If only it were so simple (100 years, part IV)

Ever since I have been enquiring into the works of Nature I have always loved and admired the Simplicity of her Ways. (1)

In his book (yes, it’s about that again), D’Arcy supports his ideas through examples, through observations on biological systems that he can either explain through mathematical equations or directly compare to purely physical phenomena such as bubble formation. You might think that these are grave simplifications.

However, even in biology, which some people might call a “complex science”, simplifications are often used. Using cell culture rather than tissue. Isolating a single player in a pathway to see what its effect is. And quite often, a simplification holds true within the limits that have been set up to define it.

As was pointed out to me recently, the definition of “complex” is that something is “composed of many interconnected parts”. Meaning that this is not necessarily the antonym to “simple”. But “complex” is often seen to mean the same thing as “difficult”, even if that’s not necessarily the definition. In any case, it is definitely not so that physics is a “simple science”:

But even the ordinary laws of the physical forces are by no means simple and plain. (2)

It makes sense to break down a complex system into its individual components and analyse these, perhaps more simple concepts, separately. There is great value in simplifying things. First of all, there is a certain beauty in simplicity:

Very great and wonderful things are done by means of a mechanism (whether natural or artificial) of extreme simplicity. A pool of water, by virtue of its surface, is an admirable mechanism for the making of waves; with a lump of ice in it, it becomes an efficient and self-contained mechanism for the making of currents. Music itself is made of simple things – a reed, a pipe, a string. The great cosmic mechanisms are stupendous in their simplicity; and, in point of fact, every great or little aggregate of heterogeneous matter involves, ipso facto, the essentials of a mechanism. (3)

When reading this paragraph, two things jumped out at me. Two weeks ago, I was at the annual meeting of the British Society for Cell Biology (joint with other associations) and heard an interesting talk by Manuel Théry. Part of his story relied on putting boundaries on a system. Without boundaries, whatever we would like to study just gets too complicated, and we are unable to understand what is happening. For example, when explaining how waves originate, it is much easier to use a system where water is confined in a box. We can then directly observe the wave patterns that start to occur and understand their interactions.

And then this: “Music itself is made of simple things – a reed, a pipe, a string. The great cosmic mechanisms are stupendous in their simplicity.” D’Arcy sure knew his way around words.

Simplifying also heavily increases our understanding of the principles of life, the universe and everything. When you think about it, it is used so often, you hardly even notice that certain simplifications have been made. D’Arcy points this out as well:

The stock-in-trade of mathematical physics, in all the subjects with which that science deals, is for the most part made up of simple, or simplified, cases of phenomena which in their actual and concrete manifestations are usual too complex for mathematical analysis; hence, even in physics, the full mechanical explanation is seldom if ever more than the “cadre idéal” towards which our never-finished picture extends. (4)

When considering biological systems, he states the following:

The fact that the germ-cell develops into a very complex structure is no absolute proof that the cell itself is structurally a very complicated mechanism: nor yet does it prove, though this is somewhat less obvious, that the forces at work or latent within it are especially numerous and complex. If we blow into a bowl of soapsuds and raised a great mass of many-hued and variously shaped bubbles, if we explode a rocket and watch the regular and beautiful configurations of its falling streamers, if we consider the wonders of a limestone cavern which a filtering stream has filled with stalactites, we soon perceive that in all these cases we have begun with an initial system of very slight complexity, whose structure in no way foreshadowed the result, and whose comparatively simple intrinsic forces only play their part by complex interaction with the equally simple forces of the surrounding medium. (5)

For many biological and non-biological systems, the initial conditions might not seem complex. It is by interactions between other – perhaps on their own relatively simple – environmental conditions, other simple systems, that it grows out to be complex. Obviously, as in the definition. But a complex system is more difficult to understand conceptually, more difficult to model. And that brings us the value of simplification, looking at smaller, simpler systems that more closely resemble the “cadre idéal”, allow us to pick apart the different players in a larger system. If we understand their individual behaviour, perhaps this can shed light on the collective behaviour.

As we analyse a thing into its parts or into its properties, we tend to magnify these, to exaggerate their apparent independence, and to hide from ourselves (at least for a time) the essential integrity and individuality of the composite whole. We divide the body into its organs, the skeleton into its bones, as in very much the same fashion we make a subjective analysis of the mind, according to the teachings of psychology, into component factors: but we know very well that the judgment and knowledge, courage or gentleness, love or fear, have no separate existence, but are somehow mere manifestations, or imaginary coefficients, of a most complex integral. (6)

As far as D’Arcy goes in his book, his simplifications hold true:

And so far as we have gone, and so far as we can discern, we see no sign of the guiding principles failing us, or of the simple laws ceasing to hold good. (7)

Of course, this does not automatically lead to complete understanding. We only get that tiny bit closer to seeing the bigger – and smaller – picture:

We learn and learn, but will never know all, about the smallest, humblest, thing. (8)

Because we must never forget that adding together those simplifications does not automatically lead to the answer to the complete problem (and I find this oddly poetic):

The biologist, as well as the philosopher, learns to recognise that the whole is not merely the sum of its parts. It is this, and much more than this. (9)

To end, D’Arcy also makes note of things beyond his comprehension:

It may be that all the laws of energy, and all the properties of matter, and all the chemistry of all the colloids are as powerless to explain the body as they are impotent to comprehend the soul. For my part, I think it is not so. (10)

Contact surfaces between four cells, or bubbles. This has nothing to do with the soul. It does have to do with how we can often simplify cells to their “shells”, and for certain principles this approximation holds true.


(1) Dr. George Martine, Medical essays and Observations, Edinburgh, 1747.

(2) On Growth and Form, p. 19

(3) On Growth and Form, p. 292

(4) On Growth and Form, p.  643-644

(5) On Growth and Form, p. 289

(6) On Growth and Form, p1018

(7) On Growth and Form, p. 644

(8) On Growth and Form, p. 19

(9) On Growth and Form, p1019

(10) On Growth and Form, p. 13

(2-10) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)


Fantastic Beasts and Where to Find Them – Part III: Basilisks

For my third Fantastic Beasts issue, I wanted to focus on another beast from a city I – albeit briefly – lived in: the basilisk.

In the meantime, the movie has been released, and I also couldn’t come up with anything more to say about the basilisk than I already have, here and here.

So I’ll just leave you with this comic:



Physics, but not vs evolution (100 years, part III)

As you may well know, because you have read it here or heard it elsewhere, this year is the 100 year anniversary of D’Arcy Thompson’s On Growth and Form. The book is over 1000 pages long, and while extremely interesting, it can be quite a task to get through. Therefore, I figured I’d share some of the thoughts I had while reading – and to be honest, this was sometimes diagonally – through this masterwork.

To place this and future posts within context, I will first focus on how its main premise (physical forces as the driver of morphology) fits into the context of the time where the general sentiment was:

No other explanation of living forms is allowed than heredity, and any which is founded on another basis much be rejected… (1)

But that is not to say that no one in the scientific community was open to the idea that physics had some part to play:

To think that heredity will build organic beings without mechanical means is a piece of unscientific mysticism. (1)

It seems D’Arcy Thompson’s book was the first major publication on this idea, and his book is an inspiration for biomathematicians and biophysicists today. Or at least it is thought-provoking: throughout the book he underlines through several – 1000 pages worth of –  analogous observations from the material (non-living) and biological (living) world his theory, that the way biological systems grow, and the shape and size they eventually take, is driven by physical principles:

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. … Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems. (2)

It is important to point out that he never claimed that physics is the only driving force of the shape and size of living things, just that it is one of the drivers, and that heredity is extremely important in understanding the processes of biology in its own right. But if outlining the physics of growth and form takes over a thousand pages, we should almost be thankful that heredity was taken out of the picture:

We rule “heredity” or any such concept out of our present account, however true, however important, however indispensable in another setting of the story, such a concept may be. (3)

Ruling it out of the picture doesn’t stop D’Arcy from occasionally musing on the limitations of heredity:

That things not only alter but improve is an article of faith, and the boldest of evolutionary conceptions. How far it be true were very hard to say; but I for one imagine that a pterodactyl flew no less well than does an albatross, and that Old Red Sandstone fishes swam as well and easily as the fishes of our own seas. (4)

This goes to show that while D’Arcy did not consider evolutionary theory in his story, it was not something he hadn’t thought about. He regularly quotes Darwin (I’m working through The Origin of Species myself at the moment… at least D’Arcy’s book had some pictures!) and as a professor in zoology, it stands to reason that he was knowledgeable on the subject.  Throughout his career, he published around 300 articles and books, and some day I’ll go through all of them to show he has written more on heredity.

To conclude, while On Growth and Form outlines an alternative theory to explain the morphology of biological systems, it is in no way trying to replace or contradict the theory of evolution or any idea of genetics-driven development. I’ll wrap up with one of D’Arcy’s final thoughts:

And though I have tried throughout this book to lay the emphasis on the direct action of causes other than heredity, in short to circumscribe the employment of the latter as a working hypothesis in morphology, there can still be no question whatsoever that heredity is a vastly important as well as a mysterious thing; it is one of the great factors in biology, however we may attempt to figure to ourselves, or howsoever we may fail even to imagine, its underlying physical explanation.  (5)

Well, that’s all folks. More on growing and forming next time! Have I mentioned that this book is over a thousand pages long?

D’Arcy in his twenties (University of Dundee Archive Services)


(1) Haller, 1888

(2) On Growth and Form, p. 10

(3) On Growth and Form, p. 284

(4) On Growth and Form, p. 873

(5) On Growth and Form, p. 1023

(2-5) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)

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

Physics of Cancer (1)

If you are confused by the title, that’s okay. Usually, when we read something about cancer, it is about something biology-related, for example about specific mutations or the environmental conditions that increase cancer risk. A lot of research is happening with regards to the biology and biochemistry of cancer: which tumour suppressor genes are mutated in certain cancers, what are the effects cancer has on someone’s health, what drugs can we use to treat a cancer, … ? But, perhaps surprisingly, studying the physics of cancer also has its merit. Why, it’s a whole field in itself!

So I’d like to talk a little bit about this topic, the physics of cancer, and in this first part, I will focus on how physical forces can change the behaviour of cells (and how this might be involved with disease).

Cells not only sense their biological environment, they also feel their physical environment. They sense the stiffness of the cells and protein structures around them, they sense how other cells are pushing and pulling on them, and then they react to it. And these mechanisms could actually be quite important for the development and progression of cancer.

Recent research showed that the cells surrounding a tumour are under mechanical stress because of the growth of the tumour. As a tumour grows, it pushes on its environment. So the – initially healthy – cells in its direct surroundings, feel a pressure. In this specific study, they showed that this pressure caused the cells to start a mechanical response pathway leading to the upregulation of a protein β-catenin. This protein is involved in activating certain pathways involved in cell proliferation.

Which is exactly what its upregulation leads to in cancer. In the case of colorectal cancer (which, if you remember, I am particularly interested in), a mutation of Apc (adenomatous polyposis coli, in case you were wondering) also leads to an accumulation of β-catenin amongst other things. The APC protein has been linked to many functions, but the best known is its involvement in forming a complex that binds to β-catenin and tagging it for destruction. That way the proteins involved in protein recycling know that the β-catenin proteins can be cut up. But when APC is mutated, β-catenin gets tagged and starts piling up and doing some of its jobs a little bit too well, including inducing proliferation pathways.

So back to the study, if healthy cells are experiencing a constant pressure (due to a big bad tumour growing into their space, or – as they tested in the study – artificially caused pressure), they start acting more “cancer-like”. This suggests that mechanical activation of a tumorigenic pathway, in this case, the β-catenin pathway, is a potential method for transforming cells.

This is just one example of how physics and cancer are potentially related. As a side note, I myself am also interested in how cells respond the mechanical stresses, which prompted me to do an experiment where I placed weights on top of cells.


Feeling the pump.


This subject was the topic of my first FameLab performance, which ended in a little song (to the tune of “Friday I’m in Love” by the Cure). It’s sung from the perspective of a cell that is stuck next to a growing tumour:

Hello there, I am a cell.
Feeling healthy, fit and well.
Life is good, yes, life is swell.
But my neighbour’s got it worse.

Something about him does not belong.
The way he pushes is just wrong.
They say in him the force is strong,
they say he’s got the force.

He takes up so much space.
And is always getting up in my face.
It’s putting me in a stressful space.

You could say he’s left his mark.
It’s like swimming with a shark.
He’s pushing me towards the dark,
the dark side of the Force,
the dark side of the Force.

Oh, have a mentioned that I like Star Wars?