It looks as if we have a method for predicting secondary structure even if you cannot do
pseudonauts. At the start of the method I said let's just maximise the number of base
pairs. That is not really enough. Let's consider a practical simple scoring scheme for secondary
structure which is liable to be closer to chemistry. So the first step is we're going
to build this up in steps. The first step is let's go from base pairs to hydrogen bonds.
Why would you do that? Because we know that a GC pair has three hydrogen bonds
but an AU pair or a wobble pair have only got two hydrogen bonds. So you would expect
a structure to be happier if it makes more GC base pairs than AU base pairs.
Or to put a number on it imagine I've got two alternative structures. One has got three GC
pairs so that's nine hydrogen bonds but an alternative structure has got four base pairs
but they're only AU base pairs so that would be eight hydrogen bonds. So this set of base pairs
would be better than that set of base pairs. Okay so we better take that into account.
That's one aspect but now the second improvement to the scoring scheme
is much harder to quantify. Look at my high resolution picture of an RNA structure here.
Everything I've said about scoring is based on a base pair here here here and here and so on
and I haven't considered this region over here. What if I've got three unpaired bases here
or maybe I've got five unpaired bases here. These were all zeros before. They don't count for
anything but now look at it from the point of view of a chemist. Are these bases interacting
with each other? Well they're not forming base pairs but are they hydrophobic interactions?
Is there some strange hydrogen bond happening across here or here? Are they interacting with
the solvent? Well there's energies associated with all of these possibilities and there's
entropy associated with an unpaired region. So there's a bit of order when I form a base
and there's a bit more disorder when I do not form a base pair. So I don't know what the energetic
contribution is from three bases or five bases. All I know is it's not zero. So we're going to
have to find some way to take that into account. It might be positive, it might be negative,
but we cannot ignore the contribution from unpaired bases up here.
Now the next thing is I mentioned stacking much earlier, this slightly mysterious term here.
So stacking, remember base stacking means the energy happiness from having a ring
flat lie against another flat ring over there. Now what does that mean when I think about scoring?
It means that the energy of looking detail here, this space here and this space here is not
independent of the bases below and above forming a base pair. So certain secondary structures will
put big purine rings on top of each other and some will put purines on top of pyrimidines which will
not have such a good stacking energy. Or we could just say that the energy of base pairing
is not well represented by saying the energy here is independent of the interactions here below
and above. So we cannot say that each base pair is independent of the base pairing of his neighbours.
So we can't say just that the energy that I get from forming base pair i and j is simply the sum
of this particular base pair i and j plus the sum of the preceding and preceding bases in this case.
They are not, this base pair is not independent of what happens at this base pair there.
So is there some easy way to account for this? Not a perfect way but just to bring
some idea into the scoring scheme. So what I want is to say that the score I give to this
base pair here depends on the base pair above and the base pair below. Just a simple way to bring
that in on average and I don't want to add too many parameters. I don't want a horrible big mess
of parameters. These three questions are going to lead to what's called the nearest neighbour
model which is the most commonly used way to score secondary structures for RNA.
Let me tell you about the nearest neighbour model. Here is a piece of RNA, it goes along here
through unpaired bases and comes back. When I spoke previously about scoring I said
the energy here is gc plus ua plus au. What I do in this model is quite different or slightly
different. I say I don't look at a gc pair alone. I say let's look at this pair and this pair at
the same time and instead of having three kinds of base pair we're going to have four times four
sixteen kinds of pairs of pairs. So in a table I look up what's the energy of gu paired with ac
and the overlapping next pair here. So the next term I add in is au sorry ua au which is ua au
so that would be this here and then I look at the next overlapping pair here. So to get the score
of this structure it would be minus 2.2 for the first pair minus 1.3 minus 2.2 minus 3.3 so the
first pair the next overlapping pair and the next overlapping pair and if you think about it
carefully what I have done is introduce the idea that the energy of this base pair here
has a contribution from the preceding base pair and the succeeding base pair over there. So
with this simple approximation I'm not looking at base pairs alone I look at the ones before
and the ones after. At the same time from a table of numbers I have a table that tells
me that unpaired bases of length two four six with a certain composition that is unfavorable
so it gives me a positive energy over there. So I would look up and score this whole structure here
with the sum of the overlapping pairs plus the unpaired loop at the end
and a reasonable question would be where do these energies come from?
How do we calculate these things? These numbers here are not calculated they are stored in tables
and where do they come from? Tedious measurements. So what people do is they take this sequence here
they measure the melting temperature and then they change this base from a c to a g and an a
and a u and with each substitution they measure the melting temperature. So they find if they
put a u here the energy is a little bit worse and then they change an entry in the table here
which would now be for a c g u g pair of pairs and then they extend this loop here by one base
put another a in here measure the melting temperature and then calculate back to the
to the change in delta g values. So it's all done by you could say painstaking experiment
or you could just say these numbers have over many years being empirically tabulated
or they are tabulated based on empirical values.
So let me summarize scoring. The most primitive scoring possibility is just count the number
of base pairs and that's what was done in the 1980s. The next improvement is to count
the number of hydrogen bonds. Then the next improvement is to take into account unpaired bases
and then we add in the idea of base stacking and when we reach this point we really have
a very modern scoring scheme the nearest neighbor model. And finally when you've reached this point
you may well ask me what about tertiary interactions? Those still remain ignored.
You do not take into account the overall folding of a molecule when you predict
the secondary structure. It's quite amazing that these methods work at all.
So how well do they work? I mean just how if you take your sequence and you feed it into one of
these programs what are the what are the errors that we're talking about? For no good reason
people say they think they have about five to ten to ten percent errors in the energies.
I don't think you should take that number too seriously. Nobody really knows what the errors
are but how good are the predictions? There is some better idea there because what you can do
is take the known crystal structures, get their sequences, feed them to the prediction programs
and then compare predicted bases with base pairs that you can see in crystal structures.
Unfortunately it very much depends on exactly what test set you use but I would say somewhere
between a half and three quarters of the base pairs that are predicted are correct. So that's
a useful number to remember. You always get an answer back from a web server or from one of these
programs but a quarter to a half of the predicted base pairs are probably wrong.
Depends on the sequence and the size and so on. So why are these measures not better or why are
these predictions not better? The first problem is that it is in terms of the physics it's surprisingly
difficult. Imagine you are an adenosine base inside an RNA sequence. You might want to make
a base pair with a uracil but there are lots of uracils in a sequence so there are many possible
base pairs that you could form. So there are we can generalize this and say for any base
there are probably lots of good partners for that base and what that means is if we look at the whole
sequence there will be many alternative structures which are almost as good energy.
So yes this predicted structure is best this one is almost as good and when we think in terms of
error it means that actually maybe the second best one was the better structure.
What we can do though is treat this in a more elegant way and we can start talking about
probabilities of bases. This is good fun because computationally the method to calculate
probabilities is very very clever and it was first done by a guy called McCaskill who lived
for many years in Jena despite having a Scottish name McCaskill and actually he was educated a
couple of miles away from me. Not that any of the glory has worn off. So what the McCaskill
algorithm does is it's like structure prediction. You can find the optimal set of base pairs
for a given sequence but what you can also do is say yes these base pairs are optimal
these are drawn here but there is a non-zero probability of an alternative base pairing here.
So if you look in this region really in great detail here you can see there's a little red spot
so this corresponds to this helix over here and it's saying that actually this bulge could be
somewhere else with a reasonable probability but you might say okay that's a very small change.
From the McCaskill algorithm what you get is other possibilities. So look along the sequence here
so go towards near base 130. The bases in this three prime end could be forming base pairs
with bases in the five prime end with a very non-zero probability. So that would correspond to
bases here forming base pairs with some of these guys over here or maybe actually over there.
So in the probability plot we have the optimal structure on one side the optimal prediction
but we have probabilities of alternative base pairs given in the top right hand side.
So half an hour ago I said this is the fourth way to represent the secondary structure
of an RNA molecule. This is strictly speaking the alternative representation of this
but the reason we like dot plots is we can get some idea of the probabilities of alternative
base pairs which correspond to either slightly different structures like here or here or
radically different foldings of the molecule over there. So interesting way of looking at the
structure and that is the additional information provided by the dot plot.
Let's continue with the question of reliability.
In RNA structures we do not have only Watson-Crick base pairs with nice hydrogen bonds.
We have all kinds of hydrogen bond possibilities which have significant energies. We have all kinds
of Van der Waals interactions. When you look at a folded molecule like this one
this is not just a set of nice base pairs like in this region. It is actually stabilized
by things like the Van der Waals interactions in this region here. And for this particular example
so for this structure here we can actually feed this structure into another program,
get out the classic base pairs in this region here and get out some of the interactions
between the helices and those would correspond to these lines here. And you can do this with a
dedicated program. You can do that there are programs which will do this for RNA very
specifically. You can also do it at home in the kitchen by reading these coordinates into a
program like chimera and just asking for the neighboring atoms for for example the bases here
and you will find they are very close to some of the atoms from residues or bases over there
or bases over there. So these interactions will affect the probability of forming helices up there.
If a helix here allows me to form favorable interactions there it will be more stable
even if this helix here is not the optimum when I just look at scoring in the algorithm that I
described earlier. So a set of tertiary interactions might make something stable
if it was only borderline possible earlier.
And these interactions are really important. You see them in every interesting structure
that you look at. If I just take a random example like this purine ribose switch here
it clearly has regular base pairing in this region and regular base pairing here. But
when it folds around that's all due to these funny tertiary interactions which are marked
on to this secondary structure representation here. The next structure again just a quick
example it has regular base pairing here some regular base pairing here but when it folds up
that's all due to these tertiary interactions here and these might change the balance of energies
in other parts of the structure here and these tertiary interactions are all ignored
by the secondary structure prediction programs. So they will lead to you making wrong predictions.
Let me summarize this issue of reliability. There are alternative structures with similar energies
and if the second best guess is actually the correct one you are just not going to see it
with one of the current structure prediction programs and the algorithm that I discussed
simply ignores tertiary interactions. So it's not surprising that the predictions are not so reliable
and well may you ask why do people keep putting them in papers? It's because it's the best you can do.
The state-of-the-art predictors are a tiny bit more sophisticated than the methods I described.
What you do in a real if you're very serious about predicting secondary structure
is you can at least get rid of some of the errors by saying if I have a sequence in this species
the same sequence in another species probably adopts the same shape. So related sequences
will fold the same way very much the same idea as with protein homology modelling. So the procedure
is if you have your particular sequence and you want to predict the sequence of your structure
you can use a program which will take closely related sequences from some data bank
and try to fold all of them simultaneously. So we'll look for an average answer and this does
make a difference. Just looking at it statistically it has to be an improvement because
if you imagine our mistakes are random then repeating the calculation averages over random errors.
So now will come the most fun part. Imagine you have solved the secondary structure prediction
problem. Could you still, could you really predict how an RNA molecule is going to behave
and what is biologically relevant.