So just to unpack this a little - there's a lot of different mechanisms going on in neural computation.
For instance one of those is spike-timing dependent plasticity. Basically the idea is that the sensitivity of a synapse gets up-regulated or down-regulated depending on the relative timing of the firing of the two neurons involved. So in the classic example, if the up-stream neuron fires before the down-stream neuron, the synapse gets stronger. But if the down-stream neuron fires first, the synapse gets weaker.
Another one is synchronization. It appears that the firing frequency of groups of neurons which are - for instance representing the same feature - become temporally synchronized. I.e. you could have different neural circuits active at the same time in the brain, but oscillating at different frequencies.
Another interesting mechanism is how dopamine works in the Nucleus Accumbens. Here you have two different types of receptors at the same synapses: one of them is inhibitory, and is sensitive at low concentrations of dopamine. The other is excitatory, and is sensitive at high concentrations. What this means is, at a single synapse, the same up-stream neuron can either increase or decrease the activation of the down-stream neuron: if the up stream neuron is firing just a little, the inhibitory receptors dominate. But if it's firing a lot, the excitatory receptors take over, and the down-stream neuron starts to activate more. Which kind of connection weight in an ANN can model that kind of connection?
My overall question would be, do you think back-propogation and markov chains are really sufficient to account for all that subtlety we have in neural computation, especially when it comes to specific timing and frequency-dependent effects?
If Markov processes won’t cut it, a Turing machine will. And an ANN can approximate a Turing machine.
To boil it down, if you really want to argue that the behaviour of a neuron can’t be simulated by an ANN, you’re arguing that a neuron is doing something non-computable. At which point you might as well argue it’s magical.
You only need to accurately simulate the input and the output.
Frankly, if that can’t be done with a Markov process I’d be very surprised, and we already know that Markov chains can be simulated with ANNs