Abstract
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 two-dimensional 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.
Highlights
The relationship between structure and function of neuronal circuits is a challenging problem in neuroscience and has two related aspects: 1) How can we identify the neuronal connections which lead to appropriate activity of a circuit? 2) How does that activity, as a dynamical pattern of spiking activity, lead to functions like cognitive behaviour? Experimental neuroscience provides knowledge on mechanisms of spike generation and propagation along the axon, synaptic transmission to other neurons and many other details of neuronal network function
The adjusted model takes into account specific details of axon growth for different spinal cord neuron types
A New Approach to Establishing Complete Connectivity In this paper we present and discuss the derivation and operation of a model for generating axons in a two-dimensional environment, under the control of a set of gradient cues
Summary
The relationship between structure and function of neuronal circuits is a challenging problem in neuroscience and has two related aspects: 1) How can we identify the neuronal connections which lead to appropriate activity of a circuit? Experimental neuroscience provides knowledge on mechanisms of spike generation and propagation along the axon, synaptic transmission to other neurons and many other details of neuronal network function. In many cases important information about large scale synaptic connectivity (contacts between neurons) is missing. One reason is that the experimental investigation of connections between large numbers of neurons is extremely difficult so there is only limited information on these connections, and their detailed mapping between all individual neurons in all but the smallest networks is absent. A way to address this problem and predict large scale network connectivity on the basis of relatively small amounts of information is through development. At the core of this developmental approach is a new biologically realistic model of axon growth
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