There is a posting in MIT Technology Review (here) about an electronic device called a memristor. It acts like a resister with a memory and was first produced about a year ago.
…it turns out that the synapses between neurons behave exactly like memristors. That raises the possibility that memristors can be connected together in a way that truly mimics the wiring of human brains.
One of the defining features of the connections between neurons is that they become stronger when neurons fire together; hence the phrase “neurons that fire together, wire together”, a phenomenon otherwise known as Hebbian learning. Various experiments have shown that this effect is most pronounced early in the learning process, when the increase in connection strength is greatest. Later learning merely reinforces the links
(there have been problems with memristor curcuits) Merrikh-Bayat and Bagheri have a simple solution: use two memristors in series. Choosing their memristance carefully allows them to reproduce Hebbian-type synapse strengthening more or less exactly.
That may turn out to be a useful insight. The first neuromorphic chips to use memristance to mimic synapse behaviour are already being built. A small change in their design may make a significant difference.
This is gives an approximation of a neuron for research but still is a long way from actual neurons. I think an electronic neuron may have to react to electrical and magnetic fields and also to many chemical gradients (or have a way to simultate these) before it can mimic a real neuron’s actual behaviour.