Are there models of single neurons on slow timescales? 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.
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.