Look into computational neuroscience, neural engineering, spiking neurons and spike-timing dependent plasticity (STDP). These are more accurate models of biological neurons and their synaptic interactions.

From the Hodgkin-Huxley (HH) neuron model to integrate and fire (I&F) you can approximate and simulate various levels of realism in artificial neural networks. There's even the Nengo library[0] which can simulate these for you in Python. Unfortunately, they're very hard to work with compared to perceptrons, artificial neural networks, and deep learning (see Neural Engineering[1] for a good framework). Additionally, they're far more computationally intensive with the HH model coming in at over 800 FLOPS to the I&F model (which lacks a lot of the behavior and dynamics of biological neurons) which has 7 FLOPS. Then try representing numbers with spiking neurons... You need several dozen, working as a population[2], to accurately represent a single floating point because they're so noisy. This makes working with data pretty difficult and expensive.

[0] https://github.com/nengo/nengo

[1] http://compneuro.uwaterloo.ca/research/nef.html

[2] https://en.wikipedia.org/wiki/Neural_coding