Branching morphogenesis in a reaction-diffusion model

Electrical stimulation of chicken embryo development supports the Inside story scenario of human development and evolution

Animal evolution is driven by random mutations at the genome level. However, it has long been suggested that there exist physical constraints which limit the set of possible outcomes. In craniate evolution, it has been observed that head features, notably in the genus homo, can be ordered in a morphological diagram such that, as the brain expands, the head rocks more forward, face features become less prognathous and the mouth tends to recede. One school of paleontologists suggests that this trend is wired somewhere structurally inside the anatomy, and that random modifications of genes push up or down animal forms along a pre-determined path. No actual experiment has been able to settle the dispute. I present here an experiment of electric stimulation of the head in the chicken embryo which is able to enhance the magnitude of tension forces during development. This experimental intervention causes a correlated brain shrinkage and rotatory movement of the head, congruent with tissue texture, which proves that head dilation and flexure are intimately linked. Numerical modelling explains why the brain curls when it dilates. This gives support to the idea that there exists, in the texture of the vertebrate embryo, a latent dynamic pattern for the observed paleontological trends in craniates towards homo, a concept known as Inside story.

A change in boundary conditions induces a discontinuity of tissue flow in chicken embryos and the formation of the cephalic fold

The morphogenesis of vertebrate body parts remains an open question. It is not clear whether the existence of different structures, such as a head, can be addressed by fundamental laws of tissue movement and deformation, or whether they are only a sequence of stop-and-go genetic instructions. I have filmed by time-lapse microscopy the formation of the presumptive head territory in chicken embryos. I show that the early lateral evagination of the eye cups and of the mesencephalic plate is a consequence of a sudden change in boundary conditions of the initial cell flow occurring in these embryos. Due to tissue flow, and collision of the two halves of the embryo, the tissue sheet movement is first dipolar, and next quadrupolar. In vivo air puff tonometry reveals a simple visco-elastic behaviour of the living material. The jump from a dipolar to a quadrupolar flow changes the topology of the early morphogenetic field which is observed towards a complex vortex winding with a trail (the eye cups and brain folds). The hydrodynamical model accounts for the discontinuity of the vector field at the moment of collision of the left and right halves of the embryo, at a quantitative level. This suggests a possible mechanism for the morphogenesis of the head of amniotes, as compared to cephalochordates and anamniotes.

Self-organization of developing embryo using scale-invariant approach

BACKGROUND

Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.

METHODS

In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing C. elegans during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.

RESULTS AND CONCLUSION

The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.

Electrochemical synthesis of dendritic zinc films composed of systematically varying motif crystals

Polycrystalline zinc films with new dendritic frameworks were electrodeposited from nonaqueous formamide media containing 0.01-0.3 M Zn(ClO4)2.6H2O as the Zn2+ source and 0.1 M LiClO4.3H2O as the supporting electrolyte. Formamide media offer a wider range of deposition temperatures and deposition potentials than aqueous solutions, which provides a higher degree of freedom in creating new polycrystalline architectures. The growth patterns of zinc crystals could be precisely controlled (e.g., faceted growth and dendritic growth) by changing the interplay between the growth rate and the mass transport rate. The effect of deposition potential, temperature, and Zn2+ concentration on the onset potential of dendritic growth and the detailed dendritic features were studied systematically. The zinc dendrites obtained in this study were composed of submicron-sized crystals of a uniform shape (motif crystals) that grow repetitively fused together to form three-dimensionally dispersed dendritic backbones. This unique organization achieves a remarkable physical and electrical continuity between crystals while generating high surface areas, which is difficult to accomplish simultaneously in polycrystalline films. The shape of motif crystals can be finely tuned from hexagons to fern-shaped leaves by the deposition potential applied, which in turn alters the overall degree of branching of dendritic backbones. Cyclic voltammetry of the resulting zinc electrodes with various growth patterns was carried out and discussed in conjunction with the films' morphological variation.

Dynamics of vascular branching morphogenesis: the effect of blood and tissue flow

Vascularization of embryonic organs or tumors starts from a primitive lattice of capillaries. Upon perfusion, this lattice is remodeled into branched arteries and veins. Adaptation to mechanical forces is implied to play a major role in arterial patterning. However, numerical simulations of vessel adaptation to haemodynamics has so far failed to predict any realistic vascular pattern. We present in this article a theoretical modeling of vascular development in the yolk sac based on three features of vascular morphogenesis: the disconnection of side branches from main branches, the reconnection of dangling sprouts ("dead ends"), and the plastic extension of interstitial tissue, which we have observed in vascular morphogenesis. We show that the effect of Poiseuille flow in the vessels can be modeled by aggregation of random walkers. Solid tissue expansion can be modeled by a Poiseuille (parabolic) deformation, hence by deformation under hits of random walkers. Incorporation of these features, which are of a mechanical nature, leads to realistic modeling of vessels, with important biological consequences. The model also predicts the outcome of simple mechanical actions, such as clamping of vessels or deformation of tissue by the presence of obstacles. This study offers an explanation for flow-driven control of vascular branching morphogenesis.