Everybody agrees that synaptic connections between neurons are needed to
access memories, but there is reason to think those connections may not be
where memories are ultimately stored, at least not important very long term
memories. The theory that memories are stored in the strengthening of
synapses based on recent activity (Long Term Potentiation) does a pretty
good job at explaining how memory can be retained for hours or days, but
when you get beyond a week or so there are problems because the proteins
associated with Long Term Potentiation (LTP) are not particularly stable,
and experiments with snails have shown that even when LTP has been
destroyed with chemicals the loss of memory is not always permanent. So
there must be an information storage mechanism other than the pattern of
synaptic strengths for at least some memories.

It’s been known for a long time that a mesh of proteins attached to
carbohydrates forms something called "the perineuronal net" which sheaths
mature brain neurons. And it's been known that synapses form through gaps
in the net; but very recently evidence has been found that very long term
memories, the sort that endures for an entire lifetime, may be encoded in
the holes in the perineuronal net, rather like old fashioned computers once
encoded information as holes in punched cards.

http://www.sciencemag.org/news/2015/10/mysterious-holes-neuron-net-may-help-store-long-term-memories

https://www.braindecoder.com/memory-perineuronal-nets-1418933042.html

The proteins that compose the Perineuronal Net are much more stable than
those in neurons, but when a synapse is strengthened it produces a small
amount of an enzyme that can break down the net, and if the synapse
increases a lot over a short amount of time there is enough enzyme to make
a small hole in the Perineuronal Net right next to the synapse, and the
hole seems to be permanent. Mice that have been genetically engineered
to lack this enzyme have normal short and medium term memory but very poor
long term memory. Even severe Alzheimer's disease has little effect
on Perineuronal Nets, so memory information might still exist in a
Alzheimer brain even if the synapses in it are so damaged they can no
longer be accessed  by them. It seems to me this may also be reason for
optimism regarding the success of Cryonics ;  the Perineuronal Net is much
tougher than neurons are and the space between brain cells where the
Perineuronal Net  is located, along with blood vessels various
glycoproteins and lots of fluid, occupies 20% of brain volume on average
but it can get 60% larger during sleep or anesthesia :

http://science.sciencemag.org/content/342/6156/373

So if a neuron shrinks or grows in volume during freezing that shouldn't be
something it hasn't seen before, and even if a shard of ice does punch a
meaningless hole in the net it should be obvious to a intelligent
nano-machine that the hole was  just caused by ice and not by synaptic
behavior because the ice would still be sticking through it.

 John K Clark

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