Computational modeling of growth in cortial cultures using the NETMORPH simulation tool

Spontaneously developing cortical cultures represent a convenient experimental model system to study the growth and maturation of neurons and neuronal networks. Different microscopical techniques in combination with cell staining provide a possibility to monitor the morphological changes of neurons as well as synaptogenesis. We study the growth in cortical cultures through mathematical models and numerical simulations, using a recently published simulator NETMORPH (Koene et al. 2009). The construction of the simulator is based on the extensive studies of neuron growth in vitro and the statistical description of relevant phenomena, such as neurite elongation rate, elongation direction, and neurite branching (van Pelt & Uylings 2005). The precise dynamics of biophysical processes involved in growth is not included, but only the statistical description of morphology. The obtained model thus has moderate complexity, with relatively low number of model parameters. Single neuron descriptions are incorporated into the computational model of neuronal cultures, consisting of around 10000 neurons, in (Koene et al. 2009). In our study we focus on the first two weeks in vitro. At the beginning of simulations neurons are disconnected, and the first synapses are formed until the end of first week in vitro. The number of synapses per cell progressively increases until the end of second week in vitro. The range of relevant model parameters is first constrained in accordance with the experimental evidences. This parameter space is systematically sampled and the statistics describing the networks of neurons at the end of the first and second week in vitro is obtained through simulations. The relevant network parameters are adopted from graph theory. Each neuron soma represents a node in the graph, and a synapse formed between a dendrite of one and the axon of another neuron represents an edge in the graph. The number of synapses between two neurons can be described as a weight of the corresponding edge. The graph measures, including in- and out-degree distributions and statistics of motifs (Milo et al. 2002), are then extracted. Our preliminary study demonstrates how precisely these parameters describe the network structure during growth. Here, we are further analyzing how the single cell growth parameters, for example the probability of branching, reflect on the network structure. Finally, the obtained results are compared to the experimental evidence describing the distribution of potential synapses developed in cortical cultures (Ichikawa et al. 1993).