Evolutionary Innovation by Polyploidy

The preferred conditions for evolutionary innovation represent a fundamental question, but little is known experimentally or theoretically. In this study, we focused on the potential role of polyploidy in the evolution of novel traits. We proposed a simple model and demonstrated that the evolutionary rate of polyploids is similar to more much slower than that of haploids under neutral selection or during gradual evolution. However, experiments using polyploid cyanobacteria demonstrated that the probability of achieving antibiotic resistance increased with the number of chromosomes and implied an optimal number of chromosomes. Then, we investigated the dynamics of the same model on a fitness landscape in which cells should jump over a lethal valley to increase their fitness. The evolutionary rate could be increased in polyploidy, and the optimal number of chromosomes was identified. Further, we proposed that the optimization for evolutionary innovation might determine the number of chromosomes in polyploid bacteria.Comment: 35 pages, 8 figures, 4 table

Linear Response Theory of Evolved Metabolic Systems

Predicting cellular metabolic states is a central problem in biophysics. Conventional approaches, however, sensitively depend on the microscopic details of individual metabolic systems. In this Letter, we derived a universal linear relationship between the metabolic responses against nutrient conditions and metabolic inhibition, with the aid of a microeconomic theory. The relationship holds in arbitrary metabolic systems as long as the law of mass conservation stands, as supported by extensive numerical calculations. It offers quantitative predictions without prior knowledge of systems.Comment: 6+6 pages, 3+4 figures, 1 tabl

A linear reciprocal relationship between robustness and plasticity in homeostatic biological networks.

In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of core genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase to provide a plastic (sensitive) response. A feedforward structure from the non-core to core genes evolved autonomously. Negative proportionality was observed between the average changes in core and non-core genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. The proportion coefficient between those genes is represented by their number ratio, as in the "lever principle", whereas the decrease in the ratio results in a transition from perfect to partial adaptation, in which only a portion of the core genes exhibits robustness against environmental changes. This reciprocity between robustness and plasticity was satisfied throughout the evolutionary course, imposing an evolutionary constraint. This result suggests a simple macroscopic law for the adaptation characteristic in evolved complex biological networks

Evolutionary process of gene regulatory networks.

(A, B) Adaptation dynamics of genes (xi(t)) of an individual with the highest fitness before (A: 0th generation) and after (B: 1000th generation) evolution. α was changed from 0 to 1 and from 1 to -1 at time 100 and 200, respectively. Black and gray lines indicate the time course of the core (NC = 10) and regulator (NR = 90) genes, respectively. (C) Changes in ΔXC from the 0th to 1000th generations and (D) the corresponding trajectory at the ΔXR–ΔXC plane. All of the trajectories start from the same point (ΔXC = ΔXR = ΔX0 ≃ 0.462). Different color lines indicate evolutionary trajectories with different NC/N: magenta for 0.1, red for 0.2, orange for 0.3, yellow for 0.4, lime for 0.5, green for 0.6, cyan for 0.7, blue for 0.8, purple for 0.9, and brown for 1.0. Gray dotted and dashed lines are given by Eq 5 for NC = 10 10 and 20, respectively.</p

Schematic representation of the gene regulatory network.

Each white circle represents a gene. Genes regulate the expression of other genes (including self-regulation). Triangular and flat arrowheads represent activating and inhibitory interactions, respectively.</p

Interactions between the core and regulator genes in evolved networks with varied <i>N</i>^C.

(A–D) Difference of the linking probabilities between two nodes in the evolved networks from the default value plink. RN indicates the random network. Each graph shows the linking probabilities (A) from the regulator to the core, (B) from the core to the core, (C) from the regulator to the regulator, and (D) from the core to the regulator. Red and cyan bars represent the linking probability for activating and inhibitory interactions, respectively. (E) ΔX of the core without every interaction from the regulator. (F) Flipping probabilities of each node from the off to on state or from the on to off state after a change in the sign of hi. Each flipping probability is averaged for every node. Cyan circles and squares represent the flipping probabilities of nodes in the core and the regulator for a change in a node in the regulator, respectively. Red circles and squares represent these flipping probabilities for a change in a node in the core, respectively. The gray dotted line represents the flipping probability measured for the random network.</p