Gradient based axon growth modelling of different cell types with specific growth features in the spinal cord of hatchling Xenopus tadpole

It is imperative to understand how simple basic mechanisms can allow primary functioning neuronal circuits to develop. To explore the 'functional connectome', we investigate anatomy and electrophysiology of young hatchling Xenopus tadpole's spinal cord. Our bottom-up approach to modelling of neuronal connectivity is based on developmental process of axon growth - we develop a gradient-based mathematical model for axon growth. It is known that in the developing developing vertebrate spinal cord, axons grow under influence of chemical morphogenes released from the dorsal roof plate ('BMP'), ventral floor plate ('Shh') and hindbrain region ('Wnt'). Distribution of these guidance molecules along the spinal cord set up a gradient field which steer the axons in appropriate locations and thus ensure formation of proper connections. The model of axon growth includes a fixed environment of the governing gradients and seven parameters describing the sensitivity of axon to different guidance molecules. Sensitivity parameters are specific for axons of each cell-type and also they are specific for the direction of axon growth (either to head or tail). A stochastic optimization programming technique is implemented to determine the values of these parameters for each cell-type and each direction of axon growth. The cost function provides a fitting of the model to the experimental measurements of axons and takes into account the projection of the axon to the Dorso-Ventral axis as well as the axon tortuisity. The model successfully generates axons of both commissural and non-commissural neurons which include stimulus receiving sensory neurons, sensory infomation processing interneurons and motorneurons. We model axons of seven types of spinal neurons believed to be involved in swimming and struggling behaviour of tadpole. Each neuron has a different axon growth feature, e.g., commissural neurons grow axons ventrally on the same side of the spinal cord at first and turn longitudinally  on the other (contralateral) side of the spinal cord and non-commissural neurons grow their axons on the same (ipsilateral) side of spinal cord. This gradient based axon growth will in fact lead to bilogical reconstruction of the connectome of the tadpole's spinal cord.