Hi David,

Basic questions are often complex when you dig into them. A few years back we developed a database of pair wise interactions of amino acids in protein structures. Clearly hydrophobic residues prefer the buried location, but about 30% of them are still found on the surface - probably because they are needed for substrate interaction or protein-protein interaction. Our database is in the form of 8-dimensional hypercube. Dimensions are amino acid 1(20), amino acid 2 (20) solvent accessibility (12) distance(10), secondary structure 1 (4) secondary structure 2 (4), sequence distance (6) and protein sequence length (11). The database can be queried any way you like - thus you can raise the question How is the solvent accessibility of TRP dependent on the protein length? Similar for other AA, or clusters of AA Thus I believe this data base contains relevant information for you. The paper can be found here :

Hyperdimensional analysis of amino acid pair distributions in proteins.

Svend B Henriksen, Rasmus J Mortensen, Henrik M Geertz-Hansen, Maria Teresa Neves-Petersen, Omar Arnason, Jón Söring, Steffen B Petersen

PLoS ONE 01/2012; 7(7):e41322.

Just don't forget to check if the protein is intrinsically disordered. If it is, than almost the whole chain is solvent accessible. Use IUPred or Pondr VSL2 predictor to check disorder propensity. There is no size limit for disordered protein regions, it could be several hundred residues long.

Hi David,

Basic questions are often complex when you dig into them. A few years back we developed a database of pair wise interactions of amino acids in protein structures. Clearly hydrophobic residues prefer the buried location, but about 30% of them are still found on the surface - probably because they are needed for substrate interaction or protein-protein interaction. Our database is in the form of 8-dimensional hypercube. Dimensions are amino acid 1(20), amino acid 2 (20) solvent accessibility (12) distance(10), secondary structure 1 (4) secondary structure 2 (4), sequence distance (6) and protein sequence length (11). The database can be queried any way you like - thus you can raise the question How is the solvent accessibility of TRP dependent on the protein length? Similar for other AA, or clusters of AA Thus I believe this data base contains relevant information for you. The paper can be found here :

Hyperdimensional analysis of amino acid pair distributions in proteins.

Svend B Henriksen, Rasmus J Mortensen, Henrik M Geertz-Hansen, Maria Teresa Neves-Petersen, Omar Arnason, Jón Söring, Steffen B Petersen

PLoS ONE 01/2012; 7(7):e41322.

The classical reference that documents the answer to your question is:

Janin J. Surface and inside volumes in globular proteins, Nature 277, 491 - 492 (08 February 1979); doi:10.1038/277491a0

The conclusions are based on the properties of global proteins, and are still valid today for the vastly larger number of known structures.

Dear David,

the relationship between protein surface and buried interior is determined by the actual 3D-shape (i.e. global Fold, local disorder). For a spherical compact protein it can be calculated easily, but for protein channels (Inside + outside surface!), active site pockets and dimers/oligomers etc. you have to know the actual 3D-structure from the pdb. Proteins are individuals, general rules can be safely only applied for one Fold class.

Hi all, great answers complementing each other. Hamid, I am not sure to know what ASA means, could you explain? Steffen, thank you for the explanations and the reference, I am definitely going to have a look at your database, this is exactly what I need. Lajos, it is good to know as if there are lost of disordered proteins in my dataset it would decrease the relationship. Marco, still don't you think there could still be a relationship despite the specifics of the structure? Shoshana, thank you for the reference, there is no way I could have found that one.

Dear David,

Your question reflects the traditional schooling and as previous participants above pointed out slightly missing the point. Modern view of proteins is that this is not a single state phase of matter. Proteins are a mixture of many characteristics that I prefer to distill as a composite of solid and liquid phases. This view is reflected in answers by Marco, Steffen, and Lajos. The classic paper by Janin focused on what at that time was dominant i.e. emerging data from the PDB. Interestingly, later Janin and Wodak papers showed nicely the dynamic component contributing to our understanding what proteins are. The PDB is a tip of an iceberg and shows probably less than 30% of proteins that are conditionally stable (mostly solid state). Even in this sample the variation is overwhelmingly large. You can have a peek at this variation in a number of papers but I would cite mine Burra et al. PNAS 2009. Your question reflects that old paradigm that amino-acid sequence (therefore its length) is a dominant descriptor of what happens. This view is outdated in does not respond to the pressures of modern science. Nowadays we realize that the fate of protein can be equally determined by its composition, the environment, (postranslational modifications, compartment, degradation pressure, physical states i.e. pH and activity of other proteins or pathogens or literally almost anything) but also systemic conditions such as regulatory RNAs and epigenetic conditions.

However, it is fruitful to ask questions like you have asked with the caveat that you fully understand the limitations of the answers. For instance an "average" protein structure has variable hydrophobic surface expose area, when it comes to individual proteins, but on average in the crystal the solvent exposed areas are 50% hydrophobic. However, what is somewhat surprising that the formation of the protein crystals is "on average" not driven by enthalpic but rather by entropic forces. It means that really knowing how much is buried does not matter that much. Also, buried hydrophobic surface, even though it is a driving force behind all local folding events, does not determine the global stability directly. Only the dynamic components of every protein do.

The only useful result you may get is a general suggestion towards how small domains are organizing themselves. However, the other caveat is that very small proteins by definition have very small interior. There are no universal scaling laws (allometric) to suggest that larger proteins are built and behave like smaller proteins. Proteins are usually built in hierarchical manner even though we may not see it that way at first. Good Luck.

Dear Steffen,

Thank you for turning my attention to this data base, I missed that paper. Congratulations on a fine work.

Dear Boguslaw, thank you for this very complete answer. I asked the question because I see very intriguing patterns in the amount of positive selection in mammalian proteins that interact with pathogens. Shorther proteins show very strong excess of positive selection compared to longer proteins, with the longest ones (i.e more than 1,000 amino acids) showing no excess. In other words, I see a negative relationship between protein length and the excess of positive selection in proteins interacting with pathogens. In your opinion, what could explain it apart from my initial question?

Hi,

I highly recommend using PACSY database from NMRFAM to query. You can check by either SAS and hydrophobic scale offered by the database. The web page is http://pacsy.nmrfam.wisc.edu

Cheers.

Dear Dave,

Neglecting the problem that statistics are always indicators but never the proof of possible associations (in common language they do not meet the standard of causal explanation) your finding is interesting. I would have to know the details of your methodology but on a general level larger proteins are composites of many domains. In order to constitute the larger entity they must interact in relatively stable manner so they are utilizing the hydrophobics to do that. On the other hand more primitive proteins by design and requirement must have been shorter (smaller) therefore you have a natural selection against older proteins. Besides, we do not really understand how many proteins are borrowed and transferred between the species and how many are just simply reinvented. There is substantial evidence form several directions (homologies of sequences and structures, domain conservation, functional transfers etc.) that many folds are reinvented many times. This must reflect the fact that the number of energetically stable folds is limited which support many results obtained in the last 25 years. Looking for some physical characteristic is just misleading. Proteins were never invented to be the most stable or most prevalent in anything. We have very lousy proteins (in their function) but because of necessity of this function they are very well conserved. Many people are following blindly the template of doing science that grew up from 18 century reductionist approach. Not all the things can be explained in isolation form other things so sometimes holistic approaches are much more successful. Life certainly cannot be explained by reductionist approaches. Good Luck.

Protein length doesn't have to be proportionate with number of buried residues. The reason being, proteins try to maintain 31.45% carbon in its local structure. To satisfy this carbon percentage the amino acids are accommodated accordingly. A length of 15 amino acids can satisfy this. Sometime hydrophobic pockets are balanced by distance (non contiguous) amino acids. This can be achieved by limited length, say 250 amino acids. You may have correlation up to 300 amino acids. Beyond that there needn't be correlation of length with buried amino acid.

I must add a completely different answer here. It has been mentioned in one of the answers that there are disordered proteins in one of the databases... Predictions of the amount of disorder in the living proteome vary around 35% to 40%. If these predictions correspond to reality, is it even possible to have a significant correlation between protein length and the proportion of residues burried? Intrinsically disordered proteins can be quite long. See "Distribution and cluster analysis of predicted intrinsically disordered protein Pfam domains", for example.

Short answer: NO

Of course, one could think the longer the sequence, the larger the percentage of buried residues. Thus, a proportionality constant between sequence length and percentage of buried residues might be considered. The point is whether or not this proportionality is general or universal. And the answer is NO.

Why NO? About 40% of protein are intrinsically (partially) disordered. For these proteins, the proportionality constant is small. In addition, intrinsically folded proteins exhibit different folds, shapes and contact orders, and each prototypical shape (sphere, ellipsoid,...) will be characterized by a different proportionality constant. In addition, many proteins assemble into multimolecular structures (homo- and hetero-oligomers), which adds another complexity layer.

For example, (quasi)spherical proteins would show the larger proportionality constant, given that the sphere is the 3D object with larger volume/external surface ratio.

Therefore, there is a correlation between sequence length and proportion of buried residues, but there is no universal law with a common proportionality constant.

In the longer answer: While i believe this is true, that about 40% of the proteome is intrinsically (meaning completely) disordered (IDPs), this is a prediction and not a scientific reality yet. It remains to be verified by experimental evidence. The entire database of experimentally verified IDPs at Disprot.org as of 05/24/2013 includes only 694 proteins, many of which have a combination of intrinscally disordered regions and ordered regions. While the predictors have been shown to have equal numbers of false positives and false negatives, this means very little when we consider the line between scientific reality and scientific prediction.

@Robert, Even if we remove the intrinsically disordered proteins from the discussion, the geometric reasoning is still valid: there is a correlation between sequence length and proportion of buried residues, but there is no universal law with a common proportionality constant (the proportionality constant will depend on the shape or contact order).

Despite many good points noted in the discussion so far, a major reason that sequence length does not correlate with surface buried is that proteins form domains that tend to be ~100 to 300 residues in size. So in general longer sequences fold into more domains rather than larger single domains. This means that the surface area expected should be based upon some notion of how many domains the sequence forms and what type of domains these are predicted to be - e.g. helical bundles, beta barrels, etc. Yet, a complication related to the previous discussion is that these domains can interact with large buried interfaces or have flexible linkers. So an algorithm to predict buried surface would first deal with prediction of domains and of unstructured regions in my view.

Dear David, Adrian, John, I am still not certain that the initial question has been answered, possibly because there are no definitive papers describing such calculations. Am I wrong? I think the goal is eventually prediction and it may be possible that a solution to this question may advance this goal, if only by sorting out all surface and buried residues. I think this must have been done, but my search has also not yielded a paper. There is much more that can be done with such information besides answering the ratio question. The work involved seems straightforward to me. Here is a start:

1. Get the download script from the PDB and edit it to get pdb coordinates:

wget ftp://snapshots.rcsb.org/rsyncSnapshots.sh

Alternatively, download these files from the rcsb ftp site, or:

rsync -rlpt -v -z --delete --port=33444 \

rsync.wwpdb.org::ftp_data/structures/divided/pdb/ ./pdb

2. Download and install a program that will find surface and buried residues. I like http://www.ccp4.ac.uk/download.php

3. If the pdb download yields the series of subdirectories filled with .ent files, use the following approach:

find "toppdbdir" -name "*.ent" -exec sh ccp4script.sh "{}" ";" > myoutput.txt

where ccp4scrip.sh is something like:

echo "END" | areaimol XYZIN $1

I've taken it this far with a few pdb files I have on hand. The output does have the information. A little perl shouldl sort it all out. If anyone is interested in pursuing this, I'll add the perl script and flesh it all out. i feel I've been a little lazy and a little uncollegial in my answers here, so I've put a little thought into this one.

@John Tainer, A small correction in "proteins form domains that tend to be ~100 to 300 residues in size". It is not 100 but 90 in the smaller side. That is lowest carbon domain correlate with 90 amino acid long.

This is not at all difficult to estimate roughly. But it is variable and you need to remember the limitations.

Assume a stretched chain like a cylinder of diameter r and length l. This length l is proportional to the number of amino acids in the protein.

Fold this spaghetti into a ball. This ball has a radius of x. We need to put some packing factor into this calculation:

pi*(r**2)*l=0.6*(4/3)*pi*x**3

I have used 0.6 as the packing factor. It is a loose packing but not so loose that it will fall off.

Surface area of this ball:

4*pi*(x**2)=(4*pi)*(((r**2)*l)/0.6)*(3/4))**(2/3))

this is proportional to the number of exposed residues.

In simple words, length/packing_factor raised to the power of 2/3.

You will get a good result. Try also instead of 0.6, 0.65 or 0.7

Still confused? Applicable only to approximately globular proteins.

Hello David, Attached to this message is a reprint of Harvey Fisher's paper, "A limiting law relating the size and shape of protein molecules to their composition", PNAS 51, 1285 - 1291 (1964), which may be useful.

Thanks to all of you for your responses. Dear Robert, how much longer would it take you to actually get a table on which I could compute the correlation? That would be truly terrific and I would properly acknowledge your work in any publication.

Adrian, I get the point that a clean rule cannot be expected. What I was asking is if there is a correlation, meaning even a small correlation.

Here is an alternative that I mentioned earlier.

You can run this SQL for 20 different amino acids. It will be easy.

I am using PACSY database (pacsy.nmrfam.wisc.edu).

Just submit this SQL to acquire number of buried Alanine residues (less than 20% hydrophobicity) in the database for 50~70 residue proteins:

select COUNT(A_STRC_DB.SND_STRC) from A_STRC_DB,SEQ_DB where A_STRC_DB.MODEL_NO=1 and A_STRC_DB.FIRSTKEY_ID=SEQ_DB.KEY_ID and A_STRC_DB.HDO_PBT BETWEEN 0 and 20 and SEQ_DB.SEQ_COUNT BETWEEN 50 and 70;

Result says 893.

For exposed Alanines,

select COUNT(A_STRC_DB.SND_STRC) from A_STRC_DB,SEQ_DB where A_STRC_DB.MODEL_NO=1 and A_STRC_DB.FIRSTKEY_ID=SEQ_DB.KEY_ID and A_STRC_DB.HDO_PBT BETWEEN 20 and 100 and SEQ_DB.SEQ_COUNT BETWEEN 50 and 70;

Result says 1831.

If you change residue count range to 70 to 100,

buried 2499, exposed 3655.

So you can tell, at least for Alanine, more exposed relatively in 50-70 residue proteins than 70-100 residue proteins.

You can do the same for Arginine by just changing A_STRC_DB to R_STRC_DB.