About a month ago kalla724 posted a number of comments on this post, many of which were highly upvoted.

Synopsis: I) I think that kalla724 is too pessimistic about the practice of cryopreservation to preserve personal identity, because we don't know what level of synapse/active zone/protein structure is preserved in human brains, and we also don't know what level is required for personal identity. II) I think kalla724 is wrong about the required detail necessary to simulate a C. elegans. This is testable in the relatively near-term, and the results of that test might yield insight into whose argument in point I is stronger. 

I

kalla724's main argument: it is not possible (p = 10^-22) that cryonics will preserve personal identity, because replacing water with cryoprotectant will cause too much damage to proteins and lipids in the brain.

My view is that kalla724 is too pessimistic. To find a specific example to expand upon this intuition, I searched for "c elegans memory". I chose one of the first reviews in the results: http://learnmem.cshlp.org/content/17/4/191.full, published in 2010 by Ardiel and Rankin. Here's their first example: 

Rankin et al. (1990) were the first to characterize learning and memory in C. elegans. They studied plasticity of the “tap-withdrawal response” (TWR), a behavior whereby worms swim backward in response to a nonlocalized mechanical stimulus generated by tapping the Petri plate containing the worm. The magnitude of this reversal response is around 1 mm (roughly the length of the worm), but this can change with experience. Repeated administration of the tap results in a decrement of both the amplitude and the frequency of the response

The specific neurons mediating this are known: 

Using the circuits described by Chalfie et al. (1985) in conjunction with the neural wiring diagram (White et al. 1986), Wicks and Rankin (1995) identified the mechanosensory cells (ALM, AVM, PLM, and PVD) and interneurons (AVD, AVA, AVB, PVC, and DVA) mediating the TWR.

Through more science, they found that: 

the locus of mechanosensory habituation is in a part of the circuit unique to the TWR, i.e., the touch cells and/or the synapses between the touch cells and the interneurons. Now the hunt for the underlying molecular mechanism could begin.

There is some evidence for how the short-term component of the tap-withdrawal response plasticity. This is it: 

repeated activation of the touch cells results in autophosphorylation of the SHW-3–MPS-1 complex, thus diminishing K+ flux and prolonging the duration of mechanoreceptor potentials. This would slow the recovery from inactivation of EGL-19 (the L-type calcium channel mediating touch-evoked calcium currents) (Suzuki et al. 2003) and dampen cell excitability

This means that the complexes of proteins, working together, add phosphate groups to themselves as a post-translational modification. Each individual complex functions as a potassium ion channel, so changing its structure can alter the excitability of the cell.

Whether vitrification will preserve this specific post-translational modification is, as far as I know, an open question. The current cryoprotectant solution, M22, is pretty physiologic, which means that it functions similarly to water. But, we don't have this data. 

It's likely that when the protein complex undergoes autophosphorylation, other changes occur in the cell as well. If this led to changes in the cell's epigenome, which is very common, and the structure of the epigenome is retained by the cryopreservation, then the cell's epigenome could allow reverse inference of the state of its ion channels. We also don't have this data. 

The authors also discuss evidence for the long-term component of the tap-withdrawal response plasticity: 

the AMPA-type glutamate receptor subunit, GLR-1, was required for long-term habituation—glr-1 loss-of-function mutants habituated but did not retain decremented responses ... long-term habituation was associated with a significant reduction in the size, but not the number, of the GLR-1::GFP clusters in the posterior ventral nerve cord

This means that the number and distribution of a well characterized protein at the synapses of cells is highly correlated with the strength of the memory. This is consistent with current paradigms of long-term memory. 

Under ideal cryopreservation conditions, synaptic vesicles and receptor distributions are likely retained, even if some of the proteins may be a bit denatured. The data is far from perfect here, either. 

It's also important to stress that this only occurs under ideal conditions. Given the current practice of cryonics, cryoprotectant will not reach many or most areas of the brain. In these cases, there is a large amount of ice damage and the information is much more likely to be irretrievable. 

II

kalla724 says:

Uploading a particular C. elegans, so that the simulation reflects learning and experiences of that particular animal? Orders of magnitude more difficult. Might be possible, if we have really good technology and are looking at the living animal.

kalla724's requirement is that we look at live C. elegans to simulate them. But, the evidence above indicates a good correlation between AMPA receptor distribution and tap-withdrawal reflex. And there is good reason to believe that these features are retained by vitrification under ideal conditions. 

So, it seems to me that if you were to emulate a particular C elegans, you could add more receptors (or just up the strength parameter) at those synapses, and thus mimic the plasticity of the tap-withdrawal reflex. Looking at live animals would not be required. 

One more note:

Extrapolating results on personal identity from C. elegans to humans is not ideal. If the results are biased in one direction, we should expect more redundancy in mammalian neural systems than there are in nematode ones, because mammals have so many more brain cells. 

Edit 6/15: fixed format of quotes. 

Edit 6/16: added synopsis to clarify main points.