Motherfather 000 Unrelated Motherchild 050 Half DNA from mother other half from father Fatherchild 050 Half DNA from father other half from mother Full siblings 050 To discuss s Expected probability of having shared alleles where shared is specifically defined as shared through direct descent l Mulitiplication rule Probability of 2 or more independent events occurring together is the product of their separate probabilities PROBABILITY RULES 2 Addition rule Probability that any 1 of 2 or more mutually exclusive events occurring together is the sum other separate probabilities 3 Conditional probability Relative frequency of an event given certain conditions or knowledge 4 Law of large numbers As sample size increases estimate of a population parameter converges onto its true value n PXaY quy Jay n trials x y n BINOMIAL x event 1 p q l EQUATION y event 2 P x y probability of x y combination 1 probability of event 1 q probability of event 2 n x y Pxyz 9 q rZ x y z n trials x y z n MULTINOMIAL x event 1 p q r l EG TRINOMIAL y event 2 P x y z probability of x y z combination EQUATION z event 3 p probability of event 1 q probability of event 2 r probability of event 3 MENDELIAN INHERITANCE 2 alleles 1 gene vs multiple alleles Complete 39 vs 39 1 and overdominance l trait 1 gene vs epistasis modifier genes and quantitative inheritance Biparental nuclear genes vs extranuclear inheritance Genotype determines phenotype vs phenotype determined by genotype environment and developmental noise 6 Independent assortmentunlinked genes vs different patterns of linkage see below I MbWNH EXTENDING MENDELIAN RULES A Phenotype Interallelic interactions intergenic interactions environment developmental noise B Linkage relationships of genes to their chromosomes and each other 1 Autosomal linkage 2 Sex linkage 3 Extranuclear linkage F2 PHENOTYPES DOMINANCE 14 AA 2 Aa 14 aa HETERO7YGOTE Complete tall tall dwarf Indistinguishable from homozygous dominant peas height Incomplete red pink white Intermediate to 2 homozygous extremes four o clocks ower color Codominance type A type AB type B Both alleles fully expressed in heterozygote humans ABO blood types Overdominance large largest small Exceeds both homozygous phenotypes Arabidapsis plant size Sex in uenced Male bald bald not bald Dominance varies with sex humans Female bald not bald not bald pattern baldness Sex limited Male N 0 milk production no milk Trait restricted to one sex mammals Female Produces milk milk capacity to produce milk SEX INFLUENCED DOMINANCE SEX LIMITED EXPRESSION Both encoded by autosomal genes not sex linked genes PHENOTYPE ABO BLOOD TYPE GENOTYPES ANTIBODIES ANTIGENS A i anti B carbohydrate A B IB 8 IB i anti A carbohydrate B AB universal recipient IA IB none carbohydrates A and B O universal donor i i anti A and anti B none ANTIBODY AB Protein produced in response to antigen ANTIGEN AG Cell surface molecule eliciting immune response Ie carbohydrate on surface red blood cells RBC l Epistasis One gene affects the expression of another gene in a non additive non independent manner 2 Modifier gene One gene increases or decreases expression of another gene EPISTASIS 3 Suppressor Modifier gene that decreases expression of mutant allele at another gene thereby restoring the normal condition at this other gene INTERGENIC INTERACTION F1 PHENOTYPES F1 GENOTYPES DESCRIPTION Sweet peas ower 916 blue 916 AB Complementary color 716 White 316 Abb 316 aaB 116 aabb epistasis Shepard s purse 1516 triangular 916 AB 3 16 Abb 316 aaB Duplicative epistasis ower color 1 16 ovoid 1 16 aabb Blue eyed Mary 9 16 blue 9 16 AB Another form of ower color 3 16 magenta 3 16 Abb complementary 416 White 3 16 aaB 1 16 aabb epistasis Fruit ies eye color 1316 red 916 AB 316 Abb 116 aabb Suppresor 316 purple 316 aaB PROBLEMS Chapter 3 2 7 8 15 l6 17 20 23 24 26 27 28 30 32 36 Chapter 4 1 3 6 10 l2 l6 17 21 22 34
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