UK Nonlinear News, February 1998

The Hierarchical Genome

By Richard Gordon

The editors of UK Nonlinear News have asked me to say a few words about my forthcoming book

Gordon, R. (1998). The Hierarchical Genome and Differentiation Waves: Novel Unification of Development, Genetics and Evolution.
Singapore: World Scientific, about 1500p.

The full outline is available on a web page of the Canadian Society for Theoretical Biology: .

Why would a mathematician want to wade through this tome, which has barely a scrap of math in it? The reason has to do with the perennial problem of how order arises from chaos, or whatever we presume precedes order. Organisms are regarded as the most highly ordered structures we know of in the universe, yet they start from what would appear to be essentially spherically symmetrical objects called eggs. Of course, there is a huge, centuries old dispute over whether the egg is ordered or not, coming under the jargon of preformationism (or cytoplasmic "determinants") versus epigenesis, and this battle continues today, if often inarticulately. I try to strip it down to essentials, and show many cases that undermine preformationism, tending to support raw epigenesis, i.e., order from chaos.

Yet it is not quite chaos, because lurking in the nucleus of the fertilised egg is the well ordered DNA, a molecule 2 meters long in each human cell, containing perhaps 100,000 genes. Alone, DNA can do nothing. As part of that cell, it (and the egg cell) produces you or me, or Tyrannosaurus rex.

We could dismiss the whole problem as mere symmetry breaking. Here's a quote from the book:

Consider the quintessential example of the development of Bénard cells in a shallow pot of water on a stove..., easily made visible by throwing in some small particles, like crushed parsley.... Now honeycomb patterns are common in nature..., so their explanation warrants some attention, and nonlinear dynamics probably play a role. The problem is simply this. An embryo is generally self-contained. To create a Bénard pattern from scratch, we must therefore consider the self-assembly of the pot, the stove, the heat source, the water, and the parsley, all at once, plus their proper orientation with respect to gravity. Clearly this is beyond the nonlinear dynamics forming Bénard cells. To claim that this can be done by bootstrapping..., with consecutive nonlinear dynamics for each item, and a grand overall nonlinear dynamics for putting the components together (however separated out from the original fertilised egg), while perhaps plausible, is undemonstrated.

Simple, nonlinear dynamics, even reiterated, are simply not going to solve the problem. Something is missing, and I think I and my colleagues have found what it is. Consider a given tissue in an embryo. Two physical, observable waves go through complementary parts of that tissue: a contraction wave and an expansion wave, leaving in their wakes two new tissues. The "newness" of the tissues comes, I propose, from the binary response of the DNA, activating one of two prepared subsets of genes. If I am right, then embryogenesis is reduced to the problem of solving what launches each wave, and what determines its trajectory (plus how the DNA gets two subsets of genes ready for action).

The trajectories of these "kink" waves (waves that change the state of a material) are indeed, peculiar. Some start at a point and spread as a single, circular furrow. Others start as a circle and come down to a point. One, the ectoderm contraction wave, which forms the neural plate (the start of the brain and spinal cord), starts at a point at the tail end, breaks into an arc, the arc becomes concave, and it closes down as a point at the head end, the whole pathway approximating a hemispherical shell.

I also present hints of wave-wave interactions that may be important in the timing of the launching of the waves, giving some embryos an extraordinary independence from temperature over a wide range.

If I were more of a mathematician (I have only a B.Sc. in math from the University of Chicago), I would be plunging into the dynamics of these waves. But I'm not, so I hope to entice some of you to look at the problem.

Richard Gordon, (, University of Manitoba.

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