3.2.3 Modelling neurons and circuits

3.2.3 Modelling neurons and circuits

Modelling Single Neurons and their Combination in Circuits

Computational modelling is important to understand how the complex membrane properties and dendritic structures of a neuron process how the input signal generates the output signal.

In a ‘compartment model’, the synapse has been conceptualised as a single compartment, with synapse strength represented by a simple multiplicative factor, a type of gain control that linearly scales incoming information. Synaptic plasticity allows for dynamic gain control, which is regulated by Hebbian activity (Tong, 2020).

The Hodgkin-Huxley model introduced two new channels; sodium channels and rectifier-delayed potassium channel whose conductance changes depends on membrane potential, and they are described by three sets of non-linear equations (Hodgkin, 1952). Our present-day understanding of neural excitability modelling is based on the work of Hodgkin and Huxley in 1952. Many active channels were discovered with various characteristics and those are modelled successfully within a similar framework.

The membrane potential varies within the neuron itself. For the membrane potential, the neuron act as an electrical cable and signal propagation can occur along with the axonal process. The cable equation determined as a discrete version would result in compartments with different properties, however, the ion channels’ maximum conductance will cause changes in the channel densities. Branching the dendrites with the cable equations can be modelled by considering the cable junction with electrical properties and the nuclear charge radii. These single-neuron computational models are widely used to get an insight into a topic that is not possible with experimental observations (Yoo, 2019)

Computational neuroscience:

Modelling single neurons and their combination in circuits is a fundamental aspect of computational neuroscience, which aims to understand the workings of the brain and nervous system through mathematical and computational methods.

Single Neuron Modeling:

  • Single-neuron modelling involves creating mathematical models that capture the electrical and biochemical behaviour of individual neurons.
  • These models can take into account various aspects of neuronal behaviour, including the resting potential, action potentials, ion fluxes, and ion channels.
  • The models can be used to study the behaviour of individual neurons in response to different stimuli, such as incoming electrical signals, and to predict the behaviour of neurons under different conditions.

Neural Circuits Modeling:

  • Neural circuit modelling involves combining single neuron models to form more complex models of networks of neurons.
  • These models can help to understand how groups of neurons interact and communicate with one another to perform specific functions.
  • Neural circuit models can be used to study the behaviour of the nervous system in response to different stimuli and to predict the behaviour of the nervous system under different conditions.

In conclusion, modelling single neurons and their combination in circuits is an important aspect of computational neuroscience that helps us to understand the behaviour of the nervous system at different levels of complexity. Single-neuron models provide insight into the behaviour of individual neurons, while neural circuit models provide insight into how groups of neurons interact and communicate to perform specific functions.

References:

(1) Hodgkin, A.L. and Huxley, A.F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, [online] 117(4), pp.500–544. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1392413/.

(2) Tong, R., Emptage, N.J. and Padamsey, Z. (2020). A two-compartment model of synaptic computation and plasticity. Molecular Brain, 13(1). doi:10.1186/s13041-020-00617-1.

(3) Yoo, Y. and Gabbiani, F. (2019) “Single Neuron Computational Modeling,” Oxford Research Encyclopedia of Neuroscience. London, England: Oxford University Press.