Abstract
BackgroundThe morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other.MethodsA variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described.ResultsSome comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development.ConclusionA unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.
Highlights
The morphological development of neurons is a very complex process involving both genetic and environmental components
In conclusion we suggest the features of a computer simulation package that could ease the pain of creating new models of neuronal development and eventually allow the exploration of whole neuron development
Modelling results and experimental data All of the models described here are aimed at understanding the biophysics of various processes underlying the morphological development of a neuron
Summary
The morphological development of neurons is a very complex process involving both genetic and environmental components. Neurites, that are fundamental to the formation of the connected networks of neurons that constitute a nervous system. A typical axon has a main trunk from which shorter side branches, or collaterals, emerge to form points of contact with appropriate target neurons. The remaining neurites of a neuron are dendrites, which form complex tree-like structures and are the recipients of most synaptic contacts from the axons of other neurons. Different types of neuron can be distinguished by the structure of their dendrites, which can be characterized in terms of segment lengths and diameters, the number of terminals (unbranched tips), the number of branch points, and topological factors such as symmetry [1,2,3]
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