Guten Tag, Wilkommen Sorek, isch gehr daufmann aus das Weil zee diese video zuschauen ist
Netflix kaput heute.
Okay, and today will be an English day, and you can still vote and change your mind in
our moodle.
What I'm going to talk about now is comparing protein structures to each other, but there
will be a lot about aligning protein structures to each other, that is putting two proteins
on top of each other so that you can compare them.
Okay, first of all, let me tell you why this is so important.
Because if you have a new protein, you find something in the lab, you know that it's involved
in some disease, but you don't know exactly what this protein does.
So you want to find similarities to other proteins.
However, at the sequence level, and at the structure level, similarity is quite different.
Structure similarity lasts longer on the evolutionary time scale.
Let me tell you why.
Here is my view of molecular evolution.
It's not really my view.
What's happening is we are all trying out mutations continuously.
We are all getting hit by cosmic rays.
We live too close to the nuclear reactor.
So we have mutations, and an amino acid is exchanged at some point in some protein.
And then you ask the question, does the structure of the protein change?
So after a mutation, does the protein fold up?
If the structure changes, it is almost unimaginable that the protein keeps working.
So your enzyme doesn't fold up properly anymore.
It's probably not going to work as an enzyme.
So after a structural change, you go into the, or your protein goes into the evolutionary
garbage bin, Pekkahut.
If the structure does not change after a mutation, there is the chance that the mutation is passed
on to the next generation.
So it might be passed on, and it might become fixed in the population.
So what's the result of evolution at this level?
Constant mutations, the ones that change the structure get thrown away.
The ones where the structure survives or does not change too much, they might get passed
on.
So the result is that nature is continuously trying out mutations and throwing away the
ones that change the structure.
So structure tends to be conserved, but sequences change relatively rapidly.
Or in other words, nature is exploring sequences that are compatible with a certain structure.
This is a simple view, and of course, it's not enough to explain how new structures are
formed.
It explains why you see so many different sequences that fold up to very similar structures.
Okay, what it means for us is when we are talking about similarity, sequence is not
very well conserved, but structure is conserved.
So if we want to find similar proteins, we often have to be able to compare their structures.
Now structure determines function, you could say, but let's ask another question.
Which is more informative?
Is it better to find structural similarity or sequence similarity?
So you have a protein, you found the gene for a protein in the lab, you are looking
for similar proteins with known function.
Do you want to find proteins of similar sequence or of similar structure?
I would say you want to find, first guess, you want to find sequence similarity, because
if they have sequence similarity, it means that the evolutionary time is not so big.
So if we have similar sequences, it means two proteins are closely related.
And then of course, the structures will be similar anyway.
If we have proteins that are not so closely related, they are still related but they are
not so similar, then the sequence similarity can be so low that you do not find it with
a sequence search.
However, you will still have structure similarity.
So in this case here, we have similarity, but it is more remote, it is weaker similarity,
so we cannot be so certain if we make a function prediction.
So sequence similarity means two proteins are really close, they have similar structures
and probably similar functions.
Structure similarity alone without sequence similarity means that two proteins are related
but the evolutionary time is longer and the function might have changed a bit or a lot.
And if two proteins have no sequence similarity and no structure similarity, then you cannot
say they are related.
So what I always want to find is sequence similarity, that is the most helpful, but
structure similarity is second best and it will let us find relationships between proteins
that you might miss otherwise.
Okay, can we align structures the way we align sequences?
The answer is going to be not really.
So in summer semester, I talk about sequence alignment methods, which are nice, fast, deterministic
methods to align two sequences on top of each other, find the corresponding residues.
Can you do that for protein structures?
Not really, let me tell you why.
So back to sequence alignment for a moment, as a reminder, and I suspect this is actually
on my folium in summer semester.
This is a sequence alignment of two proteins and you can see where there are gaps in the
sequence and these correspond to gaps if you know the structures.
There's obviously a one-to-one correspondence.
Mostly the two sequences are similar and the two structures are similar, but you can see
where the gaps come in and line up.
Now how do we calculate a sequence alignment?
This is not a sequence alignment lecture, that comes in summer semester.
This is just a reminder.
If I have two sequences, so A, B, C, D along here and a second sequence along here, the
first step involves looking at this residue here, this A, and saying how similar is A
to an L, an M, an N, and so on, and I fill out a scoring matrix and then how similar
is a residue of type C here to L, M, N, P, Q, and so on.
So I start by building a matrix of similarities.
Then this is the summer semester lecture.
There is a fancy method that lets me sum up the similarities and find the optimal path.
So I find a path that tells me I get the best score if I run along these lines here.
So I align the A to the L and the C to the M and so on, and then I put a gap in here.
And that's how I calculate out a sequence similarity.
The first step involves comparing A to L, A to M, A to N, and so on.
And I do that by looking up the similarities with a similarity matrix.
So scores from the literature that tell me that an A is similar to an L and it's not
so similar to an N, for example.
So the question is, can we do something similar for structures?
This is where we have a problem.
Consider a structure alignment.
I've got two proteins, so my black protein here and my red protein over here.
And I want to align the structures, so I'm not looking at the sequences.
By eye, you can see that this is an easy problem.
I can put the red one on top of the black one, and I have this ideal alignment down
at the bottom.
And you can see there's an insertion or a deletion in this space over here.
So that's the answer.
But how would I do this computationally?
This is not so easy.
Remember, the first step in doing an alignment is to take a site in the black protein, site
one, and compare that to one prime, two prime, three prime in the red protein, and then
to take site two and compare that to one prime, two prime, three prime, and so on, and build
up a scoring matrix.
But now look in a little bit more detail.
What is the similarity of two prime here to five, six, four, whatever?
The structure at this site here depends on his neighbors.
So the structure at site two prime depends on one prime and three prime.
But the structure then depends on the alignment.
So is site three prime aligned to four, five, or six?
Is one prime aligned to one, two, or three?
I don't know yet, because I haven't aligned them, or their alignment depends on this guy's
alignment.
And this guy's alignment depends on his neighbors.
So I can't just look at a site and say it's similar to the site in another protein, because
I don't know where the neighbors are.
So there's no obvious way to compare amino acid conformations between proteins.
But that's all right.
That's fun.
It means it's time for guesses and approximations.
The goal here is going to be, can we find a method that will let us use the techniques
from sequence alignment and apply them to structure alignment?
So can I put labels on these sites and labels on these sites and compare them?
So imagine I have some alphabet, alpha, beta, gamma, whatever.
So this is an alpha, and that's an alpha, and that's a gamma.
And I have labels over here, alpha, beta, gamma, something.
And then I have some table which tells me that an alpha is similar to an alpha, and
an alpha is a bit similar to a beta, but not so similar to a gamma, for example.
Then I could build a scoring matrix.
So I have the structure, the black structure here, the red structure here, and I could
put numbers into this matrix to tell me that this site is similar to that one, and not
so similar to that one, and not so similar to that one.
If I have similarities, I could just put in ones and zeros, and then have some primitive
scoring matrix.
Could I use secondary structure?
Could I say this is alpha helical, that's beta fault blood, that's beta strand-like,
this is a gamma turn, could I do that?
Yes you can do that.
Would it work?
Not very well.
It's not the method that people use.
Let me tell you why it does not work very well using secondary structure.
There are two reasons that people do not do structure alignments based on just secondary
structure.
So the first reason, we can summarize it and say the alphabet is too small.
What do I mean by that?
If we're talking about secondary structure, we have a very small alphabet, basically alpha
helix, beta strand, and maybe some other kinds of secondary structure, which are less common.
Now look at these two proteins here.
This guy is a little alpha helical protein.
This guy here is another alpha helical protein.
If I just align helices to helices, or helices and avoid strands, I would put this guy on
top of that guy and say, oh look, I have a perfect structure alignment.
All the alpha helical sites match.
And you would say, no, it's total rubbish.
That's just two or three little helices, and of course they are going to align well to
this protein up here.
The alphabet is too small, and it doesn't carry enough information.
You lose, for example, the geometry around this site.
If you just say it's not an alpha helix, and you ignore the fact, does it align better
to this bit here or better to that bit here?
So there are lots of alternative alignments of nearly equal score.
OK, there's a second problem, which turns out to be quite nasty.
If you want to work with secondary structure, you really need rather good coordinates.
Let me give you one of my favorite examples.
Here are two proteins, and they are really related to each other.
This guy over here is a nice regular protein.
You can see the beta sheets in the middle there, some helices up there.
This guy over here, for this guy, I just drew a picture in chimera.
chimera took the coordinates and did not recognize that there's a beta sheet over there, and
did not notice that this is an alpha helical region over here, because there's nothing
terribly wrong with these coordinates.
But they came from Cana magnetica resonance from an NMR calculation, and they're just
not very accurate.
And the authors did not try to make them any better.
They just took the coordinates as they were generated by their software.
As a human, I can look at this and say, oh, I think that's a distorted alpha helix.
And I can say, oh, that's obviously a beta sheet.
But the geometry, the local geometry, and the hydrogen bonds are just not good enough
to be recognized.
If I was to use secondary structure-based methods to align this to that, they just wouldn't
align to each other.
Because this guy over here does not have regular secondary structure, purely because
the coordinates are not very pretty.
They have not been fixed up.
So I would not be able to recognize the similarity between this protein and that protein.
So the story is, do not use secondary structure for protein alignments to problems.
Let's consider how we can put labels onto protein structures so we can align them.
What we need is a better alphabet.
And so here's the idea.
Here's a little protein, and here are the amino acids of this protein, drawn very schematically.
We can break this protein into little pieces of structure.
So this fragment here is the last few residues.
This fragment here is the next bit of structure, and so on and so on.
So we'll take this long protein and break it up into pieces.
And you can imagine that this fragment here, as an example, so in the middle, this fragment
here corresponds to this bit in blue.
And this fragment over here, perhaps that corresponds to the end over there, and this
corresponds to the next piece of structure, and so on.
So we take this larger protein and break it into little pieces like this, and it's
effectively a window that slides along the structure.
If we can do that, we can take two proteins and do some kind of comparison.
So here again are my black and red proteins.
We'll take the black protein and break it into these pieces.
And now instead of individual amino acids, we'll say here's the first fragment, and that's
going to be represented by column 1.
And the second fragment from the structure is going to be responsible for column 2 and
the third fragment for column 3.
Now let's go to the red structure, this thing up here.
We break it up into the overlapping fragments, and we say, okay, this fragment here is responsible
for this row, and the next fragment is responsible for the next row, and so on and so on.
And now what I need to do to calculate out a similarity score matrix is I need a method
that tells me is this fragment here in this column similar to the fragments here, here,
here, here, and here.
So we've broken the two proteins into fragments, and now we need to compare the pieces of proteins,
the fragments to each other.
So how would you compare little pieces of proteins?
There are lots of methods, and I'm just going to give two examples of the philosophy.
And there really is a big literature on this, and there is no accepted best method.
Different people use different methods, and different groups get different answers to
protein structure alignments.
Let's consider fragments and comparisons based on angles.
So the question is, does some arbitrary fragment resemble a fragment from a different protein?
What we can do is take this fragment here, and we can calculate out the backbone angles.
So phi and C angles in this fragment here.
So we've got phi and C, one, two, three, four, and I can write them down as a list of numbers
or a vector.
So for this fragment here, I'll say, okay, that corresponds to this set of numbers here.
So psi, i, psi, dry, maybe this thing is six residues long.
So up to angle number six, and I do that for both the phi and psi angles.
Then I take each fragment from the second protein, it's over here somewhere, and I get
out the corresponding numbers for a fragment from the second protein.
So I've got a vector here from protein one, and a vector here from protein two.
And now I need a way to say, how similar are the angles in this fragment to the angles
in a fragment from a second protein?
There are many ways you could do this.
I could just say, what's the difference between the vector, the set of numbers here from protein
one and the corresponding numbers from a fragment from protein two?
So I could just take the vector difference and say how what, which is another vector
of numbers, another set of numbers, and say how different are these two vectors to each
other and calculate a distance between them in what is actually now a space of numbers.
So I'll call that a distance.
So if two fragments are almost identical to each other, the angles will be identical,
and these two vectors will be almost identical, the difference between them, this D here,
will be very small.
So what I want is a similarity matrix.
So maybe I just take the reciprocal, I say one divided by D goes into my score matrix.
So if two fragments are very similar, the difference is small, one on D is a big positive
number, so I get a big positive value for the similarity.
And why does this work relatively well?
Because if you have regular structure, alpha helix beta strand, they have got typical angles,
so you will align typical secondary structures to each other.
If I've got something that's not regular secondary structure, like a turn here, there are still
corresponding typical angles here, and if this turn is similar in protein 1 and protein
2, then I'm going to get similar angles, small distance, and similarity here.
So it doesn't require regular secondary structure, it will also work on strange structures.
So that's one method, it's not perfect, but it does work relatively well.
Now a second method to compare fragments of proteins to each other.
The story is still the same, I have a whole protein here, and I am breaking it up into
little pieces, so here's a typical piece, the next step would be to shift this along
and look at the next piece and the next piece and so on.
Probably the most popular program for comparing and aligning protein structures does not work
with angles, it works with intramolecular distances.
Consider the middle residue in this fragment, so maybe if this fragment has a length of
5, if we are working with fragments of length 5, let's consider the third amino acid in
the middle here, and consider his alpha carbon.
I can then calculate the distance from this alpha carbon to the alpha carbon at the start
of the fragment, the alpha carbon in the next amino acid, and the next amino acid.
So that would be this list here, a list of distances from the alpha carbon in the middle
to the alpha carbon at I-3, I-2, I-1 and so on, and from this alpha carbon to the succeeding
alpha carbons.
So from this alpha carbon here, the distance to the next one, the next one, the next one.
So for this alpha carbon here, I have a set of, perhaps it's four distances to neighbors
if I'm working with fragments of length 5 as an example.
So a set of distances or a small set of numbers, I can treat that as a vector as well.
So I have a little vector, I've called it D for distances from protein 1, and this little
harpoon just means that it's a vector.
So I can compare the set of distances from a fragment here to any fragment you give me
from a second protein.
And there's going to be distances that are characteristic of secondary structures that
you know.
So for example, in an alpha helix, you know that the distance from amino acid I to amino
acid I plus 4 is very small because an alpha helix curls around itself.
So the distance from here up to there.
If I was to consider distances in a beta sheet, the distance from residue I to I plus 4 is
very large.
But more than that, if I look at turns, for example, the distance between this amino acid
and that amino acid and that amino acid will be characteristic of a turn.
So the vector of distances from a turn here will be similar to the vector of distances
in some other protein if the turns here are similar.
So distances will also work and characterize protein structure even when there is no regular
secondary structure.
So this method works very well.
It's the basis of a program with a cute name called Dali, written by a lady who lives in
Helsinki.
So using the approaches that I've mentioned, we can calculate an alignment of two structures.
This is not the same as a superposition.
Superposition means taking this set of coordinates here and this set of coordinates here and
putting them on top of each other.
This is what you normally see in a paper or a talk when people want to say two proteins
are similar to each other.
And it's what we are going to need later when I talk about how do you measure structural
similarity.
So that's the question of superposition.
What we have up to now is something different.
I've basically got a table which tells me that for these two proteins here, this amino
acid corresponds to that amino acid and this amino acid corresponds to that amino acid
and this one to this one and so on.
So I have a list of which amino acids correspond to each other.
But the next question is going to be, can I put this protein on top of that one in some
optimal manner?
And that's the question of superposition.
And I believe the word in German would be überlagro.
Now if two proteins are identical, the problem is pretty easy.
Actually it's very easy.
But if they are not identical, it is difficult.
And it's difficult in two ways.
Firstly, the maths is not so easy.
It involves some pretty horrible matrix arithmetic.
But secondly, this is fun, there may be no correct answer.
It depends what you want.
Let me show you with an example.
So what I am going to claim is that there is no perfect superposition of this structure
onto that structure.
Here are my two proteins.
Now they are colored differently.
So I have a blue protein and a pinky-red protein here.
I ask you to give me the optimal superposition.
You might say, let's put the red protein on top of the blue one down like this.
You notice that this domain here is identical in both proteins.
But they seem to be very different at the top.
On a different day, you might say, no, let's align the first parts of the protein, which
are almost identical.
And then they look very different down here.
And what's clear is there is no perfect superposition of the two proteins.
And fundamentally, there is no depiction of the differences that I can give you that tells
you the two proteins consist of two almost identical halves.
And they just differ in the middle here.
And what would you get if you ask a program to align the blue protein to the red protein?
You're probably going to get an answer that actually isn't that good.
You would say that in order to get them as similar as possible, I should calculate a
superposition that looks like this third one down here, where I have little differences
all over the two structures.
That in a sense is the optimal superposition.
But now I don't get the information I want.
I don't notice that actually this half of the protein, this domain here is almost identical
in both proteins.
And this domain here is almost identical.
I just see a lot of little differences all over the place.
So this is part of a more general problem.
When I do a superposition, if I do a superposition on a couple of residues, so this is 100 residues
long, and I put it into a program and I say, give me the best matching 50 residues, I might
actually get this alignment over here.
But if I say, do the alignment over all 100 residues, I'm probably going to get this picture
down here.
So when I do a superposition of two proteins, when I look at their similarities, it's really
an open question.
How much of the structures do I want to put on top of each other?
And there is no correct answer.
You are going to get different views, depending how much of the two proteins you use.
So don't be disappointed.
Learn to live with this uncertainty and enjoy it.
So let's summarize structure alignments.
What I didn't mention before was they tend to be much slower than sequence alignments.
In sequence alignments, to align A, B, C to D, E, F, I just look up in a table how similar
is an A to a D or an E or an F. When I'm doing structure alignments, I have to calculate
out, I have to extract all of the fragments, calculate some geometric property like angles
or distances, something that takes time.
So I can't do large scale alignments or it's not, it's going to take much more computer
time than with sequences.
It's no problem to align a pair of proteins, but multiple structure alignments will be
difficult.
The other thing is, everything I have said is based on empiricism, optimism, and what
the computer scientists call heuristics.
There is no statistical or rigorous basis.
So in summer semester when I talk about sequence alignments, there's a good statistical basis.
It's actually very easy, it comes down to how often does this kind of amino acid mutate
to that kind of amino acid.
That's easy with sequences.
When I talk about structures, I'm just inventing a similarity measure.
There is nothing from evolution that automatically tells me a number that says this kind of structural
term is similar or different to that kind of structural term.
The next thing is gap penalties.
I'm going to need penalties for deletions and insertions, but in all practical programs
that I've ever seen, this is done by trial and error.
And finally, there's no definition of what's optimal.
So am I happiest when I align 90% of structures, or am I happy when I find the best 10% of
structures, or the best 30 residues that are similar between two proteins or the whole
structures?
There is no formal definition of optimal.
When you're talking about structural alignments, you have to say, I have done it, looking to
optimize exactly this kind of score or that kind of score.
So nasty business.
In the next file, I'll talk about how do you measure the similarity of two protein structures.