N-Cadherin Orchestrates Self-Organization of Neurons within a Columnar Unit in the Drosophila Medulla.

Columnar structure is a basic unit of the brain, but the mechanism underlying its development remains largely unknown. The medulla, the largest ganglion of the Drosophila melanogaster visual center, provides a unique opportunity to reveal the mechanisms of 3D organization of the columns. In this study, using N-cadherin (Ncad) as a marker, we reveal the donut-like columnar structures along the 2D layer in the larval medulla that evolves to form three distinct layers in pupal development. Column formation is initiated by three core neurons, R8, R7, and Mi1, which establish distinct concentric domains within a column. We demonstrate that Ncad-dependent relative adhesiveness of the core columnar neurons regulates their relative location within a column along a 2D layer in the larval medulla according to the differential adhesion hypothesis. We also propose the presence of mutual interactions among the three layers during formation of the 3D structures of the medulla columns.SIGNIFICANCE STATEMENT The columnar structure is a basic unit of the brain, but its developmental mechanism remains unknown. The medulla, the largest ganglion of the fly visual center, provides a unique opportunity to reveal the mechanisms of 3D organization of the columns. We reveal that column formation is initiated by three core neurons that establish distinct concentric domains within a column. We demonstrate the in vivo evidence of N-cadherin-dependent differential adhesion among the core columnar neurons within a column along a 2D layer in the larval medulla. The 2D larval columns evolve to form three distinct layers in the pupal medulla. We propose the presence of mutual interactions among the three layers during formation of the 3D structures of the medulla columns.

Reelin transiently promotes N-cadherin-dependent neuronal adhesion during mouse cortical development.

Reelin is an essential glycoprotein for the establishment of the highly organized six-layered structure of neurons of the mammalian neocortex. Although the role of Reelin in the control of neuronal migration has been extensively studied at the molecular level, the mechanisms underlying Reelin-dependent neuronal layer organization are not yet fully understood. In this study, we directly showed that Reelin promotes adhesion among dissociated neocortical neurons in culture. The Reelin-mediated neuronal aggregation occurs in an N-cadherin-dependent manner, both in vivo and in vitro. Unexpectedly, however, in a rotation culture of dissociated neocortical cells that gradually reaggregated over time, we found that it was the neural progenitor cells [radial glial cells (RGCs)], rather than the neurons, that tended to form clusters in the presence of Reelin. Mathematical modeling suggested that this clustering of RGCs could be recapitulated if the Reelin-dependent promotion of neuronal adhesion were to occur only transiently. Thus, we directly measured the adhesive force between neurons and N-cadherin by atomic force microscopy, and found that Reelin indeed enhanced the adhesiveness of neurons to N-cadherin; this enhanced adhesiveness began to be observed at 30 min after Reelin stimulation, but declined by 3 h. These results suggest that Reelin transiently (and not persistently) promotes N-cadherin-mediated neuronal aggregation. When N-cadherin and stabilized ß-catenin were overexpressed in the migrating neurons, the transfected neurons were abnormally distributed in the superficial region of the neocortex, suggesting that appropriate regulation of N-cadherin-mediated adhesion is important for correct positioning of the neurons during neocortical development.

A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation.

We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type populations. The model is based on basic principles of localized repulsion and nonlocal attraction due to adhesion forces at the microscopic level. The new model is able to capture both qualitatively and quantitatively experiments by Katsunuma et al. (2016). We also review some of the applications of these models in other areas of tissue growth in developmental biology. We finally explore the resulting qualitative behavior due to cell-cell repulsion.

Continuous models for cell-cell adhesion.

Cell adhesion is the binding of a cell to another cell or to an extracellular matrix component. This process is essential in organ formation during embryonic development and in maintaining multicellular structure. Armstrong et al. (2006) [J. Theor. Biol. 243, pp. 98-113] proposed a nonlocal advection-diffusion system as a possible continuous mathematical model for cell-cell adhesion. Although the system is attractive and challenging, it gives biologically unrealistic numerical solutions under certain situations. We identify the problems and change underlying idea of cell movement from "cells move randomly" to "cells move from high to low pressure regions". Then we provide a modified continuous model for cell-cell adhesion. Numerical experiments illustrate that the modified model is able to replicate not only Steinberg׳s cell sorting experiments but also some phenomena which cannot be captured at all by Armstrong-Painter-Sherratt model.

A numerical algorithm for modeling cellular rearrangements in tissue morphogenesis.

Among morphological phenomena, cellular patterns in developing sensory epithelia have gained attention in recent years. Although physical models for cellular rearrangements are well-established thanks to a large bulk of experimental work, their computational implementation lacks solid mathematical background and involves experimentally unreachable parameters. Here we introduce a level set-based computational framework as a tool to rigorously investigate evolving cellular patterns, and study its mathematical and computational properties. We illustrate that a compelling feature of the method is its ability to correctly handle complex topology changes, including frequent cell intercalations. Combining this accurate numerical scheme with an established mathematical model, we show that the proposed framework features minimum possible number of parameters and is capable of reproducing a wide range of tissue morphological phenomena, such as cell sorting, engulfment or internalization. In particular, thanks to precise mathematical treatment of cellular intercalations, this method succeeds in simulating experimentally observed development of cellular mosaic patterns in sensory epithelia.