Viewing ligands in twilight electron density

In this week’s journal club we discussed an excellent review paper by E. Pozharski, C. X. Weichenberger and B. Rupp investigating crystallographic approaches to protein-ligand complex elucidation. The paper assessed and highlighted the shortcomings of deposited PDB structures containing ligand-protein complexes. It then made suggestions for the community as a whole and for researchers making use of ligand-protein complexes in their work.

The paper discussed:

The difficulties in protein ligand complex elucidation
The tools to assess the quality of protein-ligand structures both qualitative and quantitative
The methods used describing their analysis of certain PDB structures
Some case studies visually demonstrating these issues
Some practical conclusions for the crystallographic community
Some practical conclusions for non-crystallographer users of protein-ligand complex structures from the PDB

The basic difficulties of ligand-protein complex elucidation

Ligands have less than 100% occupancy – sometimes significantly less and thus will inherently show up less clearly in the overall electron density.
Ligands make small contributions to the overall structure and thus global quality measures , such as r-factors, will be affected only minutely by the ligand portion of the structure being wrong
The original basis model needs to be used appropriately. The r-free data from the original APO model should be used to avoid model bias

The following are the tools available to inspect the quality of agreement between protein structures and their associated data.

Visual inspection of the Fo-Fc and 2Fo-Fc maps,using software such as COOT, is essential to assess qualitatively whether a structure is justified by the evidence.
Use of local measures of quality for example real space correlation coefficients (RSCC)
Their own tool, making use of the above as well as global quality measure resolution

Methods and results

In a separate publication they had analysed the entirety of the PDB containing both ligands and published structure factors. In this sample they demonstrate 7.6% had RSCC values of less than 0.6 the arbitrary cut off they use to determine whether the experimental evidence supports the model coordinates.

Figure to show an incorrectly oriented ligand (a) and its correction (b)

An incorrectly oriented ligand (a) and its correction (b). In all of these figures Blue is the 2mF_oDF_c map contoured at 1σ and Green and Red are positive and negative conturing of the mF_oDF_c map at 3σ

In this publication they visually inspected a subset of structures to assess in more detail how effective that arbitrary cutoff is and ascertain the reason for poor correlation. They showed the following:

(i) Ligands incorrectly identiﬁed as questionable,false positives(7.4%)
(ii) Incorrectly modelled ligands (5.2%)
(iii) Ligands with partially missing density (29.2%).
(iv) Glycosylation sites (31.3%)
(v) Ligands placed into electron density that is likely to
originate from mother-liquor components
(vi) Incorrect ligand (4.7%)
(vii) Ligands that are entirely unjustiﬁed by the electron
density (11.9%).

The first point on the above data is that the false-positive rate using RSCC of 0.6 is 7.4%. This demonstrates that this value is not sufficient to accurately determine incorrect ligand coordinates. Within the other categories all errors can be attributed to one of or a combination of the following two factors:

The inexperience of the crystallographer being unable to understand the data in front of them
The wilful denial of the data in front of the crystallographer in order that they present the data they wanted to see

Figure to show a ligand placed in density for a sulphate ion from the mother liquor (a) and it's correction (b)

A ligand incorrectly placed in density for a sulphate ion from the mother liquor (a) and it’s correction (b)

The paper observed that a disproportionate amount of poor answers was derived from glycosylation sites. In some instances these observations were used to inform the biochemistry of the protein in question. Interestingly this follows observations from almost a decade ago, however many of the examples in the Twilight paper were taken from 2008 or later. This indicates the community as a whole is not reacting to this problem and needs further prodding.

Figure to show an incomplete glycosylation site inaccurately modeled

Conclusions and suggestions

For inexperienced users looking at ligand-protein complexes from the PDB:

Inspect the electron density map using COOT if is available to determine qualitatively is their evidence for the ligand being there
If using large numbers of ligand-protein complexes, use a script such as Twilight to find the RSCC value for the ligand to give some confidence a ligand is actually present as stated

For the crystallographic community:

Improved training of crystallographers to ensure errors due to genuine misinterpretation of the underlying data are minimised
More submission of electron-density maps, even if not publically available they should form part of initial structure validation
Software is easy to use but difficult to analyse the output

GPGPUs for bioinformatics

As the clock speed in computer Central Processing Units (CPUs) began to plateau, their data and task parallelism was expanded to compensate. These days (2013) it is not uncommon to find upwards of a dozen processing cores on a single CPU and each core capable of performing 8 calculations as a single operation. Graphics Processing Units were originally intended to assist CPUs by providing hardware optimised to speed up rendering highly parallel graphical data into a frame buffer. As graphical models became more complex, it became difficult to provide a single piece of hardware which implemented an optimised design for every model and every calculation the end user may desire. Instead, GPU designs evolved to be more readily programmable and exhibit greater parallelism. Top-end GPUs are now equipped with over 2,500 simple cores and have their own CUDA or OpenCL programming languages. This new found programmability allowed users the freedom to take non-graphics tasks which would otherwise have saturated a CPU for days and to run them on the highly parallel hardware of the GPU. This technique proved so effective for certain tasks that GPU manufacturers have since begun to tweak their architectures to be suitable not just for graphics processing but also for more general purpose tasks, thus beginning the evolution General Purpose Graphics Processing Unit (GPGPU).

Improvements in data capture and model generation have caused an explosion in the amount of bioinformatic data which is now available. Data which is increasing in volume faster than CPUs are increasing in either speed or parallelism. An example of this can be found here, which displays a graph of the number of proteins stored in the Protein Data Bank per year. To process this vast volume of data, many of the common tools for structure prediction, sequence analysis, molecular dynamics and so forth have now been ported to the GPGPU. The following tools are now GPGPU enabled and offer significant speed-up compared to their CPU-based counterparts:

Application	Description	Expected Speed Up	Multi-GPU Support
Abalone	Models molecular dynamics of biopolymers for simulations of proteins, DNA and ligands	4-29x	No
ACEMD	GPU simulation of molecular mechanics force fields, implicit and explicit solvent	160 ns/day GPU version only	Yes
AMBER	Suite of programs to simulate molecular dynamics on biomolecule	89.44 ns/day JAC NVE	Yes
BarraCUDA	Sequence mapping software	6-10x	Yes
CUDASW++	Open source software for Smith-Waterman protein database searches on GPUs	10-50x	Yes
CUDA-BLASTP	Accelerates NCBI BLAST for scanning protein sequence databases	10	Yes
CUSHAW	Parallelized short read aligner	10x	Yes
DL-POLY	Simulate macromolecules, polymers, ionic systems, etc on a distributed memory parallel computer	4x	Yes
GPU-BLAST	Local search with fast k-tuple heuristic	3-4x	No
GROMACS	Simulation of biochemical molecules with complicated bond interactions	165 ns/Day DHFR	No
GPU-HMMER	Parallelized local and global search with profile Hidden Markov models	60-100x	Yes
HOOMD-Blue	Particle dynamics package written from the ground up for GPUs	2x	Yes
LAMMPS	Classical molecular dynamics package	3-18x	Yes
mCUDA-MEME	Ultrafast scalable motif discovery algorithm based on MEME	4-10x	Yes
MUMmerGPU	An open-source high-throughput parallel pairwise local sequence alignment program	13x	No
NAMD	Designed for high-performance simulation of large molecular systems	6.44 ns/days STMV 585x 2050s	Yes
OpenMM	Library and application for molecular dynamics for HPC with GPUs	Implicit: 127-213 ns/day; Explicit: 18-55 ns/day DHFR	Yes
SeqNFind	A commercial GPU Accelerated Sequence Analysis Toolset	400x	Yes
TeraChem	A general purpose quantum chemistry package	7-50x	Yes
UGENE	Opensource Smith-Waterman for SSE/CUDA, Suffix array based repeats finder and dotplot	6-8x	Yes
WideLM	Fits numerous linear models to a fixed design and response	150x	Yes

It is important to note however, that due to how GPGPUs handle floating point arithmetic compared to CPUs, results can and will differ between architectures, making a direct comparison impossible. Instead, interval arithmetic may be useful to sanity-check the results generated on the GPU are consistent with those from a CPU based system.

PredyFlexy – Predicting Protein Flexibility

An example output of PredyFlexy

My presentation focused on a method to predict protein flexibility – PredyFlexy. There is a webserver, and it is described in their paper (de Brevern et. al 2012). The method is covered much more explicitly in the paper Predicting protein flexibility through the prediction of local structures (Bornot et al. 2011). This work builds on earlier papers (which are mentioned on the front page of the webserver, some of which I will mention later). In terms of people, Alexandre G. de Brevern, Aurelie Bornot, and Catherine Etchebest are authors common to all of these papers.

The concept is simple; there is a library of ‘Local Structure Prototypes’ or LSPs. These LSPs are 11 residue fragments, and have structure and flexibility associated with them, which are derived from a set of protein structures and molecular dynamics simulations. Each LSP has a SVM (support vector machine) ‘expert’ to score how likely a given sequence profile is to have said structure. A 21 residue window is used to determine the LSP of the central 11 residues within this window.

So, the user inputs a sequence, which gets Psi-Blasted to give a sequence profile. The 5 most probable LSPs for each atom are determined using the SVM experts. Then the predicted flexibility of each atom is given by the average flexibility of these 5 LSPs. There is a confidence index to the predictions, which comes from assessing the discriminative power of the SVMs. Regions predicted to have LSP with more accurate SVMs will have a high confidence index.

Examples of Local Structure Prototypes. Taken from the supplementary information of ‘Predicting protein flexibility through the prediction of local structures’ – Aurélie Bornot, Catherine Etchebest, Alexandre G. de Brevern, Proteins 79, 3, 839–852, 2011

So, the concept seems simple, but you are probably wondering, what are these LSPs? To answer that, we have to delve into the literature. ‘Bayesian probabilistic approach for predicting backbone structures in terms of protein blocks‘, published in 2000, and with Alexandre G. de Brevern as first author, is the sensible place to start. This introduced the concept of protein blocks, which is in effect a structural alphabet. These are 5 residue fragments (described by 8 dihedral angles), and there are 16 of them (there are pretty pictures in the supplementary data 1 of this paper). Local structure prototypes are made up of these protein blocks, which were first used to predict structure, in a 2006 paper – Assessing a Novel Approach for Predicting Local 3D Protein Structures from Sequence (again, with the same authors). LSPs are 11 residue fragments, made from 7 overlapping protein blocks. Obviously there are lots of combinations to the protein blocks that can give 11 residue fragments. These combinations are clustered into 120 groups. Each group is represented by the fragment within the cluster that is closest to all other fragments within the cluster, based on C-alpha RMSD. Hence 120 LSPs.

The other pertinent question is, where does the flexibility data come from? Well, they did some MD simulations (see Bornot et al. 2011 for details) and took b-factors from the structures. They normalised these, by calculating the number of standard deviations away from the mean for each structure. Each LSP was attributed a b-factor and RMSF, which was the mean value for the central residue of every instance of the LSP in the data set. Additionally, each fragment in the data set was classed as ‘rigid’, ‘flexible’, or ‘intermediate’ based on its normalized RMSF and B-factor. Each LSP was given a probability of belonging to each of these classes based on the frequency of fragments that belonged to that LSP being in each class. The figure here (taken from Bornot et al. 2011) shows the interesting weak correlation between normalised B-factor and normalised RMSF.

Normalised B-factor values according to normalized RMSF values as determined from molecular dynamics simulations. From Bornot et al 2011. Blue points represent rigid fragments, red flexible ones, and green points intermediate fragments.

Bornot et al. 2011 also gives us a guide to the ability of this prediction method (see table II). In predicting the class of fragments (rigid, intermediate or flexible), it gets the correct class about half the time. For 40% of rigid and flexible cases, the class is predicted as ‘intermediate’. Prediction rate is also strongly correlated with flexibility – more flexible regions have much poorer prediction rates. Which is not great, as we already know that most alpha helices are rigid. However, the confidence index does give a good guide as to what to trust. I could speculate that might results in an output that tells us that helices and sheets are definitely rigid, and other elements are possibly flexible. Which would not be particularly useful, but given there are few comparable tools, something is better than nothing.

Protein flexibility is hard; experimentally determining it is difficult (and even MD simulations take a while), and people can argue about how relevant the experimental methods are (and we frequently do in our group meetings). So, like most predictive methods, a relatively fast (and simple) way to get some information about your problem is always going to be useful. If only to guide you to where you might focus your attention.

Journal club: Simultaneous Femtosecond X-ray Spectroscopy and Diffraction of Photosystem II at Room Temperature

In the last journal club we covered the paper Simultaneous Femtosecond X-ray Spectroscopy and Diffraction of Photosystem II at Room Temperature (Kern et al., 2013), currently still in Science Express.

Structure of Photosystem II, PDB 2AXT
CC BY-SA 3.0 Curtis Neveu

This paper describes an experiment on the Photosystem II (PSII) protein complex. PSII is a large protein complex consisting of about 20 subunits with a combined weight of ca. 350 kDa. As its name suggests, this complex plays a crucial role in photosynthesis: it is responsible for the oxidation (“splitting up”) of water.

In the actual experiment (see the top right corner of Figure 1 in the paper) three experimental methods are combined: PSII microcrystals (5-15µm) are injected from the top into the path of an X-ray pulse (blue). Simultaneously, an emission spectrum is recorded (yellow, detector at the bottom). And finally in a separate run the injected crystals are treated (‘pumped’) with a visible laser (red) before they hit the X-ray pulse.

Let’s take a look at each of those three in a little more detail.

X-ray diffraction (XRD)

In a standard macromolecular X-ray crystallography experiment a crystal containing identical molecules of interest (protein) at regular, ordered lattice points is exposed to an X-ray beam. Some X-rays are elastically scattered and cause a diffraction pattern to form on a detector. By analysing the diffraction patterns of a rotating crystal it is possible to calculate the electron density distribution of the molecule in question, and thus determine its three dimensional structure.

An intense X-ray beam however also systematically damages the sample (Garman, 2010). For experiments using in-house X-ray generators or synchrotrons it is therefore recommended not to exceed a total dose of 30 MGy on any one crystal (Owen et al., 2006).

Aerial view of the LCLS site. The accelerator is 3.2 kilometres long.

The experiment described in the current paper however was not conducted using a run-of-the-mill synchrotron, but with the Linac Coherent Light Source (LCLS), an X-ray free electron laser. Here each diffraction image results from an individual crystal exposed to a single X-ray pulse of about 50 femtoseconds, resulting in a peak dose of ~150 MGy. Delivering these extreme doses in very short X-ray pulses lead to the destruction of the sample via a coulomb explosion.

As the sample is destroyed only one diffraction image can be taken per crystal. This causes two complications: Firstly, a large number of sample crystals are required. This explains why the experiment required a total beam time of 6 hours and involved over 2.5 million X-ray shots and processing an equal number of diffraction images. Secondly, the resulting set of (usable) diffraction images are an unordered, random sampling of the crystal orientation space. This presents a computational challenge unique to XFEL setups: before the diffraction data can be integrated, the orientation of the crystal lattice needs to be determined for each individual diffraction image.

X-ray diffraction allows us to obtain a electron density map of the entire unit cell, and therefore the entire crystal. But we can only see ordered areas of the crystal. To really see small molecules in solvent channels, or the conformations of side chains on the protein surface they need to occupy the same positions within each unit cell. For most small molecules this is not the case. This is why you will basically never see compounds like PEGs or Glycerol in your electron density maps, even though you used them during sample preparation. For heavy metal compounds this is especially annoying. They disproportionately increase the X-ray absorption (Holton, 2009; with a handy table 1) and therefore shorten the crystal’s lifetime. But they do not contribute to the diffraction pattern (And that is why you should back-soak; Garman & Murray, 2003).

X-ray emission spectroscopy (XES)

PSII contains a manganese cluster (Mn₄CaO₅). This cluster, as with all protein metallocentres, is known to be highly radiation sensitive (Yano et al., 2005). Apparently at a dose of about 0.75 MGy the cluster is reduced in 50% of the irradiated unit cells.

Diffraction patterns represent a space- and time-average of the electron density. It is very difficult to quantify the amount of reduction from the obtained diffraction patterns. There is however a better and more direct way of measuring the states of the metal atoms: X-ray emission spectroscopy.

Basically the very same events that cause radiation damage also cause X-ray emissions with very specific energies, characteristic for the involved atoms and their oxidation state. An Mn^IVO₂ energy spectrum looks markedly different to an Mn^IIO spectrum (bottom right corner of Figure 1).

The measurements of XRD and XES are taken simultaneously. But, differently to XRD, XES does not rely on crystalline order. It makes no difference whether the metallocentres move within the unit cell as a result of specific radiation damage. Even the destruction of the sample is not an issue: we can assume that XES will record the state of the clusters regardless of the state of the crystal lattice – up to the point where the whole sample blows up. But at that point we know that due to the loss of long-range order the X-ray diffraction pattern will no longer be affected.

The measurements of XES therefore give us a worst-case scenario of the state of the manganese cluster in the time-frame where we obtained the X-ray diffraction data.

Induced protein state transition with visible laser

Another neat technique used in this experiment is the activation of the protein by a visible laser in the flight path of the crystals as they approach the X-ray interaction zone. With a known crystal injection speed and a known distance between the visible laser and the X-ray pulse it becomes possible to observe time-dependent protein processes (top left corner of Figure 1).

What makes this paper special? (And why is it important to my work?)

It has been theorized and partially known that the collection of diffraction data using X-ray free electron lasers outruns traditional radiation damage processes. Yet there was no conclusive proof – up until now.

This paper has shown that the XES spectra of the highly sensitive metallocentres do not indicate any measurable (let alone significant) change from the idealized intact state (Figure 3). Apparently the highly sensitive metallocentres of the protein stay intact up to the point of complete sample destruction, and certainly well beyond the point of sample diffraction.

Or to put another way: even though the crystalline sample itself is destroyed under extreme conditions, the obtained diffraction pattern is – for all intents and purposes – that of an intact, pristine, zero dose state of the crystal.

This is an intriguing result for people interested in macromolecular crystallography radiation damage. In a regime of absurdly high doses, where the entire concept of a ‘dose’ for a crystal breaks down (again), we can obtain structural data with no specific radiation damage present at the metallocentres. As metallocentres are more susceptible to specific radiation damage it stands to reason that the diffraction data may be free of all specific damage artefacts.

It is thought that most deposited PDB protein structures containing metallocentres are in a reduced state. XFELs are being constructed all over the world and will be the next big thing in macromolecular crystallography. And now it seems that the future of metalloproteins got even brighter.

Good looking proteins for your publication(s)

Just came across a wonderful PyMOL gallery while creating some images for my (long overdue) confirmation report. A fantastic resource to draw sexy proteins – especially useful for posters, talks and papers (unless you are paying extra for coloured figures!).

It would be great if we had our own OPIG “pymol gallery”.

An example of one of my proteins (1tgm) with aspirin bound to it:

A javascript function to validate FASTA sequences

I was more than a bit annoyed of not finding this out there in the interwebs, being a strong encourager of googling (or in Jamie’s case duck-duck-going) and re-use.

So I proffer my very own fasta validation javascript function.

/*
 * Validates (true/false) a single fasta sequence string
 * param   fasta    the string containing a putative single fasta sequence
 * returns boolean  true if string contains single fasta sequence, false 
 *                  otherwise 
 */
function validateFasta(fasta) {

	if (!fasta) { // check there is something first of all
		return false;
	}

	// immediately remove trailing spaces
	fasta = fasta.trim();

	// split on newlines... 
	var lines = fasta.split('\n');

	// check for header
	if (fasta[0] == '>') {
		// remove one line, starting at the first position
		lines.splice(0, 1);
	}

	// join the array back into a single string without newlines and 
	// trailing or leading spaces
	fasta = lines.join('').trim();

	if (!fasta) { // is it empty whatever we collected ? re-check not efficient 
		return false;
	}

	// note that the empty string is caught above
	// allow for Selenocysteine (U)
	return /^[ACDEFGHIKLMNPQRSTUVWY\s]+$/i.test(fasta);
}

Let me know, by comments below, if you spot a no-no. Please link to this post if you find use for it.

p.s. I already noticed that this only validates one sequence. This is because this function is taken out of one of our web servers, Memoir, which specifically only requires one sequence. If there is interested for multi sequence validation I will add it.

Journal Club: Can Linear Progamming (LP) be useful to us?

Linear programming (LP) is known as a fast and powerful computational technique. It has been applied to a large range of problems in finances and economics, but it is not very popular among us bioinformaticians, computational biologists, and the likes.

Linear Programming is all about find feasible solutions that satisfy a series of constraints (usually represented by inequalities). Does it sound like a familiar problem to bioinformaticians and computational biologists out there?

Source: http://hotmath.com/hotmath_help/topics/linear-programming.html

This leaves room for some questioning: can biological phenomena be modelled or simplified under the assumption of linearity? Furthermore, can LP be used to tackle the many difficult problems posed in our field? Perhaps an even bigger question: why would any of us use Linear Programming instead of another type of linear modelling? What are the advantages of it?

I will not incur in explaining the particulars of LP here. There is a plethora of materials available online (Wikipedia and Wolfram are accessible starting points) that detail Linear Programming. For those eager for something more substantial, V. Chvatal’s Linear Programming and Dantzig’s Linear Programming and Extensions are two good texts on the subject.

During this week’s journal club, I discussed an article that attempted to use Linear Programming to devise knowledge-based Docking Potentials (DP) tailored for transient protein-protein complexes. Transient complexes tend to be under-represented on the PDB, mostly due to the inherent difficulties of crystallizing such complexes. Hence, the development of knowledge-based potentials for these special cases of protein interaction is drastically hindered by a sample size limitation.

A cartoon representation of a transient complex between Azurin (cyan) and its partner Cytochrome C551 (dark blue) from Pseudomonas aeruginosa. Transient protein complexes are hard to crystallize, hence, under-represented on the PDB.

Source: Bizzarri AR, Brunori E, Bonanni B, Cannistraro S. Docking and molecular dynamics simulation of the Azurin–Cytochrome c551 electron transfer complex. J. Mol. Recognit. 2007; 20: 122–131

To offset such limitation, it would be ideal if one could extrapolate information from decoys (non-native conformations obtained from computational docking tools) in order to improve the Docking potentials. Furthermore, in an ideal world, one would also address the bias introduced by homology/sequence similarity between the existing proteins in the available structures of transient complexes.

The author of the article “Designing coarse grained-and atom based-potentials for protein-protein docking – Tobi D. – BMC Structural Biology 2010, 10:40 doi:10.1186/1472-6807-10-40 ” claims that LP can address such issues by incorporating information from the decoys as linear constraints to the model. The article describes a linear problem, in which the aim is to minimize the variance of how much the non-native energy potentials differ from the native ones. Also, they impose the constraints that native structures must have a lower energy than all of the non-native structures for a given complex (lower in this case is good).

The energy is defined as a weighted sum of the counts of specific interaction types on the complex interface. In their work, the author employed two models: an atom-based model and a side chain-based model. These models are used to classify atoms into groups and to simplify calculations. Initially, they define boolean (one-step) interactions: two atoms interact if they are within a cutoff distance of each other. This cutoff varies according to the type of atoms involved. The initial model led to a state of infeasibility, and it was then replaced by a two-step model, where you have strong and weak interactions and two sets of cutoff (this leads to twice as many unknowns in the LP model).

Well, does it work? How does it fair against other existing knowledge-based DPs?

Source: Designing coarse grained-and atom based-potentials for protein-protein docking. – Tobi D. – BMC Structural Biology 2010, 10:40 doi:10.1186/1472-6807-10-40

Despite the lack of brilliant results or any apparent improvement compared to the state-of-art, the potentials described in the article seem to slightly outperform ZDOCK2.3’s scoring functions.

This may actually speak in favour of the applicability of LP to problems in our area. In the case presented during the journal club, an LP approach produced comparable results to more conventional techniques.

Perhaps the best answer to “why should I use LP?” is that it is an unconventional, creative solution. It is significantly fast and, therefore, easy to try out depending on your problem. Science is all about experimentation, after all. Why would you not try a different technique if you have the means to?

The moral of the story: it is good to think outside the box, as long as you keep your feet on the ground.

Image Source: http://www.designthenewbusiness.com/blog/documenting/thinking-inside-the-box.html

Check the article discussed in the post here.

Journal Club: Protein structure model refinement using fragment-guided MD

For this week’s journal club I presented this paper by Jian et al from the Zhang Lab. The paper tackles the problem of refining protein structure models using molecular dynamics (MD).

The most successful protocols for building protein structure models have been template-based methods. These involve selecting whole or parts of known protein structures and assembling them to form an initial model of the target sequence of interest. This initial model can then be altered or refined to (hopefully) achieve higher accuracy. One method to make these adjustments is to use molecular dynamics simulations to sample different conformations of the structure. A “refined” model can then be taken as a low-energy state that the simulation converges to. However, whilst physics-based potentials are effective for certain aspects of refinement (e.g. relieving clashes between side chain atoms), the task of actually improving overall model quality has so far proved to be too ambitious.

The Method

In this paper entitled “Atomic-Level Protein Structure Refinement Using Fragment-Guided Molecular Dynamics Conformation Sampling,” Jian et al demonstrate that current MD refinement methods have little guarantee of making any improvement to the accuracy of the model. They therefore introduce a technique of supplementing physics-based potentials with knowledge about fragments of structures that are similar to the protein of interest.

The method works by using the initial model to search for similar structures within the PDB. These are found using two regimes. The first is to search for global templates by assessing the TMscore of structures to the whole initial model. The second is to search for fragments of structures by dividing the initial model into continuous 3 secondary structure elements. From these sets of templates and the initial model, the authors can generate a bespoke potential for the model based on the distances between Cα atoms. By doing this, additional information about the likely global topology of the protein can be incorporated into a molecular dynamics simulation. The authors claim that this enables the MD energy landscape is therefore reshaped from being “golf-course-like” being “funnel-like”. Essentially, the MD simulations are guided to sample conformations which are likely (as informed by the fragments) to be close to the target protein structure.

A schematic of the FG-MD refinement procedure

Does it work?

As a full solution to the problem of protein structure model refinement, the results are far from convincing. Quality measures show improvement in only the second or third decimal place from the initial model to the refined model. Also, as might be expected, the degree to which the model quality is improved is dependent on the accuracy of the initial of the model.

However, what is important about this paper is that, although small, the improvements made do exist in a systematic fashion. Previously, attempts to refine a model using MD not only failed to improve its accuracy but would be likely to reduce its quality. Fragment-guided MD (FG-MD) and the explicit inclusion of a hydrogen bonding potential, is not only able to improve the conformations of side chains but also improve (or at least not destroy) the global backbone topology of a model.

Dependence of the energy of a model on its TM-Score to the native structure. In black is the energy as measure using the AMBER99 energy function. In grey is the corresponding funnel-like shape of the FG-MD energy function.

This paper therefore lays the groundwork for the development of further refinement methods that incorporate the knowledge from protein structure fragments with atomically detailed energy functions. Given that the success of the method is related to the accuracy of the initial model, there may be scope for developing similar techniques to refine models of specific proteins where modelling quality is already good. e.g. antibodies.

aRrrrgh! or how to apply a fitted model to new data

Recently I’ve been battling furiously with R while analysing some loop modelling accuracy data. The idea was simple:

Fit a general linear model to some data
Get out a formula to predict a variable (let’s call it “accuracy”) based on some input parameters
Apply this formula to new data and see how well the predictor does

It turns out, it’s not that simple to actually implement. Fitting a general linear model in R produces coefficients in a vector.

model <- glm(accuracy ~ param1 + param2 * param3, data=trainingset)
coef(model)

            (Intercept)                  param1                  param2 
            0.435395087            -0.093295388             0.148154339 
                 param3           param2:param3
            0.024399530             0.021100300

There seems to be no easy way to insert these coefficients into your formula and apply the resulting equation to new data. The only easy thing to do is to plot the fitted values against the variable we’re trying to predict, i.e. plot our predictions on the training set itself:

plot(model$fitted.values, trainingset$accuracy, xlab="score", ylab="accuracy", main="training set")

I’m sure there must be a better way of doing this, but many hours of Googling led me nowhere. So here is how I did it. I ended up writing my own parser function, which works only on very simple formulae using the + and * operators and without any R code inside the formula.

coefapply <- function(coefficients, row)
{
  result <- 0
  for (i in 1:length(coefficients))
  {
    subresult <- as.numeric(coefficients[i])
    if (!is.na(subresult))
    {
      name <- names(coefficients[i])
      if (name != "(Intercept)")
      {
        subnames <- strsplit(name, ":", fixed=TRUE)[[1]]
        for (n in subnames)
        {
          subresult <- subresult * as.numeric(row[n])
        }
      }
      result <- result + subresult
    }
  }
  return(result)
}

calculate_scores <- function(data, coefficients)
{
  scores <- vector(mode="numeric", length=nrow(data))
  for (i in 1:nrow(data))
  {
    row <- data[i,]
    scores[i] <- coefapply(coefficients, row)
  }
  return(scores)
}

Now we can apply our formula to a new dataset and plot the accuracy achieved on the new data:

model_coef <- coef(model)

# Test if our scores are the same values as the model's fitted values
training_scores <- calculate_scores(model_coef, trainingset)
sum((training_scores - model$fitted.values) < 0.000000000001) / length(scores)

# Calculate scores for our test set and plot them
test_scores <- calculate_scores(model_coef, testset)
plot(test_scores, testset$accuracy, xlab="score", ylab="accuracy", main="test set")

It works for my purpose. Maybe one day someone will see this post, chuckle, and then enlighten me with their perfectly simple and elegant alternative.

On being cool: arrows on an R plot

Recently I needed a schematic graph of traditional vs on-demand computing (don’t ask) – and in this hand waving setting I just wanted the axes to show arrows and no labels. So, here it is:

x <- c(1:5)
y <- rnorm(5)
plot(x, y, axes = FALSE)
u <- par("usr") 
arrows(u[1], u[3], u[2], u[3], code = 2, xpd = TRUE) 
arrows(u[1], u[3], u[1], u[4], code = 2, xpd = TRUE)

And here is the output

(I pinched this off a mailing list post, so this is my due reference)

Next thing I am toying with are these xkcd like graphs in R here.

Oxford Protein Informatics Group

or "OPIG" to friends