Solving the Formula of Life

This book is written by Ian Stewart on 2011 and contains 19 chapters. In this book, he discussed about the relationship of Mathematics and Biology. The chapter 8 of this book focuses on the Human Genome Project and the algorithmic challenges of DNA sequencing.

The most direct connection to theoretical computer sciences came in chapter 13 where Stewart considered Alan Turing’s famous paper entitled “The Chemical Basis of Morphogenesis”, and sketched the development of biological thought about animal markings. Stewart said that for half a century, the mathematical biologists have built on Turing’s ideas. Turing’s specific model, and the biological theory of pattern-formation that motivated it, turned out to be too simple to explain many details of animal markings, but it captured many important features in a simple context, and pointed the way to models that are biologically realistic.

Turing proposed the reaction-diffusion equations to model the creation of patterns on animal during embryonic development. Stewart also noted that Hans Meinhardt had shown that the patterns on many seashells match the predictions of variations of Turing’s equations in the book entitled “The Algorithmic Beauty of Seashells”. James Murry, a mathematician, extended Turning’s ideas with wave systems, and proved the theorem: “a spotted animal can have a striped tail, but a striped animal cannot have a spotted tail”. The explanation for this theorem is that the smaller the diameter of the tail leaves less room for stripes to become unstable whereas, this instability as more likely on the larger-diameter body.

In chapter 14, an algorithmic game theory called “Lizard Games” made an appearance. Stewart introduced the readers to Barry Siverno’s studies of side-blotched lizards. These lizards come in three different characteristics which are the orange-throated, the blue-throated, and the yellow-throated. The orange-throated males are the strongest ones while the yellow-throated males are the smallest ones and the most female-colored. The blue-throated males are the best at pair-bonding. So, when the orange-throated males fight with the blue-throated males, the orange-throated wins. The blue-throated are preferable to the yellow-throated, and the yellow-throated males (the kicker) sneak away with the females while the orange-throated fight the blue-throated. This situation suggests an evolutionary game where the orange-throated beats the blue-throated, the blue-throated beats the yellow-throated, and the yellow-throated beats the orange-throated.

Stewart introduced von Neumann’s minimax theorem, Smith’s definition of evolutionary stable strategies, and other geometric concepts. Stewart then discussed about the phrase “survival of the fittest”: what it meant in the context where there is no clear winner.

In this the same chapter, Stewart gave many examples of evidence of evolution and the ways in which evolutionary theory has developed since the time of Charles Darwin. An example of this is the conventional biological wisdom in which at one time, sympiatric speciation was impossible. Roughly, the sympiatric speciation occurs when one species develops into two distinct species in a single geographic area. For many years, it was believed that for the speciation to occur, the groups of animals had to be geographically separated. But, this conventional wisdom appeared to be false because of both the empirical evidence and the more sophisticated mathematical models. Stewart said that there are two main forces that act on populations. First is the gene flow from interbreeding tends to keep them together as a single species, and the second is the natural selection that contrasts the gene flow. This natural selection is double edged. Sometimes it keeps the species together because they adapt better to their environment collectively if they all use same strategy. But sometimes also, it levers them apart because several distinct survival strategies can exploit the environment more effectively than one. On the second case, the fate of the organism depends on the force that will win. If the gene flow will win, we will get one species, but if the natural selection will win against a uniform strategy, we will get two species. A changing environment changes the balance of these forces and will have dramatic results.

Other computer-related chapters introduced graph theory, cellular automata and von Neumann’s replicating automaton. In chapter 10, Stewart told us the story of scientists that were identifying viruses with the use of X-ray diffraction and other similar methods. In other chapters, Stewart discussed the importance of symmetry and symmetry-breaking in mathematics with no exception. An example is the herpes simplex virus is mirror-symmetric and has 120 symmetries. Many of the viruses are coated with chemicals with the icosahedron as its shape. These icosahedral coats are made of triangular arrays of capsomers. Capsomers are small self-assembling proteins.

Pure icosahedral mathematics quite did not match on what was empirically observed. In the year 1962, Donald Caspar and Aaron Klug, inspired by the geodesic domes of Buckminster Fuller, proposed a theory that the pseudo-icosahedra will be used to model the virus coats. The Caspar-Klug theory provided an excellent model of many viruses, but over the next forty years, the research teams found structures that could not be explained using this theory. In the start of the year 2000, the mathematician Reidun Twarock and his co-authors finally proposed a unifying framework by using a higher-dimensional geometry.

Reidun Twarock introduced a viral tiling theory that uses the six-dimensional icosahedral symmetry group. He then took a cut from that six-dimensional lattice and projected it into three dimensions. This kind of approach accurately “predicts” both the pseudo-icosahedral virus coats, and the exceptional virus coats that were observed after the year 1962.

Conclusion

I guess this book is a good reference in knowing the relationship between mathematics and biology because of the author’s great “talent” and his knowledge about both fields: the mathematics and the biology.

Reference

Aaron Sterling. Iowa State University. Book Review (3 pages). <http://nanoexplanations.files.wordpress.com/2012/01/mathematicsoflife.pdf>  12/29/2013