# We can model everything, right…?

### First, happy new year to all our Blopig fans, and we all hope 2016 will be awesome!

A couple of months ago, I was covering this article by Shalom Rackovsky. The big question that jumps out of the paper is, has modelling reached its limits? Or, in other words, can bioinformatics techniques be used to model every protein? The author argues that protein structures have an inherent level of variability that cannot be fully captured by computational methods; thus, he raises some scepticism on what modelling can achieve. This isn’t entirely news; competitions such as CASP show that there’s still lots to work on in this field. This article takes a very interesting spin when Rackovsky uses a theoretical basis to justify his claim.

For a pair of proteins and Q, Rackovsky defines their relationship depending on their sequence and structural identity. If and share a high level of sequence identity but have little structural resemblance, and are considered to be a conformational switch. Conversely, if and share a low level of sequence identity but have high structural resemblance, they are considered to be remote homologues.

Case of a conformational switch – two DNAPs with 100% seq identity but 5.3A RMSD.

Haemoglobins are ‘remote homolgues’ – despite 19% sequence identity, these two proteins have 1.9A RMSD.

From here on comes the complex maths. Rackovsky’s work here (and in papers prior, example) assume that there are periodicities in properties of proteins, and thus apply fourier transforms to compare protein sequences and structures.

In the case of comparing protein sequences, instead of treating sequences as a string of letters, protein sequences are characterised by an x 10 matrix. represents the number of amino acids in protein (or Q), and each amino acid has 10 biophysical properties. The matrix then undergoes Fourier Transformation (FT), and the resulting sine and cosine coefficients for proteins and are used to calculate the Euclidean distance between each other.

When comparing structures, proteins are initially truncated into length-L fragments, and the dihedral angle, bond length and bond angle for each fragment is collected into a matrix. The distribution of matrices allows us to project proteins onto a pre-parameterised principal components space. The Euclidean distance between the newly-projected proteins is then used to quantify protein structural similarity.

In both sequence and structure distances, the distances are normalised and centred around 0,0 by calculating the average distance between and its M-nearest neighbours, and then adjusted by the global average. Effectively, if a protein has an average structural distance, it will tend toward 0,0.

The author uses a dataset of 12000 proteins from the CATH set to generate the following diagram; the Y-axis represents sequence similarity and the X-axis is the structural similarity. Since these axes are scaled to the mean, the closer you are to 0, it means you’re closer to the global average sequence or structure distance.

The four quadrants: along the diagonal is a typical linear relationship (greater sequence identity = more structural similarity). The lower-right quadrant represents proteins with LOW sequence similarity yet HIGH structural similarity. In the upper-left quadrant, proteins have LOW structural similarity but HIGH sequence similarity.

Rackovsky argues that, while the remote homologue and conformational switch seem like rare phenomena, it accounts for approximately ~50% of his dataset. Although he does account for the high density of proteins within 0,0, the paper does not clearly address the meaning of these new metrics. In other words, the author does not translate these values to something we’re more familiar with (e.g.RMSD, and sequence identity % for structural and sequence distance). Although the whole idea is that his methods are supposed to be an alignment-free method, it’s still difficult to draw relationships to what we already use as the gold standard in traditional protein structure prediction problems. Also, note that the structure distance spans between -0.1 and 0.1 units whereas sequence identity spans between -0.3 and 0.5. The differences in scale are also not covered – i.e., is a difference of 0.01 units an expected value for protein structure distance, and why are the jumps in protein structure distance so much smaller than jumps in sequence space?

The author makes more interesting observations in the dataset (e.g. α/β mixed proteins are more tolerant to mutations in comparison to α- or β-only proteins) but the observations are not discussed in depth. If α/β-mixed proteins are indeed more resilient to mutations, why is this the case? Conversely, if small mutations change α- or β-only proteins’ structures to make new folds, having any speculation on the underlying mechanism (e.g. maybe α-only proteins are only sensitive to radically different amino acid substitutions, such as ALA->ARG) will only help our prediction methods. Overall I had the impression that the author was a bit too pessimistic about what modelling can achieve. Though we definitely cannot model all proteins that are out there at present, I believe the surge of new sources of data (e.g. cryo-EM structures) will provide an alternative inference route for better prediction methods in the future.