Background

Synaptic connectivity is a key determinant of the interaction between neurons, and its quantitation is pivotal to understanding the organization of brain circuits and the relationship with network function (Ascoli and Atkeson, 2005). Current knowledge of synaptic probability relies on empirical evidence, which is limited by the number of simultaneously recorded neurons (e.g., by pair recording, octopatch, multielectrode array) and affected by experimental conditions (in vitro vs. in vivo, slice orientation and thickness, distance between cells, etc.). Connections in a particular brain region are often probed by evoked responses upon stimulation of the afferent fiber tracts; however, such tests do not allow the identification of the specific neuronal types involved (Moradi and Ascoli, 2020). Alternatively, synaptic connectivity can be calculated computationally by embedding three-dimensionally (3D) reconstructed neuronal morphologies into 3D brain atlases and counting the possible locations of axonal-dendritic overlap (Ropireddy and Ascoli, 2011). Nevertheless, this approach requires a large amount of labor-intensive data, is limited by the precision of the 3D registration, and has so far proven impractical to scale up.

Despite its importance, connectivity information remains incomplete for most animal species and neural systems (Rees et al., 2017). This protocol describes a simple process for the extraction of important quantitative synaptic parameters – namely the connection probability, number of contacts per connected pair, and distance from the pre- and postsynaptic somas along the neurite paths – from commonly available two-dimensional images of axonal and dendritic morphology. To the best of our knowledge, there are no alternative solutions available to obtain the same results. Initially, this approach was used to estimate hippocampal connectivity and demonstrated high correlation of the resulting estimates with sparsely available data (Tecuatl et al., 2021).

The overall workflow of the presented pipeline consists of seven main logical components: (i) quantitation of parcel-specific axonal and dendritic lengths; (ii) determination of parcel-specific axonal and dendritic path distances; (iii) measurement of parcel-specific axonal and dendritic convex hull volume; (iv) calculation of the average number of synapses per neuronal pair in each parcel; (v) calculation of the number of contacts per connected pair; (vi) calculation of the connection probability per neuronal pair; and (vii) calculation of the confidence intervals on these values by propagation of error analysis. All steps can be carried out on a basic desktop or laptop computer using readily available software (Figure 1).

Figure 1. Flow chart of the described pipeline. The procedure starts from 2D neuronal images that are processed to quantitate axonal and dendritic lengths, path distances from the soma by parcel, and convex hull volumes. From these quantitations, we calculate the number of synapses and contacts per neuronal pair and subsequently estimate the probabilities of connection from multiple neuronal pairs. The generated information is analyzed and presented as the mean and standard deviation.