# NETMORPH

 Arjen van Ooyen and Jaap van Pelt (2015), Scholarpedia, 10(6):10213. doi:10.4249/scholarpedia.10213 revision #151967 [link to/cite this article]
Post-publication activity

Curator: Arjen van Ooyen

NETMORPH is a simulation tool for generating large-scale neuronal networks with realistic neuron morphologies.

## Introduction

The functioning of neurons and neuronal networks strongly depends on the organization of synaptic connectivity. At the network level, the connectivity structure determines how information is transmitted and what spatiotemporal patterns of activity can arise (Gaiteri and Rubin, 2011; Neymotin et al., 2011). At the neuron level, the dendritic distribution of afferent connections critically influences input integration and signal processing (Magee, 2000; Tigerholm, 2012).

During development, neurons establish synaptic connections when their axons and dendrites come into close proximity of each other (Peters, 1979). Many extracellular guidance cues, such as cell adhesion molecules and diffusible chemoattractants, are thought to be involved in steering axons prior to synapse formation (Tessier-Lavigne, 1994; Benson et al., 2001; Da Silva and Wang, 2011). In addition, the geometry of axonal and dendritic arborizations by itself shapes synaptic connectivity (Stepanyants and Chklovskii, 2005). Synapse formation requires close spatial apposition of axonal and dendritic branches, and the locations where this occurs depend on axonal and dendritic morphology. Whether the formation of synaptic connectivity in local brain circuits requires that outgrowing axons and dendrites are guided by extracellular cues, or whether accidental appositions between freely outgrowing axons and dendrites can already account for baseline synaptic connectivity, remains an issue of debate (Stepanyants et al., 2004; Hill et al., 2012; Van Ooyen et al., 2014).

NETMORPH is a simulation tool for generating neuronal networks with realistic neuron morphologies (Koene et al., 2009) in which the growth of axons and dendrites (collectively called neurites) is not guided by extracellular cues. Stochastic rules for neurite elongation and branching are used to grow neuron morphologies, and synapses are formed when axonal and dendritic branches come by chance within a threshold distance of each other. Below, a more detailed description of NETMORPH is given, including the models of neurite outgrowth and synapse formation implemented in NETMORPH, the use of the NETMORPH simulator and where it can be downloaded from, as well as a brief review of studies that have applied NETMORPH. For more information about NETMORPH, see Koene et al. (2009), Van Ooyen et al. (2014) and the NETMORPH manual (see Download). For overviews of other simulation tools for modeling neurite outgrowth, see Koene et al. (2009), Aćimović et al. (2011) and Van Pelt et al. (2014b).

## Overview

NETMORPH is a modular simulation tool for building synaptically connected networks with realistic neuron morphologies (Koene et al., 2009). Axonal and dendritic morphologies are created by using stochastic rules for the behavior of individual growth cones, the structures at the tip of outgrowing neurites that mediate neurite elongation and branching. Neurons are positioned in 3D space, grow out independently of each other, and are not guided by any extracellular cues. Synapses between neurons are formed when crossing axonal and dendritic segments come sufficiently close to each other. The neurite outgrowth model implemented in NETMORPH is based on the stochastic rules for neurite branching and elongation that have been formulated by Van Pelt et al. (Van Pelt and Uylings 2003, 2005; Van Ooyen, 2011) and that have been shown to generate realistic neuronal morphologies (Van Pelt et al., 2001a, b). The neurite outgrowth model is a phenomenological model (Van Ooyen, 2011) in which each growth cone has at each time step a probability to elongate the trailing neurite, to branch and produce two daughter growth cones, and to turn and change the direction of neurite outgrowth. The parameter values of the model can be optimized so as to obtain an optimal match with the morphology of specific neuron types.

## Neurite branching

Each terminal segment $$j$$ in an axonal or dendritic tree (see Figure 1 for terminology) branches in a discrete time step $$(t_i - \Delta t, t_i)$$ with probability $$p_{i,j} = n_i^{-E} B_{\infty} e^{-t_i/\tau} (e^{\Delta t/\tau} - 1) 2^{-S\gamma_j} / C_{n_i}$$ (for the derivation of this equation, see Koene et al., 2009). The term $$n_i^{-E}$$ makes the branching probability dependent on the momentary number $$n_i$$ of terminal segments in the tree, with parameter $$E$$ (called competition parameter) modulating the strength of this dependency. The term $$2^{-S\gamma_j}$$ makes the branching probability dependent on the centrifugal order $$\gamma$$ of the terminal segment, with parameter $$S$$ modulating the strength of this dependency. The coefficient $$C_{n_i} = 1/n_i \sum_{j=1}^{n_i} 2^{-S\gamma_j}$$ normalizes at each time point the order dependency of all tips. The term $$B_{\infty} e^{-t_i/\tau} (e^{\Delta t/\tau} - 1)$$ is the time-dependent baseline branching rate, representing all factors that influence branching but that are not covered by the dependence on the total number of terminal segments in the tree, where $$\tau$$ is a time constant and $$B_{\infty}$$ is the asymptotic expected number of branching events at a tip for $$E=0$$. The 3D outgrowth directions of the daughter branches after a branching event are determined as described in Koene et al. (2009). The values of the parameters $$B_{\infty}$$, $$\tau$$, $$S$$ and $$E$$ can be chosen so as to obtain an optimal match with the morphology of specific neuron types. The parameter optimization can be done separately for axons and dendrites, and even for different subparts of an axonal or dendritic tree (apical dendrites, basal dendrites).

Figure 1: Schematic axonal or dendritic tree illustrating tree terminology. The different kinds of segments and nodes, and the labeling of segments based on centrifugal order. The centrifugal order of a segment is the number of branch points along the path from the root to the terminal tip of the segment. Terminal tip is equivalent to growth cone. From Van Ooyen et al. (2014).

## Neurite elongation

The new daughter growth cones that are produced by a branching event are assigned individual growth rates, which they maintain until they themselves experience a branching event. The elongation rates are obtained by random sampling from a Gaussian distribution, with mean and standard deviation eri-mn and eri-sd, respectively (NETMORPH parameters; eri stands for elongation rate initialization). During elongation, neurites can also change their direction (neurite turning), as described in Koene et al. (2009). Like the branching parameters, the elongation parameters eri-mn and eri-sd can be optimized so as to obtain an optimal match with the morphology of specific neuron types.

## Synapse formation

Synapse locations are defined as those places in the 3D meshwork of axonal and dendritic arborizations at which axons and dendrites come within a threshold distance of each other. Because the model-generated neurons are represented by piecewise-linear elements (lines or cylinders, with a length of a few microns, as determined by the parameters for neurite turning; Koene et al., 2009), the proximity test needs to be performed on all pairs of axonal and dendritic line pieces. To be regarded as a synapse location, NETMORPH requires that the axonal and dendritic line pieces cross and that the orthogonal distance between them (taken from the centre lines of the axonal and dendritic cylinders) is smaller than a given threshold value (e.g., 4 μm; Figure 2). NETMORPH searches for synapse locations at the end of the growth process, when all neurons are completely formed. Alternatively, the search can be performed during outgrowth, but this yields exactly the same results because there are no interactions between cells. At each synapse location found, a single synapse between axon and dendrite is established. The algorithm for finding synapses was developed in Van Pelt et al. (2010).

Figure 2: Synapse formation in NETMORPH. An axonal (A) and a dendritic (D) branch and their projections on a plane V. The shortest distance between the axonal and the dendritic branch is defined as the orthogonal distance between a pair of crossing axonal and dendritic line pieces. If this distance is smaller than a given threshold value, the orthogonal line (purple) marks the location of a synapse. From Van Ooyen et al. (2014).

## Use of the simulator

NETMORPH is written in C++ and tailored to a Unix operating environment. Windows users can provide such an environment within Windows through Cygwin. After compilation of NETMORPH, one can grow single-neuron morphologies (Figure 3) or networks of neurons (Figure 4) with realistic morphologies. A simulation run of NETMORPH is based on a script, which is a text file containing parameter identifiers with associated values specifying such parameters as the duration of the simulation, the discrete time step, the branching and elongation rates, and the threshold distance for synapse formation. The structure of the scripts and the parameters are fully explained in the NETMORPH manual. The output of NETMORPH consists of a number of files specifying the generated neuron morphologies and synaptic connectivity. The generated neurons and network can be visualized by a basic visualization tool incorporated in NETMORPH or by a separate java program called NEURON3D.

Figure 3: Examples of NETMORPH-generated neurons. Axons are shown in green, and dendrites are depicted in red. The neurons were grown with outgrowth parameters optimized on a dataset of experimentally reconstructed L2/3 pyramidal cells from NeuroMorpho.org. From Van Ooyen et al. (2014).

NETMORPH (version 2011-06-24) and its manual (updated 2014-04-03), as well as NEURON3D, can be freely downloaded from ModelDB (accession number 182135). The manual describes how NETMORPH can be installed, provides a number of example scripts, and specifies all the parameters that control a NETMORPH simulation.

Figure 4: NETMORPH-generated network showing the spatial distribution of synapses. Cell bodies are shown as white spheres, and synapses as small blue spheres. Axons are depicted in green, and dendrites in red. The network is drawn in perspective, so cell bodies and synapses in the background are smaller than those in the foreground. From Van Pelt et al. (2010).

## Applications

The potential applications of NETMORPH include exploring to what extent typical connectivity patterns can arise from neuronal morphology alone (Van Ooyen et al., 2014); creating detailed connectivity patterns with synapses at specific axodendritic locations; examining how aberrant synaptic connectivity in brain diseases such as Alzheimer’s disease and autism (Uddin, 2015) may result from changes in neuronal morphology; investigating the complex relationship between neuronal morphology and local and global connectivity; and providing a first approximation of synaptic connectivity for cortical microcircuits in large-scale brain models (Tiesinga et al., 2015). The synaptic connectivity and neuronal morphologies produced by NETMORPH can be made available to tools such as NEURON (Hines and Carnevale, 1997) to simulate activity dynamics.

## Studies that used NETMORPH

Van Ooyen et al. (2014) showed that in a NETMORPH-generated network of L2/3 pyramidal neurons, the emerging synaptic connectivity, despite the absence of extracellular guidance cues, showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free.

NETMORPH was used by Van Pelt and Van Ooyen (2013) and McAssey et al. (2014) to validate methods for estimating neuronal connectivity from axonal and dendritic density fields (the spatial distribution of a neuron’s axonal and dendritic mass, obtained by averaging over many individual axonal and dendritic arborizations) and by Van Pelt et al. (2014a) to show how axonal and dendritic density fields can be obtained from incomplete single-slice neuronal reconstructions.

Aćimović et al. (2011) simulated the development of neocortical cultures using NETMORPH and characterized the changes in network connectivity during growth. Mäki-Marttunen et al. (2011, 2013) studied the relationships between connectivity structure and activity dynamics in NETMORPH-generated networks.

Laakso (2010) and Krieger and Laakso (2010) used the NETMORPH simulator to generate realistic morphologies of pyramidal neuron populations from mouse neocortex.

## Acknowledgements

The text of this article is partly based on Van Ooyen et al. (2014). NETMORPH was developed in the Neuroinformatics Group at the Department of Integrative Neurophysiology, VU University Amsterdam, The Netherlands, by Randal Koene, Jaap van Pelt and Arjen van Ooyen, with assistance from Betty Tijms, Peter van Hees, Frank Postma, Sander de Ridder, Sacha Hoedemaker, Andrew Carnell and Pieter Laurens Baljon. The work was supported by grants from the Netherlands Organization for Scientific Research (CASPAN: 635.100.005) and the European Union (NEURoVERS-it: 019247; SECO: 216593) awarded to Jaap van Pelt and Arjen van Ooyen.

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