Author Archives: Will Lin

Music and Math – Frequencies, ratios, and tuning

Beneath the beauty of music lies some interesting mathematics, from Fourier transforms of waveforms to ratios of frequencies. In this blog post, we’ll be discussing frequency ratios and tuning in particular!

The most simple ratio is the 1:1 ratio (perfect unison); that is, two sounds with the same frequency will sound at the same pitch. There is also the 2:1 ratio (perfect octave), the most consonant interval. Multiplying the frequency by 2 will always give a pitch an octave above, so the 4:1 ratio will be a perfect fifteenth (2 octaves above) and so forth. This means that if you play one tone at 100 Hz and another at 400 Hz, you will hear two tones separated by an interval of 2 octaves.

The just intonation (or pure intonation) tuning system utilizes similarly simple ratios for other common intervals. For example, the 3:2 ratio is the perfect fifth (the interval from C going up to G). The 4:3 ratio is the perfect fourth, and the 5:4 ratio is the major third.

However, our current twelve-tone musical system does not function very well when using these simple ratios. There are many intricacies with this tuning system that can result in some “out of tune” sounds and the music drifting away from the original pitch. One example is in a comma, which is the interval between a note being tuned in two different ways. For example, the syntonic comma is the 81:80 ratio.

In modern music, equal temperament is used. In our twelve-tone system, that means the difference in frequencies in a semitone is the twelfth root of 2.  A perfect fifth is 7 semitones up, thus the frequency difference is 7 times the twelfth root of 2, which roughly approximates 3/2. This system allows us to play in any key equally by having all intervals slightly out of tune from their just counterparts.

Arachidonic acid: a very important fatty acid

Arachidonic acid is a fatty acid (a carboxylic acid with a long carbon tail) with 20 carbons and 4 double bonds. Counting from the end without the carboxylic acid group, the first double bond appears at the 6th position from the end, making this an omega-6 fatty acid.

Chemical structure of arachidonic acid. Credits: Wikimedia (Public domain) https://commons.wikimedia.org/wiki/File:AAnumbering.png

Arachidonic acid is incorporated into phospholipids in cell membranes. In the process of some cell signalling events such as the inflammatory cascade, it is cleaved from phospholipids by phospholipase A2 (PLA2), after which it can be modified into many signalling molecules including the prostaglandins (PGs), thromboxanes (TXs), and leukotrienes (LTs). These are the most well-known and well-studied of the metabolites derived from arachidonic acid; however, there are also many other compounds including the endocannabinoids (ECs), and several less understood groups such as the eoxins (EXs)lipoxins (LXs), epoxyeicosatrienoic acids (EETs), hepoxilins (HXs), isoprostanes (IsoPs), and isofurans (IsoFs). Some of these compounds are quite recent discoveries and thus have little information available about them. Nevertheless, many of these compounds have biological activity associated with the inflammatory response, either with anti-inflammatory or pro-inflammatory effects. The latter molecules are still under active investigation in order to better understand the way they mediate actions in the body. [1]

The actions of all these molecules are too numerous to explain here. Some of the most well-known actions are those of the prostaglandins. If you have ever taken NSAIDs such as ibuprofen or naproxen, you will have affected this system. These drugs inhibit the cyclooxygenase enzyme, a critical enzyme in prostaglandin synthesis. Prostaglandins have diverse effects such as acting as pro-inflammatory mediators and regulating smooth muscle contraction and relaxation (such as PGE2), or causing vasodilation and preventing platelet aggregation (such as PGI2, also known as prostacyclin). Other molecules in the cyclooxygenase pathway, such as thromboxane, promote clotting and causing blood vessels to contract (such as TXA2). [2] The leukotrienes, synthesized from the lipooxygenase pathway, are inflammatory mediators. Some asthma medications, such as montelukast and zafirlukast, block the actions of the leukotriene LTD4 which can help with the bronchospasms in asthma. [3]

The endocannabinoid system is also a growing area of interest. The compound N-arachidonoylethanolamine, also known as anandamide, is probably the most well-known compound. The effects of this compound include pain sensation modulation, reward processes in the brain, and immune system modulation. [4]

This is only a small peek at the world of arachidonic acid metabolites: there remains much to be explained outside of this blog post, and much to be discovered!

Sources:

[1] Wang, B., Wu, L., Chen, J., Dong, L., Chen, C., Wen, Z., Hu, J., Fleming, I., & Wang, D. W. (2021). Metabolism pathways of arachidonic acids: Mechanisms and potential therapeutic targets. Signal Transduction and Targeted Therapy, 6(1), 1–30. https://doi.org/10.1038/s41392-020-00443-w
[2] Ricciotti, E., & FitzGerald, G. A. (2011). Prostaglandins and inflammation. Arteriosclerosis, Thrombosis, and Vascular Biology, 31(5), 986–1000. https://doi.org/10.1161/ATVBAHA.110.207449
[3] Dempsey, O. J. (2000). Leukotriene receptor antagonist therapy. Postgraduate Medical Journal, 76(902), 767–773. https://doi.org/10.1136/pmj.76.902.767
[4] Lu, H.-C., & Mackie, K. (2016). An Introduction to the Endogenous Cannabinoid System. Biological Psychiatry, 79(7), 516–525. https://doi.org/10.1016/j.biopsych.2015.07.028

More steroids, plants, fungi

Steroids are not only relegated to the animal world; fungi and plants synthesize many steroids as well. One particular example of clinical relevance is ergosterol, found in the cell membranes of fungi where it serves a similar role to cholesterol in animal cell membranes. This can be exploited by antifungal medications: azole drugs such as clotrimazole and miconazole function by inhibiting ergosterol synthesis. Specifically, they inhibit the 14α-demethylase enzyme that converts lanosterol to ergosterol (note the similarities to the cholesterol pathway discussed in this previous post). [1]

Ergosterol can also be converted to ergocalciferol in a UV-light dependent reaction, similarly to the synthesis of Vitamin D3 in animals. In fact, ergocalciferol is also known as Vitamin D2, and like cholecalciferol, ergocalciferol can be hydroxylated twice to 1,25-dihydroxyergocalciferol or ercalcitriol, which binds to the Vitamin D receptor and causes its effects, although the binding of Vitamin D2 may not be as strong. [2]

There are diverse steroids made by plants, some of which have toxic effects. Of note are digoxin and digitoxin produced by the foxglove plant. These two chemicals consisted of a carbohydrate chain attached to a modified steroid, and they can be fatal if ingested. They inhibit the Na+/K+ ATPase responsible for establishing the electrochemical gradient within the cell, which is exploited for the use of digoxin as a drug for arrhythmias and heart failure due to the ability of the medication to increase the contractility of the heart when given at low doses. [3]

These are only some of the steroids occurring in plants and fungi. In the future, maybe more will be discovered with important biological activities!

Sources:
[1] Herrick, E. J., & Hashmi, M. F. (2021). Antifungal Ergosterol Synthesis Inhibitors. In StatPearls. StatPearls Publishing. http://www.ncbi.nlm.nih.gov/books/NBK551581/
[2] Houghton, L. A., & Vieth, R. (2006). The case against ergocalciferol (vitamin D2) as a vitamin supplement. The American Journal of Clinical Nutrition, 84(4), 694–697. https://doi.org/10.1093/ajcn/84.4.694
[3] Hauptman, P. J., & Kelly, R. A. (1999). Digitalis. Circulation, 99(9), 1265–1270. https://doi.org/10.1161/01.cir.99.9.1265

Steroids, salt, sugar, sex

Steroids are biologically active compounds composed of four fused rings. Although the word “steroid” is commonly associated with anabolic steroids and muscle growth, steroids are in fact a diverse group of compounds with varying effects on the human body.

The steroid cholesterol can be either synthesized via the mevalonate pathway or are obtained from the diet. The mevalonate pathway starts with acetyl-CoA, which is converted in a series of steps to isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP), which are the building blocks of isoprenoids, a diverse group of compounds that include steroids. The enzyme HMG-CoA reductase, which catalyzes the step converting HMG-CoA to mevalonate, is blocked by statins which are used for the treatment of high cholesterol levels. The IPP units are combined to form farnesyl pyrophosphate, which are then used to form squalene. From there, the squalene is cyclized to form lanosterol, which is then converted to cholesterol. Cholesterol is important for moderating cell membrane fluidity, and also participates in the formation of lipid rafts which are theorized to be involved in cell signalling. [1]

Cholesterol can then be converted into a variety of signalling molecules such as neurosteroids, vitamin D, glucocorticoids, mineralocorticoids, and sex steroids. Neurosteroids modulate complex activities in the brain, such as neural plasticity. They can act in an excitatory manner (such as dehydroepiandrosterone (DHEA), which modulates NMDA receptor activity) or inhibitory manner (such as pregnanolone, which modulates GABA A receptor activity). [2]

Vitamin D is involved in calcium homeostasis, increasing calcium absorption in the intestines and modulating bone remodulating. It is synthesized from cholesterol, including a step that involves UV radiation. It is then hydroxylated twice in order to be in the active form, 1,25-dihydroxycholecalciferol, also known as calcitriol, which binds to the vitamin D receptor to produce its effects. [3]

Glucocorticoids such as cortisol modulate metabolism and immune function. Cortisol promotes gluconeogenesis, which produces glucose, as well as promoting the breakdown of lipids and proteins. It also diminishes immune function by inhibiting the effects of various cytokines that promote inflammation and immune responses. [4]

Mineralocorticoids such as aldosterone helps to maintain blood pressure and electrolyte balance. Aldosterone acts in the kidneys to increase sodium reabsorption and potassium excretion, thus increasing sodium levels and decreasing potassium levels in the blood. Because of the sodium reabsorption, water is then retained, increasing blood volume and thus increasing blood pressure. Glucocorticoids and mineralocorticoids are both synthesized from cholesterol via progestogens in the adrenal cortex by 21-hydroxylase and 11β-hydroxylase. [5]

Sex steroids are classified as progestogens (such as progesterone), androgens (such as testosterone), or estrogens (such as estradiol). Estrogens are synthesized from androgens by the enzyme aromatase, while androgens are synthesized from progestogens by 17α-hydroxylase. Progestogens are synthesized by the conversion of cholesterol by cholesterol side-chain cleavage enzyme. Sex steroids regulate a variety of activities. Progesterone is important in the secretory phase of the uterus during the menstrual cycle, where it is produced by the corpus luteum to maintain the endometrial lining for implantation. Testosterone is important for sperm development, as well as increasing muscle growth and contributing to male secondary sex characteristics. Estradiol is responsible for inducing ovulation, bone maintenance, and female secondary sex characteristics. However, all sex steroids have diverse roles in people of all genders that are not described here. [6][7][8]

Steroids are a diverse group of compounds, and this is only the beginning. You can read about more steroids here!

Sources:
[1] Russell, D. W. (1992). Cholesterol biosynthesis and metabolism. Cardiovascular Drugs and Therapy, 6(2), 103–110. https://doi.org/10.1007/BF00054556
[2] Robel, P., & Baulieu, E. E. (1995). Neurosteroids: Biosynthesis and function. Critical Reviews in Neurobiology, 9(4), 383–394.
[3] Bikle, D. (2000). Vitamin D: Production, Metabolism, and Mechanisms of Action. In K. R. Feingold, B. Anawalt, A. Boyce, G. Chrousos, W. W. de Herder, K. Dhatariya, K. Dungan, A. Grossman, J. M. Hershman, J. Hofland, S. Kalra, G. Kaltsas, C. Koch, P. Kopp, M. Korbonits, C. S. Kovacs, W. Kuohung, B. Laferrère, E. A. McGee, … D. P. Wilson (Eds.), Endotext. MDText.com, Inc. http://www.ncbi.nlm.nih.gov/books/NBK278935/
[3] Arlt, W., & Stewart, P. M. (2005). Adrenal corticosteroid biosynthesis, metabolism, and action. Endocrinology and Metabolism Clinics of North America, 34(2), 293–313, viii. https://doi.org/10.1016/j.ecl.2005.01.002
[5] Connell, J. M., Fraser, R., & Davies, E. (2001). Disorders of mineralocorticoid synthesis. Best Practice & Research. Clinical Endocrinology & Metabolism, 15(1), 43–60. https://doi.org/10.1053/beem.2000.0118
[6] Aizawa, K., Iemitsu, M., Maeda, S., Jesmin, S., Otsuki, T., Mowa, C. N., Miyauchi, T., & Mesaki, N. (2007). Expression of steroidogenic enzymes and synthesis of sex steroid hormones from DHEA in skeletal muscle of rats. American Journal of Physiology. Endocrinology and Metabolism, 292(2), E577-584. https://doi.org/10.1152/ajpendo.00367.2006
[7] Penning, T. M. (2010). New Frontiers in Androgen Biosynthesis and Metabolism. Current Opinion in Endocrinology, Diabetes, and Obesity, 17(3), 233–239. https://doi.org/10.1097/MED.0b013e3283381a31
[8] Cui, J., Shen, Y., & Li, R. (2013). Estrogen synthesis and signaling pathways during ageing: From periphery to brain. Trends in Molecular Medicine, 19(3), 197–209. https://doi.org/10.1016/j.molmed.2012.12.007

The Art of Consulting the Literature

Throughout your university years, you will undoubtedly be required to consult research articles for a paper. Although it’s tempting to just find an article that says what you need and throw in a citation, there are many situations where taking a more in-depth analysis of the paper will help your paper (and your GPA!).

SEARCHING FOR PAPERS

It can be difficult to find papers that match exactly what you’re looking for. Places to start include Google Scholar, UBC Library, or even the citations listed on Wikipedia or in other papers. As a student, you will have access to many journals through UBC Library, so this is often your best bet! Choose your keywords carefully, unless you know the exact paper or author you are looking for. On Google Scholar, you can use operators such as AND,  OR, “” , and – to refine your search. This can make finding appropriate papers a lot faster and easier!

Once you find an article you really like, take note of the authors. Often the authors have done previous work on the topic, allowing you to focus in on related articles. Getting to know the key experts on your topic is essential to writing a great paper, as this gives your paper more credibility.

If you’re struggling to find relevant articles, consider looking at literature reviews. They might contain pertinent information, which you can then track down the source of this information, hopefully leading to a relevant article. Reading literature reviews also familiarizes you with the stakeholders and experts on your topic!

ANALYZING THE PAPER

Now that you’ve found an appropriate source that says what you need, you should also analyze it! Does it come from a reputable journal? How was the study conducted? How was the data collected and analyzed? Does the data support the authors’ conclusions?

This step is time-consuming, and often it will be impractical to you as a student to thoroughly analyze every paper you cite in your assignments. Things to look out for that will also affect how you talk about the paper include:
– inclusion/exclusion criteria
– sample size (Is the sample size large enough for statistical analyses?)
– blinding and controls (Is this a double-blinded randomized trial? If not, how are they controlling for extraneous factors and biases?)
– type of study (e.g. retrospective, experimental) (Is the author correct in inferring correlation = causation?)
– duration of study
– variables measured
– implications of the data

READING THE PAPER

Always start by reading the Abstract! This gives you a summary of the paper’s research question and findings, which saves you a lot of time in determining whether the paper is relevant. It’s okay to skip most of the Introduction if you’re familiar with the background knowledge of your topic; however, make sure to identify the knowledge gap, research question, and what they propose to do in order to answer this question.

I would then advise to skip to the Discussion to quickly find out if their efforts were fruitful, and the implications of their results. You can then go back to the Results section to determine whether you agree with their conclusions. Often times, there are specific details in the Results section that aren’t mentioned in the Discussion.

Reading the Materials and Methods section is often optional and depends on your needs. If you’re writing a paper about the latest scientific findings on your topic, you can probably just skim the section. This extends to literature reviews as well. However if you’re designing your own experiment, it’s often worthwhile to see how experts in the field approach similar experimental design.

We hope you found this article helpful! Happy lit. searching 🙂

SSRIs, serotonin, and depression

SSRIs (selective serotonin reuptake inhibitors) are among the most commonly prescribed medications, used as a first-line pharmacological treatment for depression. Their basic mechanism is well-known: blocking the serotonin transporter, resulting in decreased serotonin reuptake into the neuron and thus more serotonin remains outside, allowing for more activation of serotonin receptors, and thus decreasing the depressive symptoms [1]. However, this is an oversimplification: the role of serotonin in the brain is still poorly understood.

For example, abnormally large serotonin levels in the brain may result in serotonin syndrome, a life-threatening condition characterized by neuromuscular and autonomic hyperactivity [2]. This condition may be caused by the use of drugs that act on the serotonergic system, such as SSRIs. On the other hand, serotonin deficiency may also lead to hyperactivity, as well as disrupted sleeping patterns [3].

There are also a multitude of serotonin receptors in the brain, all with different effects [1]. For instance, activation of the 5-HT1A receptor with selective agonists results in antidepressant effects [4]; however, blockade of 5-HT2C receptors with selective agonists also results in antidepressant effects, with a faster onset [5]. As well, autoreceptors modulate serotonin signalling, which further complicates the effects of increasing serotonin levels. Interestingly, the downregulation of 5-HT2C receptors appears to coincide with the onset of effects from SSRIs [6], suggesting that some abnormal signalling involving the 5-HT2C receptors may be involved in depression.

Further complicating matters is the downstream effects on serotonergic, noradrenergic, and dopaminergic pathways. It is known that NDRIs (norepinephrine/dopamine reuptake inhibitors) such as buproprion are also effective in treating depressive symptoms [7], and that activation of serotonin receptors also results in modulation of norepinephrine and dopamine signalling, such as in the case of 5-HT2C receptors [6]. This is still an active area of research, but it is still quite clear that the role of serotonin in the brain is not as simple as “serotonin = happy”.

References

[1] Sangkuhl K, Klein T, Altman R. Selective Serotonin Reuptake Inhibitors (SSRI) Pathway. Pharmacogenet Genomics. 2009;19(11):907-909. doi:10.1097/FPC.0b013e32833132cb

[2] Volpi-Abadie J, Kaye AM, Kaye AD. Serotonin Syndrome. Ochsner J. 2013;13(4):533-540.

[3] Whitney MS, Shemery AM, Yaw AM, Donovan LJ, Glass JD, Deneris ES. Adult Brain Serotonin Deficiency Causes Hyperactivity, Circadian Disruption, and Elimination of Siestas. J Neurosci. 2016;36(38):9828-9842. doi:10.1523/JNEUROSCI.1469-16.2016

[4] Kennett GA, Dourish CT, Curzon G. Antidepressant-like action of 5-HT1A agonists and conventional antidepressants in an animal model of depression. Eur J Pharmacol. 1987;134(3):265-274. doi:10.1016/0014-2999(87)90357-8

[5] Opal MD, Klenotich SC, Morais M, et al. Serotonin 2C receptor antagonists induce fast-onset antidepressant effects. Molecular Psychiatry. 2014;19(10):1106-1114. doi:10.1038/mp.2013.144

[6] Millan MJ. Serotonin 5-HT2C receptors as a target for the treatment of depressive and anxious states: focus on novel therapeutic strategies. Therapie. 2005;60(5):441-460. doi:10.2515/therapie:2005065

[7] Patel K, Allen S, Haque MN, Angelescu I, Baumeister D, Tracy DK. Bupropion: a systematic review and meta-analysis of effectiveness as an antidepressant. Ther Adv Psychopharmacol. 2016;6(2):99-144. doi:10.1177/2045125316629071

3D movie glasses and light polarization

Have you ever watched a movie in 3D at a movie theatre? You probably had to wear special glasses in order to get that 3D effect. And if you take them off, the movie looks completely blurry.

The most common way of producing the 3D image is through the use of polarized filters. This principle works by projecting the movie from two different perspectives at the same time, with the light being polarized in a different way in each projection. The polarization refers to the orientation the waves are travelling in, which means multiple light waves of different polarizations can be still travelling in the same direction! Continue reading

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Potato chips and asparaginase

Have you eaten any fried potato product recently? You do know how unhealthy those things are, right? Not only because of the fat and carbohydrate and sodium content, but possibly because of the presence of acrylamide. Acrylamide is a potent neurotoxin and a possible carcinogen, which is often used in laboratories for making gels to separate proteins. [1]

Potato chips, also known as potato crisps, are a fried potato product that may have unhealthy levels of acrylamide. Credits: Wikimedia

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Endogenous retroviruses and disease

Did you know that there are retroviruses in the human genome? In fact, there are retroviruses in the genome of all mammals. These viruses have previously integrated their DNA into our ancestors’ DNA, and have degraded to the point that they can no longer replicate and infect other cells. However, they still contain some of the characteristics of retroviruses, such as long terminal repeat (LTR) regions and gag, pol, and env genes. [1]

It has been suggested that these human endogenous retroviruses (HERVs) may modulate gene expression. [1] For example, the release of amylase into saliva may be regulated by a HERV that acts as a promoter, and apolipoprotein C1 (a protein that helps with lipid transport) may be regulated by a LTR from a HERV. [2] Continue reading