bioRxiv2017
A reduction in high-dimensional phenotypic states to a few degrees of freedom is essential to understand biological systems. One possible origin of such a reduction (as recently discussed) is the steady growth of cells that constrains each components replication rate. Here, in contrast, our aim is to investigate consequences of evolutionary robustness, which is shown to cause a stronger dimensional reduction in possible phenotypic changes in response to a variety of environmental conditions. First, we examined global protein expression changes in Escherichia coli after various environmental perturbations. Remarkably, they were proportional across components, across different types of environmental conditions, while the proportion coefficient corresponded to the change in growth rate. Because such global proportionality is not generic to all systems under a condition of steady growth, a new conceptual framework is then needed. We hypothesized that such proportionality is a result of evolution. To test this hypothesis, we analyzed a cell model--with a huge number of components, that reproduces itself via a catalytic reaction network--and confirmed that 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. Furthermore, we found that the changes in concentration across all components in response to environmental and evolutionary changes are constrained to the changes along a one-dimensional major axis within a huge-dimensional state space. On the basis of these observations, we propose a theory in which high-dimensional phenotypic changes after evolution are constrained to the points near a one-dimensional major axis that correlates with the growth rate, to achieve both evolutionary robustness and plasticity. By formulating this proposition in terms of dynamical systems, broad experimental and numerical results on phenotypic changes caused by evolution and adaptation are coherently explained.\n\nSummaryCells generally consist of thousands of components whose abundance levels 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 a few degrees of freedom has not yet been achieved for cell systems. Given that 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 change under different environmental conditions. On the basis of 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 high-dimensional state space are constrained to changes along a one-dimensional curve, representing a major axis for all the observed changes. Moreover, this one-dimensional structure emerges only after evolution and is not applicable to any system showing steady growth. This curve is determined by the growth rate of a cell, and thus it is possible to describe an evolved system by means of a growth rate function. All the observed results are consistent with the hypothesis that changes in high-dimensional states are nearly confined to the major axis in response to environmental, evolutionary, and stochastic perturbations. This description opens up the possibility to characterize a cell state as a macroscopic growth rate, as is the case for the thermodynamic potential. This approach can provide estimates of which phenotypic changes are theoretically more evolvable, as predicted simply from their observed environmental responses.