Are there models of single neurons on slow timescales?

Question

From what I've come across on the web, most models of single neurons seem to focus on the "fast timescale", where electrical signals are transmitted from one neuron to another. However, neurons are also cells, with all the associated complexity that cells bring: from gene expression to biochemical reactions happening in response to these electrical signals, albeit on a slower timescale. Are there any single neuron models that attempt to integrate these various timescales?

I'm mainly interested in knowing about more realistic abstractions of neurons than those used in Artificial Neural Networks (ANNs) and so on. A key assumption I'm making is that neurons, being a type of cell, would have biochemical processes going on on a slower timescale that would modulate their 'spiking' behavior over time. Please correct me if this assumption is wrong.

Answer 1

The search for a biologically realistic neural network is never ending. As Sydney mentioned there are many newer models of neurons that take into account activity over larger time-scales, such as the Adaptive Leaky-Intergrate-Fire neuron. The bleeding edge of this search is the Blue Brain Project, which is trying to create the most biologically detailed model of the brain possible. The project should be a good resource if you're interested in the more advanced models.

Since you're interested in Artificial Neural Networks (which implies you're also interested in computation power), I would like to point out that the Neural Engineering Framework allows you to use as detailed of a model of neuron as desired on a realistic time-scale, while still allowing you to compute and learn arbitrary functions as a typical ANN allows.

Answer 2

Given that neurons operate by means of signal transmission and not on distinctive 'slow' or 'fast' timescales, I'm assuming that you are looking for abstract models of neurons that are more 'realistic' than the time-independent artificial representations most often used in neural networks, but correct me if I'm wrong.

There are neuron models that attempt to mimic the biological processes of the neuron, and there are also abstract models of neurons that attempt to work in imperfect or specific conditions (i.e. in response to individual neurotransmitters, as demonstrated during synaptic transmission). These models usually take into account the action potentials (spikes) and refractory periods of real neurons, and thus these models are also known as 'spiking neuron models'.

Here is one model of a spiking neuron, which attempts to imitate authentic spiking as observed in cortical neurons. This model incorporates Hodgkin-Huxley-type-dynamics with integrate-and-fire-type properties. Integrate-and-fire is another popular model of neuron (probably the earliest model -- it was invented back in the early 1900s). It is represented as 'the membrane potential of a neuron in terms of the synaptic inputs and the injected current that it receives' (read more here).

By extension, you might find spiking neural networks interesting. Unlike artificial neural networks, SNNs incorporate time, and neuronal and synaptic states into their model, thus increasing biological accuracy. You might also be interested in this paper, which focuses exclusively on computing with spiking neural networks.