Genetics

Background:

One question that has always intrigued us humans is “Where did we come from?” Long ago, Hippocrates and Aristotle proposed the idea of what they called pangenes, which they thought were tiny pieces of body parts. They thought that pangenes came together to make up the homunculus, a tiny pre-formed human that people thought grew into a baby. In the 1600s, the development of the microscope brought the discovery of eggs and sperm. Antonie van Leeuwenhoek, using a primitive microscope, thought he saw the homunculus curled up in a sperm cell. His followers believed that the homunculus was in the sperm, the father “planted his seed,” and the mother just incubated and nourished the homunculus so it grew into a baby. On the other hand, Regnier de Graaf and his followers thought that they saw the homunculus in the egg, and the presence of semen just somehow stimulated its growth. In the 1800s, a very novel, “radical” idea arose: both parents contribute to the new baby, but people (even Darwin, as he proposed his theory) still believed that these contributions were in the form of pangenes.

Modern genetics traces its beginnings to Gregor Mendel, an Austrian monk, who grew peas in a monastery garden. Mendel was unique among biologists of his time because he sought quantifiable data, and actually counted the results of his crosses. He published his findings in 1865, but at that time, people didn’t know about mitosis and meiosis, so his conclusions seemed unbelievable, and his work was ignored until it was rediscovered in 1900 by a couple of botanists who were doing research on something else. Peas are an ideal organism for this type of research because they are easy to grow and it is easy to control mating.

We will be looking at the sorts of genetic crosses Mendel did, but first, it is necessary to introduce some terminology:

Alleles

alternate forms for genes

Dominant Allele

the one that’s fully expressed; symbolized by a capital letter, often the first letter of the word for which it stands

Recessive Allele

the one that’s completely masked; symbolized by the SAME letter, but lower case

Homozygote

an individual with a pair of two of the same allele (BB or bb)

Heterozygote

an individual with a pair of two different alleles (Bb)

Genotype

the organism’s actual genetic make-up: for example, is it BB, Bb, of bb?

Phenotype

the organism’s expressed traits, what it looks like, how the genes are expressed: for example, does it have brown or blue eyes?

A monohybrid cross is a genetic cross where only one gene/trait is being studied. P stands for the parental generation, while F₁ and F₂ stand for the first filial generation (the children) and second filial generation (the grandchildren). Each parent can give one chromosome of each pair, therefore one allele for each trait, to the offspring. Thus, when figuring out what kind(s) of gametes an individual can produce, it is necessary to choose one of the two alleles for each gene (which presents no problem if they are the same).

For example, a true-breeding purple-flowered plant (the dominant allele for this gene) would have the genotype PP, and be able to make gametes with either P or P alleles. A true-breeding white-flowered plant (the recessive allele for this gene) would have the genotype pp, and be able to make gametes with either p or p alleles. Note that both of these parent plants would be homozygous. If one gamete from each of these parents got together to form a new plant, that plant would receive a P allele from one parent and a p allele from the other parent, thus all of the F₁ generation will be genotype Pp, they will be heterozygous, and since purple is dominant, they will look purple. What if two individuals from the F₁ generation are crossed with each other (Pp × Pp)? Since gametes contain one allele for each gene under consideration, each of these individuals could contribute either a P or a p in his/her gametes. Each of these gametes from each parent could pair with each from the other, thus yielding a number of possible combinations for the offspring. We need a way, then, to predict what the possible offspring might be. Actually, there are two ways of doing this. The first is to do a Punnett square (named after Reginald Crandall Punnett). The possible eggs from the female are listed down the left side, and there is one row for each possible egg. The possible sperm from the male are listed across the top, and there is one column for each possible sperm. The boxes at the intersections of these rows and columns show the possible offspring resulting from that sperm fertilizing that egg. The square from this cross would look like this:

Note that the chance of having a gamete with a P allele is ½ and the chance of a gamete with a p allele is ½, so the chance of an egg with P and a sperm with P getting together to form an offspring that is PP is ½ × ½ = ¼, just like the probabilities involved tossing coins. Thus, the possible offspring include: ¼ PP, (¼ Pp + ¼ pP, which are the same, Pp, since P is dominant over p) = ½ Pp, and ¼ pp.

Another way to calculate this is to use a branching, tree diagram:

Choices for 1st allele	Choices for 2nd allele		Resulting Offspring	Probability
P (½)	P (½)	=	PP	¼
	p (½)	=	Pp	}  ½
p (½)	P (½)	=	Pp
	p (½)	=	pp	¼

Note, again, that the chance of Pp is ¼ + ¼ = ½. A shorter way of telling how many PP, Pp, and pp could be expected, would be to say that there is a 1:2:1 genotype ratio. The chance of getting at least one dominant allele (either PP or Pp) necessary for purple color (this can be written as P-) is ¼ + ½ = ¾, so we could say that there’s a 3:1 phenotype ratio. These two ratios are classic genotype and phenotype ratios for a monohybrid cross between two heterozygotes.

Based on his data, then, Mendel came up with a four-part theory of how genetics works:

Some special cases:

Testcross:

If an organism has the dominant phenotype, but an unknown genotype, cross that individual with a homozygous recessive individual. If all offspring are dominant, the individual in question probably has two dominant alleles, but if any recessive offspring show up, the individual is a heterozygote.
Either:

	D	D
d	Dd Dd Dd Dd
d

or:

	D	d
d	Dd dd Dd dd
d

Incomplete Dominance:

A red-flowered plant × white-flowered will give heterozygotes that are pink. The red allele is not completely dominant, so the heterozygote is intermediate. In many other genes, the dominant allele is instructions for “do this” while the recessive allele is instructions for “we don’t know how to do this.” However, in incomplete dominance, both the instructions for (in this case) “make red” and the instructions for “make white” are carried out. The same is true in a person who is heterozygous for sickle-cell anemia: instructions for both “make normal hemoglobin” and “make abnormal hemoglobin” are carried out, so that person’s blood has some of each.

	R	r
R	RR Rr Rr rr
r

Thus, ¼ are red (RR), ½ are pink (Rr), and ¼ are white (rr).

Multiple Alleles:

Many genes only have two alleles. An interesting exception to this (there are others) is the human ABO blood group. The alleles are I^A, I^B, and i, so the possible genotypes/phenotypes are I^AI^A or I^Ai = type A blood, I^BI^B or I^Bi = type B blood, I^AI^B = type AB blood, and ii = type O blood. These phenotypes are not all equally-distributed in all populations of humans. In the U. S., about 45% of the population is type O, 42% type A, 10% type B, and only 3% type AB. However, other cultures/ethnic groups exist in which 75% of the people are type A and 25% type 0 (no B or AB), or where 40% of the people have type B with a mixture of the other types also present.
(Rh factor, by the way, is a totally separate gene with Rh⁺ [R] and Rh^– [r] alleles [actually, that gene also has multiple alleles, but the vast majority of people are positive or negative for one particular allele called “D”]. In the U. S., about 85% of the population is Rh⁺ [RR and Rr] and 15% Rh^– [rr], thus the chances of someone being O^– [having both ii and rr] would be 45% × 15% = 6.75%. The rarest blood type in the U. S. would be AB^–, about 0.45% of the population.]
This is discussed in more depth in the human genetics notes.

Pleiotropy

The ability of one gene to have multiple effects: for example, a deaf whit cat or a cross-eyed white tiger.

Polygenic trait:

A trait controlled by several genes: for example, human skin color is controlled by about three or four genes (depending on which book you read), each of which has two alleles. The various skin colors arise from various combinations of the alleles in these several genes. Note that skin color also is influenced by environment, and exposure to sunlight will stimulate synthesis of the pigment melanin in skin.

Dihybrid Cross:

A cross where two traits/genes are under consideration. For example, in peas if R = round, so r = wrinkled, and Y = yellow, so y = green, in a cross between RRYY × rryy, the gametes must have ONE ALLELE FOR EACH GENE, so in this case, RRYY could produce gametes with one R and one Y, or RY, and rryy could produce gametes with one r and one y, or ry. The F₁ would get RY from one parent and ry from the other, thus would all be RrYy. Note that it is necessary to keep the alleles for the same gene together and put the dominant allele (capital letter) first for EACH GENE. In calculating what the F₂ generation would be, you must first figure out what gametes (eggs or sperm) each parent can make. It is very important to remember that gametes must have ONE ALLELE FOR EACH GENE, so figure out the possibilities this way:

Choices for 1st allele	Choices for 2nd allele		Resulting Gamete	Probability
R (½)	Y (½)	=	RY	¼
	y (½)	=	Ry	¼
r (½)	Y (½)	=	rY	¼
	y (½)	=	ry	¼

Thus, each parent could make four kinds of gametes, so the Punnett square would be 4 × 4 cells.

	RY	Ry	rY	ry
RY	RRYY RRYy RrYY RrYy RRYy RRyy RrYy Rryy RrYY RrYy rrYY rrYy RrYy Rryy rrYy rryy
Ry
rY
ry

This would give the following results:

Possible Offspring:	Genotype Ratio		Phenotypes	Phenotype Ratio
RRYY	1		R-Y-	9
RRYy	2		R-yy	3
RRyy	1		rrY-	3
RrYY	2		rryy	1
RrYy	4		TOTAL	16
Rryy	2
rrYY	1
rrYy	2
rryy	1
TOTAL	16

Thus the genotype ratio is 1:2:1:2:4:2:1:2:1 and the phenotype ratio is 9:3:3:1.

On your own, try I^AiRr × I^BiRr, a cross involving both the ABO blood group and Rh factor (which we will discuss a little later on).

In pedigrees, a circle represents a female and a square represents a male. Filled-in vs. open symbols are used to distinguish between two phenotypes for the gene in question, and a half-filled symbol is used to designate a carrier (a heterozygous individual who has a recessive allele for some gene, but is not showing that phenotype). Here is a sample pedigree for eye color. If the people with filled-in (dark) symbols have brown eyes and those with open (light) symbols have blue eyes, can you figure out the genotypes of the people marked with *?