The Mechanism of Evidence of a Ninth Good Will Hunting Stress pp. 6 & 7 Planet? pp. 14 & 15 Math pp. 16 &17

MiltonHelix Academy’s Science Journal Winter 2020

Page 1 Contents No More DSBs? How Base Editing Takes CRISPR to a New Level 3, 4, & 5 by Anna Yang

The Stress Mechanism 6 & 7 by Miriam Zuo

Bayes’ Theorem 8 & 9 by Nikhil Pande

Photography 10 & 11

Quantum Dots: Tiny Crystals Brightening Today’s Technologies 12 & 13 by Wilder Crosier

A Ninth Planet in our Solar System!? 14 & 15 by Luca Mostofi

Solving the Good Will Hunting Problem 16, 17, & 18 by Madeleine Cesaretti

Rising Through the Thrilling Haze (Poem) 19 by Anna Yang

Helix Editorial Board 2019-2020 Co-heads Miriam Zuo Kiran Biddinger Wilder Crosier

Senior Editors Zaki Alaoui Nikhil Pande Maya Geyling

Faculty Advisor Mr. Sando Special Thanks to. . . Mr. Edgar, Dr. Richards, Mr. Reilly, Ms. Pedersen, Mr. Kernohan, and Ms. Lockwood

Page 2 No More DSBs? vides a gene editing technique called base editing that di- How Base Editing Takes CRISPR to a New Level rectly and irreversibly con- by Anna Yang ‘23 verts a base pair into anoth- Gene editing is a process of initiate one of two responses, er, increasing the accuracy modifying DNA to correct non-homologous end joining and efficiency of HDR while or induce mutations. It has (NHEJ), or homology direct- suppressing indel formation the potential of curing many ed repair (HDR). NHEJ is from NHEJ. They synthe- genetic diseases such as Sick- initiated when a homologous sized an enzyme capable of le-cell anemia, color blind- strand is absent. Random in- in situ converting a C into a ness, Tay-Sachs disease, and sertions and deletions (in- U, which has the same base some types of cancer. These dels) were formed in the locus pairing property of a T. By in- diseases are caused by point where the sugar-phosphate activating the protein Cas-9 mutations, which are muta- backbone was broken by the (dCas-9) through Asp10Ala tions in the DNA sequence Cas-9 protein, disrupting or and His840Ala mutations (2), that involves a change in a sin- inactivating the gene. The cell the enzyme loses the ability to gle base pair. Consequently, uses the mechanism of HDR induce DSBs, but retains its point mutations may alter the when a homologous strand is DNA binding ability in con- amino acid sequence of the present, which uses an intact junction with a guide RNA translated polypeptides and homologous strand as a tem- that locates the target gene. impact its functioning. Cur- plate to complete the missing Then, dCas-9 is linked to a rently, the existing genom- bases. Although CRISPR is the cytidine deaminase, which ic editing technologies, such most widespread genome ed- directly converts the C into a as the CRISPR-Cas9 system, iting technique available, this U by atomic rearrangement edit the DNA base sequence method may lack in efficiency of the nucleotide. Under the through an engineered nu- and specificity. When NHEJ tested conditions, the enzyme clease. CRISPR, for exam- and HDR compete for DSB rat APOBEC1 shows the most ple, was originally a defense repair, indel formation always promising deamination ac- mechanism used by bacteria occur to some extent (1). This tivity compared to other cyt- against foreign pathogens, leads to gene disruption or in- idine deaminase enzymes (3). but was engineered in recent activation. To prevent the ran- years for targeted gene edit- dom insertion and deletion The G:U discrepancy in the ing. The enzyme Cas-9 acts as of nucleotides in response to target locus can be perma- a nuclease, and was associated a DSB, the target base must nently converted to the A:T Maya Geyling with a guide RNA that locates be directly converted with- pairing through the innate cel- the target sequence. Nucleas- out cleavage of the DNA lular function of DNA repair es such as Cas-9 induce dou- strand. This goal was achieved and replication. DNA repair ble-stranded breaks (DSB) by the recently developed is a process where a protein in the sugar-phosphate back- technology of base editing. complex recognizes a mis- bone of DNA as the first step match in base pairing, which to correcting mutations. DSBs A study by Komor et al. pro- is then corrected by a poly- Page 3 merase enzyme and sealed by gy has a significantly higher of successful C:G→A:T repair, DNA ligase. The maximum efficiency than Cas-9 medi- showing the highest efficiency efficiency of this method is ated HDR (see Fig.1b), with with the BE3 base editor (3). 50% yield of conversions (3), substantially fewer indels. By avoiding double-stranded and this suboptimal efficien- Fig.1: a) BE3 redirects the pref- breakages, base editing im- cy was a result of the cellular ered repair mechanism of cel- proved in efficiency and -re response of eukaryotic mis- match repair (MMR), which tends to repair the newly synthesized strand by recog- nizing its nicks before being sealed by DNA ligase (4). To prevent the MMR process from converting the edited U back to a C, the enzyme BE3 (5) was introduced to nick the unedited strand to simulate the newly synthesized strand for a higher probability of MMR repair (see Fig.1a). By inducing nicks, BE3 is used to manipulate MMR to target the original strand, thereby completing the substitution. With MMR favoring the un- edited G, the C:G point mu- tation could be corrected to A:U. The A:U base pair is then permanently converted to A:T, the desired outcome, through DNA repair and rep- lication. This method of nick- ing the target strand produces the base editor protein com- Fig.1: a) BE3 redirects the prefered repair mechanism of cellular base-excision repair plex (BE3, APOBEC–XTEN– by nicking the target strand, resulting in the desired outcome of base editing. b) Percentages of successful C:G→A:T repair, showing the highest efficiency with the BE3 dCas9(A840H)–UGI), base editor (3). augmenting the efficiency six- lular base-excision repair by duced indel formation rate in fold, while resulting in a mere nicking the target strand, re- the repair of point mutations. 1.1% average indel formation sulting in the desired outcome It has the potential to be uti- rate (6). Results confirm that of base editing. b) Percentages lized in a clinical setting to this base editing technolo- Page 4 cure genetic diseases caused affinity for oxygen. If an in- discoveries are in progress in by a single point mutation of dividual contains both copies the field of genetic engineer- A:T→C:G. Many inherited of the mutated gene, sickle ing. One recent breakthrough diseases resulting from a sin- cell disease occurs, with many is prime editing (7), which gle T→C point mutation ex- medical implications on the takes the concept of base ed- perienced advancement due organismal level. Base editing iting (the direct conversion to base editing. For example, already shows a significant of nucleotides without dou- sickle cell anemia was caused advancement in the treat- ble-stranded cleavage) and by a point mutation in the he- ment of sickle cell anemia and develops a safer and more ef- moglobin gene substituting a many similar diseases, by cor- ficient alternative. The poten- glutamic acid with valine in recting the underlying point tial of gene editing techniques the beta-globin polypeptide. mutation. This technology of such as base editing are end- Effects on the protein level are base editing was one of the less in the scientific and hemoglobin molecules that many newly developed meth- medical fields. What do you form clumps; this leads to de- ods of direct base editing that think the next step would be? formed red blood cells with a took the CRISPR technology sickle shape, and a decreased to a new level. Many more Sources Cited (1) Zaboikin, Michail, et al. “Non-Homologous End Precision Chemistry on the Genome and Transcriptome Joining and Homology Directed DNA Repair Frequen- of Living Cells.” Nature Reviews Genetics, vol. 19, no. cy of Double-Stranded Breaks Introduced by Genome 12, 2018, pp. 770–788., doi:10.1038/s41576-018-0059-1. Editing Reagents.” Plos One, vol. 12, no. 1, 2017, doi:10.1371/journal.pone.0169931. (7) Anzalone, Andrew V., et al. “Search-and-Replace Genome Editing without Double-Strand Breaks or (2) Komor, Alexis C., et al, “Improved Base Excision Donor DNA.” Nature, vol. 576, no. 7785, 2019, pp. Repair Inhibition and Bacteriophage Mu Gam Protein 149–157., doi:10.1038/s41586-019-1711-4. Yields C:G-to-T:A Base Editors with Higher Efficiency and Product Purity.” Science Advances, vol. 3, no. 8, (8) Ranzau, Brodie L., and Alexis C. Komor. “Genome, 2017, doi:10.1126/sciadv.aao4774. Epigenome, and Transcriptome Editing via Chemical Modification of Nucleobases in Living Cells.” Biochem- (3) Komor, Alexis C., et al., “Programmable Editing of a istry, vol. 58, no. 5, 2018, pp. 330–335., doi:10.1021/acs. Target Base in Genomic DNA without Double-Strand- biochem.8b00958. ed DNA Cleavage.” Nature, vol. 533, no. 7603, 2016, pp. 420–424., doi:10.1038/nature17946. (9) Cohen, Jon. “‘Base Editors’ Open New Way to Fix Mutations.” Science, vol. 358, no. 6362, 2017, pp. (4) Modrich, Paul. “Mechanisms in Eukaryotic Mis- 432–433., doi:10.1126/science.358.6362.432. match Repair.” Journal of Biological Chemistry, vol. 281, no. 41, 2006, pp. 30305–30309., doi:10.1074/jbc. (10) Pankaj, Radhika, and Yoshihisa Matsumoto. r600022200. “DNA Double-Strand Break Repair Through Non-Ho- mologous End-Joining: Recruitment and Assembly of (5) Eid, Ayman, et al. “CRISPR Base Editors: Genome the Players.” DNA Repair, 2011, doi:10.5772/21262. Editing without Double-Stranded Breaks.” Biochem- ical Journal, vol. 475, no. 11, 2018, pp. 1955–1964., (11) Liang, F., et al. “Homology-Directed Repair Is doi:10.1042/bcj20170793. a Major Double-Strand Break Repair Pathway in Mammalian Cells.” Proceedings of the National Acad- (6) Rees, Holly A., and David R. Liu. “Base Editing: emy of Sciences, vol. 95, no. 9, 1998, pp. 5172–5177., doi:10.1073/pnas.95.9.5172. Page 5 ciated with stress, although it The Stress Mechanism is also involved in other pro- by Miriam Zuo ‘20 cesses like regulating blood pressure and the sleep cycle (3). It is released by the adre- nal glands as a result of chem- ical interactions along the hypothalamic-pituitary-ad- renal (HPA) axis; this axis, as suggested by its name, in- volves the hypothalamus and pituitary gland in the brain, as well as the adrenal glands on top of the kidneys (4). The adrenal gland also produces adrenaline, otherwise known as epinephrine, which “makes the heart beat faster, increas- es blood flow to the brain and muscles, and stimulates the body to make sugar to use It often feels like there’s an end- and how it may be mitigated. for fuel”; these effects are per- less stream of stressors: may- Stress is the body’s ceived as an adrenaline rush be it’s time to take a step back. “fight-or-flight mechanism,” a (5). The least well known of the process that was evolutionari- stress hormones, noradrena- By this point in the school ly useful in surviving danger- line (or norepinephrine) has year, most students have ex- ous and challenging situations similar effects as epinephrine perienced stress, whether in (2). Though we no longer reg- but also has the additional the form of scrambling af- ularly encounter predators ability to elevate blood pres- ter deadlines, stressing about that threaten our survival, the sure (6). Combined, these grades, or running out of time modern world brings a host of three hormones produce the on a test. Perhaps unsurpris- stressors that continue to ac- symptoms of stress that many ingly, this feeling is common: tivate this mechanism. When people commonly experience: 79% of Americans report feel- a person faces a stressful sit- faster breathing, increased ing stressed sometimes or fre- uation, the “fight-or-flight alertness, anger, anxiety, and quently throughout the day mechanism” is activated by difficulty concentrating (2). (1). Yet, though the outward chemicals called hormones; While the specific ef- sensation of stress may be all in particular, it’s affected by fects of stress vary between too familiar, we are often less cortisol, adrenaline, and nor- individuals, the overall im- clear on its underlying causes, adrenaline (2). Cortisol is the pact of stress is negative, par- as well as its detrimental effects hormone most closely asso- ticularly when compounded Page 6 long-term. The Americanmore, the constantly elevated effort to reduce your stress lev- Psychological Association’s levels of cortisol attributed els yields worthwhile health first category of stress is acute to chronic stress are a potent benefits in the short-term, stress, which is short-term factor in anxiety, depression, but its primary value results stress; it induces a weaker im- weight gain, and memory and from its long-term benefits. mune system, difficulty sleep- concentration problems (3). Therefore, practicing medita- ing, sweating, and fainting Given the severely tion or going on a long walk (2). The second form of stress detrimental impact of stress lead to benefits that outweigh is episodic acute stress, and on our physical and men- the amount of time invested. it is associated with frequent tal well-being, we should be Potential stressors stress triggers, such as hav- conscious of actively manag- abound in everyday life, es- ing too many commitments; ing our stress levels. Sever- pecially in rigorous, competi- its effects are more severe, al strategies may be helpful: tive environments like Milton significantly contributing to exercise, reduced caffeineAcademy. Yet, stress is not elevated blood pressure and intake, a healthy diet, yoga, inevitable: our habits and our heart disease (2). A growing meditation, and breathing stress-coping mechanisms problem in our work-driven techniques (2). Searching for largely determine our body’s society, chronic stress occurs de-stressors – activities and response to the challenges of when someone lives in perpet- actions that lower stress lev- our surroundings. Instead of ual stress (2). This third type els – and building support passively accepting stress, we of stress is particularly harm- networks are also effective for should strive to take control ful, and it results in a higher many people (2). As a whole, over it to live healthier lives. likelihood of suicide, heart at- though it’s often challenging tacks, and strokes (2). Further- to find extra time, putting in Sources Cited (1) Saad, Lydia. “Eight in 10 Americans Afflicted (5) Cafasso, Jacquelyn. “Adrenaline Rush: Every- by Stress.” Gallup, 20 Dec. 2017, https://news. thing You Should Know.” Healthline, https://www. gallup.com/poll/224336/eight-americans-afflict- healthline.com/health/adrenaline-rush. Accessed 12 ed-stress.aspx. Accessed 12 Oct. 2019. Oct. 2019.

(2) Felman, Adam. “Why stress happens and (6) Nall, Rachel. “What’s the Difference Between how to manage it.” Medical News Today, 28 Nov. Epinephrine and Norepinephrine?” Healthline, 2017, https://www.medicalnewstoday.com/arti- https://www.healthline.com/health/epineph- cles/145855.php. Accessed 12 Oct. 2019. rine-vs-norepinephrine. Accessed 12 Oct. 2019.

(3) “What Is Cortisol?” WebMD, https://www. (7) Stress Graphic. Mindful, https://www.mindful. webmd.com/a-to-z-guides/what-is-cortisol#1. Ac- org/9-ways-mindfulness-reduces-stress/. Accessed cessed 12 Oct. 2019. 12 Nov. 2019.

(4) “Hypothalamic-Pituitary-Adrenal Axis.” Sci- ence Direct, https://www.sciencedirect.com/topics/ neuroscience/hypothalamic-pituitary-adrenal-axis. Accessed 6 Nov. 2019. Page 7 Bayes’ Theorem the probability using previous negative reading for the disease outcomes or conditions for when the patient does have it) by Nikhil Pande ‘21 the purpose of prediction (3). is 6%. If this specific individual Since many elements of life are The method of Bayesian prob- ends up testing positive for the left solely to chance, proba- ability contrasts the method disease, what is the probability bility is an important element of frequentist probability, in that he actually has it? of predicting the future. But which the probability of a cer- The following probability probabilities are always affect- tain event is derived from its tree incorporates the informa- ed by the given conditions of mere frequency of occurrence. tion of the problem to output the situation. Bayes’ Theorem, Frequentist probability has a the probabilities of testing posi- discovered by Thomas Bayes simple probability formula of tive and negative for an individ- and formalized by Pierre La- (number of outcomes)(number ual that either has the disease or place, serves as one of probabil- of opportunities) (4). In this doesn’t. ity’s fundamental theorems (1). way, frequentism assumes the The premise of this theorem randomness of all other fac- To find the probability of D giv- involves incorporating initial tors, making it insufficient as en P, or P(D | P), we can simply conditions to predict a future a predictor for more complex divide the P(D and P) by the outcome (2). Bayes’ theorem phenomena. total probability of testing posi- reads: We can examine Bayes’ theorem tive, which ultimately computes through a specific example. An to about 24% with a calculation of 0.0094/0.0394. Of all patients tested positive, only 24% do indeed have the disease. This value may seem extraordinarily low, but is quite plausible when considering the miniscule rate of this disease in society. For a test as important as a medical screening, the Source: https://wikimedia.org/api/rest_v1/media/math/render/ mere 24% chance of having the svg/87c061fe1c7430a5201eef3fa50f9d00eac78810 disease can look like a failure or incompetency of the test- The capital letters A and B individual goes into the hospital ing device. However, for one represent specific events. This and undergoes testing to see thing, the chance of a positive notation of P(A | B) means the if he has a certain disease. The test is extremely rare. If we probability that event A happens probability that any individual look at the probability tree, the given that event B has already in a total population has the P(P)=0.0394, meaning that this happened. disease is 1%. Additionally, the scenario doesn’t occur often. The formula relies on probability that the device used Furthermore, the uncertainty of the presence of other factors to to test for the disease delivers a only a 24% chance exists only determine the probability of an false positive (a positive reading for the probability of having the outcome. This method of prob- for the disease when the patient disease after testing positive, ability is called Bayesian prob- does not have it) is 3%, and the or P(D | P). For the probability ability, more generally meaning probability of a false negative (a of not having the disease when Page 8 testing negative, or P(D’ | P’), doesn’t have the disease after of having the disease, but when the Bayes’ theorem-derived testing negative. The P(D’ | P’) using it for negative tests, it value in fact delivers strong value is equal to the numerator gave us a very strong assurance confidence in the test’s result. of the Bayes’ theorem, which of accuracy, a 99.94% change of From the tree, we can divide is P(D’| P’)*P(D’). The denom- not having the disease. P(D’ | P’) by P(P’ | D’) + P(P’ | inator is equal to the ultimate Because of Bayes’ theorem, D). The calculation of 0.9994/ probability of a negative test, professionals in all fields are (0.96+0.04) comes out to a P(P’). Thus, when we used able to incorporate given con- probability of 0.9994, a value Bayes’ theorem for the accuracy ditions into probability calcu- that can be interpreted as a of a positive test, it provided us lations, which can help bring 99.94% chance that the patient with an uncertain 24% chance more certainty into diagnoses and other decisions. This the- orem can be used not only in regards to false positives, but also with the stock market, sports predictions, architecture, scientific predictions, and more. And through its versatility, it enhances the way we evaluate chance in this unpredictable world.

Sources Cited (1) McGrayne, Sharon Bertsch. “Why Bayes (3) Olshausen, Bruno A. Bayesian Probability Rules: The History of a Formula That Drives Theory. 1 Mar. 2004. Redwood Center for The- Modern Life.” Scientific American, 1 May 2011, oretical Neuroscience, www.rctn.org/bruno/ www.scientificamerican.com/article/why-bayes- npb163/bayes.pdf. Accessed 28 Oct. 2019. rules/. Accessed 28 Oct. 2019. (4) Annis, Charles. “Frequentists and Bayesians.” (2) O’Connell, Brian. “What Is Bayes Theorem Charles Annis P.E. Statistical Engineering, www. and Why Is It Important for Business and Fi- statisticalengineering.com/frequentists_and_ nance?” The Street, 3 Dec. 2018, www.thestreet. bayesians.htm. com/personal-finance/ education/what-is-bayes- theorem-14797035. Accessed 7 Feb. 2020.

Page 9 Photography

Mya Lampley ‘22

Maya Geyling ‘20

Page 10 Michaela Ocko ‘23

Kyra Geyling ‘23

Mya Lampley Page 11 known as a Stokes shift (4). Now, Quantum Dots: Tiny Crystals the excited electron relaxes back Brightening Today’s Technologies down to the ground state, releasing a photon of visible light (lower in by Wilder Crosier ‘21 energy than the incoming UV due to the Stokes shift) with a charac- teristic wavelength (color) defined by the bandgap (2,3) (see figure 2). What’s so special about QDs is that the physical size of the crystal determines the size of this electron bandgap, and therefore the color (or wavelength) of light emitted (5). Larger dots have smaller band

Figure 1: Quantum dots exhibit fluorescence. From one vial to the next (left to right) the QDs gaps, so they emit longer wave- increase in size by 10 nanometers. Smallest QDs emit violet light, largest QDs dots emit red light. lengths (lower energy light) to- Source: Wikimedia Commons https://commons.wikimedia.org/wiki/File:Quantum_Dots_with_ wards the red end of the spectrum, emission_maxima_in_a_10-nm_step_are_being_produced_at_PlasmaChem_in_a_kg_scale.jpg while smaller dots emit shorter Some of today’s largest innova- the photon causes an electron in wavelengths towards the blue end tions–more efficient solar pan- the valence band (the atom’s out- of the spectrum (6). When QDs are els, improved cancer imaging, ermost energy level in its ground synthesized, engineers can control and ever sharper TV displays–are state) to jump into an excited state the temperature and duration of a coming from a very tiny system: in the conduction band (a higher chemical reaction to make QDs of the quantum dot. But what are energy level) (3). The resulting en- desired sizes, and therefore desired quantum dots? And how are they ergy difference (the jump) between emission colors, without chang- such an effective and versatile the valence band and the conduc- ing the material from which the technology? Quantum dots (QDs) tion band is called the band gap dots are made (see figure 1) (10). are extremely tiny, semiconduct- (3). Electrons stay in the excited What makes these nano- ing crystals, called nanocrystals. state for a very short period of time crystals so eminent are their ap- And when I say tiny, I mean really (between 10-9 to 10-8 seconds), and plications in modern technology tiny–QDs range from 2-10 nano- during this time they lose some which extend across the consum- meters in diameter (about 10-50 of their energy. This energy loss is er, environmental, and medical atoms thick!) (1). The minute size and semiconductive properties of QDs give the crystals special op- tical properties that have made them such a distinctive technology. The QDs’ most employed property in modern technology is fluorescence: a property of some materials where they absorb light of one wavelength and reemit it as light of a different wavelength Figure 2: Schematic of fluorescence mechanism. An incoming UV photon excites an (2). When ultraviolet light shines electron from the valence band, across the semiconductor’s band gap, to the conduc- on a quantum dot, an atom in the tion band. The excited electron loses some energy by remaining in its excited state for a short period of time in what is called a Stokes shift. The now lower energy excited crystal will absorb a photon of this electron falls back to its ground state releasing a photon of visible light. ultraviolet light. The energy from Page 12 fields. Technology companies like ufactured solar cells” (7). The sun eventually attach drug molecules to Samsung and LG have created TV emits light over the entire elec- the antibodies and quantum dots displays that use QDs to give their tromagnetic spectrum, but tradi- for targeted drug delivery direct- screens richer colors. In a tradi- tional solar cells struggle to cap- ly to the cancerous cells. The light tional TV’s LCD display, a blue ture light from the far infrared. coming from the QDs would allow LED shines through yellow phos- Because engineers can produce scientists to monitor the delivery phor to create white light, which QDs at desired sizes, each with a of the drug to the cancer (9). How- can then be adjusted to any color specific band gap, they can cap- ever, researchers are concerned by the red, green, and blue filters ture the infrared light easily (7). with the toxicity of quantum dots; in each pixel (8). With a quantum Quantum dots also hold a quantum dots today are composed dot display (QLED), instead of us- lot of promise for medical imaging of compounds with heavy metals, ing phosphor to make white light, and drug delivery. Current research most commonly made of cadmi- the blue LED shines through QDs on cancer imaging involves bind- um selenide or indium phosphide with red and green sized band ing quantum dots to antibodies (10), and research so far has not gaps. Because each color in a quan- and injecting them into the body. fully clarified how QDs composed tum dot LCD display is a pure red, The antibodies will move about of these metals affect the body (11). green, or blue, the color coming the body and then bind to cancer Quantum dots, with their through the filters is more pure (8). cells. Because the quantum dots fine-tunable band gaps for light Quantum dots also have fluoresce, doctors could use UV emission, have found applications the ability to greatly increase the light to find and image cancer cells in technology across many fields. efficiency of today’s solar panels. at early stages (9). The color tun- Now, when you come across a Led Calderone writes for AltEn- ability and high brightness of QDs QLED TV, you can not only en- ergyMag that quantum dot solar makes them especially effective for joy the pure colors but also un- cells could be “at least three times cancer imaging over other fluoresc- derstand the science behind more efficient than existing man- ing molecules. Researchers hope to these fascinating, tiny crystals.

Sources Cited (1) “Quantum Dot.” ScienceDaily, ScienceDaily, www. sciencedaily.com/terms/quantum_dot.htm. (7) Calderone, Len. “Quantum Dot Solar Cells Are Com- ing.” AltEnergyMag, 22 May 2018, www.altenergymag.com/ (2) The Editors of Encyclopaedia Britannica. “Fluores- article/2018/05/quantum-dot-solar-cells-are-coming/28547/. cence.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 24 Mar. 2017, www.britannica.com/science/fluores- (8) Bourzac, Katherine. “Quantum Dots Go on Dis- cence. play.” Nature News, Nature Publishing Group, 15 Jan. 2013, www.nature.com/news/quantum-dots-go-on-dis- (3) J.M.K.C. Donev et al. “Conduction Band.” Conduction play-1.12216. Band - Energy Education, www.energyeducation.ca/ency- clopedia/Conduction_band. (9) “Quantum Dots and Medical Research.” Science Learning Hub, 28 May 2008, www.sciencelearn.org.nz/ (4) Ockenga, Wymke. “An Introduction to Fluorescence.” resources/1645-quantum-dots-and-medical-research. Learn & Share | Leica Microsystems, Leica Microsystems, 31 May 2011, www.leica-microsystems.com/science-lab/ (10) “How Are Quantum Dots Made?” Avantama AG, 18 an-introduction-to-fluorescence/. May 2018, www.avantama.com/how-are-quantum-dots- made/. (5) “Quantum Dots.” Sigma Aldrich, www.sigmaaldrich. com/technical-documents/articles/materials-science/nanoma- (11) Lee, Kyung-Han. “Quantum Dots: A Quantum Jump terials/quantum-dots.html. for Molecular Imaging?” Journal of Nuclear Medicine, 1 Sept. 2007, http://jnm.snmjournals.org/content/48/9/1408. (6) Woodford, Chris. “Quantum Dots: Introduction to Their full. Science and Applications.” Explain That Stuff, 28 July 2018, www.explainthatstuff.com/quantum-dots.html. Page 13 A Ninth Planet in our Solar Sys- planet would be roughly five times the Earth’s mass (4). No tem!? Or Are Some Physicists other known planet in our Jumping Too Fast To Conclusions solar system checks in at that mass; however, five earth mass by Luca Mostofi ‘21 is the single most common Ever since Pluto’s heartbreak- reasonably chalked up to the size of any planet that we have ing demotion to dwarf-planet, presence of this planet. Firstly, discovered in the universe (4). there have been eight planets the unique elliptical orbits of Thus, the ninth planet would in our solar system. Howev- certain objects in the Kuiper account for our system’s lack er, recent discoveries in the Belt (a ring of icy objects that of a planet of that size by pro- outer reaches of the solar encompasses the area beyond viding one. Perhaps the most system (tens of billions of ki- both Pluto and Neptune) damning piece of evidence in lometers beyond Neptune) could point towards this plan- support of planet nine is the indicate that there perhaps et’s existence (2). This poten- idea of a perpendicular orbit. could be an undiscovered tial revelation would account In the Kuiper belt, there are ninth planet that orbits very for the orbits of those Kuiper a few objects that orbit per- distantly from our sun (1). objects’ all pointing in a gen- pendicular to the orbit of the Supporters of this ninth erally similar direction (Fig- planets in our solar system, planet theory cite several, oth- ure 1) (1). A Cal Tech profes- and scientists say that the ex- erwise inexplicable anomalies sor, Konstantin Batygin, also istence of planet nine could in our system that could be mentions that this theoretical explain these abnormal orbit

Figure 1

Page 14 patterns (3). An object as sub- cally make this planet visible covering procedures would stantial as planet nine would (if you knew exactly where likely be impossible because possess the considerable grav- to look) have aligned on only of its remarkably minia- itational effects to account for two days. With the distance ture size: a five earth mass the unconventional orbits of and conditions proving to black hole would fit snugly those Kuiper belt asteroids (3). be such a hinderance, Baty- in the palm of one’s hand (7). Detractors of the hy- gin believes finding it could While the theories of a pothesis ask a single, critical take up to another decade (3). truly ancient, baseball sized question: why hasn’t anyone A more far-fetched yet black hole or of an undiscov- found it yet? The distant lo- equally intriguing theory is ered, relatively nearby ninth cation of this planet - so far that there is no ninth planet planet would undoubtedly sell from the sun that it would at all, but rather a primordial papers, they both seem im- take an estimated 10,000 black hole in our solar system plausible to me. Both hypoth- years to complete a single or- (5). A primordial black hole is eses are burdened by the fact bital period - means that even a black hole that formed im- that neither have any concrete, the most powerful telescopes mediately after the big bang visual evidence to cement their have a hard time picking up (6). Should one of these an- existence (such as a sighting). on it considering the lack of cient black holes be hiding Regardless, whether there sunlight in those reaches of somewhere in our solar sys- is a primordial black hole, a the solar system (3). Batygin tem, its mere presence would ninth planet, or nothing nov- notes that since 2017, the nat- impact the solar system in the el at all, our infinite universe ural conditions (for example same ways as a ninth plan- continues to yield fascinat- a calm atmosphere and no et (7). However, finding it ing theories and discoveries. moon) that could theoreti- using standard planet-dis-

Sources Cited

(1) Brad Jones, “NASA Press Release Says Our Solar nine-could-be-black-hole-scientists-say-18813596. System Has a 9th Planet,” Futurism, last modified October 13, 2017, accessed December 1, 2019, https://futurism.com/ (6) Alison Klesman, “What Are Primordial Black Holes?,” nasa-press-release-says-our-solar-system-has-a-9th-planet. Astronomy, last modified July 10, 2019, accessed December 1, 2019, http://www.astronomy.com/news/2019/07/primordi- (2) NASA, “Kuiper Belt,” NASA Science, last modified al-black-holes. November 13, 2019, accessed December 1, 2019, https://so- larsystem.nasa.gov/solar-system/kuiper-belt/overview/. (7) Ryan F. Mandelbaum, “What If Planet Nine Is a Bowling Ball-Size Black Hole?,” Gizmodo, last modified (3) Does Planet 9 Exist?, produced by Veritasium, 2019, September 27, 2019, accessed December 1, 2019, https://giz- accessed December 1, 2019, https://www.youtube.com/ modo.com/what-if-planet-nine-is-a-bowling-ball-size-black- watch?v=pe83T9hISoY&feature=youtu.be&app=desktop. hole-1838527880.

(4) Evidence of a Ninth Planet, produced by Cal Tech, Cal Tech, 2016, accessed December 1, 2019, https://www.you- tube.com/watch?v=6poHQ2h00ZA&app=desktop.

(5) Brittany Vincent, “’Planet Nine’ Could Be Black Hole, Scientists Say,” Mic, last modified September 30, 2019, accessed December 1, 2019, https://www.mic.com/p/planet- Page 15 Solving the Good Will that can exist off 10 verti- Hunting Problem ces and still be connected. by Madeleine Cesaretti ‘21 below is an example of At the start of the Acade- though? How can we go one graph with n = 10. my Award winning mov- about solving it? The prob- “Homeomorphic” means ie Good Will Hunting lem posed is as follows: that within the compar- (Miramax Films, 1997), a professor at MIT presents Draw all homeomorphically his class with a problem. The professor writes the irreducible trees of size n = 10. problem on the board and Before we get to solving ison of multiple graphs leaves it as a challenge for this question, we need to there does exist a one-to- anyone to try and solve. define a few of the words one correspondance be- Later that night, Will in there. First off, the trees tween the vertices in one Hunting, a genius janitor being described in this graph to that in another at MIT, solves the problem problem are not trees in -- meaning that the ver- and leaves his solution on the most traditional sense tices of one graph are ad- the board. The next day, of the word, but rather when none of the profes- they are connected graphs sor’s students are able to with no cycles -- meaning claim credit for the solv- that they consist of con- ing of the problem, the nected vertices and edges professor writes another but one can’t start and end problem on the board -- at the same point without this problem the profes- going over the same edge sor claims took him and twice. “N labeled verti- his colleagues two years to ces” refers to the number n = 10 prove. Again, Will solves of vertices in the tree and the problem but is caught thus “size n = 10” tells us jacent to vertices of an- in the act of doing so by that these trees will be other graph. On the next the professor, and thus made of 10 vertices and page are two examples of the events of the rest of from that we know there graphs that are homeo- the movie unfold. What is will be 9 edges as that is the morphic to each other. this “impossible” problem highest number of edges Page 16 ground and teamwork, it is actually quite feasible. Try solving this question on your own! The solu- tion is on the next page.

As you can see, vertices in I first encountered this G₅ and K₅ correspond to problem watching Good each other in the following Will Hunting with my way and are thus homeo- friends, but I didn’t pursue morphic to each other: it at the time: I had very lit- tle experience with graph theory, and the movie pri- marily uses this question and Will Hunting’s solv- ing of it as a catalyst for the events of the rest of the movie. Nevertheless, this year I took the math half course Discrete Math Seminar (MADSH) taught by Ms. Lockwood, where we explored graph theory “Irreducible” indicates and solved this question that in a graph there exists together as a class. While no vertices of degree 2; the this question was written degree of a vertice refers to to intentionally appear the number of edges con- difficult, with a little back- nected to a specific vertice. Right is an example of a graph that has a vertex of degree 2 that is then short- ened to be irreducible. Page 17 Solution to the Good Will Hunting Problem:

a) Draw all homeomorphically irreducible trees of size n = 10.

Page 18 Rising Through the Thrilling Haze by Anna Yang ‘23

In the oldest star, deepest sky, Laws of nature quietly lie. Behind the lenses atoms call, We’re the same and different after all. Straight up into the source we gaze, Up, up, past the thrilling haze.

Single cells divide and grow, Then down a one-way road they go. Microbes, eukaryotes, you and me, What decides how their fate shall be? Straight up into the source we gaze, Up, up, toward the thrilling haze.

Through the tree of life we climb, Driven by the passing time. On a field of dust, green was grown In a world observed but never known. Straight up into the source we gaze, Up, up, into the thrilling haze.

Science looks down with peering eyes And asks the questions deep and wise. She draws a bridge across the sea Where all unite to find the key. Straight up for the truth we chase, Up, up, through the thrilling haze.

Page 19 Cover photography by Maya Geyling

Helix Magazine, 2004-2020 Page 20 Milton’s Science Writers Club