Inv 2: Hardy-Weinberg

Abstract
Through the creation of our own Hardy-Weinberg Equilibrium equation, the lab group tried to better understand the process by which evolution occurs and use a program such as Microsoft Excel to model passing on of alleles for a certain gene in an extremely simple way. After establishing our usable model and testing it a few times, then more complex evolutionary factors were added, such as a heterozygous advantage, to better understand the process of evolution in the world. I made two hypotheses for my own personal Hardy-Weinberg model, that the Hardy-Weinberg model will work best with large populations because the larger the population the less wild variation can occur between two successive generations. The other hypothesis that I made was that in the case of a heterozygous advantage, the alleles of a gene will approach even percentages in the population (i.e. 50-50) because the heterozygous individuals have 50% of each allele and the heterozygous will survive to pass on their genes.

Procedure
To create the Hardy-Weinberg model, I used Microsoft Excel, a spreadsheet program that can also perform basic mathematical operations, which would be extremely useful for modeling evolution. I began by inputting the initial frequency of p (the dominant allele) and q (the recessive allele). It does not really matter what these two values are, because the operations will work regardless of the value. The p and q values both had to be between 0 and 1, and must add to equal 1. So the q value is 1-p and vice versa. Then I began creating my zygotes by randomly assigning an A (for dominant allele) or B (for recessive) by using the random number and the if functions in the program.

The random number function produces a random number between 0 and 1 in the cell it is input into. The if function checks the value of a predetermined cell and decides to show one of two outcomes. The if function can become more complicated by embedding more if functions in the original if function, allowing for a variety of outputs. In the first allele cell, I typed out =IF(RAND()<=D$2, "A","B"). This may seem like computer gibberish, but in fact this is the combination of the if and random functions. It says "if the random number generated is less than or equal to D2 (which is the allele frequency of A in this generation), then the out put is an A. If the random number is greater than D2, then the output is a B. Through this, I was able to craft a system by which I could randomly generate zygotes, and then add them up using a simple sum function, which is simply adding together the values of different cells on the spreadsheet. Here is a sample of the spreadsheet:

With simple copy and paste functions, I was able to extend the spreadsheet as far as I liked, allowing me to have an almost infant population with which to test hypotheses.

For however many individuals I had in my population, I had to add together all of the different genotypes that I produced (AA, AB, or BB) and then figure out the allele frequency for A or B in that generation so that I could use this frequency in the ensuing generation and then create more generations all linked by "common ancestors". To find the total A gametes, I added 2 times the number of AA individuals (because they have 2 A alleles) and one times the number of AB individuals (because they only have 1 A allele) and this gave me the total number of alleles in the population. I then divided the total A gametes by the total number of gametes in the population, or 2 times the population size because every individual has two gametes. Then I got a number somewhere between 0 and 1 (sound familiar?) and plugged it in for the next generation. A picture of how this looks is below.

By this method I obtained values for simple populations so that I could track allele frequencies and their changes due to randomness. There were no external variables such as natural selection or incomplete dominance accounted for in this simple spreadsheet.

After completing the simple stuff, I wanted a challenge so I moved on to something more difficult. I also modeled a heterozygous advantage situation in which the heterozygous individuals had a better survival rate than homozygous individuals for whatever reason. An example of this in real life is the gene for sickle cell anemia. If you are homozygous for this gene, you get either sickle cell anemia or susceptibility to malaria. If you are heterozygous, however, you do not have sickle cell anemia and you are also immune to malaria.

For this experiment, I would take the totals numbers of individuals of each of the three genotypes and then I would multiply them by a percentage that represented the survival rate. In my simple experiment I tested a survival rate of 75% for AA and BB and a survival rate of 100% for AB. Then the allele frequencies were calculated in much the same way, the only difference being that when I divided the total number of alleles by the population size, I divided by the surviving population size. This would make sure my numbers did not get messed up.

Results

First experiment:Changing population sizes
For the first experiment modeling different sizes of populations, I found that the Harvey Weinberg Equilibrium works much better with larger populations rather than small ones. This proved my hypothesis correct about larger populations being more stable. But how did the model show me this?

Below are the graphs for the 5 generations of an organism with only 10 individuals in the population. Also the original allele frequencies that I began with were 50% for both A and B.

As you can see, there is quite wild fluctuation in the number of individuals with each genotype. In fact, in the first population there are 0 of the AA genotype, but by generation 5, there are 3. These wild shifts in genotypic ratios showed me that a small sample size was not good. I thought then perhaps a medium sample size would be best, so I created a spreadsheet with 100 individuals per generation. I also started with the same allele frequencies at the beginning, 50% for both A and B. The graphs are given below.

Ass seen in these graphs, the wild fluctuations that were seen in the population size of 10 are gone. Though there are still some fluctuations, seen in the jump of BB individuals between generations 2 and 3, but they are much more mild than that of population of 10. I saw that increasing the population size led to less wild fluctuations, so I thought that I could increase the population size even further. I then increased the size of the population to 1000, started with equal amounts of allele A and allele B in the population, and created graphs for those five generations as well. These graphs are shown below.

As seen in the graphs above, the ratios of genotypes are much more concrete with a very large population. There is some slight fluctuation, but nothing major at all. Therefore, I concluded that the genotypic ratios proposed by Hardy-Weinberg work best in a large population because there is less of a chance for dramatic changes that are extremely possible in small populations. After this I moved onto my next experiment, that of the heterozygous advantage.

Second experiment: Heterozygous advantage
For this experiment, I created 3 sets of generations. The variable that I changed in this experiment was the ratio of A and B alleles in the starting population. I held my population size steady at 1000 and I gave the homozygous individuals a 75% chance of survival and the heterozygous individuals a survival rate of 100%. My first trial was done with allele frequencies of 50-50 to begin with. I thought this would be a good experiment because it could show that even though fluctuations may occur in the first few generations, there will be a trend of the frequencies approaching 50-50 again. Here is a graph of the allele frequencies over the 5 generations that I tested.

As I predicted, there was some initial fluctuation and the A allele, represented by the blue line, was less common than the B allele, over successive generations, I can see that the two lines are getting closer together. This means that the two frequencies are approaching more equal ratios than they began as. To test my hypothesis further, I changed the starting allele frequencies to 70% A and 30% B alleles. Here is a graph of those results.

The graph shows that the A allele began the experiment as having much more of a share of the gene pool's allele frequency, and the B as having less. Yet over every single generation, the A allele lost some of that share and the B allele gained some of that share. Therefore, the two alleles are once again approaching equality in representation in the gene pool. Finally, to really test my hypothesis, I started an experiment with the A allele being 90% of the entire gene pool, and the B only having a mere allele frequency of 10%. Here is a graph of that trial.

Once again, there is an obvious trend that shows the two allele frequencies are getting closer together. The A allele frequency, which started out so high, consistently decreased while the B frequency consistently increased. These trials proved my hypothesis was correct because eventually, all three trials will approach 50% allele frequency for both A and B. Because this is not an exact science and incorporates an element of randomness, the allele frequencies won't hit exactly 50-50 and stay there, but they will continues to fluctuate. However, the two frequencies will be quite close to one another in value and close to a 50-50 split.

Conclusion
I think that the entire experiment was a success. I successfully modeled the Hardy-Weinberg hypothesis and also proved both of my hypotheses correct. Larger populations will produce the best results for the Hardy-Weinberg equilibrium, and if there is a heterozygous advantage, no matter what the int ital allele frequencies are, the allele frequencies will approach 50-50. I think that the only part of the equation that I wish I had done was tested different evolutionary methods such as natural selection or a bottleneck effect. These would have been fun and interesting to do, but unfortunately other commitments have forced me to confine myself to only testing a single evolutionary method.

ALIEN LIFE FOUND

During our mission on the C-223 Bellarmine class starship, the Biology AP crew crash landed on an unknown planet in the far reaches of our solar system. Seeing our misfortune as an opportunity to explore and maybe take some samples, the crew did a quick search of the perimeter. During our exploration, multiple alien life forms were discovered, and these samples were bagged and brought back to the shit for further examination. Below is the video log of our ensuing dissection of the alien life form.

https://www.youtube.com/watch?v=zBaIaSfcYG4&feature=youtu.be

Why should this creature be considered life? Well, as mentioned in the log, we discovered that the organism had some digestive structures, as well as a beak to take in food, so it must digest and eat its own food. We also found some structures that looked like reproductive organs, so the organism must reproduce. Also, the creature has tentacles, used either for moving, grasping, or both, so the organism interacts with its environment under its own volition. Even though we did not see the creature move, we can infer this regardless. The creature has multiple layers of membranes separating different organs and protecting it from the outside world, so therefore there is a level of higher organization that goes along with this organism. I am not 100 percent sure of the qualities that are necessary to determine whether or not something is "alive", but i believe that this alien organism can be considered a life form.

This life form is an extremely important discovery for mankind because it shows us that we are not alone in the universe, and that there may be other similar organisms to us on planets similar to Earth. Though at first glance the alien we found does not look like a human, there is similarity. Both have bilateral symmetry, both have similarly shaped eyes, and both seem to be dependent on water. The creature was filled with many different types of nontoxic fluid, and even seemed to be covered in different fluids, so we can hypothesize that this creature consumes water to keep itself moist.

We are bringing these alien life forms back to Earth for further study, but I am happy to declare this mission a success and I hope for the C-223's safe and speedy return to Earth and our families.

Restriction Enzymes and Electrophoresis

Introduction
When talking about restriction enzymes, it is necessary to first talk about viruses. Viruses are small packets of protein and DNA that are not actually classified as lifeforms for a few reasons. Most prominent of which, viruses cannot reproduce. In order to keep the species alive and pass on genetic material to offspring, viruses infect other cells, either prokaryotic or eukaryotic, and insert their DNA into the DNA of that cell. Then the cell is forced to produce large amounts of the viral proteins and create many copies of the original virus inside of the cell until its usefulness runs out and the cell is killed by the viral DNA, allowing the new viruses produced to spread and infect others.

As a defense mechanism against viral attacks, many bacteria and eukaryotes have developed what are called restriction enzymes, or proteins that cut DNA. Therefore, when a virus inserts its DNA into a new host, that host's restriction enzymes would cut the DNA into fragments, not allowing the cell to become infected. The restriction enzymes only work at sites on the viral DNA called palindromes, or places where the base pairs are the same in one direction as they are in the opposite direction on the corresponding strand.

Restriction enzymes have become an important part of gene splicing by making it possible for scientists to connect two sets of genes of different organisms or replace harmful genes that a person has with healthy genes. Also, through a process called gel electrophoresis, in which DNA fragments are run through gel by a current, similarities or heredity can be found between people, being an important tool for paternity testing among other things.

During the week of February 8th, the lab group of Shreyan,  Mark, Vinay and Vikram returned to the lab to perform DNA cutting using restriction enzymes and also gel electrophoresis. Through this process, the group should be able to determine the size of the DNA fragments cut by the enzymes. The group was tasked with using lambda virus DNA, which is about 50,000 base pairs long.

Procedure
On the first day of the week, we gathered our materials together and then set to work. We had 3 microtubes of different restriction enzymes which were called; PstI, EcoRI, and HindIII. We also had a microtube full of uncut lambda DNA strands. For our four experiment microtubes, one we filled with Lambda DNA and a restriction buffer, and the other were filled with Lambda DNA, restriction buffer, and one of the enzymes listed above. The tubes were labeled P, E, H, and L, and below is a table of their contents.

Tube	Lambda DNA	Restriction Buffer	PstI	EcoRI	HindIII
P	4 µl	5 µl	1 µl	0 µl	0 µl
E	4 µl	5 µl	0 µl	1 µl	0 µl
H	4 µl	5 µl	0 µl	0 µl	1 µl
L	4 µl	6 µl	0 µl	0 µl	0 µl

After this we spun the tubes in a centrifuge to mix the contents completely. Having mixed the contents of each tube, the group left the tubes overnight so that the restriction enzymes could do their work.

On the second day, I was unfortunately absent due to illness, but Vinay, Shreyan and Vikram continued the experiment without me. The second day was the gel electrophroesis day. The group obtained marker DNA from our teacher, and the function of the marker DNA is to be completely split up by the enzymes we were using in order for us to estimate the length of the strands of DNA used in our experiment. The marker DNA, as well as the other DNA and restriction enzyme samples that we had, were loaded into agarose gel, pictured below. The agarose gel that was used was actually clear, but the picture below is of the gel after it has been stained so that we could see the distance traveled by the DNA fragments.

When we are ready to begin the electrophoresis, a current will be run through the gel, and because it is a negatively charged acid, the DNA will flow towards the positive electrode. However, the gel acts as a viscous buffer to the DNA, so not all of the DNA will flow to the positive electrode quickly. Instead, smaller fragments of DNA pass through the gel easier and will travel further towards the positive electrode than larger fragments of DNA.

The agarose gel, with the DNA fragments loaded up inside of it, was then put into the electrode apparatus, pictured below, and a current was run through the gel for about 20 minutes.

After the gel was removed from the electrophoresis apparatus, the gel was dunked in fast acting blue dye overnight so that the DNA bands were visible. The process by which the gel was stained is shown below.

On the third day, results were gathered and the lab group measured the lengths that the DNA traveled down the gel from the DNA wells that all of the fragments started in. This is shown below.

Data/Observations
Unfortunately, because I was absent for all but the first day of the lab, I was not able to gather data with my lab group. But, after explaining what the data meant, and also a discussion with my teacher Mr. Wong, I was able to understand the data set that resulted from the experiment.

Using the data gathered in this experiment, the group was tasked with estimating the length of the DNA strands cut by each individual restriction enzyme. To do this we had to compare the bands that we saw in our agarose gel to lengths traveled by fragments that were in the marker group. These strands were known to have a certain base pair lengths, so we could estimate the lengths of our DNA fragments through comparison and a little bit of educated guesswork. Unfortunately, our groups's marker DNA lane was not recorded correctly or simply did not perform as it was meant to, so the DNA lengths were borrowed from our classmates.

Here is a table of the distances traveled by each lane, including the marker DNA lengths obtained from our peers:

	M (Marker DNA)		L (Uncut DNA)		P (PstI)		E (EcoRI)		H (HindIII)
Bands	Distance in mm	Actual base pairs	Distance in mm	Estimated Base Pairs	Distance in mm	Estimated Base Pairs	Distance in mm	Estimated Base Pairs	Distance in mm	Estimated Base Pairs
1	14	23,130	10.2	50,000	15.2	20,000	15.2	23,000	15.2	21,000
2	16	9,416			19.1	6,000	19.1	6,000	17.8	7,000
3	18	6,557			20.3	4,000
4	22	4,361
5	27	2,332
6	Not visible	2,027

Using simple guesswork and estimation, the group assigned values of base pair lengths to the DNA fragments that were cut using restriction enzymes. But is there a better way to estimate fragment lengths? A second way that the group estimated the lengths was using what is called a semilog graph. Using the info from the marker DNA group, we created a graph relating distance traveled to base pair length of the DNA strands by plotting the points of the marker strand and creating a line of best fit. This graph is shown below. Then, by using the graph, the group was able to estimate lengths of the DNA fragments somewhat easier.

Using this graph, we estimated the base pair length of each DNA fragment, shown below.

	M (Marker DNA)		L (Uncut DNA)		P (PstI)		E (EcoRI)		H (HindIII)
Bands	Distance in mm	Actual base pairs	Distance in mm	Estimated Base Pairs	Distance in mm	Estimated Base Pairs	Distance in mm	Estimated Base Pairs	Distance in mm	Estimated Base Pairs
1	15.2	23,130	10.2	55,000	15.2	18,000	15.2	18,000	15.2	18,000
2	17.8	9,416			19.1	8,000	19.1	8,000	17.8	10,000
3	19	6,557			20.3	6,000
4	22	4,361
5	27	2,332
6	Not visible	2,027

As you can see, some of the values are extremely different in the new table of estimations.

Conclusion
I believe that the experiment can be considered a success. Though our marker DNA did not turn out as planned, we were still able to create our semilog graph and also get some good estimations of the length of our other DNA fragments. I am not completely sure whether or not any of our results are correct and that is the actual length of each fragment, but I am willing to bet we got somewhat close to the right answer. I know that our estimations for the uncut lambda DNA, about 50,000 base pairs is correct, and I think the cuts made by PstI and EcoRI were valid too. I am not sure whether or not the cuts made by HindIII, or at least the data we recorded from it, were valid. I think I remember reading somewhere that the lambda DNA is cut in many places by HindIII, but it was only cut into two fragments in our experiment.

I believe the only error made during this experiment was in collecting data from the agarose gel. I know that the data we gathered regarding the marker DNA was wildly incorrect, so much so that had to use another group's data to get the correct graph. I am also skeptical about the results gained from the HindIII cuts, as mentioned above. I think that when looking at the agarose gel, it is necessary to shine light from the bottom up through the gell so the dyed lines of DNA are extremely clear and can be recorded easily. I also think that when graphing the semilog graph, it would have been easier to graph on paper rather than the iPad so that we may use a rule and get better, more accurate results.