Good! Last video file about 15 slides, mostly about loop modeling with one last
topic at the end. So loop modeling is going to come up in all interesting
modeling exercises. Typical situation is you have your template structure here,
you have your sequence here, you've calculated the best possible alignment
but there are some gaps or insertions. So physically what does this correspond
to? Let's look at my high resolution picture here. So this is an element of
secondary structure, another one over here, and there's some unstructured less
structured loop joining the two elements of secondary structure. This
alignment jumps over a few residues which would correspond to an initial
model that goes up here and then it has to jump through space. So now we have a
problem. You do not want to change the secondary structure elements because
those tend to be well conserved but you have this loop here that effectively has
to be modeled from scratch. You somehow have to join this bit here over to this
bit over there but using the amino acids here which would correspond to these
amino acids in the alignment. So the problem is you've got some residues with
unknown structure but you can say that the end points are relatively fixed. Not
absolutely but secondary structure tends to be conserved between similar proteins.
So we have to move these residues so as to join this point up to that point. So
the loop modeling problem. We would like to avoid disturbing the regular secondary
structure. That's most likely to be correct. The end points are also not
absolutely fixed but relatively fixed and for these residues here we know
their composition. We know which amino acids are here. So what we're looking
for is an arrangement of the backbone and side chains here which is
geometrically possible and should be of low energy. I'm going to talk about three
possibilities roughly in order of difficulty or cleverness or at least the
first one is not very practical but it's what you might think of at first. So
brute force approaches then the return of distance geometry and lastly
database searches of various kinds. I don't like this approach very much but
it's something you might consider. Brute force searching for possible
configurations. Imagine I say an angle can be discretized into into 12
possibilities which would be every 30 degrees. So a small a small number not
terribly detailed. I could generate coordinates by going to the first angle
here taking the 12 possibilities the next angle the 12 possibilities here and
the next angle 12 possibilities here and so on. I can calculate all of these
things out and for every possibility I could say does the side chain come around
and reach this point here. What I would be doing for n angles is constructing an
n-dimensional grid so this would be an n-dimensional grid search. It's not
going to it's not going to work quite so well especially if you approach it
naively as I described. How many angles do you have? You've got phi and C at every
residue so it's two angles. We'll say that omega the peptide the peptide plane
angle is fixed but the number of possibilities is going to be very big
very fast. So per residue 12 times 12 possibilities for n res residues that's
144 up to the n res power so that's a big number. You can do it much more
cleverly so in the literature there are examples. You might not use 12 times 12
possibilities but you could discretize phi and C into a smaller number of
possibilities according to the Ramachandran plot. So you can make this
approach work for small pieces of loops but it's not such a nice approach there
are much nicer methods. A much nicer method is to use distance geometry so
you have probably forgotten I'm sure you have forgotten everything that I've said
in previous lectures. Remember distance geometry came up as the method for it
came up in the context of nuclear magnetic resonance calculations. You have
distances between some points and you have the distances based on the
chemistry of a structure and you generate upper and lower bound matrices
then you get up a trial matrix convert to a center of mass matrix convert to
the so-called metric matrix and get out the eigenvectors and eigenvalues. How's
that relevant here? What we have is we know the distance from here over to
there but we know the all of the inter atomic distances between everything that
is covalently bound and we know the angles and so on. So what we can do is
just calculate out a distance geometry solution here. We don't have any NMR data
but that's not what we're worried about right now we just want something that is
chemically possible. So we put in all of the chemical distances so this carbon is
one and a half angstroms from that carbon which is 1.3 angstroms from the
backbone nitrogen and so on. From the angles the bond angles we get out the
corresponding distances and we've turned it into a distance geometry problem. Now
this is actually how the program model up works. It generates 50 or 100 possible
distance geometry solutions which should all be chemically reasonable
solutions and they're chemically reasonable in that all of the bond
lengths and angles should be okay and we don't have atoms on top of each other
because of the lower bound matrix. It's far from perfect because there's been no
consideration of torsion angles so we might have built four atoms in space
like this but we have ignored the fact that this confirmation is better than
that one and not as good as that one. But that's okay we've generated something
that is plausible and if you'd like could even be improved on it by a simple
energy minimization. Third approach is used in some programs and it's also very
reasonable and does give good solutions. So this would be database searching. Let
me explain with a toy example. Imagine this region here is nine residues. So
let's go to the protein data bank and collect the coordinates of every loop
that's nine residues long. For each loop we calculate out the end-to-end distance.
So from here over to there and then we could try out those loops as possible
solutions for the unknown coordinates. Now we can do it we can be a little bit
cleverer than that. We could look at the geometry at the start and at the end of
these loops and make sure the chain is going in the correct direction. That's a
first bit of the approaches that people use actually do do that and then
you can even be a little bit cleverer. You can say for these nine residues here
I know their sequence so what I'll do is in my database search I will even look
for loops which have got almost the same sequence and that's actually that works
really well because if two things have got similar sequences they
probably have similar structures. So this is not used in too many programs but it
does seem to work. It requires a lot of tabulated data. So in order to make this
approach work you have got big tables of all the two residue loops three,
four, five and so on and probably the sequences that constituted these loops
and if you're going to make this work quickly you would have to pre-calculate
some of the geometric properties. So you're talking about storing quite a lot
of data but it's also guaranteed if your loop is not too strange it's also pretty
much guaranteed to give you something that is chemically plausible because
you're working with databases from the protein databank and fits to your
particular circumstances. So that approach I also like quite a lot.
After you've done all of this you've optimized the side chains or found
possible side chains. You've built some coordinates for the loop residues. You'll
still have to do some repairs to your structure. You'll find the some side
chains will not have fit well so you might have some atoms on top of each
other. You've got the best possible solution that you could find with your
first method but it's not that good. The loops will often be wrong. Of course when
I compare two protein structures which are related, secondary structure tends to
be conserved but it also does move around a bit and it's very common in one
structure to have an alpha helix here. In this structure it's a bit longer or
shorter or it's got a proline inserted in the middle and it's kinked a little
bit and so on. So typically for a model you do one last round of energy
minimization or some kind of refinement. If you like wasting
computer time you might do molecular dynamic simulations. What is worth
worrying about is how can you look at the quality of the structure afterwards.
Basically there are two approaches. There are statistical and energy approaches
although as I explained in summer semester they are different sides of the
same story. So you can look at you can do energy calculations or you can look at
the geometry of your structure. Are all the bond lengths and angles correct? Are
all the torsion angles in reasonable places? Does the Ramachandran plot look
like it should for a normal protein? Those are all fine things to
look at. Then there are some properties that modeling people like to talk about.
Do you know something about your protein specifically? For example in the laboratory
somebody has discovered through site-directed mutagenesis that this
amino acid is essential for activity. Is it in something that looks like an
active site? That's why I say these are vague properties. If you know that a
certain amino acid is part of a binding site, maybe talking to another protein, is
it on the surface? Is there any other kind of experimental data that you have?
So there will be certain properties for each protein which you might be able to
check with your model. But that's too vague to talk about I would say in this
course. Could you really check by energy? Well what you can think about is using a
classical energy function and that really is the focus of the start of the
next semester. If physics was perfect in our energy functions it would actually
include all of the ideas that I mentioned. So soluble residues on the
surface and torsion angles in reasonable places and atoms are just touching each
other but not on top of each other. What people normally do is they adopt a
statistical approach. So they count the number of hydrophobic residues on the
surface and the number that are buried in the middle of a protein. If there are
too many hydrophobic residues on the surface it's statistically unlikely. You
look at the distributions of phi-psi angles and you compare against
counts in the protein data bank. So are the statistical properties of your model
in agreement with what you expect from the protein data bank and this can be
well quantified. So there are lots of empirical, there are several good
empirical scoring measures. What I said in this lecture is pretty much the truth.
You could say it's a bit simple. You can combine steps and repeat steps. If you
are using a program like Modeler you're probably going to generate many models.
You might use different templates. If you're using one of the good web servers
and there are really good web servers for this problem they tend to give you
back more than one possible solution and they say you can choose between the
ones that you like. If you talk to a modeling expert you should stop doing so
immediately. The automatic methods are astonishingly good at this problem and
they also give you good quality measures. What do you get from all this? What did
I say at the start of the lecture? In the easy cases you build a model and it
looks a lot like the parent structure. What you've gained is some geometric
impression of your sequence. In the difficult cases you're going to build a
bad model. It might be folded up in general correctly but it will have lots
of errors. The reason this is all okay is just remember that if
it's a protein that's important to you you probably are an expert on that
system and you can look at properties like the chemistry and say is this
reasonable. Some proteins are so important that you're not going to wait
for the experiment or for a competitor to make some statements about the
protein. And you can even with a poor model make simple predictions. So which
residues can I modify to use my protein in a biosensor without destroying its
binding activity. And now come back just for a few seconds to my picture
of the absolute limits of modeling. So a typical modeling target. Here I'm going
to show two proteins which would be a typical task. You know you're going to
get the overall fold correct but the loops and details will be generally
quite bad. So here are two proteins. They have names if you like this kind of
thing. 2M and R and 4A and L. And here are the two structures which are known super
imposed on each other. They are obviously closely related and you could use the
blue structure as a template for the red one. On the left here is a sequence
alignment but there is a trick. This is not the sequence alignment that you
would calculate with the best alignment program in the world. This sequence
alignment corresponds to putting these two structures on top of each other and
then saying from the structural superposition this residue is aligned to
this residue and this residue is aligned to this residue and so on. So this
sequence alignment is the exact correct solution that you get from the
structural superposition and it's sort of reasonable but it's a difficult one
for a sequence alignment program to get because it has to put in a gap
of length 2 over here and a larger gap over here and so on. And a sequence
alignment program would often move this region over there so as to minimize the
gap opening penalties for example. So you would not get the correct alignment
probably with a sequence alignment program and although these two proteins
are very close to each other look at this big insertion in the blue one here.
You're not going to be able to model these blue residues very well or the
extra long helix here whereas the template structure actually has a loop
there. So the alpha helix has been shortened on the evolutionary
timescale and down here the structures somewhat diverge from each other. So
whenever you're doing modeling and you have an interesting case like this which
has got about 25% sequence identity I get that from here you're not going to
get a perfect model and this would be the absolute limit of what you could get
if you had the perfect alignment. Why do I sometimes say I try to avoid protein
modeling? There is a good reason. Imagine the following realistic scenario. I have
some coordinates from the protein data bank on the left. I have built for my
sequence the model on the right. In the protein data bank if I look at the
coordinates there's a ligand here and you can say that this residue and this
residue interact with the ligand. You go to your model you say well I assume
the ligand binds in the same place and so now in my sequence this
phenylalanine and this phenylalanine are involved in
interactions. Here's the question. Did you actually need the model to work that
out? Here's the known structure from the protein data bank and here's your
sequence. In the known structure I can go and mark the residues which are involved
in interactions with some ligand or these are part of the active site. From
my sequence alignment I can simply say that this C here has been replaced by an
F in my sequence and this S here has been replaced with an F. On the basis
of the sequence alignment alone there are often properties I can work out
without going through the sideways step of a model. People like to build
models because it lets you draw a picture of what your protein could look
at but strictly you can often get better quality answers by just looking at the
sequence alignment. I do say better quality because this kind of picture
here this alignment is a clearer indicator of the evolutionary history.
When I look at this sequence and this sequence I can say the D, E, G and H are
completely conserved and this residue here has changed. So if this one in this
conserved environment has mutated it has been replaced and this
residue here is probably now adopting the role that was taken by this residue
here. So I often try to avoid protein modeling when I work with biochemistry
groups but not always they can be quite insistent they want a picture of their
protein. Don't forget for the clausal don't forget any of the ideas about
sequence similarity when is it important how do you judge the significance. Be
prepared for questions about loop modeling and sidechain placement. Don't
worry about any of the vague statements when I said how do you look at the
specific properties of your protein or these are roughly the absolute limits of
protein modeling. For the clausal I try to find the more technical
issues and that's right for now.