Journal Club: A Novel Insight into Gene Ontology Semantic Similarity

In a past journal club, I presented a paper by Xu et al on their method of quantifying semantic similarity of proteins based on the Gene Ontology. The Gene Ontology (GO) is a directed acyclic graph (DAG, c.f. Figure 1) of terms with which a protein or a gene can be annotated. These terms are designed to describe the process the protein is involved in, what role it fulfils in this process, and where in the cell it is localized. Thus, when comparing the function of two proteins in a quantifiable way, it has become standard to refer back to the GO terms these proteins are annotated with and compare these based on their relationship in the DAG.

Schematic Diagram of a Directed Acyclic Graph (DAG).

Figure 1: Schematic Diagram of a Directed Acyclic Graph (DAG).

As opposed to many methods, which measure the importance of a node (GO-term) in the DAG as its information content given an external database, the method proposed by Xu et al measures semantic similarity independently of external resources, which gives it the appearance of an independent measure. Furthermore, it claims to be good at dealing with badly annotated proteins, which is often a big problem in functional similarity calculations.

The similarity measure is a hybrid between node-based and edge-based methods, and is seemingly inspired by Wang et al’s 2007 paper and Shen et al’s 2010 paper. It is based on what they call “Shortest Semantic Differentiation Distance” or (SSDD), which is calculated over the shortest distance between two GO-terms on the DAG. When comparing the GO-terms A and B, the shortest path is measured by traversing the DAG upwards from node A to the lowest common ancestor of both nodes and down to node B.

The SSDD calculation over the shortest path is based on their so-called semantic Totipotency values assigned to the terms in the DAG that are part of the shortest path. The semantic Totipotency, T, of a term is calculated by:

Semantic Totipotency Measure

Semantic Totipotency Measure

where the weight, ω, is given by:

Weight, ω

Weight, ω

Here, Dst(t) denotest the number of descendents of the term t, and tp denotes the parent term of term t. Thus, the T-value of every node is both an expression of the depth of the DAG in this area and the coverage.

Finally, the SSDD is calculated by:

Semantic Similarity Differentiation Distance

Shortest Semantic Differentiation Distance

And subsequently the similarity of two GO terms is measured by:

Screenshot from 2014-01-27 12:47:46

 

Results

In their paper Xu et al showed the method to be competitive compared to other methods which compute protein functional similarity by pairwise GO-term comparisons, while also outperforming a common graph-based method in simUI. While these results look promising, the biological interpretability of such a semantic similarity measure remains difficult.

The strongest advantage of the SSDD method proposed was however its alleged invariance to annotation richness of proteins, which was presented as shown in Figure 2 below (Figure 5 in the paper).

Figure 2: The performance of difference methods dealing with sets of proteins with difference annotation richness.

Figure 2: The performance of difference methods dealing with sets of proteins with difference annotation richness.

The results in this figure show that SSDD exhibits only a slight decrease in Pearson Correlation Coefficient to a set of reference similarity values for proteins which are less well annotated. This ability to deal with badly annotated proteins is the true value of the SSDD method proposed by Xu et al. However, this investigation was performed by sets of proteins selected by the authors, and should thus be validated independently to confirm these surprising results.

Journal Club: Ligand placement based on prior structures: the guided ligand-replacement method

Last week I presented a paper by Klei et al. on a new module in the Phenix software suite. This module, entitled Guided Ligand-Replacement (GLR), aims to make it easier to place ligands during the crystallographic model-building process by using homologous models of the ligand-protein complex for the initial placement of the ligand.

In the situation where ligands are being added to a crystallographic protein model, a crystallographer must first build the protein model, identify the difference electron density, and then build the ligand into this density.

The GLR approach is particularly helpful in several cases:

  • In the case of large complex ligands, which have many degrees of freedom, it can take a long time to fit the ligand into the electron density. There may be many different conformations of the ligand that fit the difference electron density to a reasonable degree, and it is the job of the crystallographer to explore these different conformations. They must then identify the true model, or perhaps an ensemble of models in the case where the ligand is mobile or present in different, distinct, binding modes. GLR makes this process easier by using a template from a similar, previously-solved structure. The ligand position and orientation is then transplanted to the new structure to give a starting point for the crystallographer, reducing the tedium in the initial placing the ligand.
  • In the case of a series of related crystal structures, where the same protein structure is determined a number of times, bound to different (but similar) ligands. This is common in the case of structure based drug-design (SBDD), where a compound is developed and elaborated upon to improve binding affinity and specificity to a particular protein. This process generates a series of crystal structures of the protein, bound to a series of ligands, where the binding modes of the ligands are similar in all of the structures. Therefore, using the position and orientation of the ligand from a structure is a good starting point for the placement of further elaborations of that ligand in subsequent structures.
  • In the case of several copies of the protein in the asymmetric unit cell of the crystal. After one copy of the ligand has been built, it can be quickly populated throughout the unit cell, removing the need for the crystallographer to undertake this menial and tedious task.

Program Description:

The required inputs for GLR are standard, as required by any ligand-fitting algorithm, namely:

  • The APO structure of the protein (the structure of the protein without the ligand)
  • A description of the ligand (whether as a SMILES string, or as a cif file etc)
  • An mtz file containing the experimental diffraction data

Overview of the program:

GLR Program Overview

Fig 1. Program Overview.

> Identification of the reference structure

Firstly, the program must determine the reference structure to be used as a template. This can be specified by the user, or GLR can search a variety of sources to find the best template. The template selection process is outlined below. Reference structures are filtered by the protein sequence identity, similarity of the molecular weights of the ligands, and finally by the similarity of the binary chemical fingerprints of the ligands (as calculated by the Tanimoto coefficient).

Template Selection

Fig 2. Reference Structure selection flow diagram.

Little justification is given for these cutoffs, although it is generally accepted that proteins with above 70% sequence identity are highly structurally similar. The Tanimoto coefficient cutoff of 0.7 presumably only serves to remove the possibly of very low scoring matches, as if multiple potential reference structures are available, the highest Tanimoto-scored ligand-match is used. They do not, however, say how they balance the choice in the final stage where they take the ligand with the highest Tanimoto score and resolution.

The method for assigning the binary chemical fingerprints can be found here (small error in link in paper).

> Superposition of Reference and Target structures

Once a reference structure has been selected, GLR uses graph-matching techniques from eLBOW to find the correspondences between atoms in the reference and target ligands. These atomic mappings are used to orient and map the target ligand onto the reference ligand.

Once the reference protein-ligand structure is superposed onto the target protein, these atomic mappings are used to place the target ligand.

The target complex then undergoes a real-space refinement to adjust the newly-placed ligand to the electron density. This allows the parts of the target ligand that differ from the reference ligand to adopt the correct orientation (as they will have been orientated arbitrarily by the graph-matching and superposition algorithms).

> Summary, Problems & Limitations

GLR allows the rapid placement of ligands when a homologous complex is available. This reduces the need for computationally intensive ligand-fitting programs, or for tedious manual building.

For complexes where a homologous complex is available, GLR will be able to quickly provide the crystallographer with a potential placement of the ligand. However, at the moment, GLR does not perform any checks on the validity of the placement. There is no culling of the placed ligands based on their agreement with the electron density, and the decision as to whether to accept the placement is left to the crystallographer.

As the authors recognise in the paper, there is the problem that GLR currently removes any overlapping ligands that are placed by the program. This means that GLR is unable to generate multiple conformations of the target ligand, as all but one will be removed (that which agrees best with the electron density). As such, the crystallographer will still need to check whether the proposed orientation of the ligand is the only conformation present, or whether they must build additional models of the ligand.

As it is, GLR seems to be a useful time-saving tool for crystallographic structure solution. Although it is possible to incorporate the tool into automated pipelines, I feel that it will be mainly used in manual model-building, due to the problems above that require regular checking by the crystallographer.

There are several additions that could be made to overcome the current limits of the program, as identified in the paper. These mainly centre around generating multiple conformations and validating the placed ligands. If implemented, GLR will become a highly useful module for the solution of protein-ligand complexes, especially as the number of structures with ligands in the PDB continues to grow.

Journal Club: Human Germline Antibody Gene Segments Encode Polyspecific Antibodies

This week’s paper by Willis et al. sought to investigate how our limited antibody-encoding gene repertoire has the ability to recognise the unlimited array of antigens. There is a finite number of V, D, and J genes that encode our antibodies, but it still has the capacity to recognise an infinite number of antigens. Simply, the authors’ notion is that an antibody from the germline (via V(D)J recombination; see entry by James) is able to adopt multiple conformations, thus allowing the antibody to bind multiple antigens.

Three antibodies derived from the germline gene 5*51-01, all binding to very different antigens.

Three antibodies derived from the germline gene 5*51-01 bind to very different antigens.

To test this hypothesis, the authors performed a multiple sequence alignment for the amino acid sequence between the mature antibodies and the germline antibody sequence from which the antibodies are derived from. if a single position from ONE mature antibody showed a difference to the germline sequence, it was identified as a ‘variable’ position, and allowed to be changed by Rosetta’s multi-state design (MSD) and single-state design (SSD) protocols.

Pipeline: align mature antibodies (2XWT, 2B1A, 3HMX) to the germline sequence (5-51) , identify 'variable' positions from the alignment, then allow Rosetta to change those residues during design.

Figure 1) from Willis et al., showing the pipeline: align mature antibodies (2XWT, 2B1A, 3HMX) to the germline sequence (5-51) , identify ‘variable’ positions from the alignment, then allow Rosetta to change those residues.

Surprisingly, without any prior information of the germline sequence, the MSD yielded a sequence that was closer to the germline sequence, and the SSD for each mature antibody had retained the mature sequence. In short, this indicated that the germline sequence is a harmonising sequence that can accommodate the conformations of each of the mature antibodies (as proven by MSD), whereas the mature sequence was the lowest energy amino acid sequence for the particular antibody’s conformation (as proven by SSD).

To further demonstrate that the germline sequence is indeed the more ‘flexible’ sequence, the authors then aligned the mature antibodies and determined the deviation in ψ-ϕ angles at each of the variable positions that were used in the Rosetta study. They found that the ψ-ϕ angle deviation in the positions that recovered to the germline residue was much larger than the other variable positions along the antibody. In other words, for the positions that tend to return to the germline amino acid in MSD, the ψ-ϕ angles have a much larger degree of variation compared to the other variable positions, suggesting that the positions that returned to the germline amino acid are prone to lots of movement.

In addition to the many results that corroborate the findings mentioned in this entry, it’s neat that the authors took a ‘backwards’ spin to conventional antibody design. Most antibody design regimes aim to find amino acid(s) that give the antibody more ‘rigidity’, and hence, mature its affinity, but this paper went against the norm to find the most FLEXIBLE antibody (the most likely germline predecessor*). Effectively, they argue that this type of protocol can be exported to extract new antibodies that can bind to multiple antigens, thus increasing the versatility of antibodies as potential therapeutic agents.

Journal Club: Large-scale analysis of somatic hypermutations

This week I presented a paper by Burkovitz et al from Bar Ilan University in Israel.  The study investigates the mutations that occur in B-cell maturation and how the propensity for a change to be selected is affected by where in the antibody structure it is located. It nicely combines analysis of both DNA and amino-acid sequence with structural considerations to inform conclusions about how in vivo affinity maturation occurs.

Before being exposed to an antigen, an antibody has a sequence determined by a combination of genes (V and J for the light chain; V, D and J for the heavy chain). Once exposed, B-cells (the cells that produce antibodies), undergo somatic hyper-mutation (SHM) to optimise the antibody-antigen (ab-ag) interaction. These mutations are commonly thought to be promoted at activation-induced deaminase (AID) hotspots.

The authors’ first finding is that the locations of SHMs do not correlate well with the positions of AID hotspots and that the distribution of their distance to a hotspot is not much different to that of the background distribution. They conclude that although perhaps a mechanism to promote mutation, AID hotspots are not a strong factor that indicate whether a mutation will fix.

Motivated to find other determinants for SHM preferences, the study turns to examining structural features and energetics of the molecules. SHMs are found to be more prevalent on the VH domain of an Fv than the VL. However, when present, the energetic importance of an SHM is not related to the domain it is on. In contrast, the contribution an SHM makes to the binding energy is related to its structural location. As one might perhaps expect, those SHMs in positions that can make contact with the antigen have more affect than those that do not. Consideration of their propensity instead of raw frequency also shows that SHMs are more prevalent in antibody-antigen interfaces than in the rest of the molecule. However, they are also likely to occur in the VH-VL interface suggesting an importance for this region in fine-tuning the geometry and flexibility of the binding site.

figure

Figure taken from Burkovitz et al shows a) the location of different structural regions on the Fv b) the energetic contribution of the SHMs in each region c) the fraction of SHMs in the regions and their relative size d) the propensity for an SHM to occur in each of the five structural regions.

Perhaps the most interesting result of this study is the authors’ conclusions about the propensity of SHMs to mutate germline residues to particular amino-acids. It is found that whilst germline amino-acid usage in binding sites is distinctive from other protein-protein interfaces, the residue profiles of SHMs are less diverged. They therefore act to bring the properties ab-ag interaction towards those seen in normal interactions. This may suggest, as proposed by other studies, that the somatic hyper-mutation process is similar to mutation properties observed in evolution. In addition, it is found that five amino-acids, asparagine, arginine, serine, threonine and aspartic acid are the most common substitutions made in SHM. Finally, positions where SHMs most often have an important effect on binding energy are presented. These positions, and the amino-acid preferences provide promising targets for use in rational antibody design procedures.

Journal Club: Quantification and functional analysis of modular protein evolution in a dense phylogenetic tree

For journal club this week I decided to look at a paper by Moore et al. on the modular evolution of proteins.

Modular evolution, or the rearrangement of the domain architecture of a protein, is one of the key drivers behind functional diversification in the protein universe. I used the example in my talk of the multi-domain protein Peptidase T, which contains a catalytic domain homologous to Carboxypeptidase A, a zinc dependent protease. The additional domain in Peptidase T induces the formation of a dimer, which restricts the space around the active site and so affects the specificity of the enzyme.

peptidase_t

The multi-domain protein Peptidase T in a dimer (taken from Bashton and Chothia 2007). The active site is circled in green. Carboxypeptidase A is made up of a single domain homologous to the catalytic domain (in blue) of Peptidase T.

 
I took this case study from a really interesting paper, The generation of new protein functions by the combination of domains (Bashton and Chothia, 2007), which explores several other comparisons between the functions of multi-domain proteins and their single domain homologues.

What this paper does not address however is the directionality of such domain reorganisations. In all these examples, it is not clear whether the multi-domain organisation has evolved from the single domain enzyme or vice versa. Which brings me back to the paper I was presenting on, which attempts a reconstruction of domain arrangements followed by a categorisation of rearrangement events.

Essentially, given a phylogenetic tree of 20 closely related pancrustacean species, the paper takes the different domain arrangements on the genomes (step 1), assigns the presence or absence of each arrangement at interior nodes on the tree (step 2), and then assigns each gained arrangement to one of four possible rearrangement events (step 3).

1. Domain Annotation
The authors use different methods to annotate domains on the genomes. They conclude the most effective methodology is to use the clan level (where families with suspected homologies are joined together… similar to our beloved superfamily classification) of Pfam-A (high quality family alignments with a manually chosen seed sequence). Moreover, they collapse any consecutive stretches of identical domains into one “pseudo-domain”, eliminating the effect of the domain repeat number on an arrangement’s definition.

2. Ancestral State Reconstruction
The ancestral state reconstruction of each domain arrangement (it’s presence/absence at each internal node on the tree) is a result of a 2-pass sweep across the tree: the first from leaves to root, and the second from the root to the leaves. On the first pass the presence of an arrangement on a parent node is decided by majority rule on the state of its children. If the arrangement is present in one child node but absent in the other, the state at the parent node is defined as uncertain. Any uncertain child nodes have a neutral impact on their parent node’s state (i.e. if a parent has a child with the arrangement and a child with an uncertain state the arrangement will be annotated as present in the parent node). On the second pass (from root to leaves) uncertain nodes are decided by the state at their parent node. An uncertain arrangement at the root will be annotated as present. For more details and a clearer explanation see Box 1 in the figure below.

FigureS2

A schematic for the assignment of domain recombination events. Box 1 gives the algorithm for the ancestral state reconstruction. Figure S2 from Moore et al. 2013.

3. Rearrangement events
For each gained event on a particular branch, the authors then postulated one of four simple rearrangement events dependent on the arrangements on the parent’s predicted proteome.

i) Fusion: A gained domain arrangement (A,B,C) on a child’s proteome is the result of fusion if the parent’s proteome contains both the arrangements (A,B) AND (C) (as one example).
ii) Fission: A gained arrangement (A,B,C) is the result of fission if the parent contains the arrangement (A,B,C,D) AND the child also contains the arrangement (D).
iii) Terminal Loss: A gained arrangement (A,B,C) is the result of terminal loss if the parent contains the arrangement (A,B,C,D) AND the child does not contain the arrangement (D).
iv) Domain gain: A gained arrangement (A,B,C) is the result of domain gain if the parent contains (A,B) but not (C).

Any gained arrangement which cannot be explained by these cases (as a single-step solution) is annotated as having no solution.

Results

The authors find, roughly speaking, that the domain arrangements they identify fall into a bimodal distribution. The vast majority are those which are seen on only one genome, of which over 80% are multi-domain arrangements. There are also a sizeable number of arrangements seen on every single genome, the vast majority of which are made up of a single domain. I do wonder though, how much of this signal is due to the relative difficulty of identifying and assigning multiple different domains compared to just a single domain. While it seems unlikely that this would explain the entirety of this observation (on average, 75% of proteins per genome were assigned) it would be interesting to have seen how the authors address this possible bias.

Interestingly, the authors also find a slight inflation in fusion events over fission events across the tree (around 1 more per million years), although there are more fusion events nearer the root of the tree, with fission dominating nearer the leaves, and in particular, on the dense Drosophila subtree.

Finally, the authors performed a functional term enrichment analysis on the domain arrangements gained by fusion and fission events and showed that, in both cases, terms relating to signalling were significantly overrepresented in these populations, emphasising the potential importance that modular evolution may play in this area.

Efficient discovery of overlapping communities in massive networks

Detecting overlapping communities is essential to analyzing and exploring natural networks such as social networks, biological networks, and citation networks. However, most existing approaches do not scale to the size of networks that we regularly observe in the real world. In the paper by Gopalan et al. discussed in this week’s group meeting, a scalable approach to community detection is developed that discovers overlapping communities in massive real-world networks. The approach is based on a Bayesian model of networks that allows nodes to participate in multiple communities, and a corresponding algorithm that naturally interleaves subsampling from the network and updating an estimate of its communities.

The model assumes there are K communities and that each node i is associated with a vector of community memberships \theta_i. To generate a network, the model considers each pair of nodes. For each pair (i,j), it chooses a community indicator z_{i \rightarrow j} from the i^{th} node’s community memberships \theta_i and then chooses a community indicator z_{i \leftarrow j} from \theta_j. A connection is then drawn between the nodes with probability \beta if the indicators point to the same community or with a smaller probability \epsilon if they do not.

This model defines a joint probability p(\theta,\beta,z,y) where y is the observed data. To estimate the posterior p(\theta,beta,z | y), the method uses a stochastic variational inference algorithm. This enables posterior estimation using only a sample of all-possible node pairs at each step of the variational inference, making the method applicable to very large graphs (e.g analyzing a large citation network of physics papers shown in the figure below identifies important papers impacting several sub-disciplines).

Community detection in a physics citation network.

Community detection in a physics citation network.

One limitation of the method is that it does not incorporate automatic estimation of the number of communities, which is a general problem with clustering algorithms. Still, enabling sophisticated probabilistic analysis of structure in massive graphs is a significant step forward.

How many bins?

As it’s known in non-parametric kernel density estimation the effect of the bandwidth on the estimated density is large and it is usually the parameter who makes the tradeoff between bias and roughness of the estimation (Jones et.al 1996). An analogous problem for histograms is the choice of the bin length and in cases of equal bin lengths the problem can be seen as finding the number of bins to use.  A data-base methodology for building equal bin-length histograms proposed by (Knuth 2013) based on the marginal of the joint posterior of the number of bins and heights of the bins. To build the histogram first the number of bins has to be selected as the the value (\hat{M} ) that maximises the following posterior distribution for the number of bins:
P(M|d,I)\, \alpha \,(M/V)^N \frac{\Gamma(M/2) \prod_{k=1}^M \Gamma(n_k+1/2)}{\Gamma(1/2)^M \Gamma(N+M/2)}

where M is the number of bins, d is the data, I is prior knowledge about the problem, i.e. in particular the use of equal length bins and the range of data V, which has the relation V=Mw where w is the width of bins, N is the number of data points and n_k is the number of observations that fall in the kth bin.

Now, the height (h_k) of the bins of the histogram is given by:
h_k=\frac{M}{V} \frac{n_k+1/2}{N+M/2}.

In the case of a normal distribution the authors suggest a sample of 150 data points to “accurately and consistently estimate the shape of the distribution”.

The following figure shows the relative log-posterior of the number of bins (left) and the estimated histogram for a mixture of three normal samples and a uniform [0,50] (right).

Optimal binning

Knuth, K. H. (2013). Optimal data-based binning for histograms. arXiv preprint physics/0605197. The first version of this paper was published on 2006.

Jones, M. C., Marron, J. S., and Sheather, S. J. (1996). A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association,91(433), 401–407.

Annotate Antibody CDR and Framework Residues

Intro

Antibodies have very well conserved structures and their binding site is chiefly comprised of the six CDRs. The great similarity between the 1700+ antibody structures that can be found in SAbDab/PDB prompted the introduction of numbering schemes which act as coordinates with respect to the sequence/structural features of antibodies. The earliest such numbering scheme was introduced by Wu and Kabat, followed by the structurally informed Chothia-scheme which was eventually amended by Abhinandan and Martin. Even though there are several of those schemes, the one currently endorsed by the World Health Organization (WHO) is this of IMGT.

The Program Downolad.

It annotates the framework and CDR residues according to three definitions: Kabat, Chothia or Contact. You can download it here.

Possible issues?

You need internet connection for this program to work since it calls the Abnum service, thus you should cite the following if you use this code:

Abhinandan, K.R. and Martin, A.C.R. (2008) Analysis and improvements to Kabat and structurally correct numbering of antibody variable domains Molecular Immunology, 45, 3832-3839.

How to use it?

As an example test case, type the following in the Framer directory:

python Framer.py --f 1A2Y.pdb --c AB --o my_first_output --d chothia

This should get the the heavy and light chains of 1A2Y (A and B) and leave the output in a folder called my_first_outupt.

Options:

–f: Antibody file
–c: Antibody chains (you can submit just one or several)
–o: Output folder name – NB this is going to be created in the directory you call Framer from!
–d: CDR definition to be used, possible options are: chothia, kabat and contact.

Output files:

There are four output files:

red_blue.pdb: The pdb with b-factor colored CDRs. The CDRs have B-factor of 100.00 and the framework 0.00.
paratope.txt: The CDR residues, given in the format [id][whitespace][chain]
framework.txt: The Framework residues, given in the format [id][whitespace][chain]
full_info.txt: Full breakdown of the annotation given in the format:

Original ID Original Chain AA Chothia ID CDR(FR=frame,or CDR id)

 

Journal club: Half a century of Ramachandran plots

In last week’s journal club we delved into the history of Ramachandran plots (Half a century of Ramachandran plots; Carugo & Djinovic-Carugo, 2013).

Polypeptide backbone dihedral angles

Polypeptide backbone dihedral angles. Source: Wikimedia Commons, Bensaccount

50 years ago Gopalasamudram Narayana Ramachandran et al. predicted the theoretically possible conformations of a polypeptide backbone. The backbone confirmations can be described using three dihedral angles: ω, φ and ψ (shown to the right).

The first angle, ω, is restrained to either about 0° (cis) or about 180° (trans) due to the partial double bond character of the C-N bond. The φ and ψ angles are more interesting, and the Ramachandran plot of a protein is obtained by plotting φ/ψ angles of all residues in a scatter plot.

The original Ramachandran plot showed the allowed conformations of the model compound N-acetyl-L-alanine-methylamide using a hard-sphere atomic model to keep calculations simple. By using two different van der Waals radii for each element positions on the Ramachandran plot could be classified into either allowed regions, regions with moderate clashes and disallowed regions (see Figure 3 (a) in the paper).

The model compound does not take side chains into account, but it does assume that there is a side chain. The resulting Ramachandran plot therefore does not describe the possible φ/ψ angles for Glycine residues, where many more conformations are plausible. On the other end of the spectrum are Proline residues. These have a much more restricted range of possible φ/ψ angles. The φ/ψ distributions of GLY and PRO residues are therefore best described in their own Ramachandran plots (Figure 4 in the paper).

Over time the Ramachandran plot was improved in a number of ways. Instead of relying on theoretical calculations using a model compound, we can now rely on experimental observations by using high quality, hand picked data from the PDB. The way how the Ramachandran plot is calculated has also changed: It can now be seen as a two-dimensional, continuous probability distribution, and can be estimated using a full range of smoothing functions, kernel functions, Fourier series and other models.
The modern Ramachandran plot is much more resolved than the original plot. We now distinguish between a number of well-defined, different regions which correlate with secondary protein structure motifs.

Ramachandran plots are routinely used for structure validation. The inherent circular argument (A good structure does not violate the Ramachandran plot; The plot is obtained by looking at the dihedral angles of good structures) sounds more daring than it actually is. The plot has changed over time, so it is not as self-reinforcing as one might fear. The Ramachandran plot is also not the ultimate guideline. If a new structure is found that claims to violate the Ramachandran plot (which is based on a huge body of cumulative evidence), then this claim needs to be backed up by very good evidence. A low number of violations of the plot can usually be justified. The Ramachandran plot is a local measure. It therefore does not take into account that domains of a protein can exert a force on a few residues and just ‘crunch’ it into an unusual conformation.

The paper closes with a discussion of possible future applications and extensions, such as the distribution of a protein average φ/ψ and an appreciation of modern web-based software and databases that make use of or provide insightful analyses of Ramachandran plots.