Robustness of spatial patterns in buffered reaction-diffusion systems and its reciprocity with phase plasticity

A linear reciprocal relationship between robustness and plasticity in homeostatic biological networks

In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of core genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase to provide a plastic (sensitive) response. A feedforward structure from the non-core to core genes evolved autonomously. Negative proportionality was observed between the average changes in core and non-core genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. The proportion coefficient between those genes is represented by their number ratio, as in the "lever principle", whereas the decrease in the ratio results in a transition from perfect to partial adaptation, in which only a portion of the core genes exhibits robustness against environmental changes. This reciprocity between robustness and plasticity was satisfied throughout the evolutionary course, imposing an evolutionary constraint. This result suggests a simple macroscopic law for the adaptation characteristic in evolved complex biological networks.

Pattern Formation through Temporal Fractional Derivatives

It is well known that temporal first-derivative reaction-diffusion systems can produce various fascinating Turing patterns. However, it has been found that many physical, chemical and biological systems are well described by temporal fractional-derivative reaction-diffusion equations. Naturally arises an issue whether and how spatial patterns form for such a kind of systems. To address this issue clearly, we consider a classical prey-predator diffusive model with the Holling II functional response, where temporal fractional derivatives are introduced according to the memory character of prey’s and predator’s behaviors. In this paper, we show that this fractional-derivative system can form steadily spatial patterns even though its first-derivative counterpart can’t exhibit any steady pattern. This result implies that the temporal fractional derivatives can induce spatial patterns, which enriches the current mechanisms of pattern formation.