If that's the case, why don't we see them more often?

From the same paper:

"Many of the characteristics of proteins that enable the avoidance of aggregation, and amyloid formation in particular, are encoded by their amino acid sequences116. The elucidation of this code has enabled the identification of factors that determine the intrinsic aggregation propensity of these molecules117, 118, 119. Hence, it has been realized that globular proteins fold into structures that sequester aggregation-prone regions in their interior; in addition, typical features of the folding process, such as very high cooperativity, generate considerable kinetic barriers to the conversion of folded proteins into aggregation-prone species50, 120. Furthermore, specific patterns of residues, such as alternating hydrophobic–hydrophilic stretches50, 121, that tend to favour the amyloid state are commonly selected against during evolution119, 121, 122 or are otherwise neutralized by the insertion of highly aggregation-resistant residues, which are known as 'gatekeepers' (Refs 50,123).

Other protective mechanisms against amyloid formation are associated with properties of the cellular environment, including the location of proteins within specific compartments124, 125, and the presence of a multitude of molecular chaperones and degradation processes, such as the ubiquitin–proteasome126, 127, 128 and the autophagy129, 130, 131 systems, which function to prevent the formation and accumulation of misfolded and aggregated polypeptide chains11, 132. Indeed, the major genetic risk factor for late-onset Alzheimer's disease is the presence of an apolipoprotein E variant that reduces the ability of cells to degrade the amyloid-β peptide133."

On topic: I'm not a biologist so here's my layman's TLDR, please tell me if this is close.

1) You can tell whether a protien has this viral property by looking at its amino acid sequence

2) Looking at this seqence has shown several reasons why proteins don't often go viral

  - The relevant region ends up on the interior of the structure
  - The relevant structure is not mechanically likely
  - Evolution has come up with tons of biological tricks to prevent it

Off-topic: That is some of the grossest academese I've seen in a while, and it makes this passage near unreadable. I'm saving this sentence as an example for students of what not to do:

> The elucidation of this code has enabled the identification of factors that determine the intrinsic aggregation propensity of these molecules

I'd have a hard time coming up with a sentence that feels more inside-out than that.

>"1) You can tell whether a protien has this viral property by looking at its amino acid sequence"

Supposedly (I have no idea how well it works), but here is an example of such a tool: http://aias.biol.uoa.gr/AMYLPRED/

>"2) Looking at this seqence has shown several reasons why proteins don't often go viral"

Yes, but to clarify a bit: It looks like all proteins have this ability, but not all are just as likely to get into that state for the reasons mentioned. IE, it should be possible to find some way to make amyloids/prions out of any protein in the lab. It just requires figuring out the necessary conditions for that protein.

>"The elucidation of this code has enabled the identification of factors that determine the intrinsic aggregation propensity of these molecules"

Translation: Being able to get the amino acid sequence of proteins and predict what type of structures such a sequence leads to has allowed researchers to also predict which are likely to form aggregates.