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Using theoretical models to analyse neural development

A Corrigendum to this article was published on 06 July 2011

This article has been updated

Key Points

  • Understanding such a complex process as the development of the nervous system requires the help of mathematical and computational models.

  • In addition to providing quantitative results, theoretical models enable us to work out the potential consequences of the multitude of interactions that exist at the molecular, cellular and network levels, and by which the nervous system constructs itself.

  • This Review gives a broad overview of contemporary models for the various stages of neural development. The models are chosen to illustrate and contrast the different approaches taken in modelling development, to indicate the insights and predictions that can be derived from these model studies, and to highlight the opportunities for future modelling

  • Computational models have been used to study neural tube formation, regionalization of the neural tube, cell proliferation, migration and differentiation, axon–dendrite differentiation, neurite elongation and branching, axon guidance, structural plasticity in network formation, synaptic competition, development of ocular dominance and orientation columns, and formation of topographic maps.

  • As well as areas in which modelling has traditionally been most fruitful, this Review also outlines new areas in which modelling is making valuable contributions and considers challenges for future modelling studies.

Abstract

The development of the nervous system is an extremely complex and dynamic process. Through the continuous interplay of genetic information and changing intra- and extracellular environments, the nervous system constructs itself from precursor cells that divide and form neurons, which migrate, differentiate and establish synaptic connections. Our understanding of neural development can be greatly assisted by mathematical and computational modelling, because it allows us to bridge the gap between system-level dynamics and the lower level cellular and molecular processes. This Review shows the potential of theoretical models to examine many aspects of neural development.

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Figure 1: Modelling neural tube formation.
Figure 2: Modelling the dorsoventral regionalization of the neural tube.
Figure 3: Modelling cell proliferation, migration and differentiation.
Figure 4: Modelling axon–dendrite differentiation and axon guidance.
Figure 5: Modelling neurite elongation and branching.
Figure 6: Models that investigate the implications of homeostatic structural plasticity for network formation.
Figure 7: Modelling synaptic competition and topographic map formation.

Change history

  • 06 July 2011

    The acknowledgment section has been added on both the html and pdf versions.

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Acknowledgements

The work was supported by the Self-Constructing Computing Systems project (216593) of the Seventh Framework Programme of the European Union, and the NETFORM project (635.100.017) of the Computational Life Sciences programme of the Netherlands Organization for Scientific Research.

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Glossary

Morphogens

Secreted factors that can induce different cell fates across a sheet of cells in a concentration-dependent manner by forming gradients.

Lamellipodia

Sheet-like extensions at the edge of a cell that contain a crosslinked F-actin meshwork and are often associated with cell migration.

Convergent extension

The process by which the tissue of an embryo is restructured so that it narrows along one axis and elongates along a perpendicular axis by cellular movement.

Delta–Notch signalling

Signalling pathway involved in cell–cell communication and cell differentiation. Because both the ligand Delta and the receptor Notch are membrane-bound proteins, cells must be adjacent for signalling to occur.

Centrifugal order

The distance of an axonal or dendritic segment from the soma, in terms of the number of branch points between the segment and the soma.

Compartmental-based models

A modelling approach in which a spatially continuous structure, such as a neurite, is divided into a large number of small compartments. Each compartment is assumed to be a homogeneous entity, and neighbouring compartments interact chemically or electrically.

Diffusion-limited aggregation

The process whereby particles undergoing random movements cluster together to form aggregates.

Chemotaxis

The phenomenon in which cells or bacteria direct their movement according to gradients of chemicals in their environment.

Bayesian ideal observer

A theoretical observer that uses the concepts of Bayesian statistical decision theory to determine optimal performance in a task, given the available stimulus information.

RHO GTPase system

The group of molecules related to the product of the oncogene RAS, which are involved in controlling the polymerization and subsequent organization of actin.

Critical connectivity

A pattern of connectivity between neurons in which each electrically active neuron causes an average of one other neuron to become active, so that network activity neither dies out nor increases.

Motor unit size

The number of muscle fibres that is contacted by a given motor neuron.

Polyneuronal innervation

In mononeuronal innervation, a target cell is innevervated by just a single neuron; in polyneuronal innervation, by more than one neuron.

Hebbian learning

Synaptic connections between a presynaptic neuron and a postsynaptic neuron are strengthened when their activity is correlated (cells that fire together wire together).

Spike timing-dependent plasticity

Changes in the strength of synapses that depend on the relative timing of the presynaptic and postsynaptic action potentials.

Competitive learning

A learning rule whereby changes in synaptic strength take place only for synapses that impinge on the output cells that respond most strongly to an input.

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van Ooyen, A. Using theoretical models to analyse neural development. Nat Rev Neurosci 12, 311–326 (2011). https://doi.org/10.1038/nrn3031

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