Is there are theoretical limit to the number of proteins possible and their respective structure?

I saw an article saying that DeepMinds AI has catatogued every protein known to science. I guess "known to science" and what is the theoretical limit is not exactly the same thing but the only way one can claim "known to science" at least as I can figure out is to have some idea what the highest value can be in the first place.

On the other hand it may be all the proteins known from every living object on the planet but I don't see how anyone could claim that when most species on the planet are not even know.

So that is why I ask is there is some theoretical limit.

As for example there is a theoretical limit for the highest possible element past the transuranics based on nuclear chemistry. I believe at some point the number of protons would not be able to stay bound long enough to get past the electrostatic repulsion. I think the number is 200 something. But that is an example and not my question. In this question I am interested in knowing how a computer algorithm could predict all protein structures if there was not a theoretical limit imposed in the first place.

I have never posted here before so if the question is inappropriate for this stackexchange my apologies

• They just mean known proteins, the simplest interpretation of the statement. Jul 30, 2022 at 23:13
• yes amazing still but that would solve my problem. You are probably right on. Thank you Jul 30, 2022 at 23:21
• Not even all known proteins! There are many proteins that exist in multiple isoforms, and they used only one isoform per protein coding gene. For a reddit q/a on this, see here. Jul 31, 2022 at 1:45
• All depends what you mean by protein - basically take a single amino acid and add another .... on to very high number. Largest known is titin I think, at about 35,000 residues, but no reason that there couldn't be 35,001 or 70,000 or 100,000 etc.
– bob1
Jul 31, 2022 at 9:24

You can certainly estimate a theoretical limit, given some assumptions.

Let's say you do not care about any post-transcriptional modifications, you are interested only in the primary sequence. There are (more or less) 20 proteinogenic amino acids, so there are $$20^N$$ possible proteins (amino acid sequences) with length $$N$$.

An "average" protein has about 400 amino acids. Therefore, there are theoretically $$20^{400} \approx 2.6\times 10^{520}$$ possible proteins with 400 amino acids.

But proteins can also be larger. Let's enumerate all possible protein sequences up to length 1000:

$$\sum_{N=1}^{1000} 20^N \approx 10^{1301}.$$

All of this is only a lower limit. We did not take into account any non-standard amino acids, none of the post-transcriptional modifications, or the ability of proteins to have multiple different stable conformations.

• Note that there are only about $10^{82}$ atoms in the visible universe. Jul 31, 2022 at 17:39