Humans’ robust cognitive and linguistic functions emerge from intricate connections among numerous neurons in the neocortex. To implement machine learning model performing such a highly cognitive tasks, clarifying theoretically mechanism for generating such a network connection is an important challenge. To address this challenge, we propose an autonomous neuron connection model inspiring biological neuronal growth mechanisms [1]. This work focuses on axon elongation and creation of the synaptic connections between source and target neurons. We believe that this approach will improve our understanding of neural connectivity and it creates the brain’s initial state for life-long learning [2].
Methods An implemented model has two types of axon guidance factor sources, the attractant and repellant ones, in a 2D space. The model is based on the self-propelled particles (SPPs) [3] and the XY model [4]. The growth direction is along the gradient of extracellular guidance factors and it subjects to the noise. A tip of the axon is regarded as an SPP and it observes only local information such as the concentration itself and its gradient around them. This process includes axon branching. The axon branching occurs with probability and it creates another SPP. They move along the gradient field avoiding each other to prevent the axon overlapping. They finally reach the dendrites of the target cells and create the synapse. Results Figure 1 exhibits snapshots of the simulation result. The black, green, and red circles are source neurons, target neurons and repulsion sources, respectively. The axon branch of each source neuron succeeds in finding the dendrites of the target neurons under the environment. The simulations are performed by using Python (Fig. 1) and our original brain simulation framework, Bramuwork (P48 in [5]), and obtain similar results. Bramuwork organizes graphs in a database. The node stores attributes and methods (programs) that define its dynamics. The edge connects nodes, arranging the network connectivity and supporting the hierarchical structure. Nodes and edges are used for modeling somas, dendrites, axons, and repellent factor sources. Discussion We note that the SPPs in the model can only observe local information, such as the density and its gradient of the chemical substances, and do not use global information. Up to now, the gradient field induced by the chemical substances does not depend on time. But the diffusion or transfer occurs during the process; it may impact the created neuronal network. We have to include these phenomena without violating causality. The proposed 2D model could be generalized to a 3D one by replacing the XY spin interaction with the spherical ones.
Bramuwork enables us to modify and examine models during running time. Neurons and connections can be created and deleted during simulation, and users can search and extract subsets of data for analysis.
Figure 1. Axons elongation under axon guidance environment Acknowledgements
