Organic spirals

Organic spirals the development of a relatively unstructured embryo into a structured and highly differentiated adult is guided to a large extent by certain cues that are intrinsic to it. This process, known as self-organisation, occurs within the embryo in micro-organisms, in groups of cells of higher animals and plants and also in larger ecological communities. The detailed examination of the factors leading to self-organisation very interesting, all the more so when the resultant structure has the mathematical simplicity and visual elegance of a spiral.

A research team from the prestigious Princeton University, usa, recently confirmed that a particular enzyme and its inhibitor play a crucial role in spiral wave formation in a soil amoeba (Proceedings of the us National Academy of Sciences , Vol 94, No 24). The amoeba, Dictyostelium discoideum , lives as a single unit as long as its food lasts.But once starvation sets in, a large number of amoebae lying within a few millimetres of one another come together and form a social group. This happens through a curious process: it seems that one amoeba "calls" to its neighbours, and the call is thus passed down to other amoebae further down. This "call" is actually a scent, a chemical signal called cyclic amp (camp) that attracts amoebae. And soon all the amoebae in a neighbourhood accumulate at the site of the first "caller".

As starvation proceeds, the amoebae first become responsive to camp, then move towards a signaller and then they become capable of both moving and relaying the signal. Finally, these amoebae are able to spontaneously relay a signal by themselves.

A spontaneous signal can be either a one-shot affair or a periodic one, like a song, perhaps. As mutual signalling picks up, concentric waves of amoebae, move inwards or in spiral-shaped waves. The concentric waves are easy to explain, because they begin from the signalling centre and then spread uniformly in all directions as the scent is relayed outwards. This movement closely resembles the waves in water. But it were the spirals that had so far baffled the experts.

There are two ways in which scientists have approached the problem. The first way stresses on the universality of spirals; if spiral waves can be found in heart-tissue, Dictyostelium amoebae and forests, their explanation must lie in universal properties of living systems - or so the argument goes.

The second approach, adopted by the research team, looks for explanation in terms of specific properties of the particular system. So the question is, where are the detailed features of Dictyostelium's aggregation that might lead to spiral wave propagation? It so happens that in addition to camp , the amoebae also release the protein phosphodiesterase (pd), that can render camp inactive, and also a small protein called phosphodiesterase inhibitor (pdi), that, in turn weakens the pd . In short, pd weakens the strength of the camp signals and pdi , by weakening pd , indirectly strengthens the camp signals. Because of their widely differing sizes, camp (the smallest) can diffuse rapidly from cell to cell whereas pd (the largest) takes a long time to diffuse.

When sufficiently starved, the amoebae signal to one another with a single pulse of camp. Because they are surrounded by a sea of pd , the signal gets rapidly degraded. Now, explains the team, one cell produces and releases some pdi. As it diffuses outwards, this pdi inactivates the pd in its neighbourhood, enhancing the camp signal strength, and travels as a concentric ring of excitation. The phenomenon can be initiated from more than one cell at a time, and if the probability that a cell makes pdi is low enough, there will be only a small number of itinerant camp waves in a large field of amoebae. If a circular wavefront is accidentally broken, either because it encounters a region of temporarily unexcitable cells, or because it partially collides with another wave front, its symmetry is broken and the end of the broken wave can curl around and generate a spiral. This explanation is based solely on the assumption that only a small fraction of the total number of cells release pdi and that the bulk of the population is not capable of producing reiterated camp signals.

The research team devised two tests to confirm this theory. In one, a plate in which spiral patterns have begun to appear is sprayed with camp. This externally supplied excess of signals dampens the system down

Gradually, the pd inactivates the added camp. Meanwhile, the amoebae have advanced further in terms of their internal physiology and a great many have reached the spontaneously oscillatory stage of development. Now many origins of concentric waves, centres of aggregation, but no spirals appear.

The second test, in some ways more demonstrative, involves a mutant strain of Dictyostelium that is unable to manufacture pdi because it lacks the necessary gene. As the theory would predict, this mutant behaves similarly to the normal strain after recovery subsequent to external application of camp: concentric waves appear but spirals remain absent.

In addition to providing a plausible mechanistic basis for the origin of spirals, this study also affords a clue as to why evolution may have moulded the system in such a manner. Spiral waves, once they get going, can act as pacemakers.

This implies that these waves can act as more effective centres than the auto-nomously oscillating amoebae. There-fore, spiral aggregates tend to be relati-vely large as they can contain many more amoebae than concentric aggregates. This promotes chances of survival after the food supply has been exhausted.

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