In a certain species of flowering plants with a diploid...

In a certain species of flowering plants with a diploid genome, four enzymes are involved in the generation of flower color. The genes encoding these four enzymes are on different chromosomes. The biochemical pathway involved is as follows; the figure shows that either of two different enzymes is sufficient to convert a blue pigment into a purple pigment. white $\rightarrow$ green $\rightarrow$ blue $\stackrel{\rightarrow}{\rightarrow}$ purple A true-breeding green-flowered plant is mated with a true-breeding blue-flowered plant. All of the plants in the resultant $\mathrm{F}_{1}$ generation have purple flowers. $\mathrm{F}_{1}$ plants are allowed to self-fertilize, yielding an $\mathrm{F}_{2}$ generation. Show genotypes for $\mathrm{P}, \mathrm{F}_{1},$ and $\mathrm{F}_{2}$ plants, and indicate which genes specify which biochemical steps. Determine the fraction of $\mathrm{F}_{2}$ plants with the following phenotypes: white flowers, green flowers, blue flowers, and purple flowers. Assume the greenflowered parent is mutant in only a single step of the pathway.

In a certain species of flowering plants with a diploid genome, four enzymes are involved in the generation of flower color. The genes encoding these four enzymes are on different chromosomes. The biochemical pathway involved is as follows; the figure shows that either of two different enzymes is sufficient to convert a blue pigment into a purple pigment.
white $\rightarrow$ green $\rightarrow$ blue $\stackrel{\rightarrow}{\rightarrow}$ purple
A true-breeding green-flowered plant is mated with a true-breeding blue-flowered plant. All of the plants in the resultant $\mathrm{F}_{1}$ generation have purple flowers. $\mathrm{F}_{1}$ plants are allowed to self-fertilize, yielding an $\mathrm{F}_{2}$ generation. Show genotypes for $\mathrm{P}, \mathrm{F}_{1},$ and $\mathrm{F}_{2}$ plants, and indicate which genes specify which biochemical steps. Determine the fraction of $\mathrm{F}_{2}$ plants with the following phenotypes: white flowers, green flowers, blue flowers, and purple flowers. Assume the greenflowered parent is mutant in only a single step of the pathway.

Key Concepts

Independent Assortment

Independent assortment is a principle stating that genes located on different chromosomes segregate independently of each other during gamete formation. This concept is crucial when considering the genetic outcomes of crosses involving several genes, as it allows for the calculation of combined phenotypic ratios in the progeny. It simplifies the analysis of inheritance patterns in polygenic traits by treating each gene’s segregation as an independent event.

Biochemical Pathways

Biochemical pathways involve a series of enzyme?catalyzed reactions that convert substrates into products. In developmental genetics, different enzymes encoded by different genes catalyze sequential steps, and a mutation in one enzyme can block or modify the pathway, leading to distinct phenotypes. Understanding these pathways is essential for predicting how changes in enzyme activities affect the final outcome of a trait such as pigment production.

Gene Interaction and Epistasis

Gene interaction, particularly epistasis, occurs when the effect of one gene masks or modifies the effect of another gene in a pathway. In traits governed by multiple sequential steps, a mutation in an upstream enzyme can prevent the production of intermediate compounds needed for later steps, thereby altering the phenotype regardless of the status of downstream genes. This concept is fundamental when analyzing complex traits where multiple genes contribute to a single visual outcome.

Mendelian Inheritance

Mendelian inheritance refers to the transmission of traits from parents to offspring based on the segregation of alleles during gamete formation. In crosses between true?breeding individuals, the F1 generation typically shows uniform phenotypes under simple dominance, while the F2 generation exhibits segregation of alleles. These principles provide the framework for predicting genotypic and phenotypic ratios, even in complex traits involving multiple genes.

Transcript

00:01 So here we have a polygenetic question where we have what we're told is four different genes who are attributing to the representation of this one trait of color.

00:11 So we have this pathway here, which leads us to believe that white is the simplest one where you have a lot of recessive alleles.

00:19 And purple is the more complicated where you have to have certain dominant alleles in order to have that purple color.

00:25 So because it's laid out in this way and we know that there's four genes, i'm assuming, that the genes are ordered in this way.

00:35 So if you don't have dominant a, you will be white in color.

00:40 If you do have dominant a, but you don't have the dominant b yet, then you'll be green.

00:47 If you have that dominant a and that dominant b, but not c and d, you'll be blue.

00:54 But if you have the precursors of a and b and then also this c and d here, you will be purple in color.

01:03 So this is how we are determining, you know, genotypically what the phenotype is.

01:10 So when we're told in the question that we're starting with a parental generation where we have a true breeding parent, and that's important, who is green, and we're crossing them with the other parent who is also true breeding, who is blue, you know, what are we going to get in our f1 and our f2 generation? so our f1, we already told, is purple, so it's a little bit easy, but we're going to determine the genotype anyways.

01:34 And then we have to figure out our f2 generation to see, you know, how many would we expect to be purple, how many would we expect to be blue, how many green, and how many white.

01:45 Since those are the four colors we're told about, we're assuming that those are all the colors possible with these particular genes.

01:53 So we're starting with the parental generation because we're told information about that.

01:57 So we know that one parent is green.

02:00 So the way that you are green, as we see here, it's having that dominant a because we have to pass that arrow, so you have to have the dominant a.

02:09 But you can't pass this arrow, and so you can't have the dominant b.

02:15 So we're assuming that they have to have a dominant a, but have to have recessive bs.

02:22 And because they're true breeding, that means that whatever type of allele they have at a gene, all their alleles matched.

02:30 So if we have to have one dominant a, then because it's true breeding, it has to be homozygous.

02:37 So we don't know about c or d yet, so we'll leave those blank, move to the next parent, who we're told is true breeding blue.

02:45 So again, we look at blue.

02:46 Blue has passed the a and the b genes, so he has to have dominant a, dominant b, but he has not passed c and d.

02:54 So we assume then that we have dominant a, dominant b, and again, because true breeding, you have to have two dominant a's and two dominant b's.

03:05 But we can't have c or d, otherwise the plant would be purple.

03:11 So recessive c's and recessive d's.

03:15 Now, based on that, because we're told that our f1 generation is purple, we know that purple comes because you have at least one dominant allele at each gene, so at least one dominant c, one dominant b, a, and d.

03:28 So that means we have to be able to get a dominant a for.

03:30 From parents, which both parents have dominant a, so that's good.

03:34 Dominant b's, one parent has dominant b's, c's and d's.

03:39 So we know that the blue parent can't have dominant c's and d's.

03:42 So we're going to assume that the first parent, who's green, has dominant c's and dominant d's.

03:49 Because even if they have these dominant c's and ds, without the blue allele here, they can't progress in that pathway, so they can't be blue or purple.

03:59 So we're going to assume that these are the genotypes.

04:04 Now, when i know that, i can fill in the blinks for the f1 generation.

04:09 So we know that they're purple.

04:11 We know they have at least one dominant allele at each gene.

04:14 But we see that both parents are homozygous dominant for a.

04:18 So both parents can only give dominant a's...

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