I think it depends heavily on 'how' the synthetic neuron is replacing an existing one. If it's just dropped in there it seems like the that neuron and whatever memory or process it was part of is gone and there's just a new 'opportunity' for a connection to be made, but overall each percent of replacement is that percent 'not you' and is just a new 'thing'.

If, on the other hand, the artificial neuron is installed with the same sensitivity and precise reactivity as the existing one, so that any trigger that would have activated the original neuron results in the exact same outputs, then 100% replacement of the neurons is still 100% you. It may also be important that the new neuron also reacts to changes the same as the organic neuron would, so that repeated excitation results in the same type of strengthening of connections, etc. If not, every 'type' of difference is simply a continuous gradient of 'not you'.

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If you change it gradually enough, i believe either type of change could be made imperceptible enough that it might still seem like 'you' just changed over time.