Architecture and Physiology in Sponges and Corals

The time has now come to see whether I have successfully bridged the gap between bioconvection and the solid structures of corals and sponges. To reprise the problem, I asserted in Chapter 4 that bioconvection cells represent a primitive type of structure, one that arises spontaneously from the interaction of a metabolic energy stream with a large-scale environmental gradient in potential energy. I suggested this model might be an organizing principle that would carry over to other, more tangible structures that animals build. In other words, external physiology of the type exemplified by bioconvection should be a common feature of life, animal life included, and perhaps it should be the apparent absence of an external physiology among certain animals that is the special case, not its existence.

The weak points of this argument are three: that there is a fundamental similarity between bio-convection cells and a putative external physiology that might occur at the larger scales characteristic of animals;that this fundamental similarity can be made incarnate in the structures that animals build;and that the structures so built are capable of doing physiological work. Up to now, I have been concerned mainly with laying the foundation I need to shore up these weak points. Let us proceed, then, point by point.

Obviously, bioconvection cells and the growth forms of sponges and corals are very different things, but they share a fundamental similarity: they are both the result of a modulated positive feedback process. I touched upon positive feedback briefly in the last chapter: I shall expand the topic now, and then turn to what a modulated positive feedback is.

As the name implies, any kind of feedback involves a feedback loop, a pathway that carries a flow of matter, information, or energy back on itself. Consider a technique popular in rock music, where a microphone (mounted, say, on a guitar) feeds into an amplifier that in turn drives a speaker (Fig. 5.14). If the microphone is placed near the speaker, sound energy will travel in a loop, from the speaker to the microphone, then to the amplifier, and back again to the speaker. You can see why it is called positive feedback—sound energy is amplified with every pass it makes through the loop.

Positive feedback also operates in the genesis of bioconvection cells and in the growth of corals and sponges. In the case of bioconvection cells, the positive feedback operates in the context of hydrodynamic focusing: the sinking of an anti-bubble draws microorganisms into it, which causes the anti-bubble's density to increase, which further increases the sinking rate, and so on. In the growth of corals and sponges, the positive feedback operates in the context of diffusion-limited aggregation: a slight elevation on a growing surface steepens the local boundary layer gradients driving accretion, which promotes local upward growth, which steepens the boundary layer gradients further, and so on. In both cases, a process (sinking of an anti-bubble, growth of a coral zooid) sets up the conditions for increasing its own rate of change.

Positive feedback has come to have a bad rap, and not just because it is frequently employed as a cheap trick to cover up a lack of musical talent. Anyone who has ever sat in an auditorium with poor acoustics has been subjected to the ear-splitting screech that results when someone on stage carries a microphone too close to the speakers. However, positive feedback can, under the right conditions, be a very creative and order-producing force. A skilled musician can use positive feedback to make an instrument emit sounds of

speaker microphone input —►effector

theoretical positive feedback response

Energy flux rate theoretical positive feedback response

limited positive feedback response

Figure 5.14 Positive feedback. a: A common positive feedback loop involves a microphone, an amplifier, and a speaker emitting sound backto the microphone. b: A schematic of a generic positive feedback loop: an effector increases the magnitude of the input to the effector. c: A positive feedback drives the energy flux rate through a system to increase exponentially. Theoretically, the energy flux rate increases without bound. In actual positive feedback systems, the response is limited by the power available to drive the system.

limited positive feedback response time

Figure 5.14 Positive feedback. a: A common positive feedback loop involves a microphone, an amplifier, and a speaker emitting sound backto the microphone. b: A schematic of a generic positive feedback loop: an effector increases the magnitude of the input to the effector. c: A positive feedback drives the energy flux rate through a system to increase exponentially. Theoretically, the energy flux rate increases without bound. In actual positive feedback systems, the response is limited by the power available to drive the system.

remarkable beauty. He does so by modulating the feedback loop so that only certain types of sounds travel through the loop and not others. As we shall see momentarily, a bioconvection cell arises from a similar modulation process. It is important, therefore, that we take a few moments to understand how a modulated feedback loop works.

The sound energy emitted by a guitar comes initially from a plucked string, which has a characteristic frequency of vibration. The string's vibration in turn sets the guitar's sound box vibrating at the same frequency, which in turn enhances the vibration of the string: the string and sound box together form a resonant system. The consequence of this mutual reinforcement is a louder sound than would be emitted by the string alone.

Resonance is not positive feedback, though, it is only a means of strengthening a particular frequency of vibration: a resonant vibration will die out as the energy fed initially into the string dissipates. Positive feedback occurs when an additional source of energy, in the form of the amplifier and speaker in our example of an electric guitar, is added to the resonant system. The presence of the resonant system (string and sound box) in the feedback loop now modulates what the positive feedback can do: sound can emerge from the speaker at any frequency, but only sounds at the guitar's resonant frequency will pass through the loop. Sounds at other frequencies will fail to set the string and sound box into resonant vibration, and the sound energy carried by those frequencies will dissipate away as heat: to introduce some jargon, these other frequencies have been "choked." Sound emerging from the speaker at the resonant frequency, however, will amplify the vibration of the sound box, which will reinforce the vibration of the string, which will feed more energy to the speakers, and so on. The result is an amplified pure tone, sustained by and limited in volume by the amplifier's ability to deliver power to the loop. We now see the high-pitched screech emerging from a simple microphone and public address system for what it really is: unmodulated feedback resulting from the absence of any resonant system to choke the passage of most frequencies through the loop. The result is the indiscriminate amplification of multiple, and often dissonant, frequencies of sound.4

Modulated positive feedback also operates in the

4. In the case of a microphone and public address system, the properties of the electronic components tend to pass high frequencies preferentially, with a high-pitched screech being the result.

genesis of bioconvection cells and in the growth of corals and sponges. Modulation is evident in the regular spacing of bioconvection cells in the culture. There is a resonance of sorts operating here, but this time it acts through the physical properties of the liquid culture—its viscosity, its density—and through the density, size, and shape of the microorganisms themselves. These properties promote the emergence of convection cells of a certain size and chokes the development of cells that are either larger or smaller than this favored size.

A similar process, albeit at a much larger scale, operates in the accretive growth of sponges and corals. In this case, the modulation is evident in the appearance of imperfections on the growing surface and not others. Corals and sponges commonly branch as they grow, and although different corals may branch in characteristic ways—at the tips or along the stems (Box 5A), say—the branches themselves frequently emerge at characteristic distances from one another. This implies that the growth of certain surface imperfections is favored over others, and that distance from a branch is somehow important in determining whether or not growth is favored. In all likelihood, the modulation arises from an interaction between a growing branch and the physical properties of the fluid in which it is immersed. A coral branch in flowing water will commonly generate turbulence in its wake, hiving off turbulent eddies at a frequency determined by its size and by the velocity, viscosity, and density of the water flowing past it (Fig. 5.15). Just as the peaks and troughs of a sound wave are separated by a particular distance,5 so too are these eddies separated from one another by a characteristic distance. The eddies will interact most strongly with the surface behind the branch at this characteristic distance. This is why, for

5. Specifically, this distance is the wavelength, X, which can be calculated from the sound wave's frequency, f (cycles per second) and the speed of sound, c (in meters per second): X = c/f. The wavelength of a middle C (f = 880 s-1) in air (c = 330 m s-1) is therefore 0.375 m; that is, every peakpres-sure in a sound wave is separated from the peak pressure in an adjacent wave by 37.5 cm.

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