Self-organizing Mechanism for Development of Space-filling Neuronal Dendrites

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Abstract
Neurons develop distinctive dendritic morphologies to receive and process information. Previous experiments showed that competitive dendro-dendritic interactions play critical roles in shaping dendrites of the space-filling type, which uniformly cover their receptive field. We incorporated this finding in constructing a new mathematical model, in which reaction dynamics of two chemicals (activator and suppressor) are coupled to neuronal dendrite growth. Our numerical analysis determined the conditions for dendritic branching and suggested that the self-organizing property of the proposed system can underlie dendritogenesis. Furthermore, we found a clear correlation between dendrite shape and the distribution of the activator, thus providing a morphological criterion to predict the in vivo distribution of the hypothetical molecular complexes responsible for dendrite elongation and branching. Neurons elaborate two types of neuronal extensions. One is axon, which sends outputs to other neurons. Another is dendrite, which is specialized for receiving and processing synaptic or sensory inputs. Like elaborated branches of trees, the shape of dendrites is quite variable from one type to another, and different dendritic geometry contributes to differential informational processing and computation. For instance, neurons of the space-filling type (e.g., retinal ganglion cells) fill in an open space to pick up spatial information from every corner of their receptive field. Therefore, dendrite development is one of the representative examples of the emergence of function through morphogenesis. Previous experiments including ours showed that competitive dendro-dendritic interactions play critical roles in shaping dendrites of the space-filling type. In the present study, we incorporated this finding in constructing a new mathematical model, in which reaction dynamics of chemicals are coupled to neuronal dendrite growth. Our numerical analysis suggested that self-organizing property of the proposed system underlies formation of space-filling dendrites. Furthermore, we provided a morphological criterion to predict the in vivo distribution of the hypothetical molecular complexes responsible for dendrite elongation and branching. We have now found a substantial number of molecules involved in dendrite development, thus it is timely to discuss the prediction from this work.

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