The Role of Weak Interactions in Biological Systems: the Dual Dynamics Model

The dual dynamics model is a random autonomous network of nodes whose dynamical behavior is determined by both strong and weak interactions. The model combines discrete decision-making features reflective of logical operations with arithmetic features that represent graded influences. Dual dynamics abstracts the ubiquitous fact that biological systems at all levels of organization consist of components that respond both to specific (strong) signals and to the cumulative effect of numerous weak interactions. We have thoroughly studied the dynamical characteristics of three-valued dual dynamics networks in the range from four to 14 nodes and have compared these characteristics to those of non-boolean three-valued networks (without weak interaction) and to Kauffman boolean networks. Properties studied include: attractor length, number of attractors, basin sizes, orbital stability, and evolutionary transformability in response both to individual and cumulative mutations (where mutations are implemented as random changes in the response of a node to the pattern of strong influences impinging on it). The introduction of weak interactions and their manner of coupling to strong interactions has major altering effects on these properties. With suitable coupling it is possible to significantly enhance equifinality and evolutionary transformability. The model demonstrates that self-organizing dynamics are compatible with evolutionary plasticity when weak interactions are taken into account.