This year marks the 100th anniversary since the landmark publication On Growth and Form by D’Arcy Wentworth Thompson, which describes the mathematical patterns seen across the natural world including in shells, seeds and bees. Now, a new study from the University of Cambridge has used the same ideas of self-organisation to give an elegantly simple solution to a problem that has taxed biologists for centuries: how complex branching patterns arise in tissues such as the lungs, kidneys and pancreas. Tom Crawford spoke to researcher Edouard Hannezo...
Edouard – We are a team of physicists and we’ve been working with developmental biologists in order to understand how complex organs are formed during development. And what we’ve found is by using real organ reconstructions and mathematical modelling is that there are incredibly simple mathematical rules that are conserved among several organs, that allow organs to self-organise in a fundamentally random manner. Which means that organs don’t follow a precise blueprint, but rather each cell making up an organ behaves in a very random manner and is able to communicate with its neighbours in a simple way in order to generate a mature organ.
Tom – So in some sense each cell is kind of doing its own thing and then somehow all of the cells together give you your organ?
Edouard – Exactly, that’s something that has been widely studied in physics. For example, if you think about a tsunami wave, individual water molecules do not know that they’re forming a tsunami wave that’s moving cohesively. Each molecule just goes randomly around and it sonly if you put a lot of water molecules in a very specific way that you can form suddenly these self-reinforced structures that make up tsunami waves. And this is an exactly similar example in biology in which each cell behaves randomly and its through very simple interaction with the neighbours that they’re able to self-organise into complex patterns.
Tom – How do we end up with these incredibly complicated structures such as the lungs and the kidneys?
Edouard – What we found is that even though the global appearance of tissues such as kidneys and mammary glands is broadly similar, actually if you look in detail its actually like snowflakes – no two organs can be superposed and are exactly similar. And that’s a signature of the fact that the underlying mechanism is fundamentally random and that from random disorder these cells are able to self-organise into something that is almost robust, but never exactly the same.
Tom – A lung roughly speaking is about the same between most people. If it is as random as your suggesting, how do these cells know when to stop when they reach a certain size or how to form a lung?
Edouard – That’s the key rule that we’ve proposed in this article. So what we think is that cells proliferate, they grow randomly in all directions and of course they need to know when to stop – you want your organs to have a given size and not too much less and not too much more. And so the rule that we’ve shown is that even though each cell explores space completely randomly and divides randomly, we’ve shown that it’s able to measure the local density, so if it arrives in a place that’s a bit too crowded, it doesn’t try to keep growing it just stops. And stops growing forever. Therefore, with this density sensing of cells the organ is able to know the regions which are already dense enough – it shouldn’t grow anymore – and the regions which are not dense enough and it should grow additionally. And it’s this intrinsic self-correcting tool that allows for the self-organisation of organs and that allows organs to robustly develop from a series of random interactions between cells.
Tom – So can we imagine for a second that we are one of these tissues growing and can you talk me through the process that that tissue would undergo and how it develops into an organ.
Edouard – You can imagine a tree, and one of these trees starts with a single bud on top of a single trunk. This bud is going to start growing, it’s going to explore a random direction. And rather frequently these buds are going to divide and give rise to two branches, four branches and then eight branches, exactly as you can imagine in a tree. Therefore, this alone would never stop and it’s only thanks to this crowding induced termination that some of the tips turn off and stop growing, while other tips that are at the outer edges of the organ have access to low density regions and continue growing. There’s actually a pretty strong resemblance to what you can think about with a real tree, where you can imagine that the tips that have access to the sun will continue growing whereas tips that are overshadowed will stop.
Tom – And in terms of other applications of this kind of work beyond just understanding how our tissues develop, have you given any thought to other ways this could be used?
Edouard – One thing that we’ve started to look at in the paper is the question of developmental disorders. In particular, in the kidney, there are quite a few conditions in which unfortunately the kidneys stop growing before they are fully mature and so patients end up with at birth kidneys which are much smaller compared to normal. Therefore, we wonder if the fundamental randomness in organ development couldn’t explain pathological cases such as these developmental disorders.
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