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Structural Plasticity

Structural plasticity in a neural network refers to the physical creation and deletion of synapses. This effect is present during brain development [3], learning and healing after lesions.

A model of structural plasticity has been proposed in [1]. In this model, neurons have contact points called synaptic elements which can be used to represent axonal boutons and dendritic spines. These elements grow and recede following homeostatic rules based on the mean electrical activity of the neuron.

Intracellular calcium concentration [Ca2+] is used to indirectly measure the mean electrical activity of the neuron, since it increases when neurons spike, and otherwise decreases over time.

When synaptic elements are available, they can create new synapses with other compatible elements. If they recede, the corresponding synapse is destroyed. Global connectivity is updated in the network on a much slower timescale than changes in electrical activity.

The algorithm consists of three repeating parts:

  1. Calcium concentration in neurons are updated based on
    electrical activity
  2. The number of synaptic elements is updated
  3. Network connectivity is updated

Using this algorithm, the network is constantly rewired until an stable configuration of connections leads to the desired average electrical activity. Using simple homeostatic rules, this algorithm can also be used to fill gaps of information in networks where detailed connectivity is absent, incomplete or has been removed to simulate lesions.

Fig. 1 shows the evolution of the average calcium concentration (solid curves) in a two populations network as the connectivity (dotted curves) in the network varies through time in order to achieve a target electrical activity (solid semi-transparent horizontal lines).

Structural Plasticity ExampleFig.1: Changes in calcium concentration related to the number of synapses created between two populations, one excitatory and one inhibitory.

Our contribution

  • We have implemented the model of structural plasticity described in [1] as part of the neural network simulator NEST as detailed in [5]. This framework is included in release version 2.10.0 [4].
  • We have measured the scalability of the framework. As an example, Fig. 2 shows execution times of a strong scaling test of a network with 100,000 neurons performed on different number of computation nodes. Following the NEST philosophy, simulations using structural plasticity can be performed at small scale in personal computers and at large scale on super computers.

    Structural Plasticity Strong ScalingFig. 2: Execution times for a network with 100,000 neurons which was simulated on 1 – 16 nodes in the JuRoPA supercomputer from JSC.

  • We maintain and give support to users of this framework.
  • We use the model to study the automatic creation of connectivity of large scale neural networks. We also use it to study the relationships between structural and functional connectivity in the Virtual Connectome (link) project.

Future work

In order to enable the simulation of large scale networks with more complex patterns and restrictions, new connectivity and growth rules should be designed and implemented.

Work is being done to combine and test the structural plasticity framework with other features of NEST like synaptic plasticity and topology.

References and related reading

[1] Butz, M., & van Ooyen, A. (2013). A simple rule for dendritic spine and axonal bouton formation can account for cortical reorganization after focal retinal lesions. PLoS Comput. Biol. 9 (10), e1003259.

[2] Butz, M., Steenbuck, I. D., & van Ooyen, A. (2014). Homeostatic structural plasticity increases the eefficiency of small-world networks. Front Synaptic Neurosci 6, 7.

[3] Hensch, T. K. (2005). Critical period plasticity in local cortical circuits. Nat. Rev. Neurosci. 6 (11), 877888.

[4] Bos, H., Morrison, A., Peyser, A., Hahne, J., Helias, M., Kunkel, S., Ippen, T., et al. 2015. NEST 2.10.0. Zenodo. doi:10.5281/zenodo.44222.

[5] Diaz Pier S, Naveau M, Butz-Ostendorf M, Morrison A. Automatic generation of connectivity for large-scale neuronal network models through structural plasticity. Frontiers in Neuroanatomy. 2016;10:57.