Catalytic reaction dynamics in inhomogeneous networks.

Biochemical reactions in a cell can be modeled by a catalytic reaction network (CRN). It has been reported that catalytic chain reactions occur intermittently in the CRN with a homogeneous random-graph topology and its avalanche-size distribution obeys a power law with the exponent 4/3 [A. Awazu and K. Kaneko, Phys. Rev. E 80, 010902(R) (2009)]. This fact indicates that the catalytic reaction dynamics in homogeneous CRNs exhibits self-organized criticality (SOC). Structures of actual CRNs are, however, known to be highly inhomogeneous. We study the influence of various types of inhomogeneities found in real-world metabolic networks on the universality class of SOC. Our numerical results clarify that SOC keeps its universality class even for networks possessing structural inhomogeneities such as the scale-free property, community structures, and degree correlations. In contrast, if the CRN has inhomogeneous catalytic functionality, the universality class of SOC depends on how widely distributed the number of reaction paths catalyzed by a single chemical species is.