Q:

What is the longest-lasting protein in a human body?

Protein life times are, on average, not particularly long, on a human life timescale.
I was wondering, how old is the oldest protein in a human body? Just to clarify, I mean in terms of seconds/minutes/days passed from the moment that given protein was translated. I am not sure is the same thing as asking which human protein has the longest half-life, as I think there might be "tricks" the cell uses to elongate a given protein's half-life under specific conditions.
I am pretty sure there are several ways in which a cell can preserve its proteins from degradation/denaturation if it wanted to but to what extent? I accept that a given protein post-translationally modified still is the same protein, even if cut, added to a complex, etc. etc.
And also, as correlated questions: does the answer depend on the age of the given human (starting from birth and accepting as valid proteins translated during pregnancy or even donated by the mother)? What is the oldest protein in a baby's body and what is in a elderly's body? How does the oldest protein lifetime does in comparison with the oldest nucleic acid/cell/molecule/whatever in our body?

A:

Crystallin proteins are found in the eye lens (where their main job is probably to define the refractive index of the medium); they are commonly considered to be non-regenerated. So, your crystallins are as old as you are! 
Because of this absence of regeneration, the accumulate damage over time, including proteolysis, cross-linkings etc., which is one of the main reasons why visual acuity decays after a certain age: that is where cataracts come from. The cloudy lens is the result of years of degradation events in a limited pool of non-renewed proteins.
Edit: A few references:
This article shows that one can use 14C radiodating to determine the date of synthesis of lens proteins, because of their exceptionally low turnover: Lynnerup, "Radiocarbon Dating of the Human Eye Lens Crystallines Reveal Proteins without Carbon Turnover throughout Life", PLoS One (2008) 3:e1529
This excellent review suggested by iayork (thanks!) lists long-lived proteins (including crystallins) and how they were identified as such:
Toyama & Hetzer, "Protein homeostasis: live long, won’t prosper" Nat Rev Mol Cell Biol. (2013) 14:55–61

A:

I like Mowgli's answer, because it is a non-obvious example. However I would also point out that there are many, many protein-based structural components in the body that we know do not regenerate due to associated pathologies; so presumably these structural proteins are as old as from when they first arose in developemnt. Take the stereocilia on hair cells in the cochlea, for instance. The stereocilia structure is actin-filament based, so is a structural protein. Hearing loss occurs due to damage to these structures, which is not repaired. In fact, birds suffer only temporary hearing loss not because they regenerate these structures, but because they grow replacement hair cells.
Once you start thinking about this then, it is pretty clear that many structural proteins will be conserved throughout life (if the cell they are attached to or within remains a part of the body). And many cells of the body remain in the body throughout life, so any proteins that join the cells together, say connexin proteins that form tight junctions between cells, would also presumably be conserved. I say this because I think the energetic cost of degrading a protein that spans two membranes would be too great for it to occur. I have not hear of tight junctions being eliminated, but I may be wrong.
Mowgli's answer is nice because it involves globular rather than fibrous proteins- though Wikipedia still classifies them as structural proteins. I was interested and read this article about them. Interesting stuff! Thank you Mowgli!
I would be interested to know if there are any conserved biochemically active proteins. I would think that extracellular proteins would probably be turned over, and the best chance of finding such a conserved protein would be within a cell that remains for life post differentiation. Perhaps a proteosome complex itself (these are the protein complexes that are involved in protein degradation)? I don;t think ribosomes are degraded either, but I don't find this a very satisfactory example!

A:

A very interesting example are the cohesin molecules holding sister chromatids together in the oocytes (so only applicable to females, sorry!). Cohesion is established in utero, and these molecules are not recycled throughout life (AFAIK only shown directly for mice, not humans - https://www.ncbi.nlm.nih.gov/pubmed/20971813, https://www.ncbi.nlm.nih.gov/pubmed/26898469, but presumably same is true for us). This is considered to be a major contributor to the maternal age effect (https://en.wikipedia.org/wiki/Age_and_female_fertility) through low level loss of cohesion throughout life (since levels of cohesin can't be restored) until chromosomes start losing association between sisters which causes high chances of their missegregation (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5536066/)

