Evolutionary dimension reduction in phenotypic space

Abstract

In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in response to environmental changes are effectively restricted to a low-dimensional subspace. Thus, uncovering the origin and nature of such a drastic dimension reduction is crucial to understanding the general characteristics of biological adaptation and evolution. Herein, we first formulated the dimension reduction in terms of dynamical systems theory: considering the steady growth state of cells, the reduction is represented by the separation of a few large singular values of the inverse Jacobian matrix around a fixed point. We then examined this dimension reduction by numerical evolution of cells consisting of thousands of chemicals whose concentrations determine phenotype. The model cells grow with catalytic reactions governed by genetically determined networks, which evolve to increase cellular fitness, i.e., growth speed. As a result of the evolution, phenotypic changes due to mutations and external perturbations were found to be mainly restricted to a one-dimensional subspace. One singular value of the inverse Jacobian matrix at a fixed point of concentrations was significantly larger than the others. The major phenotypic changes due to mutations and external perturbations occur along the corresponding leftsingular vector, which leads to phenotypic constraint, and fitness dominantly changes in the same direction. Once such phenotypic constraint is acquired, phenotypic evolution to a novel environment takes advantage of this restricted phenotypic direction. This results in the convergence of phenotypic pathways across genetically different strains, as is experimentally observed, while accelerating further evolution. We also confirmed that this one-dimensional constraint on phenotypic changes is imposed even by evolution under fluctuating conditions with environmental changes occurring every few generations, where the fitness for each condition is embedded into the evolving one-dimensional direction for major phenotypic changes. Thus, while genetic evolution can be random, phenotypic evolution appears to be constrained.

Phenotypic noise and the cost of complexity

“…Experimental studies also suggest that both amplitude and correlation of phenotypic noise on multiple characters are evolvable (Stewart-Ornstein et al 2012;Yvert et al 2013). Moreover, the ability of the genotype-to-phenotype map to shape the random distribution of phenotypes, independently from the genetic variability, has been recently suggested by Sato and Kaneko (2019) and Sakata and Kaneko (2020). They have shown with analytical and numerical approaches that due to the evolution of the genotype-to-phenotype map, the distribution of phenotypes in a population can be restricted to a subspace as a result of evolution in variables environments.…”

Functional sensitivity and mutational robustness of proteins

“…Larger conformational changes are governed by low-dimensional slow modes. Recent reports have shown that the dimensions of biologically relevant modes are reduced through evolution [67,68]. Such evolutionary dimensional reduction was also observed in the phenotypic dynamics of proteins [28,29,69].…”

Functional Sensitivity and Mutational Robustness of Proteins

“…Larger conformational changes are governed by low-dimensional slow modes. Recent reports have shown that the dimensions of biologically relevant modes are reduced through evolution [66,67]. Such evolutionary dimensional reduction was also observed in the phenotypic dynamics of proteins [28,29,68].…”