The Mad Hatter and March Hair setting up a breeding experiment in a teapot
In addition to Genetic Counseling for the cards, your lab has been investigating the genetics of the Dormouse.
Dormice have either the ability to Speak (S) – or are Mute(s).
Additionally, they are either Cruel or Kind.
You wish to map the distance between the Speech and Disposition genes and determine whether Cruelty or Kindness is dominant. (Here, not a metaphysical question)
You begin by obtaining true-breeding animals:
A Speaking , Kind Male
A Mute, Cruel Female
(oh, the cries of misogyny!)
Once bred, this coupling gives rise to a litter of six offspring. All six can speak and are unfailingly kind.
These offspring are then bred to true-breeding homozygous recessive mates. The results of these matings are:
35 Speaking, Kind
15 Speaking, Cruel
15 Mute, Kind
35 Mute, Cruel
What can you determine from these results?
In similar experiments, Cruel, Longhair and Kind,Shorthair animals were examined. Both parentals were true breeding and the F1 litter consistend entirely of Kind, Longhair animals. These F1 were then crossed with homoztgous recessives for both traits, resulting in:
20 Kind, Longhair
80 Kind, Shorthair
80 Cruel, Longhair
20 Cruel, Shorthair
What do these data add to your understanding of Dormouse genetics? Can you map the three genes to one Chromosome? What experiment do you want to do next?
Last week, we discussed the use of the Hardy Weinberg equations to estimate the rate of change in population under conditions of extreme selection, i.e. total elimination of one phenotype. This is essentially the goal of any sort of eugenics program. As an example of a way that this kind of policy could creep into culture, we watched GATTACA. Besides, it’s just a good film.
The purpose of the Hardy Weinberg equations is to model conditions under which allele frequencies can NOT change from one generation to the next. Therefore, it is evident that these are exactly those conditions that are responsible for allele frequency changes.
These conditions are:
No Selection (survival)
No Sexual Selection
No Genetic Drift –due to occasional fluctuations occurring by chance
No Gene Flow – immigration / emigration
In order to prevent the random changes in allele populations stipulated in #4, we also need a sufficiently large population, where sufficient is likely definable by someone with better probability-computing skills than my own. (I feel like going off half-cocked on notions of probability and finite vs infinite time, but I’ll spare you).
Anyway, if we know something about the population, we might be able to work out the allele frequencies and then compute our theoretical proportions for the next generation from the equations…
p+q = 1,
where p and q are the frequencies of the (only) two alleles we are calculating.
p2+2pq+q2 = 1
where each unit above represents the proportion of that genotype.
Mathematically, these equations provide insight into how rapidly the rate of an allele in a population could be eliminated if reproduction was prevented in a specific group. (This sounds completely esoteric without using an example, so let’s come up with one…)
A Healthy Gnome Couple
Imagine a population of fictional creatures – Garden Gnomes.
These gnomes have a recessive allele that makes them susceptible to a fungal disease. We’ll call the two alleles for this trait H – hearty (resistant) and h– weak (susceptible)
There was recently a new law passed amongst the gnomes forbidding susceptible gnomes from breeding (let’s imagine that the H allele is apparent by a normal complexion and the h allele is apparent by a jaundiced complexion. Like susceptibility to disease, jaundice only appears in the homozygous recessive (hh) gnomes.)
Imagine a population starting with equal allele frequencies, p=q=0.5.
p2+2pq+q2 = 1
will give us genotype frequencies of:
25% HH + 50% Hh + 25%hh = 1
for the present generation.
Now, if we start our draconian, anti-jaundiced gnome policy and prevent breeding of these individuals, then this generation‘s breeding population only consists of the HH and Hh gnomes, where only the heterozygotes will contribute the h allele to the next generation.
If we call the next generation q1, we can estimate the new proportion of the q allele in the population as the frequency of the heterozygote over the total population excluding the hh gnomes:
No wonder they want to get rid of these guys
After one generation, the frequency of the H allele is now 67%.
Since the same process would occur generation after generation (as long as the law was in place – and followed), we can determine the frequency of q at any generation, where n is the generation number.
From this information, try calculating the frequency of both alleles after the policy has been in place for 5 generations.
How long will it take to completely eliminate the h allele?
How would this change if the susceptible (h) allele is dominant?
Last week I posted a quick link about operons for my micro class to check out before taking their quiz on bacterial gene regulation This post is intended to complement that one. To go back to that post, click here. If there’s one thing to remember about operons it is that bacteria, lacking a nuclear membrane, regulate their genes differently than Eukaryotes. Having a nuclear membrane separates transcription and translation into two distinct compartments allowing for more subtle tweaking of Eukaryotic mRNAs before they are exported for translation.
Click on this figure to go to a good description of how polycistronic genes work
One thing this does is it makes it very beneficial to package genes with related function closely on the genome and use a single regulatory region to control them all together. They wind up getting packed so closely together that they are actually expressed as a single messenger RNA – known as a polycistronic (meaning ‘many gene’) message.
Upstream of this polycistronic cassette are regulatory elements. One element common to all regulatory elements is the promoter. The promoter consists of several elements which ‘promote’ the binding of an RNA polymerase to the DNA. Additional regulatory elements exist to ensure that this polymerase only transcribes the genes if they are needed. In doing so, the cell conserves energy and components (e.g. Amino Acids) for only necessary processes.
In the case of the paradigm lac operon, lactose is a fuel source, but not as good as glucose. Therefore, enzymes to digest lactose are only needed when lactose is present, but glucose is not. In order to interrogate both conditions, two additional regulatory elements are present.
First, the operator sequence. This sequence binds a repressor protein that physically blocks the polymerase’s path in the absence of lactose. However, if lactose is present, the sugar binds to the repressor, causing a conformational (shape) change that causes the protein to release its grip on the operator sequence.
Second, a catabolite activator protein (CAP) will only bind to the DNA behind the RNA polymerase if cAMP is present. Let’s not get too distracted, other than to say that cAMP levels are high in the ABSENCE of glucose, and low when that sugar is present. When cAMP binds to the CAP protein it can now bind the DNA and do it’s other job: making a nice binding site for the RNA polymerase. Without CAP, the polymerase binds very inefficiently.
Together, the production of lactase enzymes (those that digest lactose) is exquisitely controlled in a way that conserves the most energy.
Ps – take a look at this graph and tell me why (not mechanistically, but rationally) the cell does not make lactase enzymes when both glucose and lactose are present.
It’s all I can think about right now. I’m dreaming of pizza right now to possibly pre-game the event later on tonight. One of the most devastating things I’ve discovered since moving to Kansas is that it is something of a food desert.
Gene Simmons making some killer Ellio’s
What I mean by that is the East Coast Roller Rink staple, Ellio’s Pizza, is not sold anywhere near here. I looked into the Ellio’s website, hoping to find some way to set up a standing order, but my results were mixed. On the downside, I didn’t see any way to ship Ellio’s here, but I did find that there is an Ellio’s Nation to sign up for. I gather it’s something like the Kiss Army of pizza And I gather there are just about as many benefits to both groups: meaning none. But I think members of the Kiss Army at least get to post topless pictures. I couldn’t find the page where people do that on the Ellio’s site.
In population genetics there are two equations that allow us to estimate the frequency of alleles within a population and also to estimate the number of homozygotes vs heterozygotes for a recessive trait. These equations are known today as the Hardy-Weinberg equations because they were simultaneous proposed by two independent scientists. Like many equations, they assume a model that is not exactly reflective of the real world, however they do lend us an understanding of the rules of the system.
The two equations are:
q + p = 1
q2 +2pq +q2 = 1
It’s that easy. In each of these equations p stands for the frequency of one allele in a population and q stands for the frequency of the other allele. Assuming there are only two alleles, they must add up to 100%, represented by the decimal number 1 here.
In order to use these equations, certain conditions must be adhered to.
No gene flow (immigration / emigration)
No sexual selection
No survival selection
No genetic drift
The last one is the one that has been interesting me lately.
What is genetic drift? What it describes are statistical anomalies, like a run of ‘Red’ on the Roulette Wheel or an unexpectedly long string of ‘Heads’ when tossing a coin.
What happens during genetic drift is that one allele becomes favored just because of such a statistical swing. But unlike roulette or coin tosses, when an allele loses out for a number of generations, it stands a diminishing chance of being seen again. The statistical anomaly becomes ‘hard-coded’ and self-reinforcing, such that eventually alleles disappear.
The key is that small samples allow genetic drift to happen more often, while larger populations tend to not see this occur. Using out coin toss example, if you toss a coin ten times, it is not especially surprising when you get 8 ‘heads’ and 2 ‘tails’. Whereas, in a toss of 1000 coins, getting 800 ‘heads’ is nearly inconceivable.
I encountered this while coding a genetics simulation program (note: my simulation uses a Wright-Fisher model that has distinct, non-overlapping generations). I wrote the program and started testing it by allowing random breeding to occur over 100 generations or so. I started using only 100 animals in my simulation, but regularly saw one allele outcompete all others, meaning that the population had lost diversity.
Below is an example with 100 organisms with four alleles for the gene breeding randomly for 200 generations.
I was sure it was a problem with my algorithm. Then I started increasing the number of animals and the ‘problem’ went away.
Here’s a second experiment at the other end of the spectrum using 50,000 animals also with four alleles breeding for 200 generations. I’ve forced Excel to graph this out on the same axis.
All this, just to demonstrate to myself that the prohibition against genetic drift is actually another way of saying, “This only works with large populations.”
What interested me is how to know whether your population is large enough to ‘resist’ genetic drift. And, how quickly will genetic drift drive alleles to fixation / loss?
“The expected number of generations for fixation to occur is proportional to the population size, such that fixation is predicted to occur much more rapidly in smaller populations.”
Not surprisingly, there is an equation designed to predict the time (# of generations) before an allele is lost by drift.
The expected time for the neutral allele to be lost through genetic drift can be calculated as
where T is the number of generations, Ne is the effective population size, and p is the initial frequency for the given allele.
Sometimes having a computer simulation comes in handy to help get a better look at how these rules apply given different populations. I’d like to get this simulation built into a simple app for either desktop or mobile device to make public, but I have been having a lot of difficulty making the leap from a program running in the console to something worth sharing.
The Supreme Court of the United States released its ruling on the ‘Association for Medical Pathology v. Myriad Genetics, Inc.’ case today. Briefly, they ruled that Myriad’s patent is invalid as they merely discovered a natural entity. Because they did not alter the material in any way vital to their industry or possess a methods claim associated with this material, their patent fails because “laws of nature [or] natural phenomena …lie beyond the domain of patent protection” according to precedent set under United States Code.
Wait – you mean the USC clearly states that they couldn’t patent this stuff? Well, no.
“Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor…”
The applicable precedent case is Mayo v. Prometheus___566 U.S. In that case, Prometheus had a patented clinical diagnostic kit that Mayo Collaborative Services (a nonprofit affiliated with the Mayo Clinic) used for some time until they developed their own version of the kit. (A pretty close precedent). In this case, the court ruled that, “Because methods for making such determinations were well known in the art, this step simply tells doctors to engage in well-understood, routine, conventional activity previously engaged in by scientists in the field. Such activity is normally not sufficient to transform an unpatentable law of nature into a patent-eligible application of such a law.”
From these rulings it appears that in order to become a patentable entity a gene must be novelly transformed in some manner that makes it functionally distinct from the naturally occurring entity, or that the method for interrogating the gene involves some novel method beyond what is previously known art.
As you can see from my previous post, my general bio class has been delving into the molecular mechanisms of replication, transcription and translation. All of these processes were worked out in the latter half of the 20th century following the publication of DNA’s structure by Watson and Crick. Because Watson and Crick’s work was so seminal, it seems reasonable for me to make a couple of book recommendations relating to that work. The first is The Cartoon Guide to Genetics. With a title including the word ‘cartoon’, it is tempting to dismiss this book, but you would be doing yourself a disservice. This is one of the most clearly written genetics books you can ask for. Despite the apparent simplicity, it is surprisingly thorough. I am presently considering making this book required reading for a genetics / ecology course I am planning.
Another book is James Watson’s The Double Helix. This book is short and an easy read, yet it puts you right in the center of the action – both scientific and personal – that surrounded the elucidation of this molecule’s structure.
This brings me to my request… As I mentioned above, I am working on a new course which will act as a second semester to my current general bio class. The main topics of this class will be inheritance, population genetics, the dynamics of populations and how all this informs our knowledge of evolution. I have a couple ideas already, but I thought I would open this space up to accept any suggestions the peanut gallery may have. If you have a book that you like that was a good read and brought up some interesting conversations, let me know and I’ll check it out.