Math and stars

By Martín Bonfil Olivera

Published in Milenio Diario, January 20, 2010

Math has a special relation with physical reality: it allows us to describe it. This is clearly seen in astronomy: mathematical models, from Ptolemaeus, through Copernicus, up to the glorious Newtonian description and Einstein's modern vision, have allowed us to describe with ever greater precision, and to understand, with great depth, the behavior of celestial bodies. Compared to this, the foolish "predictions" of astrology look like incoherent babble.

What we still do not understand is why math is useful to describe the world. November 2009 edition of the mexican magazine Ciencia y desarrollo (Science and development), where he has written for over 30 years, José de la Herrán, a pioneer in science popularization in Mexico, describes a curious example. It is a study to verify the validity of an old astronomical mystery: the famous, Titius-Bode law.

The law, postulated by German astronomer Johann Daniel Titius in 1776 and popularized by his colleague , fellow German (and namesake!) Johann Elert Bode in 1772, asserts that the distance from the Sun to the planets of the solar system (or, to be more precise, the major semi-axes of their elliptic orbits – the major radii, but the word radius is only used for circles, not for ellipses) seems to be related with a peculiar numerical succession: 0, 3, 6, 12, 24, 48...

Initially, the "law" was not taken seriously: although it was accurate for the then-known planets (Mercury to Saturn), it predicted a non-existent planet in the fifth position, between Mars and Jupiter. But when Uranus was discovered in 1781, and it was confirmed to occupy the spot predicted by it, the law was studied again. The "lost planet" was searched for and in 1801 asteroid Ceres was found, the biggest one in the asteroid belt (today considered as a planet did not manage to form, probably due to Jupiter's great gravitational influence). In general, the law predicted, with less than 5% error, the positions of all planets.

Then, in 1846, Neptune was discovered. Its distance to the Sun did not fit with the prediction (30% error). The same thing happened with Pluto (96% error!). The prestige of this law collapsed, and it was demoted to a mere coincidence.

Here Mexican astronomer Arcadio Poveda, from the Astronomy Institute at UNAM enters the scene. In an article published in 2008 in the Revista Mexicana de Astronomía y Astrofísica (Mexican Astronomy and Astrophysics Journal, in co-authorship with Patricia Lara), he studied 55 Cancri, in the constellation of The Crab, a "nearby" star (about 12 parsecs; more than 40 light years) in whose surroundings, five more planets have been discovered between 1996 and 2007. He found that in general, their distances agree with Titius-Bode law, if it is assumed that there's a missing planet between the fourth and the fifth ones (maybe this would reveal that the gravitational dynamics of emerging planetary systems prevents the formation in certain orbits). Poveda even predicts the position of two planets surrounding 55 Cancri; lets see if these are found.

Although it has been criticised, Poveda's work is very suggestive. The Titius-Bode law is still an enigma: if it were valid, although we still don't know why (epistemologists would say that it is a phenomenological law that lacks its proper theoretical explanation), it could help discover new planets in other planetary systems.

(translated by Adrián Robles Benavides)

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The amazing ribosome

By Martín Bonfil Olivera
Published in Milenio Diario, October 14th, 2009

The chemistry Nobel prize thrilled me even more than the one for Medicine.

It was given to Venkatraman Ramakrishnan (Hindu, nationalized American, but living in Great Britain), Thomas Steitz (United States) and Ada Yonath (Israeli) because of "their studies about the structure and function of the ribosome".

If, like I mentioned last week, enzymes are amazing molecular machines that practically carry out all the functions of a living cell, ribosomes are an real automatized factories that manufacture, with absolute precision, each one of the thousands of different proteins we need to be alive.

A ribosome is a complex structure made of ribonucleic acid (the one-strand cousin of DNA) and many proteins.

It has some fixed parts, and other that move with robotic precision to assemble, in a matter of minutes, and from reading the information coming from DNA, proteins made up by thousands of amino acids, strung together as pearls in a necklace.

The achievement of the Nobel winners was to localize with great precision each one of the hundreds of thousands of atoms that form a ribosome, and this has allowed them to understand their functioning in atomic detail. They used X ray crystallography, a technique developed in the beginning of the 20^th century (and the same one that allowed Watson and Crick to discover the DNA double helix structure in 1953 --a structure, I might add, infinitely simpler than a ribosome).

To achieve this, they first had to obtain perfectly arranged crystals formed by pure ribosomes. It took them almost 20 years.

But to see atoms, one cannot use an optical microscope, not even an electron microscope. Only X rays have the necessary finesse. And no lens can focus them to form images: you have to gather the group of stains formed as the X rays travel through the crystals (originally the stains were captured on photographic film, but today they are captured by a couple charged device or CCD, the invention that this year won the Physics Nobel prize) and using computers to mathematically process data.

The result? Computerized models that reveal, with a very high level of detail, each screw and bolt of these wonderful molecular nano-factories.

As an additional benefit, these models are allowing scientist to develop new antibiotics that work like monkey wrenches tossed into the ribosomes of bacteria that make us sick.

Yes, I loved this year's chemistry Nobel. Too bad that Harry Noller, one of the giants of ribosome research, was left out of the prize, which can only be given to three persons.

(translated by Adrián Robles Benavides)

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The Nobel telomere

By Martín Bonfil Olivera
Published in Milenio Diario, October 7th, 2009

Nobel prizes are always exciting. This year's Physiology or Medicine prize reveals fascinating basic science about our cells which might have revolutionary applications in health.

It was awarded, according to the Nobel committee at the Karolinska Institute in Sweden, "for the discovery of how chromosomes are protected by telomeres and the enzyme telomerase", a discovery made by investigators Elizabeth Blackburn, her colleague Jack W. Szostak and her student Carol Greider.

The genetic information of living beings is written in the molecule of deoxyribonucleic acid, DNA, which form tangles called chromosomes within the nuclei on each of our cells.

Each chromosome is formed by a single, very long, DNA molecule. When it has to be copied, before the cell divides in two, the task is performed by an enzyme molecular machine made of protein.

Picture it like this: the famous DNA double helix is like a train railway. To copy it, both rails are separated and the enzyme slides over each one, reading the letters that form it and inserting the corresponding letters on the other side. Like a little train that advances in a rail, constructing the opposing rail. In the end, we have two complete and identical railways.

(http://www.youtube.com/watch?v=hfZ8o9D1tus)

But when the enzyme reaches the end of the rail, it cannot advance any longer, and does not construct the last span of the opposing rail. Each time that a chromosome is copied, their tips (telomeres, from the greek telos, end, and meros, part) would shorten!

Using a very ingenious experiment, Blackburn and Szostak discovered in 1982 that telomeres protect chromosomes so they are not destroyed. They constructed mini-chromosomes and added telomeres to some, but not all, of them. When they inserted the chromosomes inside cells, those with telomeres survived, but the ones that didn't have them were rapidly eliminated.

And in 1984 (Christmas day!), Blackburn and Greider discovered another enzyme that allows telomeres to maintain their size. It achieves it because it has a mold with the correct letter sequence (CCCCAA) that have to be inserted in each tip of DNA. They named it "telomerase" (the termination "ase" in biochemistry indicated an enzyme).

Today we know that telomeres and telomerase play a role in aging and cellular death (when telomeres are shortened) and influence the uncontrolled multiplication of cancerous cells (because their telomerase is very active and their telomeres are not shortened). There are even vaccines in development to try to fight cancer by inactivating the telomerase of tumors.

Basic science, motivated by simple curiosity, offers a new medical promise, although a far one.

(translated by Adrián Robles Benavides)

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Natural wonders

by Martín Bonfil Olivera
Published on Milenio Diario, March 25, 2009

I have just been to one of the 13 wonders of Mexico: the basalt prisms of Santa María Regla, in the state of Hidalgo.

When he came to Mexico in 1803, Alexander von Humboldt visited these impressive 30 meter basalt columns, of perfec hexagonal shape, that border a ravine as if God had arranged them like giants pencils. They're breathtaking.

But for a naturalist such as Humboldt, and for a relentless atheist like this columnist, the divine explanation is not satisfactory: it doesn't really explain anything. Could there be a natural process that allows hundreds of hexagonal prisms to be formed and carefully stacked ?

Basalt prisms, although rare, are not unique. There are 10 or 15 sites in the world with similar structures: the “giant's causeway”, in Ireland; the “Devils postpile”, in California; the “organ pipes”, in Australia… The formation of these structures doesn't seem to be that difficult.

A second hint is the hexagonal shape of the prisms. There is an old saying in northern Mexico, "as the wagon moves, the watermelons arrange themselves", that accurately applies to this case: spheres tend to accommodate spontaneously so that each one is surrounded by twelve more: it is the most compact arrangement. In the case of circles, the most efficient arrangement is hexagonal: the most compact form to arrange cylindrical columns is so that each one is surrounded by other 6. The hexagonal shape of the prisms is the result of this arrangement. They weren’t constructed and then arranged: they formed in their actual position.

And how could melted lava —basalt is solidified magma— form individual vertical prisms? The answer relies in the existence of self- organized structures in nature. "Bénard cells" are example : when heating a liquid from below, the convection movement —hot water goes up and cold goes down— can form hexagonal columns of water that keep circulating as long as there's a temperature difference. Prisms are fossilized convection cells that were solidified when they quickly cooled down.

The mineral world can form marvelous and arranged structures. The same thing occurs, but augmented, in the living world. Darwin, another naturalist, saw it and explained it. Because of this, and more the basalt prisms of Hidalgo are really worth visiting.

(Take a look at my pictures of the basalt prisms here)

(translated by Adrián Robles Benavides)

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