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The lung airways are characterized by long and wide proximal branches and short and thin distal branches. In this study, we investigated the emergence of this hierarchical structure through experimental observations and computational models. We focused on the branch formation in the pseudoglandular stage and examined the response of mouse lung epithelium to fibroblast growth factor 10 (FGF10) by monitoring extracellular signal-regulated kinase (ERK) activity. The ERK activity increased depending on the epithelial tissue curvature. This curvature-dependent response decreased as the development progressed. Therefore, to understand how these epithelial changes affect branching morphology, we constructed a computational model of curvature-dependent epithelial growth. We demonstrated that branch length was controlled by the curvature dependence of growth that was consistent with the experimental observations and lung morphology. However, the branching of the thin branches is suppressed in this model, which is inconsistent with the fact that thin branches in the lung are short. Thus, we introduced branch formation by apical constriction, which was shown to be regulated by Wnt signaling in our previous studies. Mathematical analysis indicated that the effect of apical constriction is cell shape-dependent, suggesting that apical constriction ameliorates the branching of thin branches. Finally, we were able to provide clarity on the hierarchical branching structure through an integrated computational model of curvature-dependent growth and cell shape regulation. We proposed that curvature-dependent growth involving FGF and Wnt-mediated cell shape regulation coordinate to control the spatial scale and frequency of branch formation.Statement of SignificanceThe lung airways exhibit a morphology in which the branch scale continuously decreases toward the distal side. This study explains the mechanism behind the hierarchical branching structure. Computational models proposed that the epithelial growth activity and apical constriction cooperatively determine branch length and tip width, consistent with the experimental observations that epithelial properties change as development progresses. The growth activity and cell shape are regulated by FGF and Wnt signaling, respectively, suggesting the importance of these pathways in patterning branch structures at a different scale. Our study provides a new perspective on the role of epithelial properties in the regulation of the mesoscale structure of the lung via FGF and Wnt signaling, thereby providing an understanding of branching morphogenesis.

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.

A root hair is a long tubular protrusion from a root hair cell established via tip growth, which is accomplished by the polarized deposition of membranous and cell wall components at the root hair apex accompanied by simultaneous hardening of the shank. The polarized secretion of materials to the root hair apex is well investigated; however, little is known about the deposition of inner cell wall materials at the root hair shank. We have previously reported that phosphatidylinositol-3,5-bisphosphate (PtdIns(3,5)P2)/ROP10 signaling is required for the regulation of cortical microtubule construction and the deposition of inner cell wall components at the root hair shank during hardening. To unravel the alternate secretion mechanism for delivery of the inner cell wall components to root hair shank, here, we demonstrate that root hair-specific Qa-SNARE, SYP123, localizes to the subapical zone and shank of elongating root hairs in Arabidopsis. SYP123-mediated root hair elongation was inhibited by the FAB1 inhibitor YM201636, and inhibition of PtdIns(3,5)P2 production impaired the plasma membrane localization of SYP123. We also showed that SYP123 forms a SNARE complex with VAMP727 on the plasma membrane, and syp123 and vamp727 mutants exhibited lower cell wall stiffness in the root hair shank because of impaired deposition of inner cell wall components. These results indicate that SYP123/VAMP727-mediated secretion is involved in the transport of inner cell wall components for hardening of the root hair shank.

We found evidence of dynamic scaling in the spreading of MDCK monolayer, which can be characterized by the Hurst exponent ${\alpha} = 0.86$ and the growth exponent ${\beta} = 0.73$, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. 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 revealed that the model could reproduce the different scaling law from ${\alpha} = 0.5, {\beta} = 0.25$ to ${\alpha} = 0.9, {\beta} = 0.75$, and the exponents ${\alpha}, {\beta}$ were determined by the two indices: $\rho t$ and $c$. Based on the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law ${\alpha} = 0.74, {\beta} = 0.68$, suggesting that cell motility increased by 9 folds. 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 proposed a new mechanism that exhibits the dynamic scaling property., Comment: 11 pages, 6 figures, and supplemental materials

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.

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.

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.

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.

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.

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.

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.

A cyanobacterial clock protein KaiC shows circadian cycling of the phosphorylation level in vitro. We first developed an observation-based model. The KaiC-KaiA complex formation consequently reduces free KaiA molecules, thereby may exert a negative feedback effect toward KaiC phosphorylation. However, this model was shown not to be adequate to generate the KaiC phosphorylation cycle. Then, we analyzed generalized models and determined necessary conditions to generate the cycle. Based on the result, we realized the observed pattern of the KaiC phosphorylation cycle and predicted an unknown state that lies between KaiC phosphorylation and the formation of the KaiC/KaiA complex.

In this paper, we present a poly-dimethylsiloxane (PDMS) microfluidic device to create a vascular network for a long-term spheroid culture, of which network and spheroid are consist of human umbilical vein endothelial cells (HUVEC) and normal human lung fibroblasts (LF), respectively. Following device design, fabrication, and fundamental evaluation of HUVEC sprouting conditions, we visualized that HUVEC networks were successfully formed by the co-culture with LFs and reached a LF-based spheroid. Moreover, perfusability of the network was evaluated by injecting fluorescent microbeads. This platform will be applicable for long-term tissue cultures to understand morphogenesis and modeling of blood vessel functions.

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.

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.

Glucose incorporation is regulated mainly by GLUT4 in skeletal muscles. Here we report that treatment of L6 myotubes with scriptide, a hydroxamic acid-based histone deacetylase (HDAC) inhibitor, stimulated 2-deoxyglucose uptake. The effect appeared only after 24 hr, resulting in 2.4-fold glucose uptake at treatment day 6. Scriptide acted synergistically with insulin, indicating it stimulated a distinct pathway from the insulin signaling pathway. It was not observed in undifferentiated myoblasts or 3T3-L1 adipocytes, suggesting a muscle-specific effect of scriptide. A five-carbon chain and hydroxamic acid, essential for histone deacetylase inhibition, were indispensable for this effect, and trichostatin A stimulated glucose uptake as well. Scriptide increased the cellular content of GLUT4, and induced GLUT4 translocation, but GLUT4 mRNA level did not change, indicating scriptide functions posttranslationally. Our results indicated a novel function for HDAC inhibitors of increasing GLUT4 content and its translocation in muscle cells, resulting in stimulation of glucose uptake.

Mutations in BSCL2/seipin cause Berardinelli-Seip congenital lipodystrophy (BSCL), a rare recessive disorder characterised by near absence of adipose tissue and severe insulin resistance. We aimed to determine how seipin deficiency alters glucose and lipid homeostasis and whether thiazolidinediones can rescue the phenotype.Bscl2 (-/-) mice were generated and phenotyped. Mouse embryonic fibroblasts (MEFs) were used as a model of adipocyte differentiation.As observed in humans, Bscl2 (-/-) mice displayed an early depletion of adipose tissue, with insulin resistance and severe hepatic steatosis. However, Bscl2 (-/-) mice exhibited an unexpected hypotriglyceridaemia due to increased clearance of triacylglycerol-rich lipoproteins (TRL) and uptake of fatty acids by the liver, with reduced basal energy expenditure. In vitro experiments with MEFs demonstrated that seipin deficiency led to impaired late adipocyte differentiation and increased basal lipolysis. Thiazolidinediones were able to rescue the adipogenesis impairment but not the alteration in lipolysis in Bscl2 (-/-) MEFs. In vivo treatment of Bscl2 (-/-) mice with pioglitazone for 9 weeks increased residual inguinal and mesenteric fat pads as well as plasma leptin and adiponectin concentrations. Pioglitazone treatment increased energy expenditure and improved insulin resistance, hypotriglyceridaemia and liver steatosis in these mice.Seipin plays a key role in the differentiation and storage capacity of adipocytes, and affects glucose and lipid homeostasis. The hypotriglyceridaemia observed in Bscl2 (-/-) mice is linked to increased uptake of TRL by the liver, offering a new model of liver steatosis. The demonstration that the metabolic complications associated with BSCL can be partially rescued with pioglitazone treatment opens an interesting therapeutic perspective for BSCL patients.

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., Author Summary It is well known that plant epidermal cells show beautiful jigsaw-puzzle like pattern. However, mechanism of this pattern formation is not well understood. In this study, we integrated known experimental information and mathematical modeling to reproduce the main features of the pattern formation—maintenance of cell wall thickness and formation of interdigitation. Interestingly, the model is mathematically equivalent to the model of human skull suture interdigitation.

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., Human molecular genetics, 19(12), pp.2516-2523; 2010

A cellular automaton model proposed by Motoike includes reaction-diffusion dynamics in a simple manner (Motoike, J. Phys. Soc. Jpn. 2007). The semi-random grid adopted in this model is designed to describe biological phenomena that involve intrinsic fluctuations. It has been shown that this model can exhibit branching patterns reminiscent of neural dendrites, whose formation may be regulated by excitation signals as suggested by experimental results. From a computational viewpoint, a random grid can be regarded as representing intrinsic spatial noise. In this study, we firstly compared the features of the patterns obtained from numerical simulations using regular and semi-random square grids. It was demonstrated that the directions of the path growth tended to be orthogonal or parallel to the grid owing to the anisotropy of the regular grid. We found that, as the parameter values are varied, the numbers of endpoints change continuously for patterns exhibited by a semi-random grid, whereas, they change discontinuously for a regular grid. Next, we investigated the patterns of path formation when excitation signals were added at spatially random points. The patterns obtained under these conditions exhibited highly complex and random shapes of branches. It was also revealed that the patterns in the case of random inputs have endpoints that are more numerous than in the case of a spatially fixed input. This result suggested that the patterns represent the history of the spatial history of excitation signal inputs.