Dynamic mode decomposition for Koopman spectral analysis of elementary cellular automata.

We apply dynamic mode decomposition (DMD) to elementary cellular automata (ECA). Three types of DMD methods are considered, and the reproducibility of the system dynamics and Koopman eigenvalues from observed time series is investigated. While standard DMD fails to reproduce the system dynamics and Koopman eigenvalues associated with a given periodic orbit in some cases, Hankel DMD with delay-embedded time series improves reproducibility. However, Hankel DMD can still fail to reproduce all the Koopman eigenvalues in specific cases. We propose an extended DMD method for ECA that uses nonlinearly transformed time series with discretized Walsh functions and show that it can completely reproduce the dynamics and Koopman eigenvalues. Linear-algebraic backgrounds for the reproducibility of the system dynamics and Koopman eigenvalues are also discussed.

STRA8-RB interaction is required for timely entry of meiosis in mouse female germ cells.

Meiosis is differently regulated in males and females. In females, germ cells initiate meiosis within a limited time period in the fetal ovary and undergo a prolonged meiotic arrest until puberty. However, how meiosis initiation is coordinated with the cell cycle to coincide with S phase remains elusive. Here, we demonstrate that STRA8 binds to RB via the LXCXE motif. Mutation of the RB-binding site of STRA8 in female mice delays meiotic entry, which consequently delays progression of meiotic prophase and leads to precocious depletion of the oocyte pool. Single-cell RNA-sequencing analysis reveals that the STRA8-RB interaction is required for S phase entry and meiotic gene activation, ensuring precise timing of meiosis initiation in oocytes. Strikingly, the results suggest STRA8 could sequester RB from E2F during pre-meiotic G1/S transition. This study highlights the gene regulatory mechanisms underlying the female-specific mode of meiotic initiation in mice.

Antagonism between DDX6 and PI3K-AKT signaling is an oocyte-intrinsic mechanism controlling primordial follicle growth†.

Oocyte maturation and subsequent ovulation during the reproductive lifespan ensure long-term reproduction in mammalian females. This is achieved by tight regulation for the maintenance and growth of primordial follicles. However, the underlying mechanisms remain unsolved. We herein report that posttranscriptional gene regulation mediated by an RNA helicase, DEAD-box helicase 6 (DDX6), and phosphoinositide-3-kinase (PI3K)-AKT signaling exhibits an antagonistic interaction in mouse primordial follicles. DDX6 forms P-body-like cytoplasmic foci in oocytes, which colocalize to a P-body component, DCP1A. Interestingly, the P-body-like granules predominantly assemble in primordial follicles, but disperse once follicle growth is initiated, suggesting that they play a role in the maintenance of primordial follicles. Oocyte-specific knockout of Ddx6 using Gdf9-iCre revealed that Ddx6-deficient oocytes are defective in foci assembly and are abnormally enlarged, resulting in premature depletion of primordial follicles. These results indicate that DDX6 is required to maintain primordial follicles. The abnormal oocyte enlargement is because of enhanced PI3K-AKT signaling, a pivotal signaling pathway in the growth of primordial follicles. Conversely, the forced activation of PI3K-AKT signaling by knocking out Pten disassembles P-body-like granules in primordial follicles. These data suggest that DDX6 and PI3K-AKT signaling mutually antagonize the assembly of P-body-like granules and the growth of primordial follicles. We propose this mutual antagonism as an oocyte-intrinsic mechanism controlling the maintenance and growth of primordial follicles, ensuring the longevity of female reproduction.

Turing instability in quantum activator-inhibitor systems.

Turing instability is a fundamental mechanism of nonequilibrium self-organization. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated mostly in classical systems. In this study, we show that Turing instability can occur in a quantum dissipative system and analyze its quantum features such as entanglement and the effect of measurement. We propose a degenerate parametric oscillator with nonlinear damping in quantum optics as a quantum activator-inhibitor unit and demonstrate that a system of two such units can undergo Turing instability when diffusively coupled with each other. The Turing instability induces nonuniformity and entanglement between the two units and gives rise to a pair of nonuniform states that are mixed due to quantum noise. Further performing continuous measurement on the coupled system reveals the nonuniformity caused by the Turing instability. Our results extend the universality of the Turing mechanism to the quantum realm and may provide a novel perspective on the possibility of quantum nonequilibrium self-organization and its application in quantum technologies.

A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint.

We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but it has not been defined explicitly for quantum nonlinear oscillators. In this study, we define the asymptotic phase for quantum oscillatory systems by using the eigenoperator of the backward Liouville operator associated with the fundamental oscillation frequency. By using the quantum van der Pol oscillator with a Kerr effect as an example, we illustrate that the proposed asymptotic phase appropriately yields isochronous phase values in both semiclassical and strong quantum regimes.

The polyol pathway is an evolutionarily conserved system for sensing glucose uptake.

Cells must adjust the expression levels of metabolic enzymes in response to fluctuating nutrient supply. For glucose, such metabolic remodeling is highly dependent on a master transcription factor ChREBP/MondoA. However, it remains elusive how glucose fluctuations are sensed by ChREBP/MondoA despite the stability of major glycolytic pathways. Here, we show that in both flies and mice, ChREBP/MondoA activation in response to glucose ingestion involves an evolutionarily conserved glucose-metabolizing pathway: the polyol pathway. The polyol pathway converts glucose to fructose via sorbitol. It has been believed that this pathway is almost silent, and its activation in hyperglycemic conditions has deleterious effects on human health. We show that the polyol pathway regulates the glucose-responsive nuclear translocation of Mondo, a Drosophila homologue of ChREBP/MondoA, which directs gene expression for organismal growth and metabolism. Likewise, inhibition of the polyol pathway in mice impairs ChREBP's nuclear localization and reduces glucose tolerance. We propose that the polyol pathway is an evolutionarily conserved sensing system for glucose uptake that allows metabolic remodeling.

Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory.

Optimal entrainment of limit-cycle oscillators by strong periodic inputs is studied on the basis of the phase-amplitude reduction and Floquet theory. Two methods for deriving the input waveforms that keep the system state close to the original limit cycle are proposed, which enable the use of strong inputs for entrainment. The first amplitude-feedback method uses feedback control to suppress deviations of the system state from the limit cycle, while the second amplitude-penalty method seeks an input waveform that does not excite large deviations from the limit cycle in the feedforward framework. Optimal entrainment of the van der Pol and Willamowski-Rössler oscillators with real or complex Floquet exponents is analyzed as examples. It is demonstrated that the proposed methods can achieve considerably faster entrainment and provide wider entrainment ranges than the conventional method that relies only on phase reduction.

Koopman spectral analysis of elementary cellular automata.

We perform a Koopman spectral analysis of elementary cellular automata (ECA). By lifting the system dynamics using a one-hot representation of the system state, we derive a matrix representation of the Koopman operator as the transpose of the adjacency matrix of the state-transition network. The Koopman eigenvalues are either zero or on the unit circle in the complex plane, and the associated Koopman eigenfunctions can be explicitly constructed. From the Koopman eigenvalues, we can judge the reversibility, determine the number of connected components in the state-transition network, evaluate the period of asymptotic orbits, and derive the conserved quantities for each system. We numerically calculate the Koopman eigenvalues of all rules of ECA on a one-dimensional lattice of 13 cells with periodic boundary conditions. It is shown that the spectral properties of the Koopman operator reflect Wolfram's classification of ECA.

NANOS2 suppresses the cell cycle by repressing mTORC1 activators in embryonic male germ cells.

During murine germ cell development, male germ cells enter the mitotically arrested G0 stage, which is an initial step of sexually dimorphic differentiation. The male-specific RNA-binding protein NANOS2 has a key role in suppressing the cell cycle in germ cells. However, the detailed mechanism of how NANOS2 regulates the cell cycle remains unclear. Using single-cell RNA sequencing (scRNA-seq), we extracted the cell cycle state of each germ cell in wild-type and Nanos2-KO testes and revealed that Nanos2 expression starts in mitotic cells and induces mitotic arrest. We identified Rheb, a regulator of mTORC1, and Ptma as possible targets of NANOS2. We propose that repression of the cell cycle is a primary function of NANOS2 and that it is mediated via the suppression of mTORC1 activity through the repression of Rheb in a post-transcriptional manner.

Decoding the transcriptome of pre-granulosa cells during the formation of primordial follicles in the mouse†.

Primordial follicles, a finite reservoir of eggs in mammalian ovaries, are composed of a single oocyte and its supporting somatic cells, termed granulosa cells. Although their formation may require reciprocal interplay between oocytes and pre-granulosa cells, precursors of granulosa cells, little is known about the underlying mechanisms. We addressed this issue by decoding the transcriptome of pre-granulosa cells during the formation of primordial follicles. We found that marked gene expression changes, including extracellular matrix, cell adhesion, and several signaling pathways, occur along with primordial follicle formation. Importantly, differentiation of Lgr5-EGFP-positive pre-granulosa cells to FOXL2-positive granulosa cells was delayed in mutant ovaries of the germ cell-specific genes Nanos3 and Figla, accompanied by perturbed gene expression in mutant pre-granulosa cells. These results suggest that proper development of oocytes is required for the differentiation of pre-granulosa cells. Our data provide a valuable resource for understanding the gene regulatory networks involved in the formation of primordial follicles.