Talked about an idea in this thread -
Could nerve damage or retrograde microtubule based transport in axons explain the delay associated with PEM? about whether the time delay associated with PEM could be linked to the amount of time it takes from nerve injury/an event at nerve terminals to the nucleus generating a transcriptional response. This was based off the possibility that organophosphates, which cause certain neurons to fire constantly and would damage synapses, seem to be able to trigger an ME like illness.
I've learnt since then that apparently some forms of synaptic plasticity - namely synaptic scaling - also occur on timescales that line up well with PEM (hours to days). This is a homeostatic mechanism to keep global firing rates of a neuron relatively stable, such that if a neuron has been firing a lot due to stimulation at any of its synapses it will begin to scale down - and vice versa (
The Self-Tuning Neuron: Synaptic Scaling of Excitatory Synapses, Turrigiano 2010)
I think it's also worth considering protein degradation, which has come up in a few forms now. The proteasome in Zhang HEAL2, and autophagy is plausibly linked to at least three genes in decode (FBXL4, CCPG1, RABGAP1L). Protein degradation appears to be a key part of synapse homeostasis.
In my opinion there are a bunch of things that point to synapses, but how clear is it really that there would be amplification, rather than attenuation or something else. It does seem like it could be quite complicated - if a lot of a neuron's synapses at the dendrites were compromised for example and connections were lost, maybe the neuron could end up firing more (erratically) later anyway due to a mechanism such as synaptic scaling as above.