Finishing up a lingering project from your PhD almost a year into your postdoc is a great feeling, especially when it has actually been about 3 years in the making.
Though somewhat outside of the usual scope of activities in OPIG, I encourage you to take a look if the below summary grabs your interest. The full paper and supporting materials (including some movies which took entirely too long to make) can be found at https://pubs.acs.org/doi/abs/10.1021/jacs.9b12264.
Tag Archives: Protein Bioinformatics
Journal Club: Large-scale structure prediction by improved contact predictions and model quality assessment.
With the advent of statistical techniques to infer protein contacts from multiple sequence alignments (which you can read more about here), accurate protein structure prediction in the absence of a template has become possible. Taking advantage of this fact, there have been efforts to brave the sea of protein families for which no structure is known (about 8,500 – over 50% of known protein families) in an attempt to predict their topology. This is particularly exciting given that protein structure prediction has been an open problem in biology for over 50 years and, for the first time, the community is able to perform large-scale predictions and have confidence that at least some of those predictions are correct.
Based on these trends, last group meeting I presented a paper entitled “Large-scale structure prediction by improved contact predictions and model quality assessment”. This paper is the culmination of years of work, making use of a large number of computational tools developed by the Elofsson Lab at Stockholm University. With this blog post, I hope to offer some insights as to the innovative findings reported in their paper.
Let me begin by describing their structure prediction pipeline, PconsFold2. Their method for large-scale structure prediction can be broken down into three components: contact prediction, model generation and model quality assessment. As the very name of their article suggests, most of the innovation of the paper stems from improvements in contact prediction and the quality assessment protocols used, whereas for their model generation routine, they opted to sacrifice some quality in favour of speed. I will try and dissect each of these components over the next paragraphs.
Contact prediction relates to the process in which residues that share spatial proximity in a protein’s structure are inferred from multiple sequence alignments by co-evolution. I will not go into the details of how these protocols work, as they have been previously discussed in more detail here and here. The contact predictor used in PconsFold2 is PconsC3, which is another product of the Elofsson Lab. There was some weirdness with the referencing of PconsC3 on the PconsFold2 article, but after a quick google search, I was able to retrieve the article describing PconsC3 and it was worth a read. Other than showcasing PconsC3’s state-of-the-art contact prediction capabilities, the original PconsC3 paper also provides figures for the number of protein families for which accurate contact prediction is possible (over 5,000 of the ~8,500 protein families in Pfam without a member of known structure). I found the PconsC3 article feels like a prequel to the paper I presented. The bottom line here is that PconsC3 is a reliable tool for predicting contacts from multiple sequence alignments and is a sensible choice for the PconsFold2 pipeline.
Another aspect of contact prediction that the authors explore is the idea that the precision of contact prediction is dependent on the quality of the underlying multiple sequence alignment (MSA). They provide a comparison of the Positive Predicted Value (PPV) of PconsC3 using different MSAs on a test set of 626 protein domains from Pfam. To my knowledge, this is the first time I have encountered such a comparison and it serves to highlight the importance the MSA has on the quality of resulting contact predictions. In the PconsFold2 pipeline, the authors use consensus approach; they identify the consensus of four predicted contact maps each using a different alignment. Alignments were generated using Jackhmmer and HHBlits at E-Value cutoffs of 1 and 10^-4.
Now, moving on to the model generation routine. PconsFold2 makes use of CONFOLD to perform model generation. CONFOLD, in turn, uses the simulated annealing routine of the Crystallographic and NMR System (CNS) to produce models based on spatial and geometric constraints. To derive those constraints, predicted secondary structure and the top 2.5 L predicted contacts are given as input. The authors do note that the refinement stage of CONFOLD is omitted, which is a convenience I assume was adopted to save computational time. The article also acknowledges that models generated by CONFOLD are likely to be less accurate than the ones produced by Rosetta, yet a compromise was made in order to make the large-scale comparison feasible in terms of resources.
One particular issue that we often discuss when performing structure prediction is the number of models that should be produced for a particular target. The authors performed a test to assess how many decoys should be produced and, albeit simplistic in their formulation, their results suggest that 50 models per target should be sufficient. Increasing this number further did not lead to improvements in the average quality of the best models produced for their test set of 626 proteins.
After producing 50 models using CONFOLD, the final step in the PconsFold2 protocol is to select the best possible model from this ensemble. Here, they present a novel method, PcombC, for ranking models. PcombC combines the clustering-based method Pcons, the single-model deep learning method ProQ3D, and the proportion of predicted contacts that are present in the model. These three scores are combined linearly, and are given weights that were optimised via a parameter sweep. One of my reservations relating to this paper is that little detail is given regarding the data set that was used to perform this training. It is unclear from their methods section if the parameter sweep was trained on the test set with 626 proteins used throughout the manuscript. Given that no other data set (with known structures) is ever introduced, this scenario seems likely. Therefore, all the classification results obtained by PcombC, and all of the reported TM-score Top results should be interpreted with care since performance on validation set tends to be poorer than on a training set.
Recapitulating the PconsFold2 pipeline:
- Step 1: generate four multiple sequence alignments using HHBlits and Jackhmmer.
- Step 2: generate four predicted contact maps using PconsC3.
- Step 3: Use CONFOLD to produce 50 models using a consensus of the contact maps from step 2.
- Step 4: Use PCombC to rank the models based on a linear combination of the Pcons and ProQ3D scores and the proportion of predicted contacts that are present in the model.
So, how well does PconsFold2 perform? The conclusion is that it depends on the quality of the contact predictions. For the protein families where abundant sequence information is available, PconsFold2 produces a correct model (TM-Score > 0.5) for 51% of the cases. This is great news. First, because we know which cases have abundant sequence information beforehand. Second, because this comprises a large number of protein families of unknown structure. As the number of effective sequence (a common way to assess the amount of information available on an MSA) decreases, the proportion of families for which a correct model has been generated also decreases, which restricts the applicability of their method to protein families with abundant sequence information. Nonetheless, given that protein sequence databases are growing exponentially, it is possible that over the next years, the number of cases where protein structure prediction achieves success is likely to increase.
One interesting detail that I was curious about was the length distribution of the cases where modelling was successful. Can we detect the cases for which good models were produced simply by looking at a combination of length and number of effective sequences? The authors never address this question, and I think it would provide some nice insights as to which protein features are correlated to modelling success.
We are still left with one final problem to solve: how do we separate the cases for which we have a correct model from the ones where modelling has failed? This is what the authors address with the last two subsections of their Results. In the first of these sections, the authors compare four ways of ranking decoys: PcombC, Pcons, ProQ3D, and the CNS contact score. They report that, for the test set of 626 proteins, PcombC obtains the highest Pearson’s Correlation Coefficient (PCC) between the predicted and observed TM-Score of the highest ranking models. As mentioned before, this measure could be overestimated if PcombC was, indeed, trained on this test set. Reported PCCs are as follows: PcombC = 0.79, Pcons = 0.73, ProQ3D = 0.67, and CNS-contact = -0.56.
In their final analysis, the authors compare the ability of each of the different Quality Assessment (QA) scores to discern between correct and incorrect models. To do this, they only consider the top-ranked model for each target according to different QA scores. They vary the false positive rate and note the number of true positives they are able to recall. At a 10% false positive rate, PcombC is able to recall about 50% of the correct models produced for the test set. This is another piece of good news. Bottomline is: if we have sufficient sequence information available, PconsFold2 can generate a correct model 51% of the time. Furthermore, it can detect 50% of these cases, meaning that for ~25% of the cases it produced something good and it knows the model is good. This opens the door for looking at these protein families with no known structure and trying to accurately predict their topology.
That is exactly what the authors did! On the most interesting section of the paper (in my opinion), the authors predict the topology of 114 protein families (at FPR of 1%) and 558 protein families (at FPR of 10%). Furthermore, the authors compare the overlap of their results with the ones reported by a similar study from the Baker group (previously presented at group meeting here) and find that, at least for some cases, the predictions agree. These large-scale efforts force us to revisit the way we see template-free structure prediction, which can no longer be dismissed as a viable way of obtaining structural models when sufficient sequences are available. This is a remarkable achievement for the protein structure prediction community, with the potential to change the way we conduct structural biology research.
CCP4 Study Weekend 2017: From Data to Structure
This year’s CCP4 study weekend focused on providing an overview of the process and pipelines available, to take crystallographic diffraction data from spot intensities right through to structure. Therefore sessions included; processing diffraction data, phasing through molecular replacement and experimental techniques, automated model building and refinement. As well as updates to CCP4 and where is crystallography going to take us in the future?
Surrounding the meeting there was also a session for Macromolecular (MX) crystallography users of Diamond Light Source (DLS), which gave an update on the beamlines, and scientific software, as well as examples of how fragment screening at DLS has been used. The VMXi (Versatile Macromolecular X-tallography in-situ) beamline is being developed to image crystals that are forming in situ crystallisation plates. This should allow for crystallography to be optimized, as crystallization conditions can be screened, and data collected on experiments as they crystallise, especially helpful in cases where crystallisation has routinely led to non-diffracting crystals. VXMm is a micro/nanofocus MX beamline, which is in development, with a focus to get crystallographic from very small crystals (~300nm to 10 micron diameters, with a bias to the smaller size), thereby allowing crystallography of targets that have previously been hard to get sufficient crystals. Other updates included how technology developed for fast solid state data collection on x-ray free electron lasers (XFEL) can be used on synchrotron beamlines.
A slightly more in-depth discussion of two tools presented that were developed for use alongside and within CCP4, which might be of interest more broadly:
ConKit: A python interface for contact prediction tools
Contact prediction for proteins, at its simplest, involves estimating which residues within a certain certain spatial proximity of each other, given the sequence of the protein, or proteins (for complexes and interfaces). Two major types of contact prediction exist:
- Evolutionary Coupling
- Take a series of sequence homologues, and identifying co-evolved residues from multiple sequence alignment of the protein family. These co-evolved residues are hypothesized to share a functional dependence. Discussed previously on BLOPIG: Predicted protein contacts: is it the solution to (de novo) protein structure prediction?
- Supervised machine learning
- Using ab initio structure prediction tools, without sequence homologues, to predict which contacts exist, but with a much lower accuracy than evolutionary coupling.
ConKit is a python interface (API) for contact prediction tools, consisting of three major modules:
- Core: A module for constructing hierarchies, thereby storing necessary data such as sequences in a parsable format.
- Providing common functionality through functions that for example declare a contact as a false positive.
- Application: Python wrappers for common contact prediction and sequence alignment applications
- I/O: I/O interface for file reading, writing and conversions.
Contact prediction can be used in the crystallographic structure determination field, during unconventional molecular replacement, using a tool such as AMPLE. Molecular replacement is a computational strategy to solve the phase problem. In the typical case, by using homologous structures to determine an estimate a model of the protein, which best fits the experimental diffraction intensities, and thus estimate the phase. AMPLE utilises ab initio modeling (using Rosetta) to generate a model for the protein, contact prediction can provide input to this ab initio modeling, thereby making it more feasible to generate an appropriate structure, from which to solve the phase problem. Contact prediction can also be used to analyse known and unknown structures, to identify potential functional sites.
For more information: Talk given at CCP4 study weekend (Felix Simkovic), ConKit documentation
ACEDRG: Generating Crystallographic Restraints for Ligands
Small molecule ligands are present in many crystallographic structures, especially in drug development campaigns. Proteins are formed (almost exclusively) from a sequence containing a selection of 20 amino acids, this means there are well known restraints (for example: bond lengths, bond angles, torsion angles and rotamer position) for model building or refinement of amino acids. As ligands can be built from a much wider selection of chemical moieties, they have not previously been restrained as well during MX refinement. Ligands found in PDB depositions can be used as models for the model building/ refinement of ligands in new structures, however there are a limited number of ligands available (~23,000). Furthermore, the resolution of the ligands is limited to the resolution of the macro-molecular structure from which they are extracted.
ACEDRG utilises the crystallorgraphy open database (COD), a library of (>300,000) small molecules usually with atomic resolution data (often at least 0.84 Angstrom), to generate a dictionary of restraints to be used in refining the ligand. To create these restraints ACEDRG utilises the RDkit chemoinformatics package, generating a detailed descriptor of each atom of the ligands in COD. The descriptor utilises properties of each atom including the element name, number of bonds, environment of nearest neighbours, third degree neighbours that are aromatic ring systems. The descriptor, is stored alongside the electron density values from the COD. When a ACEDRG query is generated, for each atom in the ligand, the atom type is compared to those for which a COD structure is available, the nearest match is then used to generate a series of restraints for the atom.
ACEDRG can take a molecular description (SMILES, SDF MOL, SYBYL MOL2) of your ligand, and generate appropriate restraints for refinement, (atom types, bond lengths and angles, torsion angles, planes and chirality centers) as a mmCIF file. These restraints can be generated for a number of different probable conformations for the ligand, such that it can be refined in these alternate conformations, then the refinement program can use local scoring criteria to select the ligand conformation that best fits the observed electron density. ACEDRG can accessed through the CCP4i2 interface, and as a command line interface.
Hopefully a useful insight to some of the tools presented at the CCP4 Study weekend. For anyone looking for further information on the CCP4 Study weekend: Agenda, Recording of Sessions, Proceedings from previous years.
Is “fragment-based” still the way forward in template-free protein structure prediction?
Out of the many questions surrounding the notion that you can predict a protein’s structure from its sequence, there is one in particular that I decided to tackle during last group meeting.
Protein structure prediction is a hard problem (do I sound repetitive?). One of the many cop outs employed by the structure prediction community is the idea that you can break down known structures into fragments and use these protein pieces to perform predictions. This is known as fragment-assembly or fragment-based template-free protein structure prediction.
As absurd as the idea may seem, there is robust evidence that suggests that this is actually a viable strategy. There is a notion that the fragment space is complete; you can reconstruct the backbone of any known structure based on the torsion angles of fragments from other structures. In less technical jargon, you can effectively use fragments and combine them to re-create any of the protein structures that we know and to a fairly acceptable level of precision.
So, technically, it is possible to predict a protein structure using fragments from other structures. In practice, you are still left with the problem of choosing the right fragments to model your sequence of interest. How easy do you think that is?
We can look at this question in light of observations that were made back in the early 80s. Kabsch and Sander reported that two protein fragments having exactly the same sequence can present completely different structures [1]. This complies with the notion that global properties can affect and even define local structure, which in turn suggests that selecting the right fragments to assemble a structure is not necessarily a straightforward process.
The starting point for protein structure prediction is a sequence. Since we are talking about template-free protein structure prediction, it is safe to assume that there is no good global sequence match to your target with a known structure (otherwise you would use that match/structure as a template). Hence, fragment selection is restricted to local sequence similarity, which, as suggested in the previous paragraph, is not necessarily ideal.
On the other hand, we are becoming increasingly more accurate in inferring one-dimensional properties from a protein’s sequence. These properties can and often are used to enhance our fragment-selection capabilities. Yet, even using the state-of-the-art in secondary structure and torsion angle prediction, fragment selection is still fairly imprecise.
During group meeting I highlighted a possible contrast between practical fragment space and general (or possible) fragment space. My premise is simple. I define practical fragment space as the fragments that we can accurately select from the possible fragment space to model protein structures. In my opinion, it would be extremely interesting to quantify the difference between the two. This would answer the fundamental question of how useful fragment-assembly actually is. More importantly, it would help the community make an educated decision in regards to whether template-free structure prediction strategies should shift from fragment-based to ones based on distance constraints, an approach that is gaining popularity due to the success of contact predictions.
I am very keen to investigate this further. Maybe for my next blog post, we will have an answer! Stay tuned.
[1] Kabsch, Wolfgang, and Christian Sander. “On the use of sequence homologies to predict protein structure: identical pentapeptides can have completely different conformations.” Proceedings of the National Academy of Sciences 81.4 (1984): 10751078.
Predicted protein contacts: is it the solution to (de novo) protein structure prediction?
So what is this buzz I hear about predicted protein contacts? Is it really the long awaited solution for one of the biggest open problems in biology today? Has protein structure prediction been solved?
Well, first things first. Let me give you a quick introduction to this predicted protein contact business (probably not quick enough for an elevator pitch, but hopefully you are not reading this in an elevator).
Nowadays, the scientific community has become very good at sequencing things (and by things I mean genetic things, like whole genomes of a bunch of different people and organisms). We are so good at it that mountains of sequence data are now available: genes, mRNAs, protein sequences. The question is what do we do with all this data?
Good scientists are coming up with new and creative ideas to extract knowledge from these mountains of data. For instance, one can build multiple sequence alignments using protein sequences for a given protein family. One of the ways in which information can be extracted from these multiple sequence alignments is by identifying extremely conserved columns (think of the alignment as a big matrix). Residues in these conserved positions are good candidates for being functionally important for the proteins in that particular family.
Another interesting thing that can be done is to look for pairs of residues that are mutating in a correlated fashion. In more practical terms, you are ascertaining how correlated is the information between two columns of a multiple sequence alignment; how often a change in one of them is countered by a change in the other. Why would anyone care about that? Simple. There is an assumption that residues that mutate in a correlated fashion are co-evolving. In other words, they share some sort of functional dependence (i.e. spatial proximity) that is under selective pressure.
Ok, that was a lot of hypotheticals, does it work? For many years, it didn’t. There were lots of issues with the way these correlations were computed and one of the biggest problems was to identify (and correct for) transitivity. Transitivity is the idea that you observe a false correlation between residues A and C because residues A,B and residues B,C are mutating in a correlated fashion. AS more powerful statistical methods were developed (borrowing some ideas from mechanical statistics), the transitivity issue has seemingly been solved.
The newest methods that detect co-evolving residues in a multiple sequence alignment are capable of detecting protein contacts with high precision. In this context, a contact is defined as two residues that are close together in a protein structure. How close? Their C-betas must be 8 Angstroms or less apart. When sufficient sequence information is available (at least 500 sequences in the MSA), the average precision of the predicted contacts can reach 80%.
This is a powerful way of converting sequence information into distance constraints, which can be used for protein structure modelling. If a sufficient number of correct distance constraints is used, we can accurately predict the topology of a protein [1]. Recently, we have also observed great advances in the way that models are refined (that is, refining a model that contains the correct topology to atomic, near-experimental resolution). If you put those two things together, we start to look at a very nice picture.
So what’s the catch? The catch was there. Very subtle. “When sufficient sequence information is available”. Currently, there is an estimate that only 15% of the de novo protein structure prediction cases present sufficient sequence information for the prediction of protein contacts. One potential solution would be to sit and wait for more and more sequences to be obtained. Yet a potential pitfall of sitting and waiting is that there is no guarantee that we will have sufficient sequence information for a large number of protein families, as they may as well present less than 500 members.
Furthermore, scientists are not very good at sitting around and waiting. They need to keep themselves busy. There are many things that the community as whole can invest time on while we wait for more sequences to be generated. For instance, we want to be sure that, for the cases where there is a sufficient number of sequences, that we get the modelling step right (and predict the accurate protein topology). Predicted contacts also show potential as a tool for quality assessment and may prove to be a nice way of ascertaining whether you have confidence that a model with correct topology was created. More than that, model refinement still needs to improve if we want to make sure that we get from the correct topology to near-experimental resolution.
Protein structure prediction is a hard problem and with so much room for improvement, we still have a long way to go. Yet, this predicted contact business is a huge step in the right direction. Maybe, it won’t be long before models generated ab initio are considered as reliable as the ones generated using a template. Who knows what promised the future holds.
References:
[1] Kim DE, Dimaio F, Yu-Ruei Wang R, Song Y, Baker D. One contact for every twelve residues allows robust and accurate topology-level protein structure modeling. Proteins. 2014 Feb;82 Suppl 2:208-18. doi: 10.1002/prot.24374. Epub 2013 Sep 10.
Hypotheses and Perspectives onto de novo protein structure prediction
Before I start with my musings about my work and the topic of my D. Phil thesis, I would like to direct you to a couple of previous entries here on BLOPIG. If you are completely new to the field of protein structure prediction or if you just need to refresh your brain a bit, here are two interesting pieces that may give you a bit of context:
A very long introductory post about protein structure prediction
and
de novo Protein Structure Prediction software: an elegant “monkey with a typewriter”
Brilliant! Now, we are ready to start.
In this OPIG group meeting, I presented some results that were obtained during my long quest to predict protein structures.
Of course, no good science can happen without the postulation of question-driving hypotheses. This is where I will start my scientific rant: the underlying hypotheses that inspired me to inquire, investigate, explore, analyse, and repeat. A process all so familiar to many.
As previously discussed (you did read the previous posts as suggested, didn’t you?), de novo protein structure prediction is a very hard problem. Computational approaches often struggle to search the humongous conformational space efficiently. Who can blame them? The number of possible protein conformations is so astronomically large that it would take MUCH longer than the age of the universe to look at every single possible protein conformation.
If we go back to biology, protein molecules are constantly undergoing folding. More so, they manage to do so efficiently and accurately. How is that possible? And can we use that information to improve our computational methods?
The initial hypothesis we formulated in the course of my degree was the following:
“We [the scientific community] can benefit from better understanding the context under which protein molecules are folding in vivo. We can use biology as a source of inspiration to improve existing methods that perform structure prediction.”
Hence came the idea to look at biology and search for inspiration. [Side note: It is my personal belief that there should be a back and forth process, a communication, between computational methods and biology. Biology can inspire computational methods, which in turn can shed light on biological hypotheses that are hard to validate experimentally]
To direct the search for biological inspiration, it was paramount to understand the limitations of current prediction methods. I have narrowed down the limitations of de novo protein structure prediction approaches to three major issues:
1- The heuristics that rely on sampling the conformational space using fragments extracted from know structures will fail when those fragments do not encompass or correctly describe the right answer.
2- Even when the conformational space is reduced, say, to fragment space, the combinatorial problem persists. The energy landscape is rugged and unrepresentative of the actual in vivo landscape. Heuristics are not sampling the conformational space efficiently.
3- Following from the previous point, the reason why the energy landscape is unrepresentative of the in vivo landscape is due to the inaccuracy of the knowledge-based potentials used in de novo structure prediction.
Obviously, there are other relevant issues with de novo structure prediction. Nonetheless, I only have a limited amount of time for my D.Phil and those are the limitations I decided to focus on.
To counter each of these offsets, we have looked for inspiration in biology.
Our understanding from looking at different protein structures is that several conformational constraints are imposed by alpha-helices and beta-strands. That is a consequence of hydrogen bond formation within secondary structure elements. Unsurprisingly, when looking for fragments that represent the correct structure of a protein, it is much easier to identify good fragments for alpha-helical or beta-strand regions. Loop regions, on the other hand, are much harder to be described correctly by fragments extracted from known structures. We have incorporated this important information into a fragment library generation software in an attempt to address limitation number 1.
We have investigated the applicability of a biological hypothesis, cotranslational protein folding, into a structure prediction context. Cotranslational protein folding is the notion that some proteins begin their folding process as they are being synthesised. We further hypothesise that cotranslational protein folding restricts the conformational space, promoting the formation of energetically-favourable intermediates, thus steering the folding path towards the right conformation. This hypothesis has been tested in order to improve the efficiency of the heuristics used to search the conformational space.
Finally, following the current trend in protein structure prediction, we used evolutionary information to improve our knowledge-based potentials. Many methods now consider correlated mutations to improve their predictions, namely the idea that residues that mutate in a correlated fashion present spatial proximity in a protein structure. Multiple sequence alignments and elegant statistical techniques can be used to identify these correlated mutations. There is a substantial amount of evidence that this correlated evolution can significantly improve the output of structure prediction, leading us one step closer to solving the protein structure prediction problem. Incorporating this evolution-based information into our routine assisted us in addressing the lack of precision of existing energy potentials.
Well, does it work? Surprisingly or not, in some cases it does! We have participated in a blind competition: the Critical Assessment for protein Structure Prediction (CASP). This event is rather unique and it brings together the whole structure prediction community. It also enables the community to gauge at how good we are at predicting protein structures. Working with completely blind predictions, we were able to produce one correct answer, which is a good thing (I guess).
All of this comes together nicely in our biologically inspired pipeline to predict protein structures. I like to think of our computational pipeline as a microscope. We can use it to prod and look at biology. We can tinker with hypotheses, implement potentials and test them, see what is useful for us and what isn’t. It may not be exactly what get the papers published, but the investigative character of our structure prediction pipeline is definitely the favourite aspect of my work. It is the aspect that makes me feel like a scientist.
Protein Structure Prediction, my own metaphorical microscope…
Kinetic Modelling of Co-translational Protein Folding (Journal Club)
Following up on last week’s entry, this post will explore the same topic: polypeptide chains assuming native-like conformations as they are extruded from the ribosome, or for the less intimate with the concept, co-translational protein folding.
Before addressing some important questions concerning co-translational protein folding, I would like to make a parenthesis: I want to dedicate a paragraph or two to talk about time.
Biological processes are dynamic. They are events that occur over a period of time. For instance, one can quantify the effect of mutations propagated and accumulated over millions of years of evolution. One can also quantify the femtoseconds in which subtle conformational changes occur in photoreceptor proteins like rhodopsin, when they respond to light. Time is fundamental to understand and model any sort of biological event.
Albeit it might seem obvious to the reader that time is so crucial to amass biological knowledge, those of us more theoretically inclined (bioinformaticians, computational biologists, biostatisticians, mathematical biologists and so on and so forth) are usually presented with models that tend to over-simplify reality. Surprisingly enough, there are many over-simplistic models that neglect the effect of time in order to “better” represent whatever they claim to model. Take Protein Docking for instance. The biological process at hand presents a complicated dynamic. There is a kinetic equilibrium, in which a vast amount of protein and ligand molecules interact, associating into complexes and dissociating. Nonetheless, Protein Docking is traditionally reduced to the binding affinity between a pair of molecules. As one might say, this is only a problem if I can present a solution… Luckily, Protein Docking is not my subject of expertise, so I will leave this question open to more tenacious minds than my own.
One of the areas in which I am truly interested in is the co-translational aspect of protein folding. If one performs a quick Google Images search, using the terms “Protein Synthesis” or “Protein Translation”, the results tell a very interesting story. The vast majority of nascent protein chains are represented as fully elongates peptide chains. In a majority of pictures, the growing peptides do not even present secondary structure. They are mostly represented by long, unfolded, almost linear polymers.
Now, any first year Biochemistry student learns about something called Hydrophobicity (or hydrophilicity depending on whether you are a glass half empty or half full type of person). It is biochemistry-introductory-text-book stuff that some residues are polar and some residues are apolar, and hence will hide from water, forming a hydrophobic core. That (hydrophobicity) is one of the main driving forces of protein folding.
Hence, most of the images that appear in our Google Images search are not very representative. They are plain wrong. It is simple physics that the growing peptide chains will form secondary and tertiary structures during the process of protein synthesis. One has to remember that this process is dynamic, it is happening over time. Under these circumstances, time should not be neglected. The time scale at which extrusion occurs is slow enough to allow the nascent chain to probe conformations and simply abide to the laws of physics. A fully elongated, completely unfolded and denatured peptide chain would not exist during protein synthesis. These nascent chains would adopt intermediate conformations simply as a result of apolar residues trying to hide from water.
Ok. Now, the BIG question that can be raised is whether those intermediate conformations actually resemble the native state of the fully elongated protein. I do not want to incur in Baby Kicking, but one thing that evolution has taught us is that cells have evolved to be highly efficient systems. There is no room for wasted energy. It makes sense to hypothesize that over millions of years, the cellular machinery has adapted to explore these intermediate conformations in order to make the process of protein folding more efficient.
Over the past couple of years, substantial evidence has been amassed that codon usage and the degeneracy of the genetic code could be exploited by cells to ensure that protein folding occurs accurately and efficiently. There are many theoretical ways that such exploitation could occur: the codon translation speed could facilitate the formation of certain intermediates that are beneficial for protein folding, that increase stability or that prevent protein aggregation. There is even a biomedical impact given that some observed pathologies have been associated with synonymous codon mutations that may lead to misfolded proteins.
In the paper I presented during this journal club [1], O’Brien and colleagues have devised and described a very interesting kinetic model for protein translation. Their model was used to describe possible scenarios in which both fast and slow translation speed codons are coordinators of co-translational protein folding. Please note that, in this context, co-translational protein folding is perceived as an enrichment of intermediate conformations of the nascent chains, which resemble the native structure of the fully elongated protein.
In the model described in the paper, they opted for a probabilistic approach instead of an analytical (differential equations) approach. The time is modelled by the use of probabilities. The authors derived a formula to quantify the expected proportion of nascent chains of a given length that would be in a Folded intermediate state (one that resembles the native structure). They have managed to express this in terms of a rate of codon translation. Therefore, they stablish a direct relationship between Co-Translational protein folding and codon translation speed.
Their analysis is robust as none of the constants and kinetic rates need to be experimentally derived in order to provide insights about the protein folding process. Overall, I think the way the model was built was quite ingenious and very interesting. I would suggest any interested reader to read the article if they want to understand how the whole modelling was carried out.
Overall, I think the authors present a compelling argument for how cells could explore codon degeneracy and co-translational aspects of protein folding to improve folding efficiency. One of their results present a scenario in which fast translation speed codons can be used to assist in the fold of unstable protein regions, preventing the formation of misfolded intermediates.
One of the many functions of mathematical models is to provide insights into the underlying biology of the phenomena they attempt to model. The lack of any experimental evidence to support this paper’s results does not make it any less interesting. The article presents to the readers a sound and solid mathematical argument as to how co-translational aspects of protein folding could be beneficial for cell efficiency. If anything, they provide interesting hypotheses that might drive experimentalists in the future.
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.