In many ways, the similarity between dividing cancer cells and my theoretical cells with their constant ratio of surface area to volume was rather difficult to escape. But I was totally foxed by this particular cancer cell:
Nasty piece of work, isn’t it? I think I may have known someone who had brain cancer like this. He said that he had spiders growing in his head. And this was probably what he meant. Fortunately, those aren’t real legs. This cancer cell doesn’t walk around.
But I couldn’t see how a cell could get to grow like this.
But then I thought that my investigation thus far had led me to believe that normal cells had a narrow growth strip around them which resulted in them developing a narrow notch, and producing perfect replicas of themselves. And that cancer cells (the kind I was looking at yesterday) had wide growth strips around them, which produced long double cones separating the two ends of the growing cell. What if some cells had growth regions dotted all over them where new internal volume and surface area were added in a constant ratio? What would these cells do?
Clearly they wouldn’t divide, because they weren’t growing in the right places that would result in division. These cells could only get bigger and bigger. But they couldn’t just swell up into spheres. But if they stuck out spikes, was it possible for them to maintain a constant ratio of surface area to volume?
And the answer, after I’d written another computer model, was Yes, they could. They could either grow long conical spikes, or they could grow shorter filamentary hairs. What might happen with these spiky ‘spider’ cells is that they’re surrounded by normal cells, and can’t grow and divide in the way most cancer cells do. So they grow in the only way that they are able to grow, which is by extending firstly small bumps, and then spikes and hairs, probably in between adjoining cells, but ultimately straight through them. Cells like this could kill everything around them as they slide daggers through them.
But if these are cells that don’t divide, how come they become very numerous? The chap I knew with brain cancer spoke of spiders in the plural. So maybe these cells can flip between two modes of growth. If they can, they develop a growth strip round their waists, and grow and divide normally. But if they can’t, they push out bumps and spikes and hairs.
Which brings me all the way back to the very first cancer cell that caught my eye.
When I first saw this cell, it was the double cone joining the two halves that caught my attention, because they were so like my dividing theoretical cells. I ignored the fluffy ends, which I didn’t understand. But now I think that the fluffy ends have grown lots of filamentary hairs (HeLa cells do this too). So most likely this cell has been unable to grow and divide, and has pushed out all these filaments instead. In fact, maybe it’s only growing and dividing now because it’s been transferred into a nice, spacious lab flask where it can grow and divide to its heart’s content (if it had a heart).
And that’s about as far as my cancer research has got. It all started with my new theory of cell growth and division, in which cells kept a constant ratio of surface area to volume. Cells like this, if they grew new surface and volume in particular places, and didn’t grow in other places, would grow and effortlessly divide.
But if I have one or two tentative answers, it seems that another 10 questions pop up for every answer I find. The biggest question now is: why do some cells have narrow growth strips, and others – cancer cells – have wide ones, and some seem to have growth regions scattered all over them?
My plan right now is to build some improved computer simulation models of growing cells. I spent much of yesterday and today constructing a 3D icosahedron of node masses and elastic ties. Tomorrow I’m going to multiply the number of triangular faces from 20 to 320. Then I’m going to figure out how to simulate an internal pressure acting from inside on all 320 triangular faces, and then inflate the icosahedron into a sphere. That’ll be my theoretical ‘stem cell’ from which all other cells grow and divide.
I’m hoping that, with judicious expansion of the surface triangles (and maybe the addition of more triangles) while keeping the cell volume and surface area in the same constant ratio (the A/V ratio of the stem cell), I’ll be able to get the stem cell to grow and divide. I’m hoping that I’ll be able to simulate normal cell growth and division, and also dual-cone cancer cell growth and division, and also spiky ‘spider’ cell growth.
And when (and if) I’ve got that working, I’ll investigate how much physical work is required to perform growth and division, and maybe estimate relative cell cycle durations. I’m supposing at the moment that it takes more work to make large cancer cells, and so they reproduce more slowly.
And maybe I’ll put the growing dual-cone cancer cells inside a matrix of cells, and see if they can muscle their way past like I think they can.
And maybe I’ll simulate heat flow too. And osmotic pressure (if I can figure out how that works).
That’s about 20 research programmes for a bunch of mathematicians and physicists and engineers and computer programmers (before the chemists and biologists and geneticists have showed up). So I’m thinking that if I get my cell growth simulation model working, I might make it available for other people to use, and do their own exploring. Maybe as a game. The Build Your Own Cancer Cell game.
Anyway, with luck, if I don’t encounter any major snags, I’ll have something working in a few weeks, and I think they’re going to be visually stunning. And everyone’s going to fall in love with cancer.