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In physics of living systems, a search for relationships of a few macroscopicvariables that emerge from many microscopic elements is a central issue. Weevolved gene regulatory networks so that the expression of target genes(partial system) is insensitive to environmental changes. Then, we found theexpression levels of the remaining genes autonomously increase as a plasticresponse. Negative proportionality was observed between the average changes intarget and remnant genes, reflecting reciprocity between the macroscopicrobustness of homeostatic genes and plasticity of regulator genes. Thisreciprocity follows the lever principle, which was satisfied throughout theevolutionary course, imposing an evolutionary constraint.

A Linear Reciprocal Relationship Between Robustness and Plasticity in Homeostatic Biological Networks