RT Journal Article
SR Electronic
T1 Formation of Dominant Mode by Evolution in Biological Systems
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 125278
DO 10.1101/125278
A1 Chikara Furusawa
A1 Kunihiko Kaneko
YR 2017
UL http://biorxiv.org/content/early/2017/04/07/125278.abstract
AB 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 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.Summary Cells generally consist of thousands of components whose abundances change through adaptation and evolution. Accordingly, each steady cell state can be represented as a point in a high-dimensional space of component concentrations. In the context of equilibrium statistical thermodynamics, even though the state space is high-dimensional, macroscopic description only by a few degrees of freedom is possible for equilibrium systems; however, such characterization by few degrees of freedom has not yet been achieved for cell systems. Given they are not in equilibrium, we need some other constraint to be imposed. Here, by restricting our focus to a cellular state with steady growth that is achieved after evolution, we examine how the expression levels of its several components are changed under different environmental conditions. Based on the analysis of protein expression levels in recent bacterial experiments as well as the results of simulations using a toy cell model consisting of thousands of components that are reproduced by catalytic reactions, we found that adaptation and evolutionary paths in a high-dimensional state space are constrained along a one-dimensional curve, representing a major axis for all observed changes. Interestingly, this one-dimensional structure emerges only after evolution and is not applicable to any system showing steady growth. This curve is given by the growth rate of a cell, and thus it is possible to describe an evolved system by a growth-rate function. All of the observed results are consistent with the hypothesis that changes in high-dimensional states are constrained along the major axis against environmental, evolutionary, and stochastic perturbations. This description opens up the possibility to characterize a cell state as a macroscopic growth rate, similar to a thermodynamic potential. This approach can provide estimates of which phenotypic changes are theoretically more evolvable, as predicted simply from their observed environmental responses.