MPIDS Colloquium: Self-organised adaptive biophysical networks

Networks are common within biological systems and have been characterized in a range of different contexts that include metabolism, protein-protein interaction, neuronal circuits and ecological food webs. However, one area that has received little attention is analysis of organisms whose entire growth form is as a network. Unlike vascular transport systems in plants and animals, these net-works are not constrained to a predictable structure, but explore space in the search for patchy and ephemeral nutrients, continuously adapting to varying external conditions, in the face of competi-tion, damage and predation. In the laboratory, the same organisms can be set various problem-solving tasks that may help to provide a mechanistic basis for their unique morphology and dynamic resource allocation, but have also been interpreted as manifestations of emergent de-centralised problem-solving in non-neuronal organisms. Some aspects of their behaviour can be captured by simple mathematical models, based on a non-linear feed-forward term and a linear decay term, that echoes emergent behaviour in agent-based models of colonial insects, notably ant-colony optimisa-tion algorithms, or even neuronal reinforcement. Furthermore, reaction-diffusion equations with sim-ilar terms are known to have rich pattern forming properties in free space, generating the well-known Turing patterns. This hints that solutions to a certain class of optimisation problems may be solved (approximately) by iteratively running reaction-diffusion equations within a network architecture, which is itself modified by the flows within it.