Abstract
This lecture and the following one explore the concept of self-organization by studying the emergence of spatial and temporal patterns in systems where chemical or mechanical instabilities operate. Throughout these lectures we present theoretical and experimental papers that illustrate the richness and complexity of these self-organizing systems.
For the sake of clarity, we first look at purely chemical spatial instabilities in reaction-diffusion systems. These instabilities, known as Turing instabilities, are characterized by local excitation from an autocatalytic loop, and remote inhibition from an inhibitor. A difference in diffusion between activator and inhibitor is sufficient to generate spatial patterns whose characteristic lengths reflect the details of interactions between activator and inhibitor and their differential diffusion. We then see steady-state temporal instabilities in so-called " excitable " systems following the FitzHugh-Nagumo heuristic model : bistability, excitability and oscillations emerge from interaction between a fast autocatalytic reaction and a slower inhibitory reaction. By adding a spatial coupling mechanism via diffusion, we see the emergence of spatio-temporal structures in the form of " trigger-wave ", which manifest themselves in a wide variety of ways as calcium waves or cell cycle waves in the Xenopus embryo, action potentials, or pigmented patterns on the surface of shellfish.
In a second place, the lecture shows the emergence of spatial patterns of a purely mechanical nature. It builds on the pioneering work of biologist Albert Harris and physicists George Oster and James Murray, on the emergence of cellular aggregates from uniformly distributed cells on an elastic substrate. The contractile cells deform the substrate, inducing locally oriented cell motility and thus forming a positive feedback loop that amplifies the formation of a local cellular aggregate. Substrate elasticity, on the other hand, acts as a long-range inhibitor. We thus find mutatis mutandi a Turing pattern characterized by competition between local excitation and global inhibition in a mechanical system. The spatial distribution of feather precursor buds in birds provides a remarkable illustration of the importance of this modus operandi.
