Instability and dynamic pattern in cellular networks

Dynamic instability of reaction and transport processes in groups of intercommunicating cells can lead to pattern formation and periodic oscillations. Turing's 1952 analysis suggests a more general theory. A powerful new method for analyzing onset of instability in arbitrary networks of compartments or model cells is developed. Network structure is found to influence interaction of intracellular chemical reactions and intercellular transfers, and thereby the stability of uniform stationary states of the network. With the theory, effects of changes in network topology can be treated systematically. Several regular planar and polyhedral networks provide illustrations. Influences of boundary conditions and intercellular permeabilities on patterns of instability are illustrated in simple networks. Non-linear aspects of instability are not treated.