Mathematical beauty (100 years part I)

Exactly a century ago, D’Arcy Thompson published his book On Growth and Form.

I’ve spoken about Mr. D’Arcy before, but as it is the 100-year anniversary of his masterwork, I feel it fitting to revisit the topic. Since mentioning him last, I have finished reading his book, and have also started to write up my thesis. I bring up my thesis because my work is related to D’Arcy’s work in the sense that I have been trying to bridge the gap between biology and physics, and I predict that some of my reading will inspire me to write more (hopefully more of my thesis but presumably also more on the general topic of bio-meets-phys).

Mr. D’Arcy wrote On Growth and Form to collect his observations on the mathematical principles of nature. He explains how biological phenomena of form and growth closely resemble physical and mathematical principles. Especially for some of the more simple examples (e.g. the shape and size of single or doublets of cells) the similarities between biology and physics (e.g. single and doublets of bubbles) are almost uncanny. These simple systems can easily be described using simple formulas, and he suggests that even more complex systems can be explained in a similar way (though he remarks that it will take a lot of formulas and paper space, luckily we have computers now). In 1917, this idea was pioneering, to say the least. Bio-mathematics and biophysics were nowhere near being the hot topics they are today.

One of the events organised for the anniversary of On Growth and Form, was the exhibition A Sketch of the Universe at the  City Art Gallery in Edinburgh, showcasing works of art that were inspired by the book, or by the idea that mathematics and biology are closely intertwined. The exhibition is closed now, but this weekend I did get the chance to go visit it.

So, I present to you, some of the highlights that I found interesting or cool-looking:

Trifolium repens L – top view – No 10 by Macoto Murayama (2016) – 2D rendering of a 3D model depicting the structure of a white clover flower.

“I know that in the study of material things number, order and position are threefold clue to the exact knowledge; and that these three, in the mathematician’s hands, furnish the first outlines for a sketch of the Universe.” (D’Arcy Thompson, On Growth and Form)

Aggregation 24/27 by Andy Lomas (2005) – These prints were “grown” using computer algorithms that simulated the paths of millions of particles flowing in a field of forces.
Untitled by Gavin Rutherford (2010) – Prints citing D’Arcy Thompson.

“For the harmony of the world is made manifest in Form and Number, and the heart and the soul and all the poetry of Natural Philosophy are emodied in the concept of mathematical beauty.” (D’Arcy Thompson, On Growth and Form)

Radiolarians by Amy Barber (2010) – The single-celled Radiolardia aggregate into complex and very diverse shapes. Their skeletons are incredibly delicate and look pretty neat.

“The waves of the sea, the little ripples of the shore, the sweeping curve of the sandy bay between the headlands, the outline of the hills, the shape of the clouds, all these are so many riddles of form, so many problems of morphology.” (D’Arcy Thompson, On Growth and Form)

Scarus, Pomacanthus by Darran McFarlane (2012) – This painting was created by subjecting an existing portrait of D’Arcy to mathematical transformations.

You can read more about D’Arcy Thompson, On Growth and Form and some of the events being organised this year in honour of the 100 year anniversary, here. And presumably in the near future on this very blog.

[Note: Again, I realise that D’Arcy Thompson’s last name is “Thompson” so “Mr. Thompson” would be a more appropriate title (or Prof. Thompson) but I just cannot resist his practically Austenesque first name.]


Physics of Cancer (2)

Two weeks ago, I told you that physics and cancer are, perhaps counterintuitively, intermingled and that this relationship has biological and clinical implications. I outlined how mechanical forces act on cells and tissue, and perhaps are responsible for one of the many ways of cancer progression.

In this post, I’d like to tell you about how being able to detect mechanical properties of tissue can help with diagnosing diseases. So while the previous post was more about how physics can influence the biology of a tissue, this time I’d like to focus on how biology can dictate physical properties of a tissue.

A very important issue to point out, before going into the differences between healthy tissue/cells and cancer, is the size scale we are considering. Depending on whether we are talking about cells (µm size range) or tissues (100s of µm to mm), we can make quite opposite conclusions: several studies have shown that tumour cells are softer than healthy cells (of the same tissue type), while tumour tissue is stiffer than healthy tissue.

First the cells. Experiments such as Atomic Force Microscopy (which I mention because I have used it myself) show that especially metastatic tumour cells are softer than healthy cells. If we consider what cells do during metastasis, this actually makes sense. (Metastasis is the process where cells migrate away from the initial tumour and spread to other parts of the body.) A softer cell is able to squeeze through other cells, and through the wall of a blood vessel, allowing it to travel to elsewhere in the body. This different mechanical property allows it to behave in its particular way. Knowing this property allows us to predict the aggressiveness (or invasiveness) of a certain cancer. If the tumour has cells that are much softer than other, it is usually a more aggressive type of cancer.

That one time that being less flexible is actually healthier!

This difference in mechanical properties not only makes sense if we consider the behaviour of the cells, it can also help make prognoses and decide on what type of treatments to use.

Next, on a larger scale, tumours are stiffer than healthy tissue. This is exactly what we feel when we are “looking for lumps”. A bit of tissue feels different, namely stiffer, than what it should be. The reason tumours are stiffer is not actually due to the (softer) cells it contains, but due to what sits in between the cells: the extracellular matrix. The extracellular matrix is a very structured meshwork of structural proteins that acts as a scaffold for the cells: it provides the tissue with structural integrity, cell organisation and mechanical strength. For example, there are a lot of extracellular matrix proteins in our skin, which is why it is, well, our skin (hurray for circular reasoning): a sturdy barrier between the outside and the inside of our body. In healthy tissue, the extracellular matrix is usually very well organised. The fibers making up the matrix are regularly cross-linked and have and neatly organised. However, the matrix in tumourous tissue is chaotic. In essence, was “built” too quickly. In this fast-growing bit of tissue, the scaffolding had to be assembled fast to support the rapidly dividing cells. As a result, the fibres are not well organised and the crosslinking is random. It is as if the scaffolding of a building was built too quickly, so rather than nicely structured, there are random beams sticking out in all directions. As a result, pushing down on the matrix does not compress it as much, and it feels stiffer.

Neatly structured, easily compressed.
Just ugh. (Also, majestic artist skills, right?)

At a tissue level, these differences in mechanical properties are very useful for diagnosing cancer. Because of different mechanical properties, we can feel lumps, but we can also image it using techniques such as ultrasound, MRI and other imaging techniques. Due to different physical properties, the cancerous tissues interacts differently with whatever wave (light, sound, …) we are using to try and detect it. Thank you physics!

To wrap this up: the physics of cancer is important, and useful, and interesting, and cool and definitely worth researching. And this is why interdisciplinary research is not only a fancy buzzword, it can also increase our understanding certain phenomena and come up with better diagnoses and treatments by approaching the problem from a completely different perspective.

This subject was the topic of my second FameLab performance (Scottish regionals), which ended in a little song (to the tune of “What a Wonderful World” by Sam Cooke), in which I wanted to highlight the importance of interdisciplinary research and how studying diseases from a physics perspective can only be productive:

You know, cancer’s about biology
And perhaps a bit of chemistry
But I’m telling you there’s physics too
There’s physics happening inside you

With one subject you can never be sure
Put them together, and we might find a cure
And what a wonderful world that would be…

Some references I used to verify that my thoughts on this subject were not completely unsubstantiated:

Baker EL, Lu J, Yu D, Bonnecaze RT, Zaman MH. Cancer Cell Stiffness: Integrated Roles of Three-Dimensional Matrix Stiffness and Transforming Potential. Biophysical Journal. 2010;99(7):2048-2057. doi:10.1016/j.bpj.2010.07.051.

Suresh S. Biomechanics and biophysics of cancer cells. Acta biomaterialia. 2007;3(4):413-438. doi:10.1016/j.actbio.2007.04.002.

Kumar S, Weaver VM. Mechanics, malignancy, and metastasis: The force journey of a tumor cell. Cancer metastasis reviews. 2009;28(1-2):113-127. doi:10.1007/s10555-008-9173-4.

Plodinec M, Loparic M, Monnier CA, Oberman EC, Zanetti-Dallenback R, Oertle P, Hyotyla JT, Aebi U, Bentires-Alj M, Lim RYH, Schoenenberger C-A. The nanomechanical signature of breast cancer. Nature Nanotechnology. 2012; (7):7 57–765. doi:10.1038/nnano.2012.167

3 minutes of Fame

In the past month, I took part in a science communication competition called  FameLab, first in the local heat and then in the Scottish final. It was a really fun and educational experience (and by educational, I mean that I learned something, even if it technically was also supposed to be educational for the audience). And even though I (unfortunately) did not make it through to the national final, it was a fabulous – or should I say famelabulous (hahahaha and I didn’t even come up with that) – thing to be part of.

Anyway, FameLab is a competition where STEMers (scientists, engineers, and mathematicians) get 3 minutes to talk about a scientific concept of their choice. Yes, only 3 minutes! And as if that wasn’t hard enough, during those 3 minutes, they get judged on content, clarity, and charisma. I mean obviously you have to talk about something worthwhile and don’t jumble things up too much, but having to be charismatic as well, that just sounds like too much of a challenge!

Without going too much into detail on what I talked about exactly – I might elaborate on that in some other post, though I’m sure you can find it with some smart googling, in any case it was about the physics of cancer, – I thought I might give my insights on how to give a 3-minute talk. And most things can be extrapolated to longer talks.

Well, it’s not like I won, so there is no reason to believe anything I tell you. Also, it’s all pretty obvious stuff that they teach you in any presentation skills course. You know: stick to the key points (the audience only remembers three things or so of what you say), don’t use too much jargon but don’t dumb it down either (be like Shakespeare, jokes for all, and the occasional clever twist for the snobs to smile about), be your own charming self (no need to act), breathe, don’t faint, imagine the audience with no clothes on,… all the obvious things.

I guess the best lesson I learned was that I have an inescapable future as a superhero. “Inevitable avenger” is an anagram of my name and that has to be the most awesome thing someone has ever used to introduce me.

I’ll be using this for everything now.

Inevitable Avenger


(Yes, the only reason for this post was to brag about my new cool nickname.)



“The only greatness for man is immortality.”

Wouldn’t we all like to be immortal?

Okay, I realise there is no easy answer to this.
But let’s assume that living forever wouldn’t turn you into a shriveled old raisin and that you wouldn’t have to watch your loved ones die and that this somehow would not lead to (even more) overpopulation.
Short story, let’s just imagine your answer to that question is: “Yes, totally!”

Unfortunately, immortality is a fictitious feat for comic book superheroes. That doesn’t keep us humans from trying to reach immortality in a certain sense, in the hope of leaving a lasting mark on the world.

I’m gonna live forever.

Immortality, or prolonged aging, is of great interest for science. Living too long isn’t too great for our cells; we stop replacing old cells and start wearing out; and longer living is associated with age-related diseases with the most pertinent being cancer.

But there could be hope: not all animals develop cancer !

Let’s start underground. Naked mole rats (Heterocephalus glaber), for example, live long past their rodent cousins such as rats and mice; up to 17 years in the wild and even over 30 years in captivity. Additionally, they don’t  develop cancer. Just for reference: mice barely make it to 4 years and often die of cancer.

Naked mole rats – let’s call them NMRs for brevity – are already quite odd creatures. Aside from being very strange looking (I don’t want to hurt their feelings too much), they are quite tough: they don’t feel the sting of acids or burn of chili. I, on the other hand, can’t seem to remember to not rub my eyes after cutting a cayenne pepper. Good thing I don’t use a lot of acids in my cooking. NMRs also seem to be the only mammal that can’t control its body temperature. And now it turns out that NMRs don’t get cancer. The trick, as it turns out, is a sugar molecule called hyaluronan. This sugar is excreted by cells as part of the extracellular matrix, which gives tissues their shape and makes our skin elastic, which is why hyaluronan is already used as an anti-wrinkling therapy. NMRs have very elastic skin thanks to large amounts of long chains of hyaluronans. These long molecules form tight cages around cells, stopping cells from replicating without passing all the proper checkpoints. Consequently, these long hyaluronans stop pre-cancerous cells from overproliferation, hence NMRs don’t develop cancer. Unless you block the production of these hyaluronans of course, which researcher have done with NMR cells in a dish. These cells did start showing cancerous treats and moreover, when implanted in mice, led to tumour development.

It should be noted that this may not be the only mechanism by which NMRs avoid developing cancer. It is more than possible that other adaptations to underground life and the development of thick skin against all the insults they get for their looks, have led to tumour-suppressing powers.

She’s running for Miss universe, the poor thing.

An example of this can be seen in another rodent: the slightly more visually appealing blind mole rat (Spalax spp), let’s call them BMRs. BMRs can live for over 20 years, and do not develop cancers. It is thought to be due thanks to genetic adaptations to hypoxia, caused by low oxygen levels in poorly ventilated underground tunnels (Who taught these moles how to dig?)

BMR cells commit suicide through the process of necrosis rather than apoptosis (the usual method of cell suicide). Research suggests that a high release of interferon-beta, usually an immune response to viruses, limits overproliferation. This interferon-beta is released by abnormal cells, triggering necrosis in themselves and their close neighbours, and therefore suppresses tumour growth.

Again, this is most probably not the only mechanism, especially because the research in question has been disputed and could not be reproduced in vivo. However, it is feasible that evolutionary adaptations to a low-oxygen environment have provided BMRs with mechanisms to avoid cancer.

So fluffy I’m gonna die (but not of cancer).

Scaling it up a bit, we come to something known as Peto’s Paradox.This states that larger animals should have more risk of developing cancer. Assuming all cells are pretty much the same size (which they are) and all cells have an equal chance of getting a mutation that would lead to cancer, animals with more cells should get more cancer. The paradox: this is not true.

Within humans, it has been shown that taller people have a higher risk (almost 20%) of getting cancer. This could be the having more cells thing, but could also be linked to growth hormones: the same processes that lead to body growth are involved in tumour growth. Luckily, six foot me shouldn’t get too worried; taller people are in general healthier (a healthy childhood leads to tallness) and other cancer risk factors weigh through more than height. Smoking, obesity, and poor diet increase the chance of developing cancer, so stay off the cigarets and deep fried mars bars and I should be okay.

So Peto is not so much a paradox for humans, but if we look further, it is. As an example, not only are mice inexplicable terrifying to elephants, they also develop more cancer. More reason for the elephants not to be scared, stick it out for less than 4 years and the mouse will have probably died of cancer anyway. One possible explanation is that some animals, such as the giant elephant and some even gianter whales, have more copies of the p53 gene. p53 is a pretty famous tumour suppressor and is often mutated in cancer. When a cell’s DNA gets damaged, p53 steps in and prevents the cell from dividing and passing on the mutation to the next generation. If the cell cannot repair the DNA damage, this sets off a cue for apoptosis (programmed cell suicide) to prevent mutations from turning into cancer. Having more copies of this gene means the risk of all copies being mutated is lower. So elephants can have a few defective p53s, but still enough working copies to prevent cancer development.

“I live to create paradoxes” – Dumbo

But not dying of cancer does not necessarily render you immortal. There are many biological processes that are involved in aging. One process is the shortening of chromosomes at each cell division. To protect genetic material, the end of chromosomes consist of a region of repetitive DNA sequences called telomeres. As cells divide, these telomeres shrink until they are too short, leading to the cells stopping multiplication or dying. To repair shortened telomeres, cells have a protein called telomerase. Most vertebrates stop producing this protein as an adult, but some animals keep it indefinitely, leading to the popular belief that they – let’s take lobsters for this example – are immortal.

Side note, lobsters are not immortal. While they are able to repair their DNA up until their old age (over 40 years), they typically die from an extreme moult. Moulting is the process of shedding their shell as they grow, preventing it from getting too tight but also repairing any damage that might have occurred. However, the larger the lobster, the larger the shell and the more energy necessary to go through the moulting. Eventually, an old lobster will die from exhaustion of this process, or they will not even bother and die from damage or infection.

Not to take away that this telomerase thing does allow them to get pretty old, though.


All I need to do is avoid getting caught.

Maybe someday soon we can learn from these animals to tackle cancer and aging. Maybe there are other animals that have evolved to do even more amazing non-aging things, but I have not mentioned them because of, well, my limited time in this world.

Live long and prosper, my friends.

(title quote attributed to James Dean)

Sources used:


Oh the irony, writing a blog post about procrastination, mostly to avoid the pile of 20 papers I don’t really feel like reading. I’m sure Alanis would have added it to her lyrics, if blogs were a thing in 1995.

Some time ago I went to a seminar called “The Seven Secrets of Highly Successful PhD students”. Usually the courses provided by the university aren’t that great. But this sounded like it could be interesting and it was an excuse to do something else for a few hours. Also, the speaker was from a university in Australia, and I don’t mind listening to Australian accents at all.

Turns out Hugh Kearns is a professor in Australia, but he’s actually Irish. Ah well. Fortunately, the lecture turned out to be extremely interesting.

One of these secrets to success, number four to be exact is: “Say no to distractions.” We all know we should away from social media. But there are a whole list of hidden distractions, that don’t seem too harmful, that we use as an excuse not to work. Like going to a course about how to avoid procrastination. Or cleaning your room because “you can’t get anything doen while it’s messy. Checking emails and reorganising outlook files. A surprising form of procrastination is to search and organise references. Just to avoid having to actually start writing.

I’m not up to writing yet, but now I am in a position where I need to do some extensive literature research.

So I’ve decided to preform random Fourier transforms on my data.

Then I worked on a presentation that to be honest is already finished and doesn’t need any more work.

And then I decided to write a blog post about how not getting any work done.

And I’ll have lunch in about half an hour so no use starting anything now.

Ugh, maybe I can read one paper by then…


You can find out more about Hugh Kearns and his secrets to succes on Thinkwell


I’ll tell you a secret. It’s not really a big secret, I think many people know. But it isn’t out there quite enough.

Here’s the secret:

Scientists are superheroes.

You probably think I’m saying this to impress you, to make you believe that am a superhero. Well, I’m not. Or at least not yet. Because, technically, I’m still a scientist-in-training. So you might say I’m a superhero-in-training. Not quite there yet.
(Side note: when does one actually truly deserve to be called a scientist? Isn’t the goal to keep on learning? Will a researcher always be a scientist-in-training? Or until he/she – I don’t know – wins a Nobel prize? #AskingTheBigQuestions)

I’ll tell you why scientists are superheroes. And I’ll do it by giving an example of one of the supervillains they are fighting: cancer.

Yes, cancer. (Disclaimer: what will follow will be both a huge generalisation, because there is no such thing as “cancer” or “the cure for cancer” because cancer is as diverse as the number of different cells in our body.)

So, if you’re like me, you might have noticed in a geeky moment that cancer cells have a number of superpowers. Officially, these are called “the hallmarks of cancer” . No, this has nothing to do with greeting cards or Kenickie’s hickeys, but are certain characteristics of cancer that can accumulate during its progression and that are typically driven by genetic instability. Like a superpower, they can originate hereditarily, through a genetic defect, through mutations caused randomly, or after exposure to a DNA-altering freak accident, including radiation or chemical exposure.
(I might have given a talk last week that was completely framed around X-men. I was called a dork. It was a good day.)

So what type of superpowers could cancer cells develop?

To start with, I would argue that cancer cells could gain the power of invisibility. Often, cancer cells have the uncanny ability to “trick” the immune system to not noticing they’re there. They also cleverly evade any growth suppressors that come their way. If this is down to superb camouflage abilities, shapeshifting talents or just pure invisibility, I do not know. But it’s definitely powerful and it can definitely be used for evil.

The also possess a type of mind control (if we imagine cells have a little will and a mind of their own). They convince their surroundings to grow new blood vessels. For their own gain, obviously, because it creates a steady flow of resources. Which they can, by the way, use in different ways as the usual (but I’m not sure “changed metabolism” is such an awesome superpower unless you really start thinking it through).

Next one: excessive self-multiplication. You know, like Multiple Man. Cancer cells just keep on making replicates of themselves. Until they take up so much space that they don’t have any room anymore, which brings me to the next power…

Cancers sometimes spread out. Certain cells, known as metastatic cancer cells, have the ability to walk through walls (or in reality, evade through cell layers to get into the blood stream and hitch a ride to some other part of the body that might have some extra living space).

And then finally (I might have skipped over a few hallmarks, though) and in my opinion, the scariest superpower: cancer cells can, and often do, acquire is the power of immortality. They find a way to resist cell death. Usually, the body is amazingly good at catching the rotten apples and getting rid of them, but a cancer cell is able to resist. It is immortal. Really difficult to kill. Which is really something to be scared of.

Which means we need to assemble our own team of superheroes to the battle. And that is exactly what is happening. Every day, a team of scientists, in reality just undercover supers, go to work on a whole range of things. Discovering new functions for proteins and unraveling their function in cancer. Discovering new diagnostic techniques. Discovering new ways to model cancer. Discovering new drugs. Discovering ways to battle that one evil in the best way possible, by assembling their expertise, their powers and working together towards that one same goal.

Even Nature, a prominent scientific journal, thinks scientists are superheroes.

Go science!