RESUMEN
The characteristic six-layered appearance of the neocortex arises from the correct positioning of pyramidal neurons during development and alterations in this process can cause intellectual disabilities and developmental delay. Malformations in cortical development arise when neurons either fail to migrate properly from the germinal zones or fail to cease migration in the correct laminar position within the cortical plate. The Reelin signalling pathway is vital for correct neuronal positioning as loss of Reelin leads to a partially inverted cortex. The precise biological function of Reelin remains controversial and debate surrounds its role as a chemoattractant or stop signal for migrating neurons. To investigate this further we developed an in silico agent-based model of cortical layer formation. Using this model we tested four biologically plausible hypotheses for neuron motility and four biologically plausible hypotheses for the loss of neuron motility (conversion from migration). A matrix of 16 combinations of motility and conversion rules was applied against the known structure of mouse cortical layers in the wild-type cortex, the Reelin-null mutant, the Dab1-null mutant and a conditional Dab1 mutant. Using this approach, many combinations of motility and conversion mechanisms can be rejected. For example, the model does not support Reelin acting as a repelling or as a stopping signal. In contrast, the study lends very strong support to the notion that the glycoprotein Reelin acts as a chemoattractant for neurons. Furthermore, the most viable proposition for the conversion mechanism is one in which conversion is affected by a motile neuron sensing in the near vicinity neurons that have already converted. Therefore, this model helps elucidate the function of Reelin during neuronal migration and cortical development.
Asunto(s)
Moléculas de Adhesión Celular Neuronal/metabolismo , Corteza Cerebral/metabolismo , Proteínas de la Matriz Extracelular/metabolismo , Modelos Biológicos , Proteínas del Tejido Nervioso/metabolismo , Neuronas/metabolismo , Serina Endopeptidasas/metabolismo , Algoritmos , Animales , Moléculas de Adhesión Celular Neuronal/deficiencia , Moléculas de Adhesión Celular Neuronal/genética , Embrión de Mamíferos/metabolismo , Desarrollo Embrionario , Proteínas de la Matriz Extracelular/deficiencia , Proteínas de la Matriz Extracelular/genética , Proteínas Fluorescentes Verdes/genética , Proteínas Fluorescentes Verdes/metabolismo , Ratones , Ratones Noqueados , Proteínas del Tejido Nervioso/deficiencia , Proteínas del Tejido Nervioso/genética , Fenotipo , Proteína Reelina , Serina Endopeptidasas/deficiencia , Serina Endopeptidasas/genética , Transducción de SeñalRESUMEN
Motivated by examples in developmental biology and ecology, we develop a model for convection-dominated invasion of a spatial region by initially motile agents which are able to settle permanently. The motion of the motile agents and their rate of settling are affected by the local concentration of settled agents. The model can be formulated as a nonlinear partial differential equation for the time-integrated local concentration of the motile agents, from which the instantaneous density of settled agents and its long-time limit can be extracted. In the limit of zero diffusivity, the partial differential equation is of first order; for application-relevant initial and boundary-value problems, shocks arise in the time-integrated motile agent density, leading to delta-function components in the motile agent density. Furthermore, there are simple solutions for a model of successive layer formation. In addition some analytic results for a one-dimensional system with non-zero diffusivity can also be obtained. A case study, both with and without diffusion, is examined numerically. Some important predictions of the model are insensitive to the specific settling law used and the model offers insight into biological processes involving layered growth or overlapping generations of colonization.