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Abstract Antisense transcripts are a unique group of non-coding RNAs and play regulatory roles in a variety of biological processes, including circadian rhythms. Per2AS is an antisense transcript to the sense core clock gene Period2 (Per2) in mouse and its expression is rhythmic and antiphasic to Per2. To understand the impact of Per2AS-Per2 interaction, we developed a new mathematical model that mechanistically described the mutually repressive relationship between Per2 and Per2AS. This mutual repression can regulate both amplitude and period of circadian oscillation by affecting a negative feedback regulation of Per2. Simulations from this model also fit with experimental observations that could not be fully explained by our previous model. Our revised model can not only serve as a foundation to build more detailed models to better understand the impact of Per2AS-Per2 interaction in the future, but also be used to analyze other sense-antisense RNA pairs that mutually repress each other.

Abstract The metameric pattern of somites is created based on oscillatory expression of clock genes in presomitic mesoderm. However, the mechanism for converting the dynamic oscillation to a static pattern of somites is still unclear. Here, we provide evidence that Ripply/Tbx6 machinery is a key regulator of this conversion. Ripply1/Ripply2-mediated removal of Tbx6 protein defines somite boundary and also leads to cessation of clock gene expression in zebrafish embryos. On the other hand, activation of ripply1/ripply2 mRNA and protein expression is periodically regulated by clock oscillation in conjunction with an Erk signaling gradient. Whereas Ripply protein decreases rapidly in embryos, Ripply-triggered Tbx6 suppression persists long enough to complete somite boundary formation. Mathematical modeling shows that a molecular network based on results of this study can reproduce dynamic-to-static conversion in somitogenesis. Furthermore, simulations with this model suggest that sustained suppression of Tbx6 caused by Ripply is crucial in this conversion.

Various factors in hobbing processes affect profile and helix deviations of hobbed gears, which prevent problems on the hobbing machine from being analyzed using them. Identifying problems requires a system that allows itself to evaluate motion errors in a hobbing machine from them. The proposed one in this study has artificial intelligence for image analysis. Thus, the developed hobbing simulation provided the data on profile and helix deviations of hobbed gears derived from the motion errors in the hobbing process, which determined correlation coefficients to express the similarities of the simulated micro-geometries between tooth flanks of a hobbed gear. These correlation coefficients are color-coded according to their magnitude and converted into images to constitute training data for artificial intelligence. However, different motion errors could lead to similar ones in tests with helical gears. The present paper describes the comparisons between images obtained for spur and helical gears computed by hobbing simulation and the comparisons between ones produced from the simulated and actual micro-geometries. As a result, the motion error that causes similar images depends on gear geometries, i.e., whether spur or helical. Furthermore, actual micro-geometries depend on hob accuracies, which require their compensation. That yields equivalent images to those produced from simulated data.

A hobbed gear has pitch, profile, and helix deviations caused by various factors. However it is hard for even experts to specify which factors cause individual deviations from the measured ones. Therefore, a hobbing-machine-diagnosis system could play a key role in identifying the factors from hobbed-gear deviations. Artificial intelligence for image recognition, which is comparatively easy to use, could be appropriate for the system. Generally, a larger number of training data for artificial intelligence could improve the system accuracy, however, it must take a longer time for learning. Besides, efficient learning requires small image data. Typical gear-deviation diagrams are large images that include unnecessary information for the diagnosis system. Therefore, the image data for training have only information on the correlation coefficients between the deviations of two teeth selected at a time. The present paper describes a method for providing image data for learning. The image is the arrangement of correlation coefficients in rows and columns as a grayscale. This paper also describes the relationship between the image and the hobbing problems; e.g., radial or face runouts. As a result, the image data showed clear characteristics for the difference in the periodicity of the hobbing problem, however, did not show clear characteristics for the difference in the directionality.

Multiple feedback loops are often found in gene regulations for various cellular functions. In mammalian circadian clocks, oscillations of Period1 (Per1) and Period2 (Per2) expression are caused by interacting negative feedback loops (NFLs) whose protein products with similar molecular functions repress each other. However, Per1 expression peaks earlier than Per2 in the pacemaker tissue, raising the question of whether the peak time difference reflects their different dynamical functions. Here, we address this question by analyzing phase responses of the circadian clock caused by light-induced transcription of both Per1 and Per2 mRNAs. Through mathematical analyses of dual NFLs, we show that phase advance is mainly driven by light inputs to the repressor with an earlier expression peak as Per1, whereas phase delay is driven by the other repressor with a later peak as Per2. Due to the complementary contributions to phase responses, the ratio of light-induced transcription rates between Per1 and Per2 determines the magnitude and direction of phase shifts at each time of day. Specifically, stronger Per1 light induction than Per2 results in a phase response curve (PRC) with a larger phase advance zone than delay zone as observed in rats and hamsters, whereas stronger Per2 induction causes a larger delay zone as observed in mice. Furthermore, the ratio of light-induced transcription rates required for entrainment is determined by the relation between the circadian and light-dark periods. Namely, if the autonomous period of a circadian clock is longer than the light-dark period, a larger light-induced transcription rate of Per1 than Per2 is required for entrainment, and vice versa. In short, the time difference between Per1 and Per2 expression peaks can differentiate their dynamical functions. The resultant complementary contributions to phase responses can determine entrainability of the circadian clock to the light-dark cycle.

Integrity of rhythmic spatial gene expression patterns in the vertebrate segmentation clock requires local synchronization between neighboring cells by Delta-Notch signaling and its inhibition causes defective segment boundaries. Whether deformation of the oscillating tissue complements local synchronization during patterning and segment formation is not understood. We combine theory and experiment to investigate this question in the zebrafish segmentation clock. We remove a Notch inhibitor, allowing resynchronization, and analyze embryonic segment recovery. We observe unexpected intermingling of normal and defective segments, and capture this with a new model combining coupled oscillators and tissue mechanics. Intermingled segments are explained in the theory by advection of persistent phase vortices of oscillators. Experimentally observed changes in recovery patterns are predicted in the theory by temporal changes in tissue length and cell advection pattern. Thus, segmental pattern recovery occurs at two length and time scales: rapid local synchronization between neighboring cells, and the slower transport of the resulting patterns across the tissue through morphogenesis.

In a hobbing process, many factors bring pitch, profile, and helix deviations to hobbed gears, and it is generally difficult to identify which factors cause the deviations. Therefore, a system that allows causal factors to be determined is required especially in the after-sales service of the hobbing machine manufactures. In the present study, a hobbing-machine-diagnosis system is being developed. Artificial intelligence will be employed in the system to easily determine the cause of deviations that occur in hobbed gears. The development of the system requires a lot of learning data for artificial intelligence. The data should be obtained in various conditions. However, collecting data from real cutting is almost impossible because of cost and time, so that hobbing simulation was carried out. The hobbing simulation has already been developed by many researchers. But those simulations are not enough for manufacturers of hobbing machines to evaluate problems in the machines. In addition, the conventional tooth profile/helix deviations diagrams are not appropriate for images used in artificial-intelligence systems, because they include redundant data. In the present paper, therefore, a network graph representing the correlation between every two teeth were discussed to examine whether the graph can be used as data for artificial-intelligence systems. As a result, an image of the network graph could be suitable for the system and could enable its data size to be reduced.

In development and disease, cells move as they exchange signals. One example is found in vertebrate development, during which the timing of segment formation is set by a ‘segmentation clock’, in which oscillating gene expression is synchronized across a population of cells by Delta-Notch signaling. Delta-Notch signaling requires local cell-cell contact, but in the zebrafish embryonic tailbud, oscillating cells move rapidly, exchanging neighbors. Previous theoretical studies proposed that this relative movement or cell mixing might alter signaling and thereby enhance synchronization. However, it remains unclear whether the mixing timescale in the tissue is in the right range for this effect, because a framework to reliably measure the mixing timescale and compare it with signaling timescale is lacking. Here, we develop such a framework using a quantitative description of cell mixing without the need for an external reference frame and constructing a physical model of cell movement based on the data. Numerical simulations show that mixing with experimentally observed statistics enhances synchronization of coupled phase oscillators, suggesting that mixing in the tailbud is fast enough to affect the coherence of rhythmic gene expression. Our approach will find general application in analyzing the relative movements of communicating cells during development and disease.

Negative feedback loops (NFLs) for circadian clocks include light-responsive reactions that allow the clocks to shift their phase depending on the timing of light signals. Phase response curves (PRCs) for light signals in various organisms include a time interval called a dead zone where light signals cause no phase shift during daytime. Although the importance of the dead zone for robust light entrainment is known, how the dead zone arises from the biochemical reactions in an NFL underlying circadian gene expression rhythms remains unclear. In addition, the observation that the light-responsive reactions in the NFL vary between organisms raises the question as to whether the mechanism for dead zone formation is common or distinct between different organisms. Here we reveal by mathematical modeling that the saturation of a biochemical reaction in repressor synthesis in an NFL is a common mechanism of daytime dead zone generation. If light signals increase the degradation of a repressor protein, as in Drosophila, the saturation of repressor mRNA transcription nullifies the effect of light signals, generating a dead zone. In contrast, if light signals induce the transcription of repressor mRNA, as in mammals, the saturation of repressor translation can generate a dead zone by cancelling the influence of excess amount of mRNA induced by light signals. Each of these saturated reactions is located next to the light-responsive reaction in the NFL, suggesting a design principle for daytime dead zone generation.

The high productivity of gear skiving has caused the process to attract a lot of attention in recent years and taper shaped skiving cutters are generally used in current gear skiving. A cutter axis in gear skiving is inclined to a gear axis and a taper shaped skiving cutter could cause tooth profile deviations of skived gears after re-sharpening of tool faces. Adjusting cutter position and/or re-profiling of cutter flanks are applied to enable tooth profile deviations of skived gears to remain within acceptable ranges when the adjustment is necessary. Adjusting cutter position is preferred to re-profiling of cutter flanks due to desire for low production cost. However, the universality of the current methods of calculating cutter positions is still not confirmed. The present study explains that the current methods for obtaining cutter positions could require individual calculating formulas according to cutter specifications for each particular gear. A universal method which avoids such complexity of making various formulas could contribute to permit gear skiving to become more useful in the gear machining field. Then such a desirable method is proposed and the reasonability of the method is confirmed by experiments. In addition, this study discusses the existence of scope in which the method can be applied and a method for checking collisions between cutter flanks and gear tooth flanks being cut after adjustment of cutter position.

Taper shaped skiving cutters are commonly used in gear skiving because they provide clearance angles under a simple gear arrangement and they could have lower cutting resistance than cylindrical skiving cutters. Their tooth flanks are generally ground by the same method of generation grinding with a trapezoidal wheel as ones for pinion cutter tooth flanks for gear shaping. In gear skiving, however, the process of tool-face re-grinding could increase profile deviations of cut gears due to the lack of an appropriate change in cutter profiles along the facewidth. In the present paper, computer programs were developed to simulate the generation grinding and the skiving with the cutting edges ground by the method. Skiving with a cutter ground by the method were carried out and skived tooth forms were compared with those calculated by the developed program. As a result, the comparisons could guarantee the reliability of the program. Furthermore, the program has revealed that the increase in a helix angle of a cutter yields the increase in tooth profile deviations of skived gears after regrinding the tool faces. Therefore, taper shaped cutters should be applied to internal gear skiving with extra caution.

Many questions in developmental biology depend on measuring the position and movement of individual cells within developing embryos. Yet, tools that provide this data are often challenged by high cell density and their accuracy is difficult to measure. Here, we present a three-step procedure to address this problem. Step one is a novel segmentation algorithm based on image derivatives that, in combination with selective post-processing, reliably and automatically segments cell nuclei from images of densely packed tissue. Step two is a quantitative validation using synthetic images to ascertain the efficiency of the algorithm with respect to signal-to-noise ratio and object density. Finally, we propose an original method to generate reliable and experimentally faithful ground truth datasets: Sparse-dense dual-labeled embryo chimeras are used to unambiguously measure segmentation errors within experimental data. Together, the three steps outlined here establish a robust, iterative procedure to fine-tune image analysis algorithms and microscopy settings associated with embryonic 3D image data sets.

[This corrects the article DOI: 10.1371/journal.pone.0150853.].

In vertebrate somitogenesis, the expression of segmentation clock genes oscillates and the oscillation is synchronized over nearby cells. Both experimental and theoretical studies have shown that the synchronization among cells is realized by intercellular interaction via Delta-Notch signaling. However, the following questions emerge: (i) During somitogenesis, dynamic rearrangement of relative cell positions is observed in the posterior presomitic mesoderm. Can a synchronized state be stably sustained under random cell movement? (ii) Experimental studies have reported that the synchronization of cells can be recovered in about 10 or fewer oscillation cycles after the complete loss of synchrony. However, such a quick recovery of synchronization is not possible according to previous theoretical models. In this paper, we first show by numerical modeling that synchronized oscillation can be sustained under random cell movement. We also find that for initial perturbation, the synchronization of cells is recovered much faster and it is for a wider range of reaction parameters than the case without cell movement. When the posterior presomitic mesoderm is rectangular, faster synchronization is achieved if cells exchange their locations more with neighbors located along the longer side of the domain. Finally, we discuss that the enhancement of synchronization by random cell movement occurs in several different models for the oscillation of segmentation clock genes. [ABSTRACT FROM AUTHOR]

Individual biological oscillators can synchronize to generate a collective rhythm. During vertebrate development, mobile cells exchange signals to synchronize a rhythmic pattern generator that makes the embryonic segments. Previous theoretical works have shown that cell mobility can enhance synchronization of coupled oscillators when signal exchange is instantaneous. However, in vertebrate segmentation, the exchange of signals is thought to comprise delays from signal sending and processing, which could alter the effect of mobility on synchronization. Here, we study synchronization dynamics of mobile phase oscillators in the presence of coupling delays. We find that mobility can speed up synchronization when coupling delays are present. We derive an analytical expression for the characteristic time of synchronization dynamics, which is in very good agreement with numerical simulations. This analytical expression suggests a subdivision of the mobility range into different dynamical regimes and reveals that, with delayed coupling, synchronization is enhanced at a lower mobility rate than with instantaneous coupling. We argue that these results may be relevant to the synchronization of mobile oscillators in vertebrate segmentation. [ABSTRACT FROM AUTHOR]

We study the dynamics of mobile, locally coupled identical oscillators in the presence of coupling delays. We find different kinds of chimera states in which coherent in-phase and antiphase domains coexist with incoherent domains. These chimera states are dynamic and can persist for long times for intermediate mobility values. We discuss the mechanisms leading to the formation of these chimera states in different mobility regimes. This finding could be relevant for natural and technological systems composed of mobile communicating agents. [ABSTRACT FROM AUTHOR]