The Hox genes are responsible for determining the anterior-posterior identity of body regions
(segments) in the developing insect embryo. Different Hox genes are turned on (expressed) in
different segments of the body, and in this way they determine which segments become head and
which thorax, which develop legs and which antennas. One surprising thing about the Hox genes
is that they usually occur in a row on the same chromosome and in the same order as the body
regions that they control. For example, the fruit fly Drosophila Melanogaster has eight Hox
genes located on a chromosome in exactly the same order as the body regions in which they are
expressed, from head to tail. If the eight genes were thrown randomly onto the same
chromosome, what is the probability that they would line up in the same order as the segments in
which they expressed?
Solution
This is a permutations problem, where you can think of each Hox gene being \"chosen\" for a
\"slot\" in the chromosome has its own probability. Contrast this to combinations problems,
where order does NOT matter. Here\'s the formula for the number of possible permutations:
P = n! / (n-k)! where n = the pool of genes, and k = the number of genes we\'re pulling out. There
are 8 genes we\'re working with, and we\'re putting them all in a chromosome. So the number of
permutations is:
P = 8! / (8-8)! = 8! / 0! = 8!/1 = 8*7*6*5*4*3*2*1 = 40320 different permutations.
So, that\'s how many different ways these genes can be chaotically and randomly oriented. But
we want them in a very specific order - one after the next, specifying a position for each and
every gene. Normally in permutations problems, you\'d have some leeway with how many
different ways the proposed sequence can be achieved (e.g. drawing a red then blue marble,
when there are 20 red marbles and 10 blue marbles). But in our case, this number is 1, because
there\'s only one way to achieve our proposed sequence. Therefore, the probability is 1/40320, or
0.0025% (about a 400th of a percent). Notice that this has logical implications for the function of
these Hox genes; they were probably slowly built off one another in an evolutionary sequence as
opposed to randomly falling into place. An organism with a mutation in their Hox genes will
have grotesque limb abberations - an example is a Drosophila mutant with a leg coming out of its
head..
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The Hox genes are responsible for determining the anterior-posterior.pdf
1. The Hox genes are responsible for determining the anterior-posterior identity of body regions
(segments) in the developing insect embryo. Different Hox genes are turned on (expressed) in
different segments of the body, and in this way they determine which segments become head and
which thorax, which develop legs and which antennas. One surprising thing about the Hox genes
is that they usually occur in a row on the same chromosome and in the same order as the body
regions that they control. For example, the fruit fly Drosophila Melanogaster has eight Hox
genes located on a chromosome in exactly the same order as the body regions in which they are
expressed, from head to tail. If the eight genes were thrown randomly onto the same
chromosome, what is the probability that they would line up in the same order as the segments in
which they expressed?
Solution
This is a permutations problem, where you can think of each Hox gene being "chosen" for a
"slot" in the chromosome has its own probability. Contrast this to combinations problems,
where order does NOT matter. Here's the formula for the number of possible permutations:
P = n! / (n-k)! where n = the pool of genes, and k = the number of genes we're pulling out. There
are 8 genes we're working with, and we're putting them all in a chromosome. So the number of
permutations is:
P = 8! / (8-8)! = 8! / 0! = 8!/1 = 8*7*6*5*4*3*2*1 = 40320 different permutations.
So, that's how many different ways these genes can be chaotically and randomly oriented. But
we want them in a very specific order - one after the next, specifying a position for each and
every gene. Normally in permutations problems, you'd have some leeway with how many
different ways the proposed sequence can be achieved (e.g. drawing a red then blue marble,
when there are 20 red marbles and 10 blue marbles). But in our case, this number is 1, because
there's only one way to achieve our proposed sequence. Therefore, the probability is 1/40320, or
0.0025% (about a 400th of a percent). Notice that this has logical implications for the function of
these Hox genes; they were probably slowly built off one another in an evolutionary sequence as
opposed to randomly falling into place. An organism with a mutation in their Hox genes will
have grotesque limb abberations - an example is a Drosophila mutant with a leg coming out of its
head.
