I’ve long believed that the war on smoking will only ever end when it’s finally and conclusively proved that smoking doesn’t cause lung cancer, and that something else does. The police are looking for a serial killer, and they’ve arrested Mr Tobacco, because Mr Tobacco was present at 90% of the crime scenes, right inside the lungs where the dirty deed was done, and Mr Tobacco is a man of known bad character, who spends his days with Mr Booze and Mr Curry and Mr Pizza and other ne’er-do-wells of the Fast Food franchise. It’s going to need a Lieutenant Columbo to show that Mr Tobacco couldn’t have done it, and that the real killer was… somebody else. And he has to do it soon, because Mr Tobacco is now facing the electric chair.
Columbo, in this case, is going to have to be a cancer researcher. But who’s researching lung cancer these days? Hardly anybody. And why aren’t they researching lung cancer? Well, because everybody knows that Mr Tobacco was the culprit, and the case is closed.
So who’s going to find out what really causes lung cancer? Nobody, it seems. Mr Tobacco is just going to have to fry. And so are all the smokers.
But what if a few amateur investigators decide to find out for themselves? Why wait for highly-paid researchers in universities? Smokers have all the skills of such researchers. They’re biologists and microbiologists and geneticists and chemists and physicists and mathematicians and engineers and artists and historians. They can do anything. What’s to stop a bunch of people with these diverse skills from setting up their own research programme? Particularly when the professionals seem to be completely stuck, and getting nowhere fast.
Over the next few days I’d like to outline a research programme. I’m not going to ask for volunteers. I’m just going to try to explain why I’ve become utterly fascinated by cancer over the past few months, and why I can see the hazy outlines of a research project emerging.
It all started over 20 years ago, when I got interested in living things, and doing what I always do whenever I get interested in something – I started building computer simulation models. These were simple models of exponentially growing populations of theoretical critters whose numbers grew 1, 2, 4, 8, 16, 32 and so on. Sometimes the critters were plants, and sometimes grazers, and sometimes predators. And sometimes they were just tiny cells.
And I had a puzzle back then I couldn’t solve. It was the puzzle of how one cell grows and divides to become two cells. I wasn’t asking how two biological cells divided in two, but how a bag of water grew and divided in two. It wasn’t a biological puzzle: it was a geometrical puzzle. Because I thought of cells as being little plastic bags full of water. The problem was that there had to be just enough water and just enough plastic sheet to make two cells (and no more), and the growing cell also had to somehow divide in two.
And I couldn’t figure it out. But it didn’t really matter, because it didn’t really affect my models. So I’d pick up the problem every now and then, and have another shot at it, and get nowhere again.
Until last March, that is, when I picked up the ancient and seemingly insoluble problem once again, and had a new idea. I noticed that when a cell has grown from one sphere or cube to become two spheres or cubes of exactly the same size as the parent cell, the two daughter cells have the exactly twice the surface area and twice the volume as the parent cell. And I thought: what if a cell maintains the same ratio of surface area to volume throughout the whole cell cycle? Could that be done? Was there a geometric configuration whereby the ratio of surface area to volume stayed constant?
I remembered that real biological cells form a notch when they grow and divide, and so I started fooling around with pencil drawings of a growing cubical cell which formed a notch in it, working out the surface area and volume. Pretty soon, I’d written yet another computer programme to explore it numerically.
And it rapidly emerged that, yes, it was possible for a cubical cell with a notch in it to grow in such a way that it kept the same ratio of surface area to volume as it grew. What was really astonishing was that, if it did that, it automatically divided in two.
I had solved my insoluble puzzle! Delighted, I posted my discovery on my blog on 1 April 2012, All Fools’ day.
A month or two later I adapted a 3D display programme to show the entire sequence of cell growth and division. It’s shown at right. The cell starts off cubical, and I’ve coloured the different surfaces in different colours, so that you can see how the sizes of them change. If you wind the page up and down with a mouse wheel, it gives the appearance of an animation.
The important thing about this sequence of images is that they are all of a cell which maintains the exact same ratio of surface area to volume from start to finish.
At the end of the growth cycle, the two halves of the cell are connected only by the vertex of a pyramid: they are connected by nothing at all. The cells have divided to become two cells.
And in this particular case, the cell hasn’t divided into two cells exactly the same size as the parent cell, but into ones which are in total 1.76 times the volume of the parent. A new kind of cell has been produced, a bit smaller than the parent.
Further investigation showed that two exact replicas were only ever produced if the width of the notch was kept to zero. If the notch was a bit wider, the daughter cells were smaller than the parent cell. If the notch was wider still, the daughter cells were larger than the parent. In fact, they could be huge. And yet they all had exactly the same ratio of surface area to volume.
So these kinds of cells could grow and divide to form an entire zoo of different cells, some bigger, some smaller, some long and thin, some wide and flat. Yet while there were some ways that they could grow, and there were lots more ways in which they couldn’t grow. For example, a cube with side length 1 and volume 1 and surface area 6 and A/V ratio 6 couldn’t become a cube with side length 2, because the volume would have become 8 and the surface area would have become 24, and the A/V ratio 24/8 or 3 – which was not allowed. Cubes couldn’t grow into bigger cubes. Spheres couldn’t grow into bigger spheres.
Now, this was just me wondering how a cubical polythene bag of water could grow to become two cubical bags. But the more I looked at this model of cell growth and division, the more I thought: Never mind bags of water, this must be how real biological cells grow and divide. And as far as I could make out from watching online videos of dividing cells, they usually developed a very narrow notch between their two halves.
All of which was quite interesting in an academic sort of way, until I came across the following photo of dividing cells online one day.
And I looked at these dividing cells and immediately thought: The fluffy ends of these cells are a bit strange, but the middle bits of those cells are just like the pyramidal middle bits of many of my theoretical cells. Like the ones I’ve just shown growing and dividing.
But… these cells were cancer cells.