divulgatum está dedicado a la difusión de conocimiento científico en español e inglés, mediante artículos que tratan en detalle toda clase de temas fascinantes pero poco conocidos.
divulgatum is devoted to the dissemination of scientific knowledge in Spanish and English, through articles that go into the details of all sorts of fascinating, if not
widely known, subjects.

Monday, December 18, 2017

The origin of shape

An image of a human brain (left) next to a computer simulation generated by reproducing the physical forces acting on the brain's surface (right). Colours indicate analogous brain regions in both images.
Nature Physics 12, 588–593.)

THE HUMAN BODY is composed of around ten trillion cells – more than a hundred times the number of stars in the Milky Way. These cells are not all identical, but are classified into a myriad of different cell types: the cells making up, for example, the skin, the eye, and the brain, are strikingly different from each other, both in structure and in function. Even within a same tissue there are tens of distinct cell types, each performing a different role. It is certainly hard to imagine that such an immense organisation of specialised units can have stemmed from a single cell: the fertilised zygote arising from the fusion of an ovum (an egg cell) and a spermatozoon (a sperm cell). During the first days of embryonic development, this zygote multiplies to produce a sphere covered by a single layer of identical cells, called the blastula; not much later, this develops into a more complex structure, the gastrula, which is made up of multiple layers, each one composed of a different type of cells. The layers in the gastrula subsequently give rise to the different tissues and organs in the embryo.

Understanding the whole process by which the different parts of an organism, each composed of specialised cells with specific roles and structures, originate from a clump of undifferentiated cells, is clearly one of the most compelling scientific questions. The technical name for it is morphogenesis, from the Greek terms morpho, ‘shape’, and genesis, ‘origin’: the origin of shape.

It may come as a surprise that the first mechanistic explanation for morphogenesis was not to arrive until the mid-twentieth century. It should hardly surprise, however, that such breakthrough would be the product of the gifted mind of the mathematician Alan Turing, best remembered as the ‘father’ of computer science. In an article published in 1952, two years before his premature death, Turing proposed a system of chemical substances, called morphogens, that would explain how certain patterns of shape arise in living organisms. He described such system as evolving in time through a series of chemical reactions and diffusions; this results in a particular distribution across space of two different chemical signals, one of them promoting tissue growth, the other suppressing it. The outcome is a pattern of differential growth – some groups of cells multiplying faster than others – leading to the formation of a certain shape in the living tissue. Amazingly, Turing was able to predict some of these patterns decades before they could be first observed in the laboratory.

The term morphogen is still employed today to refer to those substances or molecules which partake in morphogenesis. We now know that the way in which many morphogens operate is by regulating cell differentiation, that is, the process whereby a cell of a ‘generic’ type transforms into a cell of a more specialised type. A family of proteins known as transcription factors are pivotal in the cell differentiation process. Transcription factors interact with cellular DNA, being able to ‘switch’ genes ‘on’ or ‘off’ in the cell. In some cases, those genes, in turn, regulate the activation of yet other genes, giving rise to genetic regulatory networks. In consequence, the action of a few transcription factors, or even a single one, can drastically affect the cell’s fate – for example, by determining important properties, such as the ability to adhere to other cells. This is especially true during what is perhaps the most crucial period in embryonic development: the process by which the blastula develops into the gastrula, known as gastrulation. To give rise to the multilayered structure of the gastrula, the cells in the blastula need to transiently ‘switch off’, by means of specific transcription factors, adhesion to their neighbour cells. This done, they can move to their new positions in the gastrula, where they regain their adhesion capabilities.

As the name indicates, morphogenesis does not only involve the differentiation of cells and their organisation into groups of distinct cell types, but also the formation of the very biological shapes which keep organisms alive and working. Interestingly, chemicals are not the only players in this process; physics has been discovered to have a considerable part in how living tissues, such as the gut or the brain, acquire their characteristic shapes. The human small intestine, for instance, is a tube between five and eleven metres in length, which folds and loops in a particular manner that allows it to fit in the abdominal cavity. It has been shown that the pattern of loops observed in the developing intestine of chick embryos can be explained by the physical forces that arise when a semirigid tube – in this case, the intestine itself – experiences substantial growth, while attached to an elastic material that does not change size. In the case of the intestine, the role of such elastic material corresponds to the mesentery, a tissue whose function is to anchor the intestine to the abdominal wall. Although this finding was largely proven using computer simulations, a simple physical analogy may be useful here. Let us imagine an elastic flat rubber band, with a flexible plastic tube sewn to one of its edges; if this tube started to grow, while the size of the rubber band remained unchanged, the shape adopted by the tube would soon match the shape in which the intestines are folded in the chick embryo. This suggests that the way in which the intestine folds is simply a physical consequence of the substantial growth experienced by this organ during early development.

The shape adopted by a flexible plastic tube when sewn to a stretched elastic rubber band, once this has been allowed to return to its original size (top) matches the pattern of loops seen in the developing intestine of chick embryos (bottom). (Source: Nature 476, 57–62.)

Another striking example of the physics underlying organic shapes is the mammalian brain. Two important regions of this are the white matter, located inside the brain, and the grey matter, which forms its outer layer (the cortex). The latter normally folds into the characteristic pattern of curved grooves that we immediately associate with this organ. Recent research has shown this morphological pattern to be the result of the physical tensions that arise when a layer of soft material increases in size, while anchored to a core of another soft material whose size does not vary. Because the outer layer – in this case, the grey matter – is firmly attached to the inner core – the white matter – it cannot expand freely in all directions. Instead, a compressive tension builds up that opposes the growth of the outer layer. To minimise such tension, the material must fold drastically in long, deep creases known as invaginations; the resulting shape allows the volume to increase while alleviating the physical stress generated in the process. When this physical system is simulated on a computer, the resulting structures look staggeringly similar to the surface of the brain. Moreover, by simulating the proportions of white and grey matter observed in different mammalian species, the shape of their brains can be reproduced; for instance, mice have much smoother brains than humans, because the proportion of grey matter in their brains is much lower. The peculiar shape of the human brain hence seems to be the solution provided by physics to the problem of achieving large volumes of grey matter.

There is certainly much more to be learned about the physical and chemical mechanisms behind morphogenesis. The inconceivably complex, marvellously tuned nine-month programme by which a single-celled zygote becomes a fully formed foetus baffles us still today. From the subtle patterns of gene regulation to the chemical and physical interactions between cells and tissues across space and time, deciphering the mathematical basis of the origin of organic shapes will always be counted among the most beautiful and captivating missions of science.

Turing, A.M. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London (1952).
Wolpert, L. The triumph of the embryo (Courier Corporation, 2008).
Savin, T., Kurpios, N.A., Shyer, A.E., Florescu, P., Liang, H., Mahadevan, L., Tabin, C.J. On the growth and form of the gut. Nature (2011).
Tallinen, T., Biggins, J.S. Mechanics of invagination and folding: Hybridized instabilities when one soft tissue grows on another. Physical Review E (2015).
Tallinen, T., Chung, J.Y., Rousseau, F., Girard, N., Lefèvre, J., Mahadevan, L. On the growth and form of cortical convolutions. Nature Physics (2016)