A lot. A nice example of the power of aldehyde fixatives to preserve fine molecular detail is Helm et al 2021.
Dendritic spines, which are often considered the functional units of neuronal circuits, strongly vary in size and shape. This study used electron microscopy, super-resolution microscopy, and quantitative proteomics to characterize > 47,000 spines at > 100 synaptic targets, helping to quantify variation in biomolecular composition across spines. Their study is amazing in part because of their technical advances, which allow for the beautiful visualization of biomolecules across neuronal membranes.
People often say that connectomics is not enough for brain information preservation because each dendrite has its own spread of ion channels. This distribution of ion channels will tell you whether a dendritic spike will occur, which is incredibly important to figure out synapse function.
If the local dendritic tree goes over a certain threshold of depolarization, then the local ion channels will open up and amplify what would have come in with the synapses alone. This also could synergize with clusters of synapses.
Theoretically, each neuron could have a unique spread of ion channels along dendrites, which could potentially make synaptic connectivity data alone insufficient, even if you have or can accurately infer synapse molecular information.
It’s hard to find examples of real evidence in the literature for or against how important these effects are. But the nonlinear effect of clusters of synapses is something that we potentially can’t account for with electron microscopy data alone.
This is a reasonable/principled objection to the idea of brain information preservation via connectivity. Personally, I find it quite plausible. A way to address this objection is to say that super-resolution microscopy techniques like those used by Helm et al 2021 could be applied to decoding memories from fixed brain tissue via measuring biomolecules, without necessarily assuming that synapses alone will be sufficient.