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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., 35 pages, 8 figures, 4 tables

Cellular adaptation to stressful environments such as starvation is essential to the survival of microbial communities, but the uniform response of the cell community may lead to entire cell death or severe damage to their fitness. Here, we demonstrate an elaborate response of the yeast community against glucose depletion, in which the first adapted cells kill the latecomer cells. During glucose depletion, yeast cells release autotoxins, such as leucic acid and L-2keto-3methylvalerate, which can even kill the clonal cells of the ones producing them. Although these autotoxins were likely to induce mass suicide, some cells differentiated to adapt to the autotoxins without genetic changes. If nondifferentiated latecomers tried to invade the habitat, autotoxins damaged or killed the latecomers, but the differentiated cells could selectively survive. Phylogenetically distant fission and budding yeast shared this behavior using the same autotoxins, suggesting that latecomer killing may be the universal system of intercellular communication, which may be relevant to the evolutional transition from unicellular to multicellular organisms.

When organisms face crises, such as starvation, every individual should adapt to environmental changes (1, 2), or the community alters their behaviour (3–5). Because a stressful environment reduces the carrying capacity (6), the population size of unicellular organisms shrinks in such conditions (7, 8). However, the uniform stress response of the cell community may lead to overall extinction or severely damage their entire fitness. How microbial communities accommodate this dilemma remains poorly understood. Here, we demonstrate an elaborate strategy of the yeast community against glucose starvation, named the voluntary triage. During starvation, yeast cells release some autotoxins, such as leucic acid and L-2keto-3methylvalerate, which can even kill the cells producing them. Although it may look like mass suicide at first glance, cells use epigenetic “tags” to adapt to the autotoxin inheritably. If non-tagged latecomers, regardless of whether they are closely related, try to invade the habitat, autotoxins kill them and inhibit their growth, but the tagged cells can selectively survive. Phylogenetically distant fission and budding yeast (9) share this strategy using the same autotoxins, which implies that the universal system of voluntary triage may be relevant to the major evolutional transition from unicellular to multicellular organisms (10).

Living organisms optimize their survivability through evolutionary processes. In particular, intracellular metabolic systems are rationally regulated to maximize the cellular growth rate. Correspondingly, the field of microeconomics investigates the behavior of individuals assumed to act rationally to maximize their utility. Therefore, microeconomics can be applied to analyze the metabolic strategies of cells. Toward this end, we developed a microeconomics-based theory of cellular metabolism by precisely mapping the regulation of metabolic systems onto the theory of consumer choice in microeconomics. As a representative example, we focus on overflow metabolism, a seemingly wasteful strategy in which cells utilize fermentation instead of the more energetically efficient respiration (so-called Warburg effect in cancer). To resolve this apparent contradiction, we formulate overflow metabolism as an optimization problem of the allocation of carbon fluxes under the guidance of microeconomic theory. Accordingly, we demonstrate that over-flow metabolism corresponds to Giffen behavior in economics, the strange consumer behavior by which greater amounts of goods are consumed as their price increases. We reveal the general conditions required for both overflow metabolism and Giffen goods: trade-off and complementarity, i.e., the impossibility of substitution for different goods, among multiple objectives. Based on the correspondence with Giffen behavior, a counterintuitive response of metabolism against the leakage and degradation of intermediate metabolites, which corresponds to the change in the price of a consumer good, is predicted. Over-all, this demonstration highlights that application of microeconomics to metabolic systems will offer new predictions and potentially new paradigms for both biology and economics.

Polyploidy has evolved many times across the kingdom of life. The relationship between cell growth and chromosome replication in bacteria has been studied extensively in monoploid model organisms such as Escherichia coli but not in polyploid organisms. Our study of the polyploid cyanobacterium Synechococcus elongatus demonstrates that replicating chromosome number is restricted and regulated by DnaA to maintain a relatively stable gene copy number/cell volume ratio during cell growth. In addition, our results suggest that polyploidy confers resistance to UV, which damages DNA. This compensatory polyploidy is likely necessitated by photosynthesis, which requires sunlight and generates damaging reactive oxygen species, and may also explain how polyploid bacteria can adapt to extreme environments with high risk of DNA damage., Homologous chromosome number (ploidy) has diversified among bacteria, archaea, and eukaryotes over evolution. In bacteria, model organisms such as Escherichia coli possess a single chromosome encoding the entire genome during slow growth. In contrast, other bacteria, including cyanobacteria, maintain multiple copies of individual chromosomes (polyploid). Although a correlation between ploidy level and cell size has been observed in bacteria and eukaryotes, it is poorly understood how replication of multicopy chromosomes is regulated and how ploidy level is adjusted to cell size. In addition, the advantages conferred by polyploidy are largely unknown. Here we show that only one or a few multicopy chromosomes are replicated at once in the cyanobacterium Synechococcus elongatus and that this restriction depends on regulation of DnaA activity. Inhibiting the DnaA intrinsic ATPase activity in S. elongatus increased the number of replicating chromosomes and chromosome number per cell but did not affect cell growth. In contrast, when cell growth rate was increased or decreased, DnaA level, DnaA activity, and the number of replicating chromosomes also increased or decreased in parallel, resulting in nearly constant chromosome copy number per unit of cell volume at constant temperature. When chromosome copy number was increased by inhibition of DnaA ATPase activity or reduced culture temperature, cells exhibited greater resistance to UV light. Thus, it is suggested that the stepwise replication of the genome enables cyanobacteria to maintain nearly constant gene copy number per unit of cell volume and that multicopy chromosomes function as backup genetic information to compensate for genomic damage.

A hierarchy of timescales is ubiquitous in biological systems, where enzymatic reactions play an important role because they can hasten the relaxation to equilibrium. We introduced a statistical physics model of interacting spins that also incorporates enzymatic reactions to extend the classic model for allosteric regulation. Through Monte Carlo simulations, we found that the relaxation dynamics are much slower than the elementary reactions and are logarithmic in time with several plateaus, as is commonly observed for glasses. This is because of the kinetic constraints from the cooperativity via the competition for an enzyme, which has different affinity for molecules with different structures. Our model showed symmetry breaking in the relaxation trajectories that led to inherently kinetic transitions without any correspondence to the equilibrium state. In this paper, we discuss the relevance of these results for diverse responses in biology., 23 pages, 13 figures

Circadian rhythms are a fundamental property of most organisms, from cyanobacteria to humans. In the unicellular obligately photoautotrophic cyanobacterium Synechococcus elongatus PCC 7942, essentially all promoter activities are controlled by the KaiABC-based clock under continuous light conditions. When Synechococcus cells are transferred from the light to continuous dark (DD) conditions, the expression of most genes, including the clock genes kaiA and kaiBC , is rapidly down-regulated, whereas the KaiC phosphorylation cycle persists. Therefore, we speculated that the posttranslational oscillator might not drive the transcriptional circadian output without de novo expression of the kai genes. Here we show that the cyanobacterial clock regulates the transcriptional output even in the dark. The expression of a subset of genes in the genomes of cells grown in the dark was dramatically affected by kaiABC nullification, and the magnitude of dark induction was dependent on the time at which the cells were transferred from the light to the dark. Moreover, under DD conditions, the expression of some dark-induced gene transcripts exhibited temperature-compensated damped oscillations, which were nullified in kaiABC -null strains and were affected by a kaiC period mutation. These results indicate that the Kai protein-based posttranslational oscillator can drive the circadian transcriptional output even without the de novo expression of the clock genes.

Circadian clocks exhibit the robustness of period and plasticity of phase against environmental changes such as temperature and nutrient conditions. Thus far, however, it is unclear how both are simultaneously achieved. By investigating distinct models of circadian clocks, we demonstrate reci- procity between robustness and plasticity: higher robustness in the period implies higher plasticity in the phase, where changes in period and in phase follow a linear relationship with a negative coef- ficient. The robustness of period is achieved by the adaptation on the limit cycle via a concentration change of a buffer molecule, whose temporal change leads to a phase shift following a shift of the limit-cycle orbit in phase space. Generality of reciprocity in clocks with the adaptation mechanism is confirmed with theoretical analysis of simple models, while biological significance is discussed., 11 pages, 12 figures

Circadian clocks ubiquitous in life forms ranging bacteria to multi-cellular organisms, often exhibit intrinsic temperature compensation; the period of circadian oscillators is maintained constant over a range of physiological temperatures, despite the expected Arrhenius form for the reaction coefficient. Observations have shown that the amplitude of the oscillation depends on the temperature but the period does not---this suggests that although not every reaction step is temperature independent, the total system comprising several reactions still exhibits compensation. We present a general mechanism for such temperature compensation. Consider a system with multiple activation energy barriers for reactions, with a common enzyme shared across several reaction steps with a higher activation energy. These reaction steps rate-limit the cycle if the temperature is not high. If the total abundance of the enzyme is limited, the amount of free enzyme available to catalyze a specific reaction decreases as more substrates bind to common enzyme. We show that this change in free enzyme abundance compensate for the Arrhenius-type temperature dependence of the reaction coefficient. Taking the example of circadian clocks with cyanobacterial proteins KaiABC consisting of several phosphorylation sites, we show that this temperature compensation mechanisms is indeed valid. Specifically, if the activation energy for phosphorylation is larger than that for dephosphorylation, competition for KaiA shared among the phosphorylation reactions leads to temperature compensation. Moreover, taking a simpler model, we demonstrate the generality of the proposed compensation mechanism, suggesting relevance not only to circadian clocks but to other (bio)chemical oscillators as well., 21 pages, 12 figures