## Biology and Mathematics

Perhaps mathematics can explain certain biological phenomenon.

While the chemistry and physics students suffered through semester after semester of mathematics, the biology students finished their calculus sequence and moved on. The idea was that biology does not lend itself to mathematical application in the same way chemistry and physics does, so students didn't need very much math. However, that may be old news. According to an article in *New Statesman* by Ian Stewart, biology may be undergoing another revolution and the result will be "biomathematics":

Maths has played a leading role in the physical sciences for centuries, but in the life sciences it was little more than a bit player, a routine tool for analysing data. However, it is moving towards centre stage, providing new understanding of the complex processes of life.

Stewart mentions at the beginning of the article that biology has undergone five great revolutions:

• Invention of the microscope

• Classification

• Evolution

• Discovery of the Gene

• Discovery of the structure of DNA

He contends that mathematics may be the new, sixth revolution in biology. If we are talking about scientific revolutions in the sense that Thomas Kuhn describes them in *The Structure of Scientific Revolutions*, then the important point here is while the prior revolutions may have provided a greater understanding of biology they did not account for certain other observations. The next revolution provides a different framework by which that field of science operates, and opens the door for asking different kinds of questions.

What drives the research questions is the framework through which you are asking the questions. Stewart indicates that mathematics provides an apt framework for looking at the complexity of biological systems and for bringing up new research questions. He provides three interesting examples of research that was guided by questions that came out of mathematical theory. This post will look at one of them, animal markings. This particular theory had to do with work based on Alan Turing's equations and Mendelbrot's fractals.

Two scientists from Japan wanted to study the striking stripe pattern on a particular type of tropical angelfish (*Pomacanthus imperator*). They applied Turing's mathematical models to the patterns on the angelfish, but came up with odd results. The Turing model predicted that the angelfish's stripes move along its body. So the scientists decided to test this theory. From the article:

It seemed wildly unlikely, but when Kondo and Asai photographed specimens of the angelfish over periods of several months, they found that the stripes slowly migrated across its surface. Moreover, defects in the pattern of otherwise regular stripes, known as dislocations, broke up and re-formed exactly as Turing's equations predicted. They did this because the pigment proteins leaked from cell to cell, drifting from the fish's tail towards its head. (In animals whose stripes are fixed, this does not happen; but once the size of the animal and other factors are known, the maths can predict whether its markings will move.)

Most likely these scientists would not have considered the possibly of the angelfish's markings migrating across its body had they not used the mathematical models which pointed towards this research.

As scientists delve deeper into biological systems, they find more and more layers of complexity. Mathematics can help scientists understand the mechanisms behind the function.

Stewart mentions how DNA had changed the way we do biology. DNA, and genetics in general, turned biology into a micro-scale endeavor. Biochemistry emerged as a prominent discipline. Stewart points out that while we are able to identify the DNA sequence, we still do not understand how the genes work together:

A creature's genome is fundamental to its form and behaviour, but the information in the genome no more tells us everything about the creature than a list of components tells us how to build furniture from a flat-pack. What matters is how those components are used, the processes that they undergo in a living creature. And the best tool we possess for finding out what processes do is mathematics.

Stephen Meyer discusses how mathematics, particularly information theory, can help our understanding of DNA in chapter 4 of his book, *Signature in the Cell*. One of the important features to applying information theory to DNA is that DNA is mathematically similar to text (he compares it to English text) because it is not only non-compressible information, but is capable of carrying information. But it doesn't just carry information, it also conveys functional information. This leads to new research questions, particularly in origin of life research.

From a philosophical standpoint, what does it mean that these biological systems can be explained by mathematical theories (DNA and information theory, animal markings and fractals, viruses and geometry, plankton and chaos theory)? The mathematical predictability certainly implies non-randomness. It also seems to imply layers of complexity and layers of information. These layers of complexity seem to indicate something more than unguided or random processes. It seems to indicate either a front-loading of information or at least some kind of mechanism that has the end goal in mind.