The current total is 155,618 structures and new ones are added at a rate of 12000 structures per year, which means that, assuming a constant growth, in 125 years —(36 ^ 4 - 155,618 ) / 12,000 —the PDB will finish codes to allocate.
2145. That is a few years after the setting of Kim Robinson's New York 2140, where New York is a flooded super-Venice, so I am guessing the RCSB PDB, in San Diego, will have long been flooded so lack of 4-letter codes is not top of their concerns.
The date may be a bit sooner. There are no codes starting from zero (the first public entry is PDB:100D).
A fair chunk of codes are burnt as they correspond to predicted models that got remove and albeit random there are a few older structures that have non-random names, like 1UBQ and 1GFL. The highest number is PDB:9XIM. But the latest entries are on the 6Pxx range. 7 * 36 ^ 3 is 320,000, which means that about half the entries are skipped or private, so a more accurate estimate is in 60 years time.
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