Simulation of Brain Development

Development of the brain is controlled by the genotype in a highly indirect manner. By indirect we mean that no part of the genotype corresponds to individual neurons and synapses, and that only gross statistical and topographical properties of the brain are encoded in the genes. Individual brains are sampled from this statistical description. The neurogenesis phase goes on as follows. Neurons are situated in a layered topographic neural space mimicking real cortical layers but low-level biological mechanisms shaping the cortex such as concentration gradient dependence in neurogenesis are not present in the simulation. Instead, neuron classes define a probability density function over the neural space from which individual neuron soma positions are sampled. Neurons possess morphologies, i.e. there is some function over neural space describing their dendritic arborisation. This morphology is applied to each neuron relative to its sampled soma position. Synaptogenesis exploits two mechanisms, just as in biology: a long-range one (called projections) and a subsequent short-range one (lock-and-key mechanism). Each neuron class has an associated list of projections. Projections are probability density functions over neural space, used in the following way. They can be defined either in absolute coordinates or in coordinates relative to a neuron's soma. When a neuron's efferents are to be determined, putative synapse locations are sampled from its projections (determined by its neuron class). Neurons having dendritic arborisation near these putative locations become candidate efferents. Then the short-range mechanism selects from competing candidates at each synapse location. The short-range lock-and-key mechanisms mimic the receptor/ligand-based binding mechanisms present in

Fig. 4 Neurogenesis and long-range mechanism of synaptogenesis. (a) Probability distribution of positions. (b) Sampled soma positions. (c) Morphology added to soma. (d) Projection (onto layer 2) from a presynaptic cell, marked with white. (e) Putative synapse location (X mark) is sampled from projection. (f) Candidate postsynaptic cells are determined (Szathmary et al., 2007)

Fig. 4 Neurogenesis and long-range mechanism of synaptogenesis. (a) Probability distribution of positions. (b) Sampled soma positions. (c) Morphology added to soma. (d) Projection (onto layer 2) from a presynaptic cell, marked with white. (e) Putative synapse location (X mark) is sampled from projection. (f) Candidate postsynaptic cells are determined (Szathmary et al., 2007)

real synaptogenesis. Locks and keys are strings of 30bits. Every candidate postsynaptic neuron's lock is matched to the presynaptic neuron's key. Binding probability is then a decreasing function of the Hamming distance between the key and the lock. The complete ontogenetic algorithm is depicted in Fig. 4.

Unlike the majority of approaches to evolve neural networks we maintain the full topographic information of our networks, i.e. neurons are situated in a layered neural space. Topographical information in a neural network can have a number of advantages. First, the interpretation of the structure can be easier. Second, developmental processes can model biological processes of neuron and synapse growth more accurately. Models, which acknowledge spatial information in biological systems yield various scale-free and small-world network attributes like the ones that are common in brain structure (Sporns et al., 2004).

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