Family Genetics

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I recently read a very interesting article, The Incredible Expanding Adventures of the X Chromosomeby Christopher Badcock, Ph.Din Psychology Today.

The article explores some of the implications of the fact that fatherspass their sex chromosome undiluted to their offspring, whereasin all other situations, the offspring receives a random mix of genesfrom both parents.

The article generated considerable discussion within our household.I decided that a picture would help make things clearer. It turns outto be rather subtle: I had to re-read the article carefully and re-draw mypicture several times.

Here's how it works. Each person has 46 chromosomes arranged in 23pairs. We will ignore the 22 ordinary pairs and concentrate on thepair that determines sex. Everyone has at least one X chromosome;women have two, while men have one X and one Y. The X and Ychromosomes are quite different in length, so during reproduction theydo not inter-combine the way ordinary pairs do. In particular, themother's two X chromosomes get randomly mixed, but the father's X andY stay "undiluted": each offspring either gets the father's X,becoming a girl, or the father's Y, becoming a boy.

This apparently simple observation turns out to make for quitecomplicated mixing patterns over a couple of generations. ThePsychology Today article gives a nice text example, but lacks adiagram. Here is my attempt to fill that gap.

Let's start with your four grandparents. Assuming they are allunrelated individuals, their various X and Y chromosomes are alldifferent, indicated here by eight distinct colors. There are two Ychromosomes in the mix, from your two grandfathers: pink for thepaternal and orange for the maternal. There are also six Xchromosomes: one each for the grandfathers (purple and cyan,respectively), and two each for the grandmothers (red/blue on thepaternal side, yellow/green on the maternal side).

Now let's move to your parents. Your father, since he is male,inherited your paternal grandfather's "pink" Y. Like everyone, he getsa mix of his two maternal X chromosomes, shown here as a "red/blueflag". This mix is different for each person, so for his brothers andsisters (your paternal aunts and uncles) I have rotated the red/blueflag to make it look different. For example, your uncle is not identicalyour father, even though they share the pink Y.

You mother, since she is female, inherited your maternal grandfather's"cyan" X. Like everyone, she gets a mix of her two maternal Xchromosomes, shown here as a "yellow/green flag". Once again, this mixis different for each person, so for her brothers and sisters (yourmaternal aunts and uncles) I have rotated the yellow/green flag tomake it look different. For example, your aunt is not identicalyour mother, even though they share the cyan X.

Now it is your turn. If you are male, you will have inherited yourfather's pink Y, plus an X that is a mix of your mother's two Xchromosomes. Note that this new X is half cyan (from your maternalgrandfather), and completely lacks red, blue and purple: you havereceived contributions from only 5 of the original 8 colors. Inparticular, you have no sex chromosomes at all from your paternalgrandmother. Of course, you do share other genes of hers, on the other22 chromosome pairs - it is just the 23rd pair we are discussing here.

Similarly, if you are female, you get the red/blue X from your father,plus an X that mixes your mother's two X chromosomes. Again, I rotated thecyan/yellow/green flag to remind us that your mix is different fromthat of your siblings. Nonetheless, it still is half from yourmaternal grandfather (cyan), just as for your other siblings. Overall,you have contributions from 6 colors: you only lack the pink Y andpurple X from your paternal grandfather. Of course, you share othergenes with him, on the other 22 chromosome pairs.

That's an interesting asymmetry right there: girls have 6 of the 8colors, boys just have 5.

Also, your brothers have the same pink Y as your father andpaternal grandfather, undiluted (except for mutations) stretching backfor many generations. In contrast, although your sisters received yourfather's undiluted X chromosome, that X itself is a random mix of yourpaternal grandmother's X chromosomes, so it is not the sameas any of your grandparent's individual X chromosomes.

It's also interesting that boys share none of their colors withtheir paternal aunts. Girls, in contrast, do have some color overlap withtheir maternal uncles.

We also see that none of the grandchildren inherit any portionof the purple X belonging to the paternal grandfather. Similarly, none of the grandchildren inherit any portion of the orange Ybelonging to the maternal grandfather.

As a mathematician, I have focused here on telling a simplestory about the way the patterns change, assuming the simple rule thatfathers pass their sex chromosome undiluted to their offspring,whereas mothers pass on a random mix of theirs. In fact, an expert ingenetics would point out that real genetics is more complex than ourpicture suggests. Biology is not so "black and white" as math is!Just to hint at some of the complexities:

• Some genes on the Y chromosome may actually mix with some on the X, so not all of them are "sex-linked" in the manner described above.
• Some people have mutations that result in XY females, XX males, XYY males, and even other combinations.
• In females, some cells inactivate (most of) the mother's X and other cells inactivate (most of) the father's X. This explains the phenomenon of "calico cats", where a female (XX) cat has patches of different colored hair depending on which X is expressed in that patch; as a result, there are no male calico cats.
• The Y chromosome is much shorter than the X. That means each Xcarries lots more genes than any Y does, and men, in particular, havemany un-paired genes, where their Y lacks a counterpart to a gene onthe X.

Genetic disorders (mutations) on the X chromosome often show up inmales, because the Y chromosome does not have corresponding genes thatcould compensate for the defect. For instance, red-green colorblindness in men is actually X-linked, and hence is inherited fromtheir mothers, rather than being a defect in their father's Y.The Psychology Today article draws some interesting conclusions fromthis about intelligence and other characteristics that have somesex-linked components. You should read the original article to learn more; note that the print version in the magazine islonger and has more examples than the version available on the web.

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