A developmental approach to predicting brain connectivity from small biological datasets: a gradient-based neuron growth model: Neuron Growth Model and Neuronal Connectivity

Relating structure and function of neuronal circuits is a challenging problem. It requires demonstrating how dynamical
patterns of spiking activity lead to functions like cognitive behaviour and identifying the neurons and connections that lead
to appropriate activity of a circuit. We apply a ‘‘developmental approach’’ to define the connectome of a simple nervous
system, where connections between neurons are not prescribed but appear as a result of neuron growth. A gradient based
mathematical model of two-dimensional axon growth from rows of undifferentiated neurons is derived for the different
types of neurons in the brainstem and spinal cord of young tadpoles of the frog Xenopus. Model parameters define a twodimensional
CNS growth environment with three gradient cues and the specific responsiveness of the axons of each neuron
type to these cues. The model is described by a nonlinear system of three difference equations; it includes a random
variable, and takes specific neuron characteristics into account. Anatomical measurements are first used to position cell
bodies in rows and define axon origins. Then a generalization procedure allows information on the axons of individual
neurons from small anatomical datasets to be used to generate larger artificial datasets. To specify parameters in the axon
growth model we use a stochastic optimization procedure, derive a cost function and find the optimal parameters for each
type of neuron. Our biologically realistic model of axon growth starts from axon outgrowth from the cell body and
generates multiple axons for each different neuron type with statistical properties matching those of real axons. We
illustrate how the axon growth model works for neurons with axons which grow to the same and the opposite side of the
CNS. We then show how, by adding a simple specification for dendrite morphology, our model ‘‘developmental approach’’
allows us to generate biologically-realistic connectomes.