A generative growth model for thalamocortical axonal branching in primary visual cortex

Axonal morphology displays large variability and complexity, yet the canonical regularities of the cortex suggest that such wiring is based on the repeated initiation of a small set of genetically encoded rules. Extracting underlying developmental principles can hence shed light on what genetically encoded instructions must be available during cortical development. Within a generative model, we investigate growth rules for axonal branching patterns in cat area 17, originating from the lateral geniculate nucleus of the thalamus. This target area of synaptic connections is characterized by extensive ramifications and a high bouton density, characteristics thought to preserve the spatial resolution of receptive fields and to enable connections for the ocular dominance columns. We compare individual and global statistics, such as a newly introduced length-weighted asymmetry index and the global segment-length distribution, of generated and biological branching patterns as the benchmark for growth rules. We show that the proposed model surpasses the statistical accuracy of the Galton-Watson model, which is the most commonly employed model for biological growth processes. In contrast to the Galton-Watson model, our model can recreate the log-normal segment-length distribution of the experimental dataset and is considerably more accurate in recreating individual axonal morphologies. To provide a biophysical interpretation for statistical quantifications of the axonal branching patterns, the generative model is ported into the physically accurate simulation framework of Cx3D. In this 3D simulation environment we demonstrate how the proposed growth process can be formulated as an interactive process between genetic growth rules and chemical cues in the local environment.Author summary: The morphology of axonal arborizations is highly variable and complex, yet the canonical regularities of the cortex imply that axonal branching patterns have developed based on a small set of simple rules. Extracting such growth rules is fundamental, as it can shed light on the genetically encoded instructions for cortical developmental, necessary for subsequent cortical function. We propose in this work a generative model for branching patterns of thalamic afferents in cat area 17, fundamental for the synaptic connections of the ocular dominance stripes, and for a conservation of receptive field properties. The model is optimized for the segment-length distribution as well as for a length-weighted asymmetry quantification of the axonal morphologies, and can hence capture global morphological properties of the entire dataset, as well as morphologies of individual axons. We can show that our mechanistic model clearly surpasses the statistical accuracy of the Galton-Watson model, the most employed model for biological growth processes, a result which underlines the plausibility of the proposed growth rules. Our model is implemented in MATLAB as well as ported into Cx3D, a physically realistic simulation environment, where biophysical interactions with the environment are incorporated in the growth process to shape the final axonal morphology.