# Formation of Dominant Mode by Evolution in Biological Systems

## TL;DR

This paper demonstrates that evolutionary processes shape biological systems to exhibit a proportional response in component concentrations to environmental changes, constrained along a major axis linked to growth rate, supported by experiments and models.

## Contribution

It introduces a new theoretical framework explaining how evolution constrains high-dimensional phenotypic changes along a major axis related to growth rate.

## Key findings

- Global proportionality in protein expression is observed across various stresses.
- Evolution shapes concentration changes to maximize growth and fitness.
- Phenotypic changes are constrained along a one-dimensional axis in high-dimensional space.

## Abstract

Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering a linear response to it, a common proportionality in such expression changes was derived and partially verified by experimental data. Here, we examined global protein expression in ${\it Escherichia coli}$ under various environmental perturbations. Remarkably they are proportional across components, even though these environmental changes are not small and cover different types of stresses, while the proportion coefficient corresponds to the change in growth rate. However, since such global proportionality is not generic to all systems under a condition of steady growth, a new conceptual framework is needed. We hypothesized that such proportionality is a result of evolution. To validate this hypothesis, we analyzed a cell model with a huge number of components that reproduces itself via a catalytic reaction network, and confirmed that the common proportionality in the concentrations of all components is shaped through evolutionary processes to maximize cell growth (and therefore fitness) under a given environmental condition. Further, we found that the concentration changes across all components in response to environmental and evolutionary changes are constrained along a one-dimensional major axis within a huge-dimensional state space. Based on these observations, we propose a theory in which high-dimensional phenotypic changes after evolution are constrained along a one-dimensional major axis that correlates with the growth rate, which can explain broad experimental and numerical results.