What can be said on the length differences between interacting proteins? Are they usually of similar sequence lengths or not at all?
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1$\begingroup$ What do you mean by length difference? Interacting proteins which are different in size? And why should this be a problem? Additionally: Proteins fold into a 3D structure, which is much more important for protein-protein interactions than the size. $\endgroup$– Chris ♦Commented Feb 27, 2014 at 10:08
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$\begingroup$ Each protein has a sequence. Sequences have lengths (amount of amino acids). Some proteins interact by forming physical bonds to each other. I'm asking if something can be said about size differences between interaction proteins. E.g. - usually very small proteins would not connect with each other, but only with a bigger protein. This is not "a problem". I'm simply wondering because I want to understand what would be a good descriptor for proteins when trying to model physical interactions. $\endgroup$– UriCommented Feb 27, 2014 at 10:41
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$\begingroup$ I think that if you did an analysis of this it would be dominated by interactions involving the same protein (dimers, trimers). Apart from that I know of no bias towards similar sizes. $\endgroup$– Alan BoydCommented Feb 27, 2014 at 11:47
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$\begingroup$ @Uri it seems like you mean to ask about 3D size rather than sequence length, is that correct? In other words, you are using sequence length as a proxy for some 3D size property. $\endgroup$– BitwiseCommented Feb 27, 2014 at 13:48
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$\begingroup$ No, I'm asking about sequence length. $\endgroup$– UriCommented Feb 27, 2014 at 18:37
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At least in a human protein interaction network, it appears that proteins indeed mostly bind to proteins of similar sequence length. Consider the figure below, based on analysis of a human protein interaction network from the Protein Interaction Network Analysis (PINA) platform. In the data set, the median relative protein size (the largest amino acid sequence length divided by the smallest in each interacting pair) was 1.9, the maximum value was 293.6 and the 99th percentile, which is the cutoff for the plot, was at 15.2.
Edit: As per stords comment below, you get essentially the same result for a random network: 
In this case, the network was generated by picking two proteins at random from the original network, creating an interaction between them, and repeating until the random network has the same number of interactions as the original.
Immediately, it might look like the PINA PIN is dominated by random interactions. I would run some network analysis to determine its characteristics, but seeing as it's a rather large network it would take more time than I have right now. The results are similar for two additional networks with interactions in Saccharomyces cerevisiae and Caenorhabditis elegans respectively downloaded from PINA. Note that all three networks have been constructed from databases with varying levels of curation (See the original publication for PINA: http://www.nature.com/nmeth/journal/v6/n1/full/nmeth.1282.html). As such, many of the interactions might not be biologically meaningful.
Taking into account the above, you might want to define "interacting proteins" more precisely. One might expect that a better curated network only containing interactions with a known function or effect might give a different picture. However, using a more strigently constructed human "functional interaction" network published by Wu et al. (http://genomebiology.com/content/11/5/R53, FIs_043009.txt in Additional file #3) still gave a similar result.
Method: I made a Python script to calculate the relative amino acid sequence lengths for all interactions in a human protein-protein interaction network (PIN) available from PINA ((http://cbg.garvan.unsw.edu.au/pina/interactome.stat.do). The network file is located at: http://cbg.garvan.unsw.edu.au/pina/download/Homo%20sapiens-20121210.sif. PINs for other organisms are also available at the same site and many other places. The script can be used with any PIN in SIF format using UniProt identifiers.
The script can be downloaded here: https://github.com/jarlemag/misc-bioinformatics/blob/master/ProteinInteractionNetwork.py
The most time-consuming part was downloading the sequence lengths from UniProt. To avoid having to do that, the protein sequence lengths can be saved to and loaded from a text file. The list of protein sequence lengths is here: https://github.com/jarlemag/misc-bioinformatics/blob/master/protlengths.txt To create the figure, place all three files in the same directory and run the script using Python 2.7.
Keep in mind that the PIN data may not be entirely reliable.
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$\begingroup$ Did you in any way correct for the natural distribution of protein sizes? There are many fewer large proteins than small proteins, so just by random interactions I could imagine a plot like this. $\endgroup$– stordsCommented Feb 27, 2014 at 20:46
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$\begingroup$ No, I took a very simple approach - suggestions for improvement are certainly appreciated. How would you do that, specifically? $\endgroup$– jarlemagCommented Feb 27, 2014 at 20:51
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$\begingroup$ I'm not very good at statistics, so take my advice with a grain of salt, but what I would do is simulate this kind of plot, but just use random interactions between proteins in your dataset rather than using known interactions. If the random plot looks the same, then the effect is likely due to the natural length distribution. If the random plot looks different, then the effect is likely real. Its qualitative, and I'm sure that there is a better way, but its quick and would be informative, I think. $\endgroup$– stordsCommented Feb 27, 2014 at 21:00
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$\begingroup$ Seems like you might be right. I've updated my answer. $\endgroup$– jarlemagCommented Feb 27, 2014 at 23:34
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$\begingroup$ On the topic of PIN quality, the following articles may be of interest: ncbi.nlm.nih.gov/pmc/articles/PMC2683745, nature.com/nmeth/journal/v6/n12/full/nmeth1209-934.html $\endgroup$– jarlemagCommented Feb 28, 2014 at 12:50