Figure 1. High-throughput screen for reaction-diffusion patterning networks using RDNets.
(a) Schematic representation of the software RDNets to identify pattern-forming networks. RDNets exploits a computer algebra system for high-throughput mathematical analysis of reaction-diffusion networks with N nodes and k edges. Diffusion and reaction constraints, including the number of diffusible (blue) and non-diffusible (red) nodes and quantitative parameters (here: k2, k8), can be specified as inputs. Additionally, the phase of the resulting periodic pattern can be selected. A list of reaction-diffusion networks is given as output. (b) Bar charts summarizing the number of networks for the 2-, 3-, and 4-node signaling network cases. Resulting networks can be of three types: Type I requires differential diffusivity, Type II allows for equal diffusivity, and Type III is diffusivity-independent. Type II and Type III networks are more robust to parameter changes than Type I networks. (c) Simulations of the possible topologies associated with a given network show that the minimal three-node systems can form in-phase and out-of-phase periodic patterns depending on the network topology. See Appendix 6 for a full list of parameters.
Figure 1—figure supplement 1. Catalog of all 3-node networks with two diffusible nodes (blue), one non-diffusible node (red) and six interactions.
Figure 1—figure supplement 2. Comprehensive catalog of 4-node Type I reaction-diffusion networks with two diffusible (blue) and two non-diffusible (red) nodes representing the interaction between two signaling pathways.
Figure 1—figure supplement 3. Comprehensive catalog of 4-node Type II reaction-diffusion networks with two diffusible (blue) and two non-diffusible (red) nodes representing the interaction between two signaling pathways.
Figure 1—figure supplement 4. Comprehensive catalog of 4-node Type III reaction-diffusion networks with two diffusible (blue) and two non-diffusible (red) nodes representing the interaction between two signaling pathways.
