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.

Automated summary

In the physics of living systems, understanding the relationship between macroscopic variables and microscopic elements is crucial. By evolving gene regulatory networks, we observed that certain core genes remained stable while other genes exhibited plasticity in response to environmental changes. An autonomous feedforward structure evolved from non-core to core genes. This study revealed a reciprocity between the robustness of homeostatic genes and the plasticity of regulator genes, which is constrained by the ratio of these genes.