We present a macroscopic theory to characterize the plasticity, robustness, and evolvability of biological responses and their fluctuations. First, linear approximation in intracellular reaction dynamics is used to demonstrate proportional changes in the expression of all cellular components in response to a given environmental stress, with the proportion coefficient determined by the change in growth rate as a consequence of the steady growth of cells. We further demonstrate that this relationship is supported through adaptation experiments of bacteria, perhaps too well as this proportionality is held even across cultures of different types of conditions. On the basis of simulations of cell models, we further show that this global proportionality is a consequence of evolution in which expression changes in response to environmental or genetic perturbations are constrained along a unique one-dimensional curve, which is a result of evolutionary robustness. It then follows that the expression changes induced by environmental changes are proportionally reduced across different components of a cell by evolution, which is akin to the Le Chatelier thermodynamics principle. Finally, with the aid of a fluctuation-response relationship, this proportionality is shown to hold between fluctuations caused by genetic changes and those caused by noise. Overall, these results and support from the theoretical and experimental literature suggest a formulation of cellular systems akin to thermodynamics, in which a macroscopic potential is given by the growth rate (or fitness) represented as a function of environmental and evolutionary changes.
Keywords: dimension reduction; fluctuation; phenotypic evolution; plasticity; robustness.