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.zebrafish | somitogenesis | Delta-Notch | mathematical models I n vertebrate development, somites bud off from the anterior end of the tissue not yet differentiated to somites, called the presomitic mesoderm (PSM), one by one moving posteriorly. The time interval between the formation of one somite and the next is almost constant during somitogenesis, and it is species-specific. In the PSM, there are segmentation clock genes with oscillating expression, and the timing of segmentation is considered to be controlled by the oscillatory expression of these genes because their period of oscillation is very close to the period of segmentation (1-5).The oscillatory expression of the segmentation clock genes is known to be caused by the negative feedback regulation by their own products (6-8). Neighboring cells are in contact with each other (9, 10). In the PSM, oscillatory expressions are synchronized among neighboring cells. This synchronized oscillation is necessary for normal segmentation, and disruption of the synchronization results in a defective somite boundary (11-13).Theoretical models of segmentation in vertebrates have been developed to explain the spatiotemporal periodicity of the segmentation process (14-18), the oscillatory expression of segmentation clock genes (19)(20)(21)(22)(23)(24), and the wave-like gene expression observed in the anterior PSM (23,(25)(26)(27)(28)(29). Previous theoretical studies have also addressed mechanisms of synchronization of the segmentation clock between cells (13,24,25,30). In zebrafish, the synchronization of the segment...

In the neocortex, higher-order areas are essential to integrate sensory-motor information and have expanded in size during evolution. How higher-order areas are specified, however, remains largely unknown. Here, we show that the migration and distribution of early-born neurons, the Cajal-Retzius cells (CRs), controls the size of higher-order areas in the mouse somatosensory, auditory, and visual cortex. Using live imaging, genetics, and in silico modeling, we show that subtype-specific differences in the onset, speed, and directionality of CR migration determine their differential invasion of the developing cortical surface. CR migration speed is cell autonomously modulated by vesicle-associated membrane protein 3 (VAMP3), a classically non-neuronal mediator of endosomal recycling. Increasing CR migration speed alters their distribution in the developing cerebral cortex and leads to an expansion of postnatal higher-order areas and congruent rewiring of thalamo-cortical input. Our findings thus identify novel roles for neuronal migration and VAMP3-dependent vesicular trafficking in cortical wiring.

Cardiomyocytes are susceptible to apoptosis caused by hypoxia during the acute and subacute phases of myocardial infarction (MI). Angiogenesis can reduce MI-induced damage by mitigating hypoxia. It has been speculated that the ischemic border zone is a unique area rescued by angiogenic therapy. However, the mechanism and timing for new vessel formation in the mammalian heart following hypoxia are unclear. Identifying targets that benefit from angiogenesis treatment is indispensable for the development of revolutionary therapies. Here, we describe a novel circulatory system wherein new vessels develop from the endocardium of the left ventricle to perfuse the hypoxic area and salvage damaged cardiomyocytes at 3–14 days after MI by activating vascular endothelial growth factor signaling. Moreover, enhanced angiogenesis increased cardiomyocyte survival along the endocardium in the ischemic zone and suppressed ventricular remodeling in infarcted hearts. In contrast, cardiomyocytes in the border zone’s hypoxic area underwent apoptosis within 12 h of MI, and the border area that was amenable to treatment disappeared. These data indicate that the non-perfused area along the endocardium is a site of active angiogenesis and a promising target for MI treatment.

The crack growth dynamics of the carbon-black (CB) filled elastomers is studied experimentally and analyzed while focusing on both kinetics and crack tip profiles. The CB amounts are varied to change the mechanical properties of the elastomers. Static crack growth measurements simultaneously reveal the discontinuous-like transition of the crack growth rate v between the "slow mode" (v≈10^{-5}-10^{-3} m/s) and "fast mode" (v≈10^{-1}-10^{2} m/s) in a narrow range of the input tearing energy Γ and the accompanying changes in the crack tip profiles from blunt to sharp shapes. The crack tip profiles are characterized by two specific parameters, i.e., the deviation δ from the parabolic profile and the opening displacement a in the loading direction. The analysis based on the linear and weakly nonlinear elasticity theories of fracture dynamics demonstrates that the Γ dependence of δ and a is simply classified into three groups depending on the mode (slow or fast) and the magnitudes of δ, independent of CB volume fractions. The theories well explain the results in the slow and fast modes with small magnitudes of δ, while they fail to describe the data in the fast mode with large magnitudes of δ, where the contributions of the strong nonlinearity and/or energy dissipation become significant. The correlation between a power-law relationship Γ∼v^{α} observed in the fast mode and the linear viscoelasticity spectrum is also discussed. The correlation in elastomers with low CB volume fractions is quantitatively explained by the theory of Persson and Brener [Phys. Rev. E 71, 036123 (2005)PLEEE81539-375510.1103/PhysRevE.71.036123], whereas the deviation from the theory becomes appreciable for elastomers with higher CB volume fractions which exhibit strong nonlinear viscoelasticity.

Stretching experiments with various geometries are performed using a custom-built tensile tester to reveal the intriguing features of the mechanical softening phenomena of filled elastomers in loading-unloading cycles, commonly known as the Mullins effect. The dissipated energy (D), residual strain (ε), and dissipation factor (Δ; the ratio of D to input strain energy) in the loading-unloading cycles are evaluated as a function of the maximum stretch in cyclic loading (λ) using three types of extension, i.e., uniaxial, planar, and equibiaxial extension, for silica-filled elastomers with various filler contents, and with or without a silane coupling agent. The dissipated energy D and ε increase with an increase in λ, and they depend on the type of extension when compared at the same λ: D and ε increase in the order of equibiaxial, planar, and uniaxial extension. In contrast, the values of Δ obtained for various degrees and types of extension are collapsed into a single curve when the first invariant of the deformation tensor (I) corresponding to λ is employed as a variable: Δ steeply increases with an increase in I in the small deformation regime of I < 3.2, while Δ levels off in the large deformation regime of I > 3.5. The plateau values of Δ increase with an increase in filler content. The characteristic dependence of Δ on I in each of the small and large deformation regimes is expected to reflect the destruction process of the inherent structures, including filler networks and the filler-polymer interface, and the friction between the fillers and the rubber matrix, respectively.

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In early lung development, epithelial tubes (lung buds) intrude into mesenchyme covered with pleural cells (lung border), and form tree‐like networks, by means of repeated use of morphogenetic processes: “elongation,” “terminal bifurcation,” and “lateral budding.” When a bud is elongating, a peak of Fgf10 expression is formed in the mesenchyme near the tip; whereas when terminal bifurcation and lateral budding occur, two separate peaks are formed instead. To explain the spatial pattern of Fgf10 expression, we developed a mathematical model for the regulation of Fgf10 expression with geometrical conditions including shapes of the lung buds and the lung border. Different localization patterns of Fgf10 expression can be explained by the geometrical conditions. Fgf10 expression has a single peak when a length between the tip of lung bud and the lung border is large. When the length is small, Fgf10 expression has two peaks, whose location depends on the curvature of lung border. Developmental Dynamics 238:2813–2822, 2009. © 2009 Wiley‐Liss, Inc.