Photoreception Chemosensation Body axis outgrowth Heart

Mesodermal structures

Summed combinations of Hox gene expression specifies region along the axis; Segmentation behind CNS: Hairy, Engrailed

Sog/chordin dorsal, dpp/TGFb ventral

Para-hox genes: Anterior, Lab/Gsx; central, Bcd/Xlox, and perhaps an Antp/Ubx-like gene; posterior, Cdx/Abd-B.

Pax6, opsin

Odorant receptors

Dll/Dlx, Fgf


Snail, Twist, Slug

See (Arendt and Nubler-Jung 1994;Campbell 2002;Carroll, Grenier et al. 2001;De Robertis and Sasai 1996;Gerhart 2000;Scott 1994;Wilkins 2002).

similar gene hierarchies and inductions; but they are very different in their details: your legs and a fly's are not the same.

Repeated Structures Produced by Periodic Patterning Processes

Many traits—plant and animal—have periodic (repeated) and/or hierarchically nested patterns. What might be responsible at the gene level? Modular structures can develop Roman candle fashion by being generated from a source region and growing away from that region; the continued replacement of reptile teeth is an example. Combinatorial expression of TFs like the Hox genes can be responsible for initiating different cascades in the repetitive elements along an axis. However, neither combinatorial enhancer binding nor signal concentration gradients can explain all periodic patterning. For traits like hair, scales, feathers, intestinal villi, leaves, or fly sensory bristles or ommatidia (individual units of the compound eye), it is not plausible that each individual unit would be programmed by its own unique gene combination. There are too many units, and they are also often too similar to each other. Some other patterning process must be responsible.

In one such process the individual elements develop from initiation sites periodically spaced along an axis or in a tissue field. Once an initiation site becomes committed for the appropriate differentiation cascade, the unit can proceed autonomously without communication among the individual units; for example, the structure may develop when isolated experimentally.

Bateson developed an "undulatory" theory of life (Bateson 1894; 1913; Hutchinson and Rachootin 1979; Webster et al. 1992; Webster 1992; Weiss 2003a). He likened repetitive systems to interference patterns seen in wavelike phenomena being studied intensely according to field theories of late nineteenth century physics (Bateson had some notions derived from his time, that are not far from a kind of vitalistic inherency of built-in patterning, but we need not accept all of someone's views to see where perceptiveness may lie). Diffusion usually establishes simple gradients, as described earlier, but in 1952 the famous computer scientist Alan Turing (Turing 1952) suggested a reaction-diffusion process in which the interaction between two chemicals with different diffusion characteristics could establish spatially heterogeneous and/or repetitive patterns. Essentially, interference waves are established. In the archetypal simple model, the pattern can be described by two differential equations, one for the dynamics of change of concentration in space and time of each factor.

In a basic activator-inhibitor system of that type (Figure 9-6A) the interacting elements are SFs. One, the activator, catalyzes its own production in cells that detect it and also induces the production of a second signal that inhibits the activator. Both diffuse from sources of production across a cellular field. In this basic model, pattern formation requires that the inhibitor diffuse faster than the activator. This single process can in principle generate a series of spaced initiation sites in which an organ element will develop (that is, sites where the activator exceeds some expression threshold), surrounded by inhibition zones where no structure develops. The nature and stability of the resulting pattern depends on the production and turnover rates of these key substances (or on how many of them there are, and so on) (e.g., Bar-Yam 1997; Meinhardt 1996; 2003; Murray 1993).

That such processes were involved in biological patterning was suggested by the striking similarity between mathematical models and computer simulations and a host of observed traits including natural pattern traits such as the locations of hair, feather, teeth, butterfly spots, fish coloration, seashell and mammalian fur patterning, and others (see, e.g., Figure 9-6B and Kondo 1995; Asai 1999; Meinhardt 1996; Meinhardt 2003; Meinhardt 2000; Murray 1993; Nijhout 1991; Salazar-Ciudad 2002; Jung 1998).Very different patterns like butterfly wing patterns, fish stripes, and seashell coloration can be generated by similar processes worked in different ways. At the same time, small changes in the characteristics of a single process can generate very different patterns—just what one would want of a system that can evolve, can generate complex outcomes, but is itself not so complicated.

As one example, the mantle edge of a seashell is also a kind of linear progress zone in relation to shell color patterns. The shell grows out from the mantle forming a hollow spiral (hollow except for the organism itself). The mantle constitutes a line of cells along which periodic waves of different color generation are produced by a reaction-diffusion-like process. Wavelike color differences form along this line but then grow out and away from the mantle to become the new part of the shell. As the linear process "unrolls" from the mantle like a window shade, a two-dimensional color pattern results (Meinhardt 1996).

Simulations by various authors attempting to model different living patterns have used variations on the basic equations, and the process may never be exactly as specified by simple differential equations. But the nature, or logic of the patterning processes is probably similar to what is modeled. In fact, processes of this general time 2

time 1

inhibitor (I)

inhibitor (I)

activator (A)'

activator (A)'

time 3



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