Smooth Elongation of Pavement Cells Induced by RIC1 Overexpression Leads to Marginal Protrusions of the Cotyledon in Arabidopsis thaliana.

The interdigitated pavement cell shape is suggested to be mechanically rational at both the cellular and tissue levels, but the biological significance of the cell shape is not fully understood. In this study, we explored the potential importance of the jigsaw puzzle-like cell shape for cotyledon morphogenesis in Arabidopsis. We used a transgenic line overexpressing a Rho-like GTPase-interacting protein, ROP-INTERACTIVE CRIB MOTIF-CONTAINING PROTEIN 1 (RIC1), which causes simple elongation of pavement cells. Computer-assisted microscopic analyses, including virtual reality observation, revealed that RIC1 overexpression resulted in abnormal cotyledon shapes with marginal protrusions, suggesting that the abnormal organ shape might be explained by changes in the pavement cell shape. Microscopic, biochemical and mechanical observations indicated that the pavement cell deformation might be due to reduction in the cell wall cellulose content with alteration of cortical microtubule organization. To examine our hypothesis that simple elongation of pavement cells leads to an abnormal shape with marginal protrusion of the cotyledon, we developed a mathematical model that examines the impact of planar cell growth geometry on the morphogenesis of the organ that is an assemblage of the cells. Computer simulations supported experimental observations that elongated pavement cells resulted in an irregular cotyledon shape, suggesting that marginal protrusions were due to local growth variation possibly caused by stochastic bias in the direction of cell elongation cannot be explained only by polarity-based cell elongation, but that an organ-level regulatory mechanism is required.

The SYP123-VAMP727 SNARE complex delivers secondary cell wall components for root hair shank hardening in Arabidopsis.

The extended tubular shape of root hairs is established by tip growth and concomitant hardening. Here, we demonstrate that a syntaxin of plants (SYP)123-vesicle-associated membrane protein (VAMP)727-dependent secretion system delivers secondary cell wall components for hardening the subapical zone and shank of Arabidopsis (Arabidopsis thaliana) root hairs. We found increased SYP123 localization at the plasma membrane (PM) of the subapical and shank zones compared with the tip region in elongating root hairs. Inhibition of phosphatidylinositol (PtdIns)(3,5)P2 production impaired SYP123 localization at the PM and SYP123-mediated root hair shank hardening. Moreover, root hair elongation in the syp123 mutant was insensitive to a PtdIns(3,5)P2 synthesis inhibitor. SYP123 interacts with both VAMP721 and VAMP727. syp123 and vamp727 mutants exhibited reduced shank cell wall stiffness due to impaired secondary cell wall component deposition. Based on these results, we conclude that SYP123 is involved in VAMP721-mediated conventional secretion for root hair elongation as well as in VAMP727-mediated secretory functions for the delivery of secondary cell wall components to maintain root hair tubular morphology.

Analyzing the effect of cell rearrangement on Delta-Notch pattern formation.

The Delta-Notch system plays a vital role in many areas of biology and typically forms a salt and pepper pattern in which cells strongly expressing Delta and cells strongly expressing Notch are alternately aligned via lateral inhibition. In this study, we consider cell rearrangement events, such as cell mixing and proliferation, that alter the spatial structure itself and affect the pattern dynamics. We model cell rearrangement events by a Poisson process and analyze the model while preserving the discrete properties of the spatial structure. We investigate the effects of the intermittent perturbations arising from these cell rearrangement events on the discrete spatial structure itself in the context of pattern formation and by using an analytical approach, coupled with numerical simulation. We find that the homogeneous expression pattern is stabilized if the frequency of cell rearrangement events is sufficiently large. We analytically obtain the balanced frequencies of the cell rearrangement events where the decrease of the pattern amplitude, as a result of cell rearrangement, is balanced by the increase in amplitude due to the Delta-Notch interaction dynamics. Our framework, while applied here to the specific case of the Delta-Notch system, is applicable more widely to other pattern formation mechanisms.

Computational Model Exploring Characteristic Pattern Regulation in Periventricular Vessels.

The developing neocortical vasculature exhibits a distinctive pattern in each layer. In murine embryos, vessels in the cortical plate (CP) are vertically oriented, whereas those in the intermediate zone (IZ) and the subventricular zone (SVZ) form a honeycomb structure. The formation of tissue-specific vessels suggests that the behavior of endothelial cells is under a specific regulatory regime in each layer, although the mechanisms involved remain unknown. In the present study, we aimed to explore the conditions required to form these vessel patterns by conducting simulations using a computational model. We developed a novel model framework describing the collective migration of endothelial cells to represent the angiogenic process and performed a simulation using two-dimensional approximation. The attractive and repulsive guidance of tip cells was incorporated into the model based on the function and distribution of guidance molecules such as VEGF and Unc ligands. It is shown that an appropriate combination of guidance effects reproduces both the parallel straight pattern in the CP and meshwork patterns in the IZ/SVZ. Our model demonstrated how the guidance of the tip cell causes a variety of vessel patterns and predicted how tissue-specific vascular formation was regulated in the early development of neocortical vessels.

Mathematical Modeling of Dynamic Cellular Association Patterns in Seminiferous Tubules.

In vertebrates, sperm is generated in testicular tube-like structures called seminiferous tubules. The differentiation stages of spermatogenesis exhibit a dynamic spatiotemporal wavetrain pattern. There are two types of pattern-the vertical type, which is observed in mice, and the helical type, which is observed in humans. The mechanisms of this pattern difference remain little understood. In the present study, we used a three-species reaction-diffusion model to reproduce the wavetrain pattern observed in vivo. We hypothesized that the wavelength of the pattern in mice was larger than that in humans and undertook numerical simulations. We found complex patterns of helical and vertical pattern frequency, which can be understood by pattern selection using boundary conditions. From these theoretical results, we predicted that a small number of vertical patterns should be present in human seminiferous tubules. We then found vertical patterns in histological sections of human tubules, consistent with the theoretical prediction. Finally, we showed that the previously reported irregularity of the human pattern could be reproduced using two factors: a wider unstable wavenumber range and the irregular geometry of human compared with mouse seminiferous tubules. These results show that mathematical modeling is useful for understanding the pattern dynamics of seminiferous tubules in vivo.

Excess Pyrophosphate Restrains Pavement Cell Morphogenesis and Alters Organ Flatness in Arabidopsis thaliana.

In Arabidopsis thaliana, the vacuolar proton-pumping pyrophosphatase (H+-PPase) is highly expressed in young tissues, which consume large amounts of energy in the form of nucleoside triphosphates and produce pyrophosphate (PPi) as a byproduct. We reported that excess PPi in the H+-PPase loss-of-function fugu5 mutant severely compromised gluconeogenesis from seed storage lipids, arrested cell division in cotyledonary palisade tissue, and triggered compensated cell enlargement; this phenotype was recovered upon sucrose supply. Thus, we provided evidence that the hydrolysis of inhibitory PPi, rather than vacuolar acidification, is the major contribution of H+-PPase during seedling establishment. Here, examination of the epidermis revealed that fugu5 pavement cells exhibited defective puzzle-cell formation. Importantly, removal of PPi from fugu5 background by the yeast cytosolic PPase IPP1, in fugu5-1 AVP1pro::IPP1 transgenic lines, restored the phenotypic aberrations of fugu5 pavement cells. Surprisingly, pavement cells in mutants with defects in gluconeogenesis (pck1-2) or the glyoxylate cycle (icl-2; mls-2) showed no phenotypic alteration, indicating that reduced sucrose production from seed storage lipids is not the cause of fugu5 epidermal phenotype. fugu5 had oblong cotyledons similar to those of angustifolia-1 (an-1), whose leaf pavement cells display an abnormal arrangement of cortical microtubules (MTs). To gain insight into the genetic interaction between ANGUSTIFOLIA and H+-PPase in pavement cell differentiation, an-1 fugu5-1 was analyzed. Surprisingly, epidermis developmental defects were synergistically enhanced in the double mutant. In fact, an-1 fugu5-1 pavement cells showed a striking three-dimensional growth phenotype on both abaxial and adaxial sides of cotyledons, which was recovered by hydrolysis of PPi in an-1 fugu5-1 AVP1pro::IPP1. Live imaging revealed that cortical MTs exhibited a reduced velocity, were slightly fragmented and sparse in the above lines compared to the WT. Consistently, addition of PPi in vitro led to a dose-dependent delay of tubulin polymerization, thus supporting a link between PPi and MT dynamics. Moreover, mathematical simulation of three-dimensional growth based on cotyledon proximo-distal and medio-lateral phenotypic quantification implicated restricted cotyledon expansion along the medio-lateral axis in the crinkled surface of an-1 fugu5-1. Together, our data suggest that PPi homeostasis is a prerequisite for proper pavement cell morphogenesis, epidermal growth and development, and organ flattening.

Mechanism underlying dynamic scaling properties observed in the contour of spreading epithelial monolayer.

We found evidence of dynamic scaling in the spreading of Madin-Darby canine kidney (MDCK) cell monolayer, which can be characterized by the Hurst exponent α=0.86 and the growth exponent ß=0.73, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. Dynamic scaling refers to the roughness of the surface scales, both spatially and temporally. During the spreading of the monolayer, it is known that so-called leader cells generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation shows that the model can reproduce different scaling laws from (α=0.5,ß=0.25) to (α=0.9,ß=0.75), where the exponents α and ß are determined by two dimensionless quantities determined by the microscopic cell behavior. From the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law, α=0.74,ß=0.68, suggesting that cell motility increased ninefold. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and we propose a mechanism that exhibits the dynamic scaling property.

Mark1 regulates distal airspace expansion through type I pneumocyte flattening in lung development.

During the later stages of lung development, two types of pneumocytes, cuboidal type II (AECII) and flattened type I (AECI) alveolar epithelial cells, form distal lung saccules. Here, we highlight how fibroblasts expressing MAP-microtubule affinity regulating kinase 1 (Mark1) are required for the terminal stages of pulmonary development, called lung sacculation. In Mark1-knockout (KO) mice, distal sacculation and AECI flattening are significantly impaired. Fetal epithelial cells generate alveolar organoids and differentiate into pneumocytes when co-cultured with fibroblasts. However, the size of organoids decreased and AECI flattening was impaired in the presence of Mark1 KO fibroblasts. In Mark1 KO fibroblasts themselves, cilia formation and the Hedgehog pathway were suppressed, resulting in the loss of type I collagen expression. The addition of type I collagen restored AECI flattening in organoids co-cultured with Mark1 KO fibroblasts and rescued the decreased size of organoids. Mathematical modeling of distal lung sacculation supports the view that AECI flattening is necessary for the proper formation of saccule-like structures. These results suggest that Mark1-mediated fibroblast activation induces AECI flattening and thereby regulates distal lung sacculation.

Author Correction: PtdIns(3,5)P2 mediates root hair shank hardening in Arabidopsis.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

PtdIns(3,5)P2 mediates root hair shank hardening in Arabidopsis.

Root hairs elongate by tip growth and simultaneously harden the shank by constructing the inner secondary cell wall layer. While much is known about the process of tip growth1, almost nothing is known about the mechanism by which root hairs harden the shank. Here we show that phosphatidylinositol-3,5-bisphosphate (PtdIns(3,5)P2), the enzymatic product of FORMATION OF APLOID AND BINUCLEATE CELLS 1 (FAB1), is involved in the hardening of the shank in root hairs in Arabidopsis. FAB1 and PtdIns(3,5)P2 localize to the plasma membrane along the shank of growing root hairs. By contrast, phosphatidylinositol 4-phosphate 5-kinase 3 (PIP5K3) and PtdIns(4,5)P2 localize to the apex of the root hair where they are required for tip growth. Reduction of FAB1 function results in the formation of wavy root hairs while those of the wild type are straight. The localization of FAB1 in the plasma membrane of the root hair shank requires the activity of Rho-related GTPases from plants 10 (ROP10) and localization of ROP10 requires FAB1 activity. Computational modelling of root hair morphogenesis successfully reproduces the wavy root hair phenotype. Taken together, these data demonstrate that root hair shank hardening requires PtdIns(3,5)P2/ROP10 signalling.

Integrating perfusable vascular networks with a three-dimensional tissue in a microfluidic device.

Creating vascular networks in tissues is crucial for tissue engineering. Although recent studies have demonstrated the formation of vessel-like structures in a tissue model, long-term culture is still challenging due to the lack of active perfusion in vascular networks. Here, we present a method to create a three-dimensional cellular spheroid with a perfusable vascular network in a microfluidic device. By the definition of the cellular interaction between human lung fibroblasts (hLFs) in a spheroid and human umbilical vein endothelial cells (HUVECs) in microchannels, angiogenic sprouts were induced from microchannels toward the spheroid; the sprouts reached the vessel-like structures in a spheroid to form a continuous lumen. We demonstrated that the vascular network could administer biological substances to the interior of the spheroid. As cell density in the spheroid is similar to that of a tissue, the perfusable vasculature model opens up new possibilities for a long-term tissue culture in vitro.

Exogenous Cellulase Switches Cell Interdigitation to Cell Elongation in an RIC1-dependent Manner in Arabidopsis thaliana Cotyledon Pavement Cells.

Pavement cells in cotyledons and true leaves exhibit a jigsaw puzzle-like morphology in most dicotyledonous plants. Among the molecular mechanisms mediating cell morphogenesis, two antagonistic Rho-like GTPases regulate local cell outgrowth via cytoskeletal rearrangements. Analyses of several cell wall-related mutants suggest the importance of cell wall mechanics in the formation of interdigitated patterns. However, how these factors are integrated is unknown. In this study, we observed that the application of exogenous cellulase to hydroponically grown Arabidopsis thaliana cotyledons switched the interdigitation of pavement cells to the production of smoothly elongated cells. The cellulase-induced inhibition of cell interdigitation was not observed in a RIC1 knockout mutant. This gene encodes a Rho-like GTPase-interacting protein important for localized cell growth suppression via microtubule bundling on concave cell interfaces. Additionally, to characterize pavement cell morphologies, we developed a mathematical model that considers the balance between cell and cell wall growth, restricted global cell growth orientation, and regulation of local cell outgrowth mediated by a Rho-like GTPase-cytoskeleton system. Our computational simulations fully support our experimental observations, and suggest that interdigitated patterns form because of mechanical buckling in the absence of Rho-like GTPase-dependent regulation of local cell outgrowth. Our model clarifies the cell wall mechanics influencing pavement cell morphogenesis.

Modulation of apical constriction by Wnt signaling is required for lung epithelial shape transition.

In lung development, the apically constricted columnar epithelium forms numerous buds during the pseudoglandular stage. Subsequently, these epithelial cells change shape into the flat or cuboidal pneumocytes that form the air sacs during the canalicular and saccular (canalicular-saccular) stages, yet the impact of cell shape on tissue morphogenesis remains unclear. Here, we show that the expression of Wnt components is decreased in the canalicular-saccular stages, and that genetically constitutive activation of Wnt signaling impairs air sac formation by inducing apical constriction in the epithelium as seen in the pseudoglandular stage. Organ culture models also demonstrate that Wnt signaling induces apical constriction through apical actomyosin cytoskeletal organization. Mathematical modeling reveals that apical constriction induces bud formation and that loss of apical constriction is required for the formation of an air sac-like structure. We identify MAP/microtubule affinity-regulating kinase 1 (Mark1) as a downstream molecule of Wnt signaling and show that it is required for apical cytoskeletal organization and bud formation. These results suggest that Wnt signaling is required for bud formation by inducing apical constriction during the pseudoglandular stage, whereas loss of Wnt signaling is necessary for air sac formation in the canalicular-saccular stages.

A Theoretical Model of Jigsaw-Puzzle Pattern Formation by Plant Leaf Epidermal Cells.

Plant leaf epidermal cells exhibit a jigsaw puzzle-like pattern that is generated by interdigitation of the cell wall during leaf development. The contribution of two ROP GTPases, ROP2 and ROP6, to the cytoskeletal dynamics that regulate epidermal cell wall interdigitation has already been examined; however, how interactions between these molecules result in pattern formation remains to be elucidated. Here, we propose a simple interface equation model that incorporates both the cell wall remodeling activity of ROP GTPases and the diffusible signaling molecules by which they are regulated. This model successfully reproduces pattern formation observed in vivo, and explains the counterintuitive experimental results of decreased cellulose production and increased thickness. Our model also reproduces the dynamics of three-way cell wall junctions. Therefore, this model provides a possible mechanism for cell wall interdigitation formation in vivo.

Tooth germ invagination from cell-cell interaction: Working hypothesis on mechanical instability.

In the early stage of tooth germ development, the bud of the dental epithelium is invaginated by the underlying mesenchyme, resulting in the formation of a cap-like folded shape. This bud-to-cap transition plays a critical role in determining the steric design of the tooth. The epithelial-mesenchymal interaction within a tooth germ is essential for mediating the bud-to-cap transition. Here, we present a theoretical model to describe the autonomous process of the morphological transition, in which we introduce mechanical interactions among cells. Based on our observations, we assumed that peripheral cells of the dental epithelium bound tightly to each other to form an elastic sheet, and mesenchymal cells that covered the tooth germ would restrict its growth. By considering the time-dependent growth of cells, we were able to numerically show that the epithelium within the tooth germ buckled spontaneously, which is reminiscent of the cap-stage form. The difference in growth rates between the peripheral and interior parts of the dental epithelium, together with the steric size of the tooth germ, were determining factors for the number of invaginations. Our theoretical results provide a new hypothesis to explain the histological features of the tooth germ.

Dendritic gates for signal integration with excitability-dependent responsiveness.

The shape and excitability of neuronal dendrites are expected to be responsible for the functional characteristics of information processing in the brain. In the present study, we proposed that excitable media with branching patterns mimicked the multi-signal integration of neuronal computation. We initially examined the conditions of the coincidence detection of two inputs as the simplest form of signal integration. We considered a gate with two channels that was bound by a circular joint with uniform excitability and demonstrated that the time window for the coincidence detection was controlled by the geometry and excitability of the gate. The functions of the gate were due to the unique property of the excitation waves, known as the curvature effect. The expanded spatial spread diluted the incoming excitation signals to insufficient levels to sustain wave advancement. Next, we applied dendritic gates that were reminiscent of neuronal dendrites for multi-signal integration. The irregular dendritic patterns were produced by a cellular automaton model of self-organizing pattern formation that adopted the semi-random grid in numerical simulations. We demonstrated that the threshold operation for multiple inputs was conducted by the dendritic pattern. The thresholds varied among gates owing to their irregular patterns, and were adjusted by changing the excitability without changing the gate geometry. The materializable model may provide a novel biomimetic approach for developing fuzzy hardware with adjustable responsiveness.

The FOXE1 locus is a major genetic determinant for radiation-related thyroid carcinoma in Chernobyl.

Papillary thyroid cancer (PTC) among individuals exposed to radioactive iodine in their childhood or adolescence is a major internationally recognized health consequence of the Chernobyl accident. To identify genetic determinants affecting individual susceptibility to radiation-related PTC, we conducted a genome-wide association study employing Belarusian patients with PTC aged 0-18 years at the time of accident and age-matched Belarusian control subjects. Two series of genome scans were performed using independent sample sets, and association with radiation-related PTC was evaluated. Meta-analysis by the Mantel-Haenszel method combining the two studies identified four SNPs at chromosome 9q22.33 showing significant associations with the disease (Mantel-Haenszel P: mhp = 1.7 x 10(-9) to 4.9 x 10(-9)). The association was further reinforced by a validation analysis using one of these SNP markers, rs965513, with a new set of samples (overall mhp = 4.8 x 10(-12), OR = 1.65, 95% CI: 1.43-1.91). Rs965513 is located 57-kb upstream to FOXE1, a thyroid-specific transcription factor with pivotal roles in thyroid morphogenesis and was recently reported as the strongest genetic risk marker of sporadic PTC in European populations. Of interest, no association was obtained between radiation-related PTC and rs944289 (mhp = 0.17) at 14p13.3 which showed the second strongest association with sporadic PTC in Europeans. These results show that the complex pathway underlying the pathogenesis may be partly shared by the two etiological forms of PTC, but their genetic components do not completely overlap each other, suggesting the presence of other unknown etiology-specific genetic determinants in radiation-related PTC.

Branching pattern formation that reflects the history of signal propagation.

In living organisms, branching structures are often observed in open systems. During the process of structure formation/deformation, signal propagation can be observed. Branching paths often deform depending on the history of signal propagation. To gain a better understanding of the process of pattern formation that results in characteristic geometrical paths, we adopt a system in which the dynamics of path formation are correlated with signal propagation. This model involves both branch-generation dynamics and signal-propagation dynamics, and we introduced positive feedback between these two dynamic processes. We studied the geometrical properties of path deformation and the pattern of signal propagation using a discretized reaction-diffusion model. The proposed model can qualitatively reproduce different branching patterns and means of signal propagation. One remarkable result is that the mutual interaction of these two dynamic processes leads to autonomous wave generation, similar to a pacemaker or the generation of spiral waves. Because the autonomous wave generation in the signal is spontaneous, the shapes of the branching paths become distorted. We discuss the correlation between path deformation and signal propagation as a first step in understanding signal processing for such complex deformable paths.

Predicting regulation of the phosphorylation cycle of KaiC clock protein using mathematical analysis.

Abstract The cyanobacterial clock protein KaiC regulates the circadian cycle by exhibiting rhythms in transcription, translation, and phosphorylation. KaiC phosphorylation persists in circadian cycling even under transcription-less conditions and was reconstituted in vitro by incubating KaiC, KaiA, and KaiB. This presents a novel perspective for circadian oscillation occurring due to interactions between clock proteins. Using mathematical models, the authors investigated the mechanism for the transcription-less KaiC phosphorylation cycle. They developed a simple model based on the possible KaiC behavior, which is experimentally suggested by Kitayama et al. (2003, EMBO J, 22:2127-2134). They hypothesized that the KaiC-KaiA complex formation, followed by a decrease in free KaiA molecules, may attenuate the KaiC phosphorylation rate, and it acts as negative feedback in the system. However, this model was shown not to be adequate to generate the KaiC phosphorylation cycle. The authors developed the general version of the model and determined the necessary condition to generate the KaiC phosphorylation cycle. Linear stability analysis revealed that oscillations can occur when the distance of feedback between the recipient reaction and the effector is far enough. Furthermore, they classified negative feedback regulations in the closed system into 2 types: destabilizing inhibition and stabilizing inhibition. Based on this result, the authors predicted that, in addition to the identified states of KaiC, another unknown state must be present between KaiC phosphorylation and the complex formation. By incorporating the unknown state into the previous model, they realized the periodic pattern reminiscent of the KaiC phosphorylation cycle in computer simulation. This result implies that the KaiC-KaiA complex formation requires more than 1 step of posttranslational modification, including phosphorylation or conformational change of KaiC.

Transcriptional autoregulation by phosphorylated and non-phosphorylated KaiC in cyanobacterial circadian rhythms.

Cyanobacteria are the simplest organisms known to exhibit circadian rhythms, which is the fundamental process of homeostasis adapting to daily environmental changes. The cyanobacterial clock gene products, KaiA, KaiB, and KaiC interact with each other, and regulate KaiC phosphorylation and kaiBC expression in a circadian fashion. Molecular genetic study recently proposed that KaiC protein may enhance and repress transcription of clock genes depending on KaiC's phosphorylation status, however, the precise mechanism is still unknown. We developed a mathematical model for the dynamics of cyanobacterial circadian rhythms focusing on the transcriptional regulation by KaiC. We investigated the model using numerical methods, and predicted the transcriptional regulation mechanism by KaiC. We searched for conditions for generating circadian oscillation and concluded that only two mechanisms of the transcriptional regulation are the possible pictures. One is the Transcriptional Repression Model where KaiC represses transcription of the clock genes after phosphorylation, and the other is the Transcriptional Activation Model where KaiC induces transcription after phosphorylation. The Transcriptional Repression Model includes self-repression similarly to the circadian oscillator models that have been proposed previously, and dynamical oscillation is easy to understand. However, the Transcriptional Activation Model does not include any direct repression in its interactive circuit, and is distinct from the previous ideas for circadian clocks. Subsequent computer simulation showed that the Transcriptional Activation Model explains most of the observed mutant phenotypes, and the Transcriptional Repression Model realizes only a half of them. It was also revealed that oscillations in the Transcriptional Activation Model is much more robust against the disruption by cell division or cell elongation than the Transcriptional Repression Model. It suggests that the Transcriptional Activation Model may reflect the essence of the actual transcriptional mechanism of the kai oscillator in cyanobacteria.