Batch 2 - Class 63 - Math in Genetics

Preclass Exercise:

Draw all the cross sections that result from slicing a cylinder
Answer:

(MC Diaries: Problem 7) We have three bottles: one has a circular opening, another a square opening, and the third has an opening in form of an isosceles triangle. See below. Design a bottle stopper that fits all the three bottles.
What if we should be able to push the stopper into each of the bottles?

Answer:

Attendance: Tishyaa, Smiti, Anisha, Kushaan, Shubham, Praharsh, Khushi, Nandini, Diya (skype)

Class Notes:

What happens if you combine yellow color with blue color?
What happens if you cross-pollinate yellow flowers with blue flowers?
Lets see an actual experiment done by Gregor Mendel around 1860s
Mendel took yellow and green peas and cross-pollinated themWhat would you expect?This is what Mendel saw

Can you explain this?
Lets see what happened in next generation (might have to explain self-pollination, as against cross-pollination which was done initially)

Why are we not getting mix of green and yellow color? (Kids should get to the point that there are different elements which lead to yellow and green color, and they don't combine)

Just like if two kids are shouting, you dont get a mix of voices, but two distinct voices
But why are all in first generation yellow? - Introduce the notion that yellow might be overpowering green

Just like your younger sibling who always shouts harder than you

And why do we suddenly see a green come back in second generation, when there were no greens in first generation?

Something was still there not getting expressed

Introduce the notion of two genes per flower for color, one from each parent, and of dominance

Lets try to recreate the above pattern basis this

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Interestingly, Mendel observed the same thing for other traits

1.	flower color is purple or white	5.	seed color is yellow or green
2.	flower position is axil or terminal	6.	pod shape is inflated or constricted
3.	stem length is long or short	7.	pod color is yellow or green
4.	seed shape is round or wrinkled

Where could we see this principle in human beings?
Lets examine an application to diseases - Cystic Fibrosis is causes by a recessive allele (explain).
- Explain notion of a carrier, a non-carrier healthy, and someone expressing the disorder.
- Let kids work on what happens for different combination of parents
- How can we use this to predict probability of a child getting a disorder?
- How about a disorder which may be caused by a dominant allele? (such as Huntington disease)
Intermediate Expression - all genes don't express as dominant or recessive. Sometimes intermediate expressions occur, such as in pitch of human males
Additive Expression - Sometimes AA is more expressive than Aa, such as in color of human skin
Some characteristics are polygenic - i.e. multiple genes effect the feature - eg: height of human beings, color of skin
- Skin color is controlled by 4 genes. Let us work with two and assume their effect is additive
- What are the different skin colors we can get?

How many would we get with four genes? - 17 (2^n+1)
Is it possible for children to be lighter or darker than both parents? Lets work this out

Human Blood Group - Single gene, two alleles, but each can have three values - A, B, or O (O is just absence of A and B). A and B are dominant over O, but if both A and B are present then both express into AB group. Lets draw a chart of what can happen in inheritance

Remember, all genes are not equally probable (50-50). It depends on evolution - for example hot climates prefer dark skins (melanin protects against UV A/B radiation), and cold climates prefer lighter skin (With lack of UV B in cold areas, low melanin to enable absorption of UV B, so that Vitamin D can be produced)

Homework:

(Geoffrey - 143) Three dutchmen and their wives go shopping hogs, and each buys as many hogs as he or she pays for each hog. Each husband spends Rs 63 more than respective wife. Husbands are Hendrick, Elas and Cornelius. Wives are Gurtrun, Katrun and Anna. Hendrick buys 23 more hogs than Katrun, while Elas buys 11 more than Gurtrun. What are the names of each man's wife?
Answer: Pairs are 32/31, 12/9, and 8/1 - we can now see integers that differ by 23 and 11. So its Hendrick-Anna, Elas-Katrun and Cornelius-Gurtrun

References:

http://anthro.palomar.edu/mendel/mendel_1.htm

http://www.slideshare.net/gurustip/polygenic-inheritance-ahl-7933636

http://www.ted.com/talks/nina_jablonski_breaks_the_illusion_of_skin_color?language=en

Mathematical Puzzles, Geoffrey Mott-Smith

Mathematical Circle Diaries, Year 1, by Anna Burago