Examining the probability of inheriting Psoriasis within my family
MATH SL: INTERNAL ASSESMENT
HARIS ISHFAQ
In this assignment, I used Microsoft Excel, ProgenyGeneticsTool and SmartDraw to create graphs, charts and diagrams, respectively.
Candidate declaration: I confirm that this work is my own and is the final version. I have acknowledged each use of the words or ideas of another person, whether written, oral or visual.
Candidate’s signature:………………………………….. Date:……………………………
Introduction:
Our body is very complex, it consists of 23 pairs of chromosomes divided from both of your parents. While this process is amazing, it may come with some negatives too. Genetic diseases can be defined as “A disease caused by an abnormality in an individual's genome” (MedicineNet, 2018). These diseases may be passed down to offspring during reproduction during the pairing of chromosomes within both parents. An example of a genetic disease is Psoriasis, which can be defined as “a common, chronic, genetic, systemic inflammatory disease that is characterized by symptoms and signs such as elevated itchy plaques of raised red skin covered with thick silvery scales” (Cole, 2018). With this being said, there is many ways to control this disease, however, it is not curable, but there is many ways psoriasis can be treated to decrease the damage it may cause. Some examples of this are avoiding the heat, or not staying in the heat for too long, as the heat can further deteriate the flaky skin.
Some other items may be prescribed, such as gel to control the psoriasis, an example of this gel is Dovobet. This is applied directly onto the infected areas twice a day every day until the flare from the disease dies down. If that doesn’t work, your doctor may send you to receive intense laser treatment as the Dovobet might not be enough to control the disease.
Background Information:
Some general knowledge must be acquired to complete this investigation. To pass down genetic diseases. During reproduction, both gametes (sperm and egg cells) have 23 pairs of chromosomes, a total of 46. When fused together, they create a zygote, which only inherits 23 of the chromosomes, 23 different chromatids (thread like strands that are combined with a centromere to create a chromosome) from the father and the mother.
, this is referred as a zygote. This entire process is called fertilization (Your Genome, 2017).
During the process, the zygote may inherit the gene for a genetic disease through the pairing of the chromosomes as it is varied. The disease being looked at throughout this experiment is Psoriasis, which is a dominant sex-linked gene. In terms of the father, if they carry the gene, they will always have the disease, this is because the disease dominant, this means that the gene is restricted to the single X chromosome the male possesses. However, in the case of the female, they have 2 X chromosomes. This means that with regular genetic diseases, there would be a chance of receiving a recessive allele (different form of a gene which is less effective than a dominant allele) which would mask (limit the effects) a dominant gene if present, this would cause the female to become a carrier (ex; the genotype of a female carrier would look like “Ff”, whereas the genotype of a diseased female would be “FF”). However, as the Psoriasis only comes in dominant form, there is no chance of the female receiving the recessive allele. This means that the female also can either have the disease or not have it at all.
When determining the probability of inheriting the disease, some other factors may be taken into account, such as determining whether or not the parents carry the gene (as it may show up later their life). Other factors such as the sex of the child is irrelevant in this situation as the disease is dominant, meaning that regardless of the gender, if the child inherits the gene for the disease they will have it. The reason behind the irrelevancy of the child’s gender is the because the trait of a dominant sex-linked allele.
Rationale:
Psoriasis is a disease that has ran through my families’ bloodline for generations, from myself to my father, it has had a great impact on our lives. With the pain that the open sores cause, it required intensive care at all times to make sure the sores don’t deteriate.
Although this disease caused pain to each individual in my family who possessed it, it also affected the ones who didn’t. When my grandfather was struggling to make money back in Pakistan, he had to look for a better job to provide for my mother and her siblings at the time. He then went to enlist into the army. He had passed all the tests, but when it came to the medical exam, he fell short due to the scaly sores of Psoriasis running up his legs. He was then declared medically unfit to serve for Pakistan and had to find another job.
With all of this being said, it can be concluded that this disease has had its impact on my family and affects us all to this day. This made me wonder the possibility myself or my elders not having the disease, or even the possibility of them getting it in the first place. This led me to my aim.
Aim of Investigation:
The aim of the investigation is to determine the probability of myself inheriting Psoriasis from my parents, as well as determining the probability of my future children inheriting the disease.
Focus of the investigation:
To determine the inheritance probability by using knowledge acquired from research and through previous courses that I have taken.
To complete this investigation, I will research within the bloodline of both my fathers and my mother’s family to determine who had the disease and who didn’t, by doing this I can determine how the disease was passed down through both families. With the results acquired from this experiment, I can determine the risk of my future children having the disease, as well as the chance that I had of inheriting/not inheriting the disease.
Modelling my family:
As this experiment is directed personally towards my own family, I will attempt to model my family with the little knowledge of my family’s genetic history, starting with my parents and moving down to my generation. As my mother does not have the disease and my father does, that already gives me a basis to start with. As for my siblings, none of my 3 sisters have the disease, leaving myself to be the only one with the disease. Although, this model will be made with the knowledge of my sisters and my mother not having the disease, there is still a possibility that it may show up later in life for them. Since there is no way of predicting whether or not they will inherit the disease, the model will have to be created in terms of the most recent updated history of my family. The model would end up looking like the following:
Diagram 1: Pedigree Chart of 2nd and 3rd generation
As seen above, my family is modeled by showing my mother, my father and my 3 siblings. It can be seen that the only people to have the disease as of right now are myself and my father. However, after doing some further investigation it can be seen that other members which go further down my family also have inherited the same disease. Therefore, the updated family will be modeled as followed.
Diagram 2: Pedigree chart of 1rst, 2nd and 3rd generation.
The new pedigree chart above accounts for all known Psoriasis carriers within my family’s bloodline. This now accounts for my maternal grandmother, maternal grandfather along with his siblings and my fraternal uncle. This chart brings up an interesting find as it shows that not every male is affected by this disease in my family, as my grandfather’s brother did not have it and so did my father’s brother. It also shows that not all females are unaffected as my grandfather’s sister was also affected. With all the new information above, the probability calculations can be made.
Probability of Inheriting the Disease:
After finding all history of the disease running throughout my family, I can finally calculate the probability of inheriting the disease within my family. As said previously, recessive alleles cannot mask the effects of the dominant gene. Some factors that have to be taken into consideration such as the history of the disease within the family, whether my parents had the disease or not. However, the gender of the person does not matter in this situation as the recessive allele cannot mask the effects of the dominant allele. To help determine the probability of inheriting the disease, I will use a punnet square (the process of crossing the different genotypes of both parents to find 4 new possible genotypes) to model my family (2nd generation). To model the family, I will use the letters “F”, to represent the dominant allele and “f” to represent the recessive allele.
Diagram 3: Punnet Square of Family.
Ff
ff
Ff
ff
In the diagram above, it shows that the possibility of myself and my sisters of having the disease while being homozygous is 0 as my mother is not a carrier of this disease. As shown as the diagram, none of the genotypes are carrying 2 of the dominant alleles. Furthermore, the probability of having the disease with a recessive allele, or being heterozygous, is 50%. The probability of not having the disease with homozygous recessive alleles is 50%, this can be seen by using a formula P(A B)= P(A) + P(B) (International Baccalaureate, 2018), where P(A) is the chance of having the disease and P(B) is the chance of not having the disease. The total probability, which is represented by P(A B), will always equal 1, using this and either the probability of inheriting the disease or the probability of not inheriting the disease.
P (A B) = P(A) + P(B)
1 = 0.50 + P(B)
P(B) = 1 – 0.50
P(B) = 0.50
As seen above, the chance of having the disease while being heterozygous is 0.5, the chance of being affected while being homozygous is 0 and finally the chance.
Now to find some variation within the data, I will repeat the same process but I will make the mother diseased with Psoriasis to see how the results would change compared to the mother not having the disease in the first place. The reason I will be doing this is because my mother does not have the disease as of right now, but it may show up later in life. Therefore, the following results show us how the probabilities may change if the disease is later inherited by my mother.
Diagram 4: Punnet Square of Family.
FF
Ff
Ff
ff
Now if we look at the new diagram above, where the new punnet square has been made to give my mother the disease, we can see that the chance of myself and my siblings being affected by the disease while being homozygous is 0.25, while the probability of being affected while being heterozygous is 0.50. Finally, the probability of being completely unaffected of the disease is 0.25. Once again, if we use the same variables as above (P(A) is the chance of having the disease, P(B) is the chance of not having the disease and P(A B) is the total probability, which will always equal to 1), we can find missing variables.
P (A B) = P(A) + P(B)
1= P(A) + 0.25
P(A)= 1 – 0.25
P(A) = 0.75
With the use of the punnet squares, the following table can be made to help model the situation. Where P(A) is being used to represent the probability of genotypes that have the disease and are heterozygous (Ff), P(B) will be used to represent the genotypes that are completely unaffected (ff) and finally P(C) will be used to represent the probability of the genotypes that do have it while being homozygous. (FF).
Table 1: Probabilities for genotypes
Situation
P(A)
P(B)
P(C)
Mother without Psoriasis
0.5
0.5
0
Mother with Psoriasis
0.5
0.25
0.25
If we are to analyze the table, its shows us how the data can significantly change when the mother possess the disease. It can be seen that the children have a better chance of being unaffected while the mother does not have psoriasis, this is most likely because of the vacancy of the dominant psoriasis allele within the chromosomes.
With the following data, we can create a tree diagram of both situations, where either the mother is infected or not, and see how the children of the infected child, being myself, would turn out and the probability of them being diseased
Diagram 5: Tree Diagram (Mother without Psoriasis)
Diagram 6: Tree Diagram (Mother with Psoriasis)
Using all of these probabilities from these diagrams, I can determine that probability of the grandchildren being affected by the disease through the following equations
1. Heterozygous Grandchildren:
P(A) = [P(A) x P (A|A)] + [P(B) x P(B|A)] + [P(C) x P(C|A)]
2. Homozygous Grandchildren
P(B) = [P(A) x P (A|B)] + [P(B) x P(B|B)] + [P(C) x (P(C|B)]
3. Unaffected
P(C) = [P(A) x P(A|C)] + [P(B) x P(B|B)] + [P(C) x P(C|C)]
Sample Calculation for Heterozygous affected with diseased Mother:
P(A) = [P(A) x P (A|A)] + [P(B) x P(B|A)] + [P(C) x P(C|A)]
P(A) = [(0.5) (0.5)] + [(0.25) (1)] + [(0.25) (0)]
P(A) = [0.25] + [0.25] + [0]
P(A)= 0.5
Table 2: Probabilities of the Grandchildren inheriting the disease
Situation
P(A)
P(B)
P(C)
Mother with Psoriasis
0.5
0
0.5
Mother without Psoriasis
0.25
0
0.75
Processing the following data:
To analyze the data, I will graph it along with the probabilities pervious found, to see whether or not one generation is better off compared to the other. The new tables will be below along with their corresponding graphs.
Table 3: Probabilities of 3rd and 4th generation inheriting the disease (Mother without Psoriasis)
Situation
P(A)
P(B)
P(C)
3rd generation
0.5
0.5
0
4th Generation (predicted)
0.25
0
0.75
Graph 1: Probabilities of 3rd vs 4th generation inheriting the disease (Mother without Psoriasis)
If we look at the following graph, we can see that the 4th generation had a higher chance of becoming homozygous affected (FF) compared to my generation which had no chance. Although, my generation had a higher chance of becoming heterozygous affected (Ff). However, these situations almost become obsolete as we are mainly looking at affected vs unaffected, and in this case the 3rd generation has a higher chance of being unaffected (ff) compared to the 4th.
Table 4: Probabilities of 3rd and 4th Generation inheriting the disease (Mother with Psoriasis)
Situation
P(A)
P(B)
P(C)
3rd generation
0.5
0.25
0.25
4th Generation (predicted)
0.5
0
0.5
Graph 2: Probabilities of 3rd vs 4th generation inheriting the disease (Mother with Psoriasis)
While analyzing this graph, the results stay similar to the previous graph. Once again, the 3rd generation is still better off as it has a higher chance of being unaffected compared to the 4th, which has no chance. The only changes are that the third generation has a lower chance of being unaffected if the mother has Psoriasis, and there is higher chance of being homozygous and heterozygous affected compared to the mother not having Psoriasis.
Extension Idea
After completing the following experiment, it made me wonder the different types of scenarios that can be modeled, for example, the probability of one child being affected with Psoriasis in a family of 4 kids.
The following can be done using the binomial distribution equation, (International Baccalaureate, 2018). In this equation, N will represent the number of trials (or in this case, the number of kids), r will represent the number which we are looking for (1) and p will represent the probability of inheriting the disease (0.5). The equation will look like the following.
As we can see in the following results, once completing binomial distribution, the probability of one child being affected in a family of 4 kids is 0.25. This is very similar to myself as I am the only child out of 4 kids who is affected by Psoriasis as of right now. This means that there was a 25% chance of only me (or one of my siblings) being affected out of all 4 of us.
Reflection:
As we look back in the report, many conclusions and results were found. Firstly, it was discovered that the probability of being affected by Psoriasis varies on whether or not the mother possesses the disease. When looking at the 3rd generation, it could be seen that there was a higher chance of not possessing the disease (Please refer to Table 1) when the mother did not have the disease compared to the mother possessing the disease. As for the predicted generation (future children), it can be seen that their parents would be better off than them as they have a high chance of not inheriting the disease whatsoever, whether the mother has Psoriasis or not.
These results could be helpful in the future for myself or my siblings, as we can see the probability of our future children inheriting the disease depending on whether or not the spouse has the disease.
Many limitations can be found within the lab, such as the assumptions made. The report was conducted using the most updated version of my family, however there is always a chance of my mother or my siblings showing signs of the disease later on in life. My grandfather was not diagnosed with the disease until near his death after he retired at the age of 75, this means that if my family members do possess the disease, such as my sisters, the results may change.
These results may relate to different diseases too. As many diseases can be sex linked and only be available in dominant form, these results could be the exact same as another disease. An example of this is Retts Syndrome, a dominant sex-linked disorder which is causes impairment issues later on in life (Rettsyndrome.org, 2018). The results would be very similar if it were to be done with Retts Syndrome as it has the same genetic properties as Psoriasis.
A possible future extension to this experiment is to later on in life examine the actual results of my children, niece and nephews and compare the results of Psoriasis existing within them to the predicted results made many years before they were born.
Conclusion:
This experiment was very insightful as it provided myself with many different results that could have occurred, which made me realize how much different the lives of myself and my family could have been.
Works Cited
“About Rett Syndrome.” RettSyndrome.org, www.rettsyndrome.org/about-rett-syndrome.
“Definition of Genetic Disease.” MedicineNet, www.medicinenet.com/script/main/art.asp?articlekey=31302.
“Definition of Proband – NCI Dictionary of Cancer Terms.” National Cancer Institute, www.cancer.gov/publications/dictionaries/genetics-dictionary/def/proband.
Ewens, Warren J. “Mathematics, Genetics and Evolution.” SpringerLink, Humana Press, 6 Feb. 2013, link.springer.com/article/10.1007/s40484-013-0003-5.
“What Is Inheritance?” Stories, The Public Engagement Team at the Wellcome Genome Campus, 3 Mar. 2017, www.yourgenome.org/facts/what-is-inheritance.