2 Kings 6 17 17 And Elisha prayed

Mendelian Genetics Timothy G. Standish, Ph. D. © 2000 Timothy G. Standish

Biography - Gregor Mendel �Father of classical genetics. �Born 1822 to peasant family in

Biography - Gregor Mendel: �Attended Education University of Vienna 1851 1853. Influenced by: –

Biography - Gregor Mendel: Research �Studied peas which he grew in a garden outside

Biography - Gregor Mendel: � 1865 Publication and Death first reported results of his

Biography - Gregor Mendel: �Mendel’s Rediscovery work was rediscovered in 1900 by three botanists:

Why Peas? � Mendel used peas to study inheritance because: � True breeding commercial

Why Peas? � Pea flowers are constructed in such a way that they typically

Why Peas? � By removing the anthers of one flower and artificially pollinating using

Mendel’s Results � When crossing purple-flowered peas with white-flowered peas, Mendel got the following

Interpreting Mendel’s Results � Because the F 1 generation did not produce lightpurple flowers

Interpreting Mendel’s Results � In the F 1 generation, the white allele was hidden

Trait Mendel’s Results F 1 Results F 2 Results Dominent traits round/wrinkled All Round

F 2 Results Mendel’s Results Seeds F 2 Ratios Seeds 5, 474 Round 1,

� Statistics Chi Square fall into two categories: 1 Descriptive - Summarize characteristics of

Chi Square: On Mendel’s Seed Texture Data 2 Chi Square: d = = 2

Chi Square: On Mendel’s Flower Color Data 2 Chi Square: d = = 2

Mendel’s Conclusions 1 Phenotypic traits are controlled by pairs of genes which act as

Mendel’s Experiment: A Case Study In Good Science �Gregor Mendel’s investigation of principles of

Mendel’s Dihybrid Cross � Mendel chose to see if the round and yellow seed

3 Reasons Mendel’s Work Was Ignored �Mendel was not on the ball �Biologists were

Reasons Mendel’s Work Was Ignored: 1) Mendel was not on the ball �Wrote in

Reasons Mendel’s Work Was Ignored: 2) Biologists were idiots �Biologists didn’t understand math �Biologists

Reasons Mendel’s Work Was Ignored: 3) Lack of independent supporting discoveries: �There was no

Chromosomes: The Physical Basis of Inheritance � 1866 Mendel published his work � 1875

Chromosomal Theory of Inheritance �Genes have specific loci on chromosomes. �Chromosomes undergo segregation (meiosis)

r r e e h ot ath M F E Chromosomal Theory of Inheritance

Independent Assortment Eggs As long as genes are on different chromosomes, they will assort

Two Genes On One Chromosome Telophase I Prophase I Replication r r e e

� Because Laws Of Probability alleles are usually distributed randomly, the laws of probability

Determination of Gamete and Zygote Variability Number of Heterozygous Pairs n 1 2 3

Laws Of Probability: 1 Product Law l l l The “and” law Describes the

Laws Of Probability: 2 Sum Law l l l The “or” law Describes the

Laws Of Probability: 3 Conditional Probability l l Probability of events in which both

Laws Of Probability: 4 Binomial Expansion The probability of a set of events arranged

Slides: 42

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2 Kings 6: 17 17 And Elisha prayed, "O LORD, open his eyes so he may see. " Then the LORD opened the servant's eyes, and he looked and saw the hills full of horses and chariots of fire all around Elisha. © 2000 Timothy G. Standish

Biography - Gregor Mendel �Father of classical genetics. �Born 1822 to peasant family in the Czech village of Heinzendorf (now called Hyncice), northern Moravia, part of the Austro. Hungarian empire at the time � 1843 - Admitted to the St. Thomas Augustinian Monastery in Brunn (Brno), southern Moravia, now in the Czech Republic �Studied mathematics in Olmutz college © 2000 Timothy G. Standish

Biography - Gregor Mendel: �Attended Education University of Vienna 1851 1853. Influenced by: – Franz Unger, a plant physiologist who believed new species could come about via hybridization. – Christian Doppler, physicist who discovered the Doppler effect. Sharpened his math skills. � 1854 Returned to Brunn © 2000 Timothy G. Standish

Biography - Gregor Mendel: Research �Studied peas which he grew in a garden outside of the Abbey where he lived starting 1856 (3 years prior to publication of Origin of Species). �Showed that the traits he studied behaved in a precise mathematical way and disproved theory of "blended inheritance. " © 2000 Timothy G. Standish

Biography - Gregor Mendel: � 1865 Publication and Death first reported results of his work �Published rules of transmission of genes in 1866 (handwritten in German, not Latin!). Work was totally ignored. � 1868 - Elected Abbot of the monastery and ceased investigation of inheritance � 1884 - Died of kidney failure © 2000 Timothy G. Standish

Biography - Gregor Mendel: �Mendel’s Rediscovery work was rediscovered in 1900 by three botanists: – Carl Correns (Germany) – Erich von Tschermak (Austria) – Hugo de Vries (Holland) © 2000 Timothy G. Standish

Why Peas? � Mendel used peas to study inheritance because: � True breeding commercial strains were available � Peas are easy to grow � Peas have many easy to observe traits including: – Seed color - Green or yellow – Seed shape - Round or wrinkled – Pod color - Green or yellow – Pod shape - Smooth or constricted – Flower color - White or purple – Flower position - Axial or terminal – Plant size - Tall or dwarf © 2000 Timothy G. Standish

Why Peas? � Pea flowers are constructed in such a way that they typically self fertilize � Because of this, it is relatively easy to control crosses in peas Anthers Pea flower Stigma © 2000 Timothy G. Standish

Mendel’s Results � When crossing purple-flowered peas with white-flowered peas, Mendel got the following results: � In the first filial (F 1) generation all offspring produced purple flowers � In the second generation (second filial or F 2): – 705 purple – 224 white � Approximately a 3: 1 ratio of purple to white © 2000 Timothy G. Standish

Interpreting Mendel’s Results � Because the F 1 generation did not produce lightpurple flowers and because white flowers showed up in the F 2 generation, Mendel disproved blended inheritance. � Mendel said that the parents had two sets of genes, thus two copies of the flower color gene � Each gene has two varieties called alleles � In the case of the flower color gene the two alleles are white and purple © 2000 Timothy G. Standish

Interpreting Mendel’s Results � In the F 1 generation, the white allele was hidden by the purple “dominant” allele � In the F 2 generation, 1/4 of the offspring wound up with two copies of the white allele thus they Heterozygous parents were white Homozygous parents make gametes either Gametes F 1 Generation from the P generation C C c Cc Cc can only make one or the other allele gametes with one F 2 Generation type of allele The F 1 Generation is all heterozygous C C c CC Cc cc © 2000 Timothy G. Standish

Trait Mendel’s Results F 1 Results F 2 Results Dominent traits round/wrinkled All Round 5, 474 Round 1, 850 wrinkled mask recessive yellow/green All Yellow 6, 022 Yellow 2, 001 green traits full/constricted All Full 882 Full 299 constricted Masked recessive Pods traits reappear Seeds green/yellow axial/terminal All Green All Axial 428 Green 651 Axial 152 yellow 207 terminal violet/white All Violet 705 Violet 224 white Tall/dwarf All Tall 787 Tall 277 dwarf Flowers Stem © 2000 Timothy G. Standish

F 2 Results Mendel’s Results Seeds F 2 Ratios Seeds 5, 474 Round 1, 850 wrinkled 2. 96: 1 Round: wrinkled 6, 022 Yellow 2, 001 green 3. 01: 1 Yellow: green 882 Full 299 constricted 2. 95: 1 Full: constricted Pods 428 Green 651 Axial 152 yellow 207 terminal 2. 82: 1 Green: yellow 3. 14: 1 Axial: terminal Flowers 224 white Stem 787 Tall l Pods Flowers 705 Violet l 3. 15: 1 Violet: white Stem 277 dwarf 2. 84: 1 Tall: dwarf l Ratios are not exactly 3: 1 How do we decide if the ratios are close enough to 3: 1 to support and not reject our theory? The chi square statistical test provides the tool used for this purpose © 2000 Timothy G. Standish

� Statistics Chi Square fall into two categories: 1 Descriptive - Summarize characteristics of a data set – Mean, standard deviation. . . 2 Decision making - Assist in deciding whether a set of data is consistent or inconsistent with a hypothesis called the null hypothesis – T test, f test, chi square. . . � Called chi square after the Greek letter “c” or “X” 2 Chi Square: d = = 2 å å C e 2 (Obs. Ex. ) Ex © 2000 Timothy G. Standish

Chi Square: On Mendel’s Seed Texture Data 2 Chi Square: d = = 2 å å C e 2 (Obs. Ex. ) Ex Obs. Ex. O-E (O-E)2/E Round 5, 474 (1, 850+5, 474) x 3/4 = 5, 493 5, 474 - 5, 493 =-19 -192/5, 493 = 0. 066 wrinkled 1, 850 (1, 850+5, 474) x 1/4 = 1, 831 1, 850 - 1, 831 = 19 192/1, 831 = 0. 20 X 2 = 0. 266 � Degrees of freedom = N - 1 = 2 - 1 = 1 � 0. 90 > p > 0. 50 that this amount of deviation is due to chance � In this case we retain the hypothesis that this data represents a 3: 1 ratio © 2000 Timothy G. Standish

Chi Square: On Mendel’s Flower Color Data 2 Chi Square: d = = 2 å å C e 2 (Obs. Ex. ) Ex Obs. Ex. O-E (O-E)2/E Violet 705 (705+224) x 3/4 = 697 705 - 697 = 8 82/697 = 0. 092 white 224 (705+224) x 1/4 = 232 224 - 232 =-8 -82/232 = 0. 276 X 2 = 0. 368 � Degrees of freedom = N - 1 = 2 - 1 = 1 � 0. 90 > p > 0. 50 that this amount of deviation is due to chance � In this case we retain the hypothesis that this data represents a 3: 1 ratio © 2000 Timothy G. Standish

Mendel’s Conclusions 1 Phenotypic traits are controlled by pairs of genes which act as individual units of inheritance 2 In genes that have multiple alleles (variations) the presence of some traits, called dominant traits, masks the presence of recessive traits 3 Gene pairs segregate randomly during gamete formation with either member of a pair equally likely to end up in a given gamete �But do multiple genes assort independently? © 2000 Timothy G. Standish

Mendel’s Experiment: A Case Study In Good Science �Gregor Mendel’s investigation of principles of inheritance is a case study in how science should be done: �He asked a good question �Chose an appropriate organism to work with �Practiced reductionism �Made good use of his data and allowed it (not prevailing theory) to drive his conclusions © 2000 Timothy G. Standish

Mendel’s Dihybrid Cross � Mendel chose to see if the round and yellow seed genes segregated independently P Generation F 1 F 2 Ratio Round green All Round Yellow 315 Round Yellow 9/16 RRyy Rr. Yy RRYy or Rr. YY 101 wrinkled Yellow 3/16 X wrinkled Yellow rr. Yy or rr. YY 108 Round green 3/16 RRyy or Rryy 32 wrinkled green 1/16 rryy � In other dihybrid crosses a 9: 3: 3: 1 ratio was also found © 2000 Timothy G. Standish

Reasons Mendel’s Work Was Ignored: 1) Mendel was not on the ball �Wrote in an obscure journal (Proceedings of the Natural History Society of Brunn). �Wrote in German, not Latin. �Mendel was not well known and did not persevere in his attempt to push his ideas. © 2000 Timothy G. Standish

Reasons Mendel’s Work Was Ignored: 2) Biologists were idiots �Biologists didn’t understand math �Biologists were interested in the explaining the transmission of continuous traits like height, esp. after publication of Origin of Species in 1859. Mendel suggested that inherited characteristics were discrete units (discontinuous). © 2000 Timothy G. Standish

Reasons Mendel’s Work Was Ignored: 3) Lack of independent supporting discoveries: �There was no physical element in which Mendel’s inherited particles could be identified. �By the turn of the century, chromosomes had been discovered (physical particles) and biologists were better at math. © 2000 Timothy G. Standish

Chromosomes: The Physical Basis of Inheritance � 1866 Mendel published his work � 1875 Mitosis was first described � 1890 s Meiosis was described � 1900 Mendel's work was rediscovered � 1902 Walter Sutton, Theodore Boveri and others noted parallels between behavior of chromosomes and alleles. © 2000 Timothy G. Standish

Chromosomal Theory of Inheritance �Genes have specific loci on chromosomes. �Chromosomes undergo segregation (meiosis) and independent assortment, �Thus alleles of genes are independently assorted. © 2000 Timothy G. Standish

Independent Assortment Eggs As long as genes are on different chromosomes, they will assort independently Sperm N E n e e N n EN En e. N en E EN EENn Ee. NN Ee. Nn E En EENn EEnn Ee. Nn Eenn e. N Ee. Nn ee. NN ee. Nn en Ee. Nn Eenn ee. Nn eenn N n e N e n E © 2000 Timothy G. Standish

Two Genes On One Chromosome Telophase I Prophase I Replication r r e e oth ath M F E E e e e E e A A E a A a a A A a As long as genes on the same chromosome are located a long distance apart, they will assort independently due to crossing over during Prophase I of meiosis E e A A a a Telophase II a E e A A a a © 2000 Timothy G. Standish

� Because Laws Of Probability alleles are usually distributed randomly, the laws of probability can describe their behavior: 1 Product Law - Describes the probability of two or more independent events occurring in a defined sequence or way 2 Sum Law - Describes the probability of two or more individual mutually exclusive events 3 Conditional Probability - Probability of events in which both events share some dependent condition 4 Binomial Expansion - The probability of a set of events arranged in no specified order © 2000 Timothy G. Standish

Determination of Gamete and Zygote Variability Number of Heterozygous Pairs n 1 2 3 4 Number of Different Gametes 2 n 2 4 8 16 Number of Different Genotypes 3 n 3 9 27 81 Number of Different Phenotypes 2 n 2 4 8 16 © 2000 Timothy G. Standish

Laws Of Probability: 1 Product Law l l l The “and” law Describes the probability of two or more independent events occurring in a defined sequence or way. Example - What is the probability of flipping a coin and getting heads and then tails? Probability of getting heads on the first flip = 0. 5 Probability of heads on the second flip = 0. 5 Total probability = 0. 5 x 0. 5 = 0. 25 © 2000 Timothy G. Standish

Laws Of Probability: 2 Sum Law l l l The “or” law Describes the probability of two or more individual mutually exclusive events Example - What is the probability of flipping a coin and getting heads or tails? Probability of getting heads = 0. 5 Probability of tails on the same flip = 0. 5 Total probability = 0. 5 + 0. 5 = 1. 0 © 2000 Timothy G. Standish

Laws Of Probability: 3 Conditional Probability l l Probability of events in which both events share some dependent condition Example - If one card in a deck of 52 is the queen of hearts, and hearts make up 1/4 of the deck, if you have a card with hearts on it, what are the odds that it is the queen of hearts? Probability queen of hearts/probability of hearts = (1/52)/(1/4) = 4/52 = 1/13 © 2000 Timothy G. Standish

Laws Of Probability: 4 Binomial Expansion The probability of a set of events arranged in no of any one way specified order: p. Probability = probability a = probability of Number of n = number of events outcome a n! s t a b s = number of outcome a b = probability of possible p = s!t! ways t = number of outcome b l l l �xample - If James and Bertha have 12 children, E what is the chance they will have 8 boys and 4 girls? n = 12, a = prob of boy = 0. 5, b = prob of girl = 0. 5, s = no. boys = 8, t = no. girls Number of ways to have 8 boys and 4 girls p = n! asbt = 12! 0. 58 x 0. 54 = 495 x 0. 00024 = 0. 121 s!t! 8!4! Probability of any specific order of 8 boys and 4 girls © 2000 Timothy G. Standish