I recently wrote an algorithm that compares multiple protein sequences in a multialignment and assigns a value for each amino acid position depending on the variation in that position. If only one single amino acid is found in a certain position, "100%" is assigned (= 100% conservation). If more than one amino acid is found in a certain position, this number drops. It drops stronger if amino acids of very different character occupy the position (e.g. arginine and tryptophan). It drops lesser if relatively similar amino acids occupy the position (e.g. tyrosine and phenylalanine).
My question is: Can I claim that my results depict the "conservation" of the protein sequence? With other words, is the term "conservation" strictly defined? Or is it a vague term carrying a lot of flexibility and requiring definition in a certain context?
I am asking because people may argue, for instance, over questions like "what is a similar amino acid"? Probably everybody would agree that valine is similar to leucine (both hydrophobic and aliphatic). But is valine also similar to tryptophan? In an way yes, because both are hydrophobic. In a way no, because one is aliphatic and the other is aromatic. For my algorithm I had to make some arbitrary decisions about similarity. Not everybody might agree with my decisions. Therefore, I am wondering, is the term "similar" clearly defined in the field? Or do evolutionary biologists define the term "similar" in a flexible way, according to their needs?
Wouldn't, for instance, someone interested in tyrosine phosphorylation claim that tyrosine is vastly different from phenylalanine, whereas someone interested in protein folding might consider those amino acids very similar?
Several ways of quantifying site-dependent "conservation" in protein alignments have been proposed and used over the years, including some that sound like yours (at least in the features considered). A review comes to mind: http://www.ncbi.nlm.nih.gov/pubmed/12112692
Below I essay a quick-and-dirty categorization of current methods. Regarding your question, I can just make some comments:
1) I'd say a site is conserved if it is more conserved than expected.
2) Therefore, one of the keys is to define your "null model". The weakness of most methods is, to my mind, that they either not use a null model (i.e. they use an implicit null model, not spelled out) or they use an inadequate null model (e.g. assuming that there's no "phylogenetic structure" underlying a given set of sequences).
3) Several methods have been devised to take into account: amino-acid frequencies, amino-acid similarities or substitution probabilities, phylogenetic information. In my experience, taking tree topology into account is key, even more important than amino-acid similarity.
4) Often overlooked: conservation/variability measures often depend very much on the quality of the multiple sequence alignment.
5) There is no single way nor a definitive measure of sequence variability/conservation. This does not mean they are "subjective" nor that any measure can do. At the end of the day, what measure to use will depend on your intended purpose and should be checked accordingly. For example, if you aim to identify active site residues, you could run your algorithm on enzymes with known catalytic sites (e.g. CSA database: http://www.ebi.ac.uk/thornton-srv/databases/CSA/) and see whether you can "predict" the correct catalytic sites and how often (true positives, false positives, etc depending on a "conservation cutoff" parameter).
6) It is very difficult to identify catalytic sites this way. I predict you'll have a very large number of "false positives". That's because, many sites are very conserved just due to structural or thermodynamic reasons, which are among the main determinants of site-dependent conservation patterns (sorry for the self-promotion, but see e.g. http://biorxiv.org/content/early/2014/09/19/009423 and a few other recent papers on the determinants of sequence conservation in my researchgate page).
Coarsely, I'd say there are three main classes of method:
1) Information-theoretic methods: you assume each column of a multiple sequence alignment represents correctly the stationary (equilibrium) distribution of amino-acids allowed at the site. Then you can calculate the sequence entropy H = - Sum(p log p) where p are the probabilities (frequencies) of the different amino-acids at the site. There are variations of this to take into account amino-acid "similarity". For example, a "reduced alphabet" can be used, clustering together "similar" amino-acids (e.g. Polar, Non Polar, Positive, Negative: a few alternative classifications have been used). When you calculate H for each column of the alignment you get a conservatism (actually a variability, since H is larger for more variable sites) profile (H1,H2...).
The main theoretical problem with such a method is that by assuming all sequences are equally informative when calculating amino-acid frequencies, you're implicitly assuming that they're so divergent they've become sort of independent realizations of the "allowed" sequence space. Thus, you just not consider the possibility that some of the conservation is "phylogentic signal", i.e. historically determined: sites may be conserved just because they haven't had the chance to diverge yet. Also, you're implicitly assuming a "star-tree", i.e. all sequences have diverged from a single common ancestor and they are very diverged from each other...
The problem is that even if your set includes sequences that are very diverged from each other (400 Myrs in your case) I doubt all pairs of sequences are so dissimilar: if they were, you'd find it difficult to even align them. If you have a reasonable alignment, it's probably because even though some pairs are 400 Myrs appart, you have "intermediate steps", in other words, you have a phylogenetic tree that is nothing like a star tree, then your conservation measure will suffer from the wrong assumption.
1.a) Entropy with Tree Info
The topology of the phylogenetic tree is a key issue. A way of taking it into account is to somehow weight-down info coming from sequences that are closer together. This is the basis of the Evolutionary Trace method. The idea is to cluster sequences together into groups with roughly similar divergence, calculate their entropies, then do a sort of weighted average where more weight is given to more divergent groups (see e.g. http://www.ncbi.nlm.nih.gov/pubmed/22183528) for a recent application.
2) Sum of Pairs Methods - No Tree info
One way to deal with the issue of amino-acid "similarity" (or, if you wish "exchangeability" ) that is more nuanced than just grouping them together into reduced amino-acid alphabets is to consider some sort of amino-acid similarity matrix. Sum-of-pairs measures then calculate a score that is of the form Score = Sum(M_{ij}) where the sum is done separately for each column alignment, and what's summed is the similarity score for the similarity matrix M values for all pairs of sequences of the alignment. (described in the previous review by Valdar) Different sum-of-pairs methods are based on different M matrices.
2.a) Sum of Pairs - with Tree info
The sum-of-pairs score can easily deal with phylogenetic info: if you've got a phylogenetic tree, you can just do a weighted sum where the weight for a pair of sequences decreases with their divergence time (I don't know if it has been done).
3) Site-dependent evolutionary rates.
In this methods you quantify (rigorously, I'd say) the variability of a rate by its rate of substitutions, e.g. the number of amino-acid substitutions at each site per Myr. Given an alignment, these rates can be inferred using a model of amino-acid substitution (there are a number, e.g. JTT, which is a matrix of probabilities of substitution of each amino-acid by another), and a phylogenetic tree. Inference is made using either Maximum Likelihood (what site-specific rates lead to the maximum likelihood of the observed alignment?) or Bayesian approaches. See, e.g., http://www.ncbi.nlm.nih.gov/pubmed/12169533
Trying to determine amino acid similarity through structure for this seems to not be the best way to determine conservation. It would be easier to claim conservation by looking at the transition/transversion state of the amino acid change.
As it is "easier" for a Transition to happen (TC; AG) than a Transversion (PurinePyrimidine), it would be more correct to say that a change from Phenylalanine or Leucine to Serine (UU* to UC*) is more conserved (or similar, to use your verbaige) than a change from Phenylalanine to Tyrosine (UUU/UUC to UAU/UAC).
Depending on how in-depth you want to get, you can even provide time scales for the amino acid shift to show that something is more or less conserved on an evolutionary timescale according to whether a transition or transversion happened in each of the three positions..
Hi Rich, thanks for your feedback. I am really not an evolutionary biologist, which is why am asking how terms such as "conservation" and "similarity" are actually defined in the field (if they are clearly defined at all).
In my case, I am comparing protein sequences of a certain protein that is present from coelacanth and fish on up to humans. I have >100 sequences in my alignment. In my naive thinking, more than 400 million years of evolution should be more than sufficient time to let all kinds of transversions and transitions happen. Nevertheless, some key residues in the protein never changed (much), probably because they are functionally relevant. This is in fact what I am trying to do. Using my algorithm, I am trying to predict functionally relevant amino acids. I thought it would be correct to call such amino acids "conserved". Hence, my question.
However, you seem to have a totally different definition of conservation based not on "preservation during evolution" but on codon similarity and the probability that one codon mutates into another. Am I simply using an incorrect definition of the term "conservation" and you are using the correct one? Or is the term "conservation" just so flexible that it can mean all kinds of things?
The most fundamental signal of evolutionary conservatism is the extent to which
"similarity" is homology. Darwin was explicit in stating that his theory was based in part on the assumption that most similarities were due to common ancestry ("inheritance") - homology - and not due to common environments - homoplasy. In the 6th edition, Darwin actually discussed the "new" terminology of homoplasy proposed by Ray Lankester. If this were not true, we would not get consistent support for particular sets of phylogenetic relationships. And, although taxonomists love to argue strongly about very small disagreements, there is strong support for a consistent phylogenetic signal. Now, this does not imply and quantitative regularity about the degree of conservatism in any particular gene or other trait, or in any particular taxon. Like most things in evolutionary biology, those assessments need to be comparative. Perhaps when we have a large enough database we will see some regularities emerge - that would be exciting.
Raif, I apologize for the confusion. I read your original question as clarification on if you can call a 100% sequence match conserved (you can), and whether you can compare AA similarity (you can, just in several ways), agreed with your position, and answered a different part of the question... You are correct in your supposition that 400 million years is plenty of time for transitions and transversions, and the reasoning as to why they haven't happend - that their function is important enough that a significant change would be deliterious.
I didn't make clear that I was saying you could do and claim what your algorithm does (which is pretty cool), before going into a suggestion on how to change the determination of similarity from subjective (comparing the form of the AA to each other) to objective (comparing the rate of codon change).
Hi Rich, thanks so much for your feedback. This really helped me!
Also, thanks to Daniel for your comments.
Several ways of quantifying site-dependent "conservation" in protein alignments have been proposed and used over the years, including some that sound like yours (at least in the features considered). A review comes to mind: http://www.ncbi.nlm.nih.gov/pubmed/12112692
Below I essay a quick-and-dirty categorization of current methods. Regarding your question, I can just make some comments:
1) I'd say a site is conserved if it is more conserved than expected.
2) Therefore, one of the keys is to define your "null model". The weakness of most methods is, to my mind, that they either not use a null model (i.e. they use an implicit null model, not spelled out) or they use an inadequate null model (e.g. assuming that there's no "phylogenetic structure" underlying a given set of sequences).
3) Several methods have been devised to take into account: amino-acid frequencies, amino-acid similarities or substitution probabilities, phylogenetic information. In my experience, taking tree topology into account is key, even more important than amino-acid similarity.
4) Often overlooked: conservation/variability measures often depend very much on the quality of the multiple sequence alignment.
5) There is no single way nor a definitive measure of sequence variability/conservation. This does not mean they are "subjective" nor that any measure can do. At the end of the day, what measure to use will depend on your intended purpose and should be checked accordingly. For example, if you aim to identify active site residues, you could run your algorithm on enzymes with known catalytic sites (e.g. CSA database: http://www.ebi.ac.uk/thornton-srv/databases/CSA/) and see whether you can "predict" the correct catalytic sites and how often (true positives, false positives, etc depending on a "conservation cutoff" parameter).
6) It is very difficult to identify catalytic sites this way. I predict you'll have a very large number of "false positives". That's because, many sites are very conserved just due to structural or thermodynamic reasons, which are among the main determinants of site-dependent conservation patterns (sorry for the self-promotion, but see e.g. http://biorxiv.org/content/early/2014/09/19/009423 and a few other recent papers on the determinants of sequence conservation in my researchgate page).
Coarsely, I'd say there are three main classes of method:
1) Information-theoretic methods: you assume each column of a multiple sequence alignment represents correctly the stationary (equilibrium) distribution of amino-acids allowed at the site. Then you can calculate the sequence entropy H = - Sum(p log p) where p are the probabilities (frequencies) of the different amino-acids at the site. There are variations of this to take into account amino-acid "similarity". For example, a "reduced alphabet" can be used, clustering together "similar" amino-acids (e.g. Polar, Non Polar, Positive, Negative: a few alternative classifications have been used). When you calculate H for each column of the alignment you get a conservatism (actually a variability, since H is larger for more variable sites) profile (H1,H2...).
The main theoretical problem with such a method is that by assuming all sequences are equally informative when calculating amino-acid frequencies, you're implicitly assuming that they're so divergent they've become sort of independent realizations of the "allowed" sequence space. Thus, you just not consider the possibility that some of the conservation is "phylogentic signal", i.e. historically determined: sites may be conserved just because they haven't had the chance to diverge yet. Also, you're implicitly assuming a "star-tree", i.e. all sequences have diverged from a single common ancestor and they are very diverged from each other...
The problem is that even if your set includes sequences that are very diverged from each other (400 Myrs in your case) I doubt all pairs of sequences are so dissimilar: if they were, you'd find it difficult to even align them. If you have a reasonable alignment, it's probably because even though some pairs are 400 Myrs appart, you have "intermediate steps", in other words, you have a phylogenetic tree that is nothing like a star tree, then your conservation measure will suffer from the wrong assumption.
1.a) Entropy with Tree Info
The topology of the phylogenetic tree is a key issue. A way of taking it into account is to somehow weight-down info coming from sequences that are closer together. This is the basis of the Evolutionary Trace method. The idea is to cluster sequences together into groups with roughly similar divergence, calculate their entropies, then do a sort of weighted average where more weight is given to more divergent groups (see e.g. http://www.ncbi.nlm.nih.gov/pubmed/22183528) for a recent application.
2) Sum of Pairs Methods - No Tree info
One way to deal with the issue of amino-acid "similarity" (or, if you wish "exchangeability" ) that is more nuanced than just grouping them together into reduced amino-acid alphabets is to consider some sort of amino-acid similarity matrix. Sum-of-pairs measures then calculate a score that is of the form Score = Sum(M_{ij}) where the sum is done separately for each column alignment, and what's summed is the similarity score for the similarity matrix M values for all pairs of sequences of the alignment. (described in the previous review by Valdar) Different sum-of-pairs methods are based on different M matrices.
2.a) Sum of Pairs - with Tree info
The sum-of-pairs score can easily deal with phylogenetic info: if you've got a phylogenetic tree, you can just do a weighted sum where the weight for a pair of sequences decreases with their divergence time (I don't know if it has been done).
3) Site-dependent evolutionary rates.
In this methods you quantify (rigorously, I'd say) the variability of a rate by its rate of substitutions, e.g. the number of amino-acid substitutions at each site per Myr. Given an alignment, these rates can be inferred using a model of amino-acid substitution (there are a number, e.g. JTT, which is a matrix of probabilities of substitution of each amino-acid by another), and a phylogenetic tree. Inference is made using either Maximum Likelihood (what site-specific rates lead to the maximum likelihood of the observed alignment?) or Bayesian approaches. See, e.g., http://www.ncbi.nlm.nih.gov/pubmed/12169533
I agree with Gaurav's view, except that even 100% conservation doesn't necessarily mean functional importance. Unless the number of sequences is very large and the set very divergent (that may well be this case), one could have 100% conservation just by chance. Moreover, even for a case of a divergent set of sequences, one could have highly conserved sites for reasons other than functional (e.g. sites participating in the folding nucleus, essential for folding, may well be very conserved).
That said, If you do find 100% conservation (or similarly high) of certain sites, that may have heuristic value for experimental tests, even in the absence of a null model and statistical tests. Such conservation PLUS potential experimental evidence could support a claim of "functional importance" of sites.
Hey Gaurav and Julian, thanks for your very extensive and detailed answers. This really helped me! Your efforts explaining the matter are very much appreciated.
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