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.

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.

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.

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.

Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators.

Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase-reduction theory recently developed for quantum nonlinear oscillators [Y. Kato, N. Yamamoto, and H. Nakao, Phys. Rev. Res. 1, 033012 (2019)10.1103/PhysRevResearch.1.033012], two types of optimization problems, one for the stability and the other for the phase coherence of the entrained state, are considered. The optimal waveforms of the periodic amplitude modulation can be derived by applying the classical optimization methods to the semiclassical phase equation that approximately describes the quantum limit-cycle dynamics. Using a quantum van der Pol oscillator with squeezing and Kerr effects as an example, the performance of optimization is numerically analyzed. It is shown that the optimized waveform for the entrainment stability yields faster entrainment to the driving signal than the case with a simple sinusoidal waveform, while that for the phase coherence yields little improvement from the sinusoidal case. These results are explained from the properties of the phase sensitivity function.

Optimization of linear and nonlinear interaction schemes for stable synchronization of weakly coupled limit-cycle oscillators.

Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase-reduction theory. By generalizing our previous study [S. Shirasaka, N. Watanabe, Y. Kawamura, and H. Nakao, Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling, Phys. Rev. E 96, 012223 (2017)2470-004510.1103/PhysRevE.96.012223] on the optimization of cross-diffusion coupling matrices between the oscillators, we consider optimization of mutual coupling signals to maximize the linear stability of the synchronized state, which are functionals of the past time sequences of the oscillator states. For the case of linear coupling, optimization of the delay time and linear filtering of coupling signals are considered. For the case of nonlinear coupling, general drive-response coupling is considered and the optimal response and driving functions are derived. The theoretical results are illustrated by numerical simulations.

ELAVL2-directed RNA regulatory network drives the formation of quiescent primordial follicles.

Formation of primordial follicles is a fundamental, early process in mammalian oogenesis. However, little is known about the underlying mechanisms. We herein report that the RNA-binding proteins ELAVL2 and DDX6 are indispensable for the formation of quiescent primordial follicles in mouse ovaries. We show that Elavl2 knockout females are infertile due to defective primordial follicle formation. ELAVL2 associates with mRNAs encoding components of P-bodies (cytoplasmic RNP granules involved in the decay and storage of RNA) and directs the assembly of P-body-like granules by promoting the translation of DDX6 in oocytes prior to the formation of primordial follicles. Deletion of Ddx6 disturbs the assembly of P-body-like granules and severely impairs the formation of primordial follicles, indicating the potential importance of P-body-like granules in the formation of primordial follicles. Furthermore, Ddx6-deficient oocytes are abnormally enlarged due to misregulated PI3K-AKT signaling. Our data reveal that an ELAVL2-directed post-transcriptional network is essential for the formation of quiescent primordial follicles.

Requirement of the 3'-UTR-dependent suppression of DAZL in oocytes for pre-implantation mouse development.

Functional oocytes are produced through complex molecular and cellular processes. In particular, the contribution of post-transcriptional gene regulation mediated by RNA-binding proteins (RBPs) is crucial for controlling proper gene expression during this process. DAZL (deleted in azoospermia-like) is one of the RBPs required for the sexual differentiation of primordial germ cells and for the progression of meiosis in ovulated oocytes. However, the involvement of DAZL in the development of follicular oocytes is still unknown. Here, we show that Dazl is translationally suppressed in a 3'-UTR-dependent manner in follicular oocytes, and this suppression is required for normal pre-implantation development. We found that suppression of DAZL occurred in postnatal oocytes concomitant with the formation of primordial follicles, whereas Dazl mRNA was continuously expressed throughout oocyte development, raising the possibility that DAZL is dispensable for the survival and growth of follicular oocytes. Indeed, follicular oocyte-specific knockout of Dazl resulted in the production of normal number of pups. On the other hand, genetically modified female mice that overexpress DAZL produced fewer numbers of pups than the control due to defective pre-implantation development. Our data suggest that post-transcriptional suppression of DAZL in oocytes is an important mechanism controlling gene expression in the development of functional oocytes.

Sexual Fate Change of XX Germ Cells Caused by the Deletion of SMAD4 and STRA8 Independent of Somatic Sex Reprogramming.

The differential programming of sperm and eggs in gonads is a fundamental topic in reproductive biology. Although the sexual fate of germ cells is believed to be determined by signaling factors from sexually differentiated somatic cells in fetal gonads, the molecular mechanism that determines germ cell fate is poorly understood. Herein, we show that mothers against decapentaplegic homolog 4 (SMAD4) in germ cells is required for female-type differentiation. Germ cells in Smad4-deficient ovaries respond to retinoic acid signaling but fail to undergo meiotic prophase I, which coincides with the weaker expression of genes required for follicular formation, indicating that SMAD4 signaling is essential for oocyte differentiation and meiotic progression. Intriguingly, germline-specific deletion of Smad4 in Stra8-null female germ cells resulted in the up-regulation of genes required for male gonocyte differentiation, including Nanos2 and PLZF, suggesting the initiation of male-type differentiation in ovaries. Moreover, our transcriptome analyses of mutant ovaries revealed that the sex change phenotype is achieved without global gene expression changes in somatic cells. Our results demonstrate that SMAD4 and STRA8 are essential factors that regulate the female fate of germ cells.

Dazl is a target RNA suppressed by mammalian NANOS2 in sexually differentiating male germ cells.

Evolutionally conserved Nanos RNA-binding proteins play crucial roles in germ cell development. While a mammalian Nanos family protein, NANOS2, is required for sexual differentiation of male (XY) germ cells in mice, the underlying mechanisms and the identities of its target RNAs in vivo remain elusive. Using comprehensive microarray analysis and a bacterial artificial chromosome transgenic system, here we identify Dazl, a germ cell-specific gene encoding an RNA-binding protein implicated in translation, as a crucial target of NANOS2. Importantly, removal of the Dazl 3'-untranslated region in XY germ cells stabilizes the Dazl mRNA, resulting in elevated meiotic gene expression, abnormal resumption of the cell cycle and impaired processing-body formation, reminiscent of Nanos2-knockout phenotypes. Furthermore, our data suggest that NANOS2 acts as an antagonist of the DAZL protein. We propose a dual system of NANOS2-mediated suppression of Dazl expression as a pivotal molecular mechanism promoting sexual differentiation of XY germ cells.

NANOS2 promotes male germ cell development independent of meiosis suppression.

NANOS2 is an RNA-binding protein essential for fetal male germ cell development. While we have shown that the function of NANOS2 is vital for suppressing meiosis in embryonic XY germ cells, it is still unknown whether NANOS2 plays other roles in the sexual differentiation of male germ cells. In this study, we addressed the issue by generating Nanos2/Stra8 double knockout (dKO) mice, whereby meiosis was prohibited in the double-mutant male germ cells. We found that the expression of male-specific genes, which was decreased in the Nanos2 mutant, was hardly recovered in the dKO embryo, suggesting that NANOS2 plays a role in male gene expression other than suppression of meiosis. To investigate the molecular events that may be controlled by NANOS2, we conducted a series of microarray analyses to search putative targets of NANOS2 that fulfilled 2 criteria: (1) increased expression in the Nanos2 mutant and (2) the mRNA associated with NANOS2. Interestingly, the genes predominantly expressed in undifferentiated primordial germ cells (PGCs) were significantly selected, implying the involvement of NANOS2 in the termination of the characteristics of PGCs. Furthermore, we showed that NANOS2 is required for the maintenance of mitotic quiescence, but not for the initiation of the quiescence in fetal male germ cells. These results suggest that NANOS2 is not merely a suppressor of meiosis, but instead plays pivotal roles in the sexual differentiation of male germ cells.

Posttranscriptional regulation of histone lysine methyltransferase GLP in embryonic male mouse germ cells.

The epigenetic status of germ cells changes dynamically during development. In this study, we analyzed the dynamics of histone H3 lysine 9 dimethylation (H3K9me2), a highly conserved mark of epigenetic silencing, and the expression of two lysine methyltransferases, G9a/Ehmt2/KMT1C and GLP/Ehmt1/KMT1D, in murine male embryonic germ cells after sex determination. Our previous studies established that G9a and GLP are the primary enzymes for H3K9me2 and predominantly exist as a G9a-GLP heteromeric complex that appears to be a functional H3K9 methyltransferase in vivo. During the period from Embryonic Day (E) 13.5 to E18.5 in mice, gonadal H3K9me2 levels were substantially lower in germ cells than in cells of nongerm lineage. Immunohistochemical analysis showed that during this phase in development, GLP level, but not G9a level, was also significantly lower in male germ cells. However, GLP mRNA was present in E13 and E16 male germ cells, with levels similar to those in cells of nongerm lineage. Interestingly, GLP is upregulated in embryonic male germ cells deficient for Nanos2, which encodes a germ cell-specific RNA-binding protein. Our data suggest that GLP protein expression is posttranscriptionally regulated in murine embryonic male germ cells after sex determination and that low H3K9me2 level results from the absence of GLP (severe reduction of the G9a-GLP heteromeric complex).

Distinct DNA methylation dynamics of spermatogenic cell-specific intronless genes is associated with CpG content.

In mammals, DNA methylation is restricted to cytosines of CpG dinucleotides, which are frequently found in short genomic regions including gene promoters. Methylation within CpG-rich regions around promoters tends to repress gene expression; thus, the CpG islands of housekeeping genes are normally unmethylated. We previously described a testis-specific single-exon gene containing a CpG-rich sequence that is methylated and thus repressed in somatic cells, whereas its expression in spermatogenic cells requires that it be hypomethylated. However, the relationship among the specific expression of spermatogenic genes, their methylation dynamics, and their CpG frequencies are poorly understood. Here, we analyzed the methylation patterns of the sphort genomic region around the transcription start site in spermatogenic cell-specific single-exon genes of various CpG contents. By using UniGene and Ensembl database analyses of the mouse genome and reverse transcription-PCR, we identified 39 single-exon genes that are exclusively expressed in spermatogeniccells. Regardless of their specific expression characteristics, genes containing higher (7 to 14 CpGs in 200 bp; mean = 12) and lower (2 to 6 CpGs in 200 bp; mean = 3.1) number ofCpG were hypo- and hyper-methylated, respectively, in all cell types examined, including spermatogeniccells. We found that genes with intermediate number of CpG (2 to 11 CpGs in 200 bp; mean = 6.9) are methylated in somatic cells, but not in male germ cells. These results suggest that DNA methylation dynamics of spermatogenic cell-specific single-exon genes are associated with CpG content, and the methylation status are stably maintained throughout male germ cell development.

Rhox13 is translated in premeiotic germ cells in male and female mice and is regulated by NANOS2 in the male.

Male and female germ cells enter meiosis in response to an extrinsic cue by retinoic acid (RA), but the pathways downstream of RA signaling that regulate early gametogenesis remain uncertain. We identified a novel reproductive homeobox gene, Rhox13, transcribed in the prenatal ovary and testis beginning on Embryonic Day (E) 13.5. Translation of RHOX13 also begins in female germ cells on E13.5 but is suppressed in male germ cells until Postnatal Day 3. Translation of RHOX13 coincides with initiation of RA signaling in both male and female gonads in vivo but occurs precociously in neonatal testes exposed to RA in vitro or in fetal male germ cells when NANOS2 is absent in vivo. Conversely, RHOX13 translation in female germ cells is suppressed in the presence of ectopically induced NANOS2. These results strongly suggest that RHOX13 expression is regulated at a posttranscriptional step by direct interaction of NANOS2 with Rhox13 mRNA to suppress translation.