A Morpho-Density Approach to Estimating Neural Connectivity

Abstract

Neuronal signal integration and information processing in cortical neuronal networks critically depend on the organization of synaptic connectivity. Because of the challenges involved in measuring a large number of neurons, synaptic connectivity is difficult to determine experimentally. Current computational methods for estimating connectivity typically rely on the juxtaposition of experimentally available neurons and applying mathematical techniques to compute estimates of neural connectivity. However, since the number of available neurons is very limited, these connectivity estimates may be subject to large uncertainties. We use a morpho-density field approach applied to a vast ensemble of model-generated neurons. A morpho-density field (MDF) describes the distribution of neural mass in the space around the neural soma. The estimated axonal and dendritic MDFs are derived from 100,000 model neurons that are generated by a stochastic phenomenological model of neurite outgrowth. These MDFs are then used to estimate the connectivity between pairs of neurons as a function of their inter-soma displacement. Compared with other density-field methods, our approach to estimating synaptic connectivity uses fewer restricting assumptions and produces connectivity estimates with a lower standard deviation. An important requirement is that the model-generated neurons reflect accurately the morphology and variation in morphology of the experimental neurons used for optimizing the model parameters. As such, the method remains subject to the uncertainties caused by the limited number of neurons in the experimental data set and by the quality of the model and the assumptions used in creating the MDFs and in calculating estimating connectivity. In summary, MDFs are a powerful tool for visualizing the spatial distribution of axonal and dendritic densities, for estimating the number of potential synapses between neurons with low standard deviation, and for obtaining a greater understanding of the relationship between neural morphology and network connectivity.

The effects of neuron morphology on graph theoretic measures of network connectivity: the analysis of a two-level statistical model

“…The connectivity is quantified using the standard graph theoretic measures like motif counts, clustering coefficient, harmonic path length, and the two definitions of small-world coefficient. Neurites are represented as neurite fields in accordance with the model already addressed in the literature (Snider et al, 2010 ; Teeter and Stevens, 2011 ; Cuntz, 2012 ; van Pelt and van Ooyen, 2013 ; McAssey et al, 2014 ). Such model provides a low-resolution and low-dimensional representation of neurites.…”

“…Our model is constructed to capture general properties of neuronal morphology suggested by Snider et al ( 2010 ), while the studies in Herzog et al ( 2007 ) and Voges et al ( 2010 ) focus on the specific types of pyramidal cells with long patchy projections and the neuronal connectivity derived from this property. In a recent study (McAssey et al, 2014 ), a similar model that uses neurite density fields to represent axons and dendrites is analyzed through simulations. The authors carefully fitted the density fields using the reconstructed neuronal morphologies fed to the simulator (Koene et al, 2009 ).…”

“…The model we considered in this study is very similar to those described in Herzog et al ( 2007 ), Voges et al ( 2010 ), and McAssey et al ( 2014 ), but we opted for a different approach to analyzing the model. Instead of simulating the model for different parameter sets, we derived the analytical solution that allows us to fully understand the significance of the individual model parameters.…”

“…Another concept is the scale-free network that installs system dynamics on the edge between order and disorder, thus maximizing the repertoire of dynamical regimes that a system can exhibit as well as the information diversity in the system (Boccaletti et al, 2006 ; Mäki-Marttunen et al, 2011 ). Small-world networks were first introduced in Watts and Strogatz ( 1998 ), and then addressed in other studies, also in the neuroscience context (Boccaletti et al, 2006 ; Herzog et al, 2007 ; Kriener et al, 2009 ; Voges et al, 2010 ; Sporns, 2011 ; McAssey et al, 2014 ). They were often examined in the context of the large-scale recordings of whole-brain activity, or the anatomical large-scale connectivity between brain regions (Sporns, 2011 ).…”

Excess neuronal branching allows for innervation of specific dendritic compartments in cortex

“…All-to-all putative connectivity Bird, Deters, & Cuntz whilst obeying optimality principles in volume, length, and signal delays (Chklovskii, 2004;Budd et al, 2010;447 Cuntz et al, 2010). The specific layout of axonal inputs and branching principles can combine to create diverse 448 dendritic shapes (Cuntz, 2012;Cuntz et al, 2012), which in turn lead to the connectivity patterns seen in neuronal 449 circuits (Hill et al, 2012;McAssey et al, 2014;Potjans & Diesmann, 2014). Whilst the design principles leading 450…”