Lecture 12: Mendel, dominance versus recessiveness of genes, Hardy Weinberg equation, etc.

 

In the mid-later 1800s (about the time of the US civil war, & soon after Darwin had proposed natural selection as the main mechanisms of evolution), a monk at a monastery in Brno did a long series of genetic experiments on garden peas, & these peas' inheritance of seven discrete properties; flower color, pea color, pea wrinkling, pod color, pod shape, pod position, and stem length.

For each of these seven characters, he found a certain abstract pattern of inheritance, following consistent quantitative rules.

For each of the 7 characters he found two alternative genes (but the word gene was not invented until later)

For each of the 7 characters, one of the 2 genes was "dominant" to the other, so you can't tell the difference whether a given pea plant was carrying two copies of the dominant gene, or one copy of the dominant gene, and one copy of the "recessive" gene.

To use the modern vocabulary, heterozygotes looked the same as plants homozygous for the dominant gene.

For example, the gene for smooth peas is dominant to its "allele", the gene for wrinkledness of peas. And the gene for purpleness of flowers is dominant to its allelic gene, which causes flowers to be white.

If you cross plants only to themselves, or close kin (inbreeding) and keep selecting only those plants with desired properties, then you can eventually get more or less "pure" lines in which all the plants have a given character, whether the gene for it is recessive or dominant. People had been noticing this for 100s of years, and also noticing that one often got "throwbacks" with some genes, until you had done enough inbreeding to "fix" characters.

For example, Darwin comments on this pattern, as well as that the throwbacks often occur preferentially in one sex, which we now recognize as resulting from sex linked genes.

Mendel looked for arithmetic patterns in the world, and also kept detailed records of the weather, & many other things, hoping to find patterns.

In the cross-bred pea plants, he DID find simple patterns:

cross (pure=inbred) purple with (pure=inbred) white: (parental generation = P generation)

all offspring have purple flowers (F1 generation)

cross these F1 plants to each other (or to selves)

75% of offspring have purple flowers
25% of offspring have white flowers (F2 generation)

But of this 75%, 1/3rd are pure purple ("homozygous") and 2/3rds are "heterozygous"

Note that in the F1 generation, all were heterozygous. (in terms of modern vocabulary)

He found this same pattern with all 7 genetic differences. for each there was one recessive and one dominant allele. (although there is no fundamental reason for that!
Dominance and recessiveness are a real phenomenon, but it is a coincidence that he didn't find more than one of each kind for each of the 7 characters; and also that he didn't find any examples of co-dominance.
(co-dominance is what you call it when the phenotype of heterozygous individuals is intermediate between the two kinds of homozygous individuals)

Mendel also reported "independent assortment" of genes
(no apparent tendencies of different genes to stick together)

Textbooks call this "The Principle of Independent Assortment"
but actually he barely missed finding "genetic linkage".

Coincidentally, peas have 7 chromosomes, and he had one gene on each of the 7. If two or more of his gene pairs had happened to be near each other on the same chromosome, then he should have found "linkage", as did later researchers.

Many people suspect maybe Mendel (or the gardeners who did much of the work for him) DID find some other genes that didn't fit the patterns, and therefore ignored them.
(In research, such things are often unavoidable; but you should mention them somewhere in your research papers! You can't follow every variation, but also must not lie or deceive)

Mendel published his research in good journals, sent copies to leading scientists, and met them personally to ask advice. One told him that the results would only be important if he could discover what chemicals were carrying the genetic information.

Almost 40 years later, long after Mendel died, 3 or 4 leading researchers more or less simultaneously re-discovered his work. Bateson, DeVries, Correns, Tschermak- Some had gotten similar results; but the main reason was they wanted or needed such results, partly so evolution could go faster, in jumps, because the physicists said the world was only 40 million years old! (but were wrong by >100-fold, of course)

If you discover facts that confirm hopes or expectations, then it may go right into the textbooks or CNN!

But if what you discover does NOT fit expectations, prepare to be ignored! (or maybe misinterpreted!)

(But NOT always! Einstein's 3 major papers in 1905 went mostly against the current "trend-think", but Max Planck and the other referees made sure they got public attention)

After 1900, other scientists found evidence that genes are carried on chromosomes; and that contradictions to Mendel's "independent assortment" could be explained by linkage of genes located near each other on the same chromosome!

A.H. Sturtevant (an undergraduate in Morgan's Biology 11 at Columbia, made the first linkage map as extra-credit homework!)

Several excellent books on the history of genetics have been published; one of the best by Sturtevant; the best by Carlson.

An interesting historical pattern is that breakthroughs often seemed at first to be contradictions to earlier discoveries. (but were then realized to confirm them beyond doubt) WHY?

Many years later, it was realized that giant chromosomes in fly larva salivary glands (& some other tissues, too!) are big enough to see bands corresponding to genes, deletions, inversions, etc.

In flies as well as mammals, females have 2 X chromosomes, while males have one X and one Y. (ironically, we and they are almost the only animals that do this!)

Because males only have one X chromosome, recessive genes can be expressed even when we only have one copy!

"Sex linked genes" like those for color-blindness and hemophilia!

These phenotypes are MUCH more common in males than females.

A female would only express the recessive gene if homozygous.
Females carrying one recessive and one dominant gene are "carriers"

If you are a color blind male, then probably your mother is a carrier (you got your one X from her) (or maybe you are a mutant!) and if you have brothers, about half are color blind.

But if your mother were herself color blind, then probably all your brothers would be, too.

Unless your wife is either color blind or a carrier, then your own sons will probably NOT be color blind, but your daughters WILL be carriers.

The Hardy-Weinberg Equation: As Mendel's rules were becoming appreciated in the early 1900s, lots of people wondered why the frequency of phenotypes for different genes had no particular tendency to be 1:3.

Please notice this expectation is illogical and even stupid!!
The 1:3 ratio is expected in F2 crosses, OR if the ratio of genes in the population happened to be about 50:50, or something!
Others thought that gene frequencies should gravitate toward 50:50 ratios, or that dominant genes should become more and more prevalent, although there would be absolutely no reason.
(people in groups can be very dumb)

Two men simultaneously published the true equation. (one of whom was the famous mathematician G.H. Hardy, who could barely believe biologists could be so stupid)

If p is proportion of one allele of a gene (lets say .3)
and q is the proportion of the other allele (lets say .7)

Then if these breed randomly, then the expected frequency of homozygotes for the first gene will be p squared (0.09)
and those homozygous for the other gene will be 0.49
and heterozygous individuals will be 2 x 0.3 x 0.7 = 0.42

If the gene frequencies were .1 and .9 then
p squared = 1%
q squared = 81%
2pq=18%

If the gene frequencies were each 50%
then p squared and q squared are both 25%
& expected frequency of heterozygous individuals would be 50%

If there is some bias in breeding, this will make the equation wrong. Selective survival will also throw it off.

The genetic disease cystic fibrosis results from being homozygous for a recessive form of a gene coding for a certain protein (that uses ATP energy to pump chloride ions)

If one person in about 2500 has this disease, then how many carriers would be expected in a class this size?

If p squared = 0.0004% (percent homozygous people)
then what % of genes in the population are of this kind?
(one over what) squared ,,, equals one over 2500

Such a high gene frequency could never be produced in a gene which is lethal in double recessives, UNLESS heterozygotes have some advantage, such as greater resistance to disease.
(heterozygosity for sickle cell trait gives resistance to malaria)

Why do genes come in LUMPs, like this?
What does it tell us about the underlying causal mechanisms?

"One gene, One enzyme" slogan of George Beadle & Edward Tatum;
Later: "One gene, One protein"

For example, presumably there is an enzyme that synthesizes the blue pigment in the pea flowers.
White flowers result from the gene being mutated in some way that makes this enzyme not work, & not make the pigment.

Why does it makes sense that the blue allele is dominant? Apparently enough enzyme can be made with one copy of the gene for the functional form of the enzyme.

If flowers were more blue when they had 2 copies of the "good gene, then the alternative alleles would be "co-dominant".

If you needed two genes worth of enzyme to get any pigment, then the white allele would be dominant.

Likewise, suppose that enzymes form clumps (dimers, tetramers) and the "good" enzymes got inactivated by binding to one of the inactive kind, what then? (such things can happen)

Many (most?) genes code for enzymes, that allow specific chemical reactions to occur.

But other genes code for structural proteins.

And other genes code for proteins that bind DNA and either stimulate or block expression of other genes.

And some genes are sites on DNA that don't code for proteins
(& nevertheless have effects, can be mutated & have phenotypes)

++++++++++++++++++++++++++++++++++++++++++++++

A question for class discussion:
It was mentioned that 90%+ of human cancers are caused by somatic mutations in certain genes called "oncogenes"

Would you expect these mutations to be dominant or recessive,
when a cancer cell is fused with a non-cancerous cell?

 

Questions you should be able to answer about Mendelian genetics

1) About when did Mendel publish his research results? (1865)

2) About when did main-line science realize it was important? (1902+)

3) Mendel studied the genetics of what organism?

4) Do we now believe that the same basic phenomena could also have been discovered in other kinds of plants or animals?

5) What were some special advantages of the ones Mendel used?

Can you correctly use each of the following word pairs? (#s 6, 7, 8, 9)

6) Dominant versus recessive? (and versus co-dominance?)

7) Homozygous versus heterozygous?

8) Phenotype versus genotype?

**9) Allele versus gene? (versus genetic locus?)

*10) The following are quotes from Darwin's "Origin of Species": What do we now know about the genetic mechanisms of such phenomena?

No one can say...why the child often reverts in certain characters to its grandfather...or more remote ancestor; (or) why a character is often transmitted from one sex to both sexes, or to one sex alone...often transmitted either exclusively, or in a much greater degree, to males alone.
...the well-known principle of reversion to ancestral characters...
...the tendency to revert to some character that has been lost during some former generations, this tendency, for all that we can see to the contrary, may be transmitted undiminished for an indefinite number of generations.

11) If we represent the "P generation" cross as CC x cc
so that the members of the F1 generation are all Cc
and half the members of the F2 generation are 1/2 Cc,
then what are the genotypes of the other 50% of the F2 generation?

12) Suppose that the members of the P generation differed at two different genetic loci?
CC DD x cc dd
then what percentage of the F1 generation will be Cc Dd?

Can you make a list of all the different genotypes that should occur in the F2 generation?
CC DD
CcDD
ccDD etc.?

13) Which of these different genotypes are homozygous for both alleles? Which are heterozygous for one allele, but homozygous for the other?

*14) If there were no linkage between the C and D genes (= independent assortment occurred), then what would be the average percentages of each of the different genotypes in the F2 generation?

*15) What would be the expected percentages of the different phenotypes? (the appearances of the individuals? Hint: which genotypes look the same as each other?)

*16) Suppose that the C and D genes had happened to be on the same chromosome, and for some reason there was no genetic crossing over: then what different genotypes would occur in the F1 generation? What about in the F2 generation?

*17) Suppose that the C and D genes were on the same chromosome, but far enough apart that chiasmata (and crossing over) occurred between these two genes in about 1% of meiotic divisions, then small percentages of which phenotypes would occur in the F2 generation?

**18) About what percentage of these rare phenotypes would you predict, based on only one percent crossing over?

**19) If genes A and B were far enough apart that 10% crossing over occurred, and C was far enough on the other side of B that 20% crossing over occurred between B and C, then can you predict about how often crossing over should occur between A and C?

**20) In the preceding question, does it affect your answer if two chiasmata and cross-overs could sometimes occur between two genes? HINT: yes! But why?

*21) If two genes are on the same chromosome, but far enough apart that crossing over occurs between them in about half of meioses, then how does the result resemble what would happen if they were on the same chromosomes?

**22) Suppose that some magical mechanism controls crossing-over so that only even numbers of cross-over events are allowed to occur! (2, or 4, or 6 cross-overs; never just one, never 3 or 5)
Suppose that genes A and Z happen to be located at the extreme opposite ends of a chromosome, figure out whether they will be genetically linked to each other, in terms of the results of crosses? If you had a whole series of other genes B, C, D, E, in that order along the chromosome, with small percentages of crossing-over occurring between each and its neighbors, and you used these frequencies to make a genetic map, why would this map seem to be a ring?

*23) Bacterial chromosomes (and those of some but not organelles) really are closed rings! What restriction has to be placed on the number of crossing-over events that can occur between such chromosomes in a given exchange of genes?
(Hint: If the 2 rings are not to be fused into one big ring!)

24) If the phenotype of those heterozygous for a given pair of genes are indistinguishable from those homozygous for one of these genes, then that gene is said to be ______ relative to the other gene.

25) Did Mendel describe any cases in which heterozygous individuals WERE intermediate in properties between the two kinds of homozygous individuals? Can that sometimes happen? What is it called, when it does happen?

26) How can color blindness occur in human males, even though they have only one copy of the defective gene, and that gene is recessive?

**27) "Hemi" is the Greek root for "half"; so what is meant by saying such color blind males are "hemizygous"?

28) If a woman is not color blind, but has a son that is color blind, then what is the probability that if she has another son, then he will be color blind?

29) Does the answer to this question depend on whether the other son has the same father?

30) If a woman is herself color blind, then what percentage of her sons will be color blind?
What percentage of her daughters will be color blind (If her husband were ALSO color blind?
If her husband were NOT color blind?)?
If her husband is NOT color blind, but a woman IS, then what percentage of her daughters will be color blind?

31) If one person in 100, on the average, is homozygous for a certain gene, then what percentage of the general population is a carrier of that gene?

32) What about if half the population is heterozygous for a given allele of a gene, then what % should be homozygous for that form of the gene? (assuming no bias in who marries whom)

33) If a genetic disease is caused by a autosomal recessive gene, and an average of 2 students in a class of 80 are (heterozygous) carriers of this mutation (one person in 40), so that if these two were to marry each other and have children half their kids would have the disease, then about what should be the frequency of this disease in the general population?

**34) Imagine a future world in which college students all get tested to find out which harmful genes each is heterozygous for, then how should this information be marked on their name tags at mixers? (so that nobody will get too serious about the wrong potential spouse)?

**35) If such a harmful recessive gene were carried, on the average, by one person in ten, then compare the probability (expected frequency) of the disease in the general population as compared with among children born to couples who were first cousins to each other. In other words, how much does it increase the frequency of the genetic disease for first cousins to marry?

 

 

 

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