As regular readers of this blog will know (I know you’re out there somewhere!), one of the main focusses of OPIG at the moment is antibody structure. For the last ten weeks (as one of my short projects for the Systems Approaches to Biomedical Science program of the DTC) I have been working on predicting the structure of the CDR-H3 loop.

So, a quick reminder on antibody structure: antibodies, which have a characteristic shape reminiscent of the letter `Y’, consist of two identical halves, each containing a heavy and a light chain. Heavy chains are made up of four domains (three constant domains, CH1, CH2 and CH3; and one variable domain, VH), while light chains have two (one constant domain, CL; and one variable domain, VL). The variable domains of both the heavy and light chain together are known as the Fv region; most naturally occurring antibodies have two. At the ends of these Fv regions are six loops, known as the complementarity determining regions, or CDRs. There are three CDRs on each of the VH and VL domains; those located on the VL domain are labelled L1, L2 and L3, while those found on the VH domain are labelled H1, H2 and H3. It is these loops that form the most variable parts of the whole antibody structure, and so it is these CDRs that govern the binding properties of the antibody. Of the six CDRs, by far the most variable is the H3 loop, found in the centre of the antigen binding site. A huge range of H3 lengths have been observed, commonly between 3 and 25 residues but occasionally much longer. This creates a much larger structural diversity when compared to the other CDRs, each of which has at most 8 different lengths. It is the H3 loop that is thought to contribute the most to antigen binding properties. Being able to model this loop is therefore an important part of creating an accurate model, suitable for use in therapeutic antibody design.

Predicting the structure of the loop requires three steps: sampling, filtering and ranking. There are two types of loop modelling method, which differ in the way they perform the sampling step: knowledge-based methods, and ab initio methods. Knowledge-based methods, or database methods, rely upon databases of known loop structures that can be searched in order to find fragments that would form feasible structures when placed in the gap. Whilst predictions are made relatively quickly in this way, one disadvantage is that the database of fragments may not contain anything suitable, and in this situation no prediction would be made. Ab initio (or conformational searching) methods, on the other hand, do not rely upon a set of previously known loop structures – loop conformations are generated computationally, normally by sampling dihedral angles from distributions specific to each amino acid. The loops generated in this way, however, are not ‘closed’, i.e. the loop does not attach to both anchor regions, and therefore some sort of loop closure method must be implemented. The assumption is made that the native loop structure should represent the global minimum of the protein’s free energy. Ab initio methods are generally much slower than knowledge-based ones, and their accuracy is dependent on loop length (long loops are harder to predict using this method), however unlike the database methods, an answer will always be produced.

For my project, I have examined the performance of FREAD (a knowledge-based method) and MECHANO (an ab initio method) when predicting the structure of the H3 loop. At the moment, FREAD produces better results than MECHANO, however we hope to improve the predictions made by both. By optimising the performance of both methods, we hope to create a ‘hybrid’ loop modelling method, thereby exploiting the advantages of both approaches. Since I’ve decided that this is the project I want to continue with, this will be the aim of my DPhil!

Last time I gave a presentation about different papers describing Molecular Dynamics simulations of TCRpMHC (http://blopig.com/blog/?p=648&preview=true). This time I extended this to more of my own work. The focus of this talk was about the motivation why to choose a certain system and which requirements if must fulfíl for reliable conclusions. In short they are:

1) A larger number (>100) of experimental values (e.g. some kind of binding, immunogenicity, etc) of a certain TCRpMHC system. These values should be provided by:
– the same group
– the same HLA/MHC batches
– the same binding conditions
– in the ideal case in the same manuscript

The values should NOT be from a database since different experimental groups come to extremely different results for the same complexes as several examples show e.g.:
The binding IC50 affinity values of PKYVKQNTLKLAT to DRB1*01:01 range from 1nM and 600nM (IEDB entries).

2) Structural data exactly matching the systematic experimental data mentioned above. If multiple structures are involved they should be published by:

– the same group (in the ideal case even published together with the above mentioned data by the same group)
– be contemporary

Data which fulfil the above mentioned criteria is quite hard to find since most biologists are mainly interested in some fancy, however, rather anecdotal examples and rarely in systematic data production.

Once one has found such a system a large number of Molecular Dynamics simulations can be performed which will yield systematic differences not just differences originating from random events or data bias.

If you ask someone who works with membrane protein structures what they think a helix kink is, you will probably get a fairly vague answer. They would probably tell you something like a kink is a point in the helix where there is a sharp change in the direction of the helix axis. Like the helix on the right in the picture.

Two example helices

There are a number of published methods to identify kinks in helices (ProKink, Helanal, MC-Helan, and TMKink, to name a few). The detail of identifying kinks (and hence the definition of kinks) differs a lot between the methods. That would be fine if they all identified the same helices as having kinks, and the same positions in each helix as kinked, but they do not. Even the number of helices that are kinked differs a lot – anything from 6 to 60%. It would be easy if all α-helices were like the two in the figure – clearly kinked or straight. Generally the methods agree on these ‘easy’ helices. But there are lots of helices that are difficult to classify.

Why do we want to computationally identify them? Well, kinks are functionally important in membrane proteins. Membrane proteins are both medicinally important, and hard to experimentally determine the structure of. So, modelling their structures is a useful thing to do, and their structure includes kinks. But also, they are a structural motif. If we can write down what we think a kink is, use that definition to identify kinks, and then use information from those kinks we identified to (reliably) predict the existence of other kinks, we will know that we fully understand to motif.

There are a remarkably large number of perfectly sensible ways to identify a sharp change in the axis of an α-helix, given the coordinates of the backbone atoms.
The published methods (mentioned above) are a bit cumbersome (they require you to create input files, and parse at least one, if not many, output files), so from my experience people tend to make their own methods (That is not just me with Kink Finder, but many of the people who need to identify kinks that I have spoken to at conferences do not use a published method).

A short summary of ways to identify kinks:

1. Fit axes to short sections of helix (4-8 residues). Give each residue an angle calculated from the angle between the axis of the section before it, and the axis of the section after it. If the largest angle in the helix is greater than a threshold, annotate the helix as kinked, at the residue with the largest angle
2. Methods similar to (1), but using a measure other than an angle. For example, the curvature of a line fitted to the helix, or the distance between the ith and (i+4)th Cα residue
3. Identify sections of the helix that are ‘straight’. Where a helix contains more than on section, it is kinked
4. Look at them, and classify

Even for (1), there are lots of ways to calculate a helix axis. You can us least-squares (very sensitive to the number of residues used in the fit), or fitting to a cylinder (better, but slower), or a vector method using 4 Cαs. Similarly for (2), you could fit a spline, or just a polynomial. This is before you decide on (e.g.) how many residues you are going to fit axes to (6?, 7? 8?), or what smoothing parameter to use in the spline fit, or what order polynomial.

How should we classify this helix?

The point is, there are lots of ways to do it, but there is no consensus definition. You can use one method, or 2, or more, but they will give you different answers. Because we have no concise definition, it is hard to say which helix classification is ‘right’ and which one is ‘wrong’. Take this helix, it is not perfectly straight, but is it not straight enough to be kinked? Or is the change in axis over a number of turns, making it curved rather than kinked?

There are a few ways round this problem, where your computer program is struggling to ‘correctly’ classify helices. Rather than using a computer, you could manually curate a set, which has been done. However, there are a few issues here. First, their definition of a kink was a bit vague – and certainly difficult to turn into a computer program. Second, humans are very good at seeing patterns, even when they are not really there. Third, the end aim, at least for me, is to incorporate this into structure prediction, where a computational formulation of a kink is necessary. Another solution is to accept that your program is deficient, and put the borderline (i.e. difficult) cases into a third group, and removing them from your analysis. This does help to improve your signal, but is a little unsatisfactory.

To conclude, there are not two types of helices, there is more of a spectrum, from very straight, through a bit kinked, to very kinked. Classifying them is a hard problem, with lots a different approaches available. But, while the methods give different answers (particularly in identifying the position of the kink in the helix), and they do not indicate the same causes of kinks, there is work to be done.

If you need to cite R, there is a very useful function called citation().

> citation()

To cite R in publications use:

  R Core Team (2013). R: A language and environment for statistical
  computing. R Foundation for Statistical Computing, Vienna, Austria.
  URL http://www.R-project.org/.

A BibTeX entry for LaTeX users is

  @Manual{,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2013},
    url = {http://www.R-project.org/},
  }

We have invested a lot of time and effort in creating R, please cite it
when using it for data analysis. See also ‘citation("pkgname")’ for
citing R packages.

If you want to cite just a package, just pass the package name as a parameter, e.g.:

> citation(package = "cluster")

To cite the R package 'cluster' in publications use:

  Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M., Hornik,
  K.(2013).  cluster: Cluster Analysis Basics and Extensions. R package
  version 1.14.4.

A BibTeX entry for LaTeX users is

  @Manual{,
    title = {cluster: Cluster Analysis Basics and Extensions},
    author = {Martin Maechler and Peter Rousseeuw and Anja Struyf and Mia Hubert and Kurt Hornik},
    year = {2013},
    note = {R package version 1.14.4 --- For new features, see the 'Changelog' file (in the package source)},
  }

This will give you BibTeX entries you can copy and paste in your BibTeX reference.  If you are using M$ Word, good luck to you.