Abstract
We developed a two-level statistical model that addresses the question of how properties of neurite morphology shape the large-scale network connectivity. We adopted a low-dimensional statistical description of neurites. From the neurite model description we derived the expected number of synapses, node degree, and the effective radius, the maximal distance between two neurons expected to form at least one synapse. We related these quantities to the network connectivity described using standard measures from graph theory, such as motif counts, clustering coefficient, minimal path length, and small-world coefficient. These measures are used in a neuroscience context to study phenomena from synaptic connectivity in the small neuronal networks to large scale functional connectivity in the cortex. For these measures we provide analytical solutions that clearly relate different model properties. Neurites that sparsely cover space lead to a small effective radius. If the effective radius is small compared to the overall neuron size the obtained networks share similarities with the uniform random networks as each neuron connects to a small number of distant neurons. Large neurites with densely packed branches lead to a large effective radius. If this effective radius is large compared to the neuron size, the obtained networks have many local connections. In between these extremes, the networks maximize the variability of connection repertoires. The presented approach connects the properties of neuron morphology with large scale network properties without requiring heavy simulations with many model parameters. The two-steps procedure provides an easier interpretation of the role of each modeled parameter. The model is flexible and each of its components can be further expanded. We identified a range of model parameters that maximizes variability in network connectivity, the property that might affect network capacity to exhibit different dynamical regimes.
Highlights
We analyze how the low-resolution properties of single neuron morphology constrain the connectivity within a large population of neurons
Quantitative measures such as the expected number of synapses, the effective radius of the connectivity area, and the node degree are derived as functions of the neurite model parameters
The concept derived in the first step, the effective radius, is related to the typical measures used to quantify connectivity in networks, motif counts, clustering coefficient, path length, and small-world coefficient
Summary
We analyze how the low-resolution properties of single neuron morphology constrain the connectivity within a large population of neurons. Each axon and each dendrite is represented by a single neurite field, the probability distribution that describes the density of the neurite branches within a limited area of the neurite. This way each neuron consists of one neurite field for the dendrite, one for the axon, and the parameter that determines the average distance between the dendrite and axon centers. In van Pelt and van Ooyen (2013) the realism of the obtained synaptic distributions and connectivity probabilities was tested for neurons modeled using density fields
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