Tag Archives: Protein

Slow and steady improvements in the prediction of one-dimensional protein features

What do you do when you have a big, complex problem whose solution is not necessarily trivial? You break the problem into smaller, easier to solve parts,  solve each of these sub-problems and merge the results to find the solution of the original, bigger problem. This is an algorithm design paradigm known as the divide and conquer approach.

In protein informatics, we use divide and conquer strategies to deal with a plethora of large and complicated problems. From protein structure prediction to protein-protein interaction networks, we have a wide range of sub and sub-sub problems whose solutions are supposed to help us with the bigger picture.

In particular, prediction of the so called one-dimensional protein features are fundamental sub-problems with a wide range of applications such as protein structure modelling,  homology detection, functional characterization and others. Here, one-dimensional protein features refer to secondary structure, backbone dihedral and C-alpha angles, and solvent accessible surface area.

In this week’s group meeting, I discussed the latest advancements in prediction of one-dimensional features as described in an article published by Heffernan R. and colleagues in Scientific Reports (2015):

“Improving prediction of secondary structure, local backbone angles, and solvent accessible surface area of proteins by iterative deep learning.”

In this article, the authors describe the implementation of SPIDER2, a deep learning approach to predict secondary structure, solvent accessible surface area, and four backbone angles (the traditional dihedrals phi and psi, and the recently explored theta and tau).

“Deep learning” is the buzzword (buzz-two-words or buzzsentence, maybe?) of the moment. For those of you who have no idea what I am talking about, deep learning is an umbrella term for a series of convoluted machine learning methods. The term deep comes from the multiple hidden layers of neurons used during learning.

Deep learning is a very fashionable term for a reason. These methods have been shown to produce state-of-the-art results for a wide range of applications in several fields, including bioinformatics. As a matter of fact, one of the leading methods for contact prediction (previously introduced in this blog post), uses a deep learning approach to improve the precision of predicted protein contacts.

Machine learning has already been explored to predict one-dimensional protein features, showing promising (and more importantly, useful) results. With the emergence of new, more powerful machine learning techniques such as deep learning, previous software are now becoming obsolete.

Based on this premise, Heffernan R. and colleagues implemented and applied their deep learning approach to improve the prediction of one-dimensional protein features. Their training process was rigorous: they performed a 10-fold cross validation using their training set of ~4500 proteins and, on top of that, they also had two independent test sets (a ~1200 protein test set and a set based on the targets of CASP11).  Proteins in all sets did not share more than 25% (30% sequence identity for the CASP set) to any other protein in any of the sets.

The method described in the paper, SPIDER2, was thoroughly compared with state-of-the art prediction software for each of the one-dimensional protein features that it  is capable of predicting. Results show that SPIDER2 achieves a small, yet significant improvement compared to other methods.

It is just like they say, slow and steady wins the race, right? In this case, I am not so sure. It would be interesting to see how much the small increments in precision obtained by SPIDER2 can improve the bigger picture, whichever your bigger picture is. The thing about divide and conquer is that if you become marginally better at solving one of the parts, that doesn’t necessarily imply that you will improve the solution of the bigger, main problem.

If we think about it, during the “conquer” stage (that is, when you are merging the solution of the smaller parts to get to the bigger picture),  you may make compromises that completely disregard any minor improvements for the sub-problems. For instance, in my bigger picture, de novo protein structure prediction, predicted local properties can be sacrificed to ensure a more globally consistent model. More than that, most methods that perform de novo structure prediction already account for a certain degree of error or uncertainty for, say, secondary structure prediction. This is particularly important for the border regions between secondary structure elements (i.e. where an alpha-helix ends and a loop begins). Therefore, even if you improve the precision of your predictions for those border regions, the best approach for structure prediction may still consider those slightly more precise border predictions as unreliable.

The other moral of this story is far more pessimistic. If you think about it, there were significant advancements in machine learning, which led to the creation of ever-more-so complicated neural network architectures. However, when we look back to how much improvement we observed when these highly elaborate techniques were applied to an old problem (prediction of one-dimensional protein features), it seems that the pay-off wasn’t as significant (at least as I would expect). Maybe, I am a glass half-empty kind of guy, but given the buzz surrounding deep learning, I think minor improvements is a bit of a let down. Not to take any credit away from the authors. Their work was rigorous and scientifically very sound. It is just that maybe we are reaching our limits when it comes to applying machine learning to predict secondary structure. Maybe when the next generation of buzzword-worthy machine learning techniques appear, we will observe an even smaller improvement to secondary structure prediction. Which leaves a very bitter unanswered question in all our minds: if machine learning is not the answer, what is?

SAS-5 assists in building centrioles of nematode worms Caenorhabditis elegans

We have recently published a paper in eLife describing the structural basis for the role of protein SAS-5 in initiating the formation of a new centriole, called a daughter centriole. But why do we care and why is this discovery important?

We, as humans – a branch of multi-cellular organisms, are in constant demand of new cells in our bodies. We need them to grow from an early embryo to adult, and also to replace dead or damaged cells. Cells don’t just appear from nowhere but undergo a tightly controlled process called cell cycle. At the core of cell cycle lies segregation of duplicated genetic material into two daughter cells. Pairs of chromosomes need to be pulled apart millions of millions times a day. Errors will lead to cancer. To avoid this apocalyptic scenario, evolution supplied us with centrioles. Those large molecular machines sprout microtubules radially to form characteristic asters which then bind to individual chromosomes and pull them apart. In order to achieve continuity, centrioles duplicate once per cell cycle.

Similarly to many large macromolecular assemblies, centrioles exhibit symmetry. A few unique proteins come in multiple copies to build this gigantic cylindrical molecular structure: 250 nm wide and 500 nm long (the size of a centriole in humans). The very core of the centriole looks like a 9-fold symmetrical stack of cartwheels, at which periphery microtubules are vertically installed. We study protein composition of this fascinating structure in the effort to understand the process of assembling a new centriole.

Molecular architecture of centrioles.

SAS-5 is an indispensable component in C. elegans centriole biogenesis. SAS-5 physically associates with another centriolar protein, called SAS-6, forming a complex which is required to build new centrioles. This process is regulated by phosphorylation events, allowing for subsequent recruitment of SAS-4 and microtubules. In most other systems SAS-6 forms a cartwheel (central tube in C. elegans), which forms the basis for the 9-fold symmetry of centrioles. Unlike SAS-6, SAS-5 exhibits strong spatial dynamics, shuttling between the cytoplasm and centrioles throughout the cell cycle. Although SAS-5 is an essential protein, depletion of which completely terminates centrosome-dependent cell division, its exact mechanistic  role in this  process remains  obscure.

IN BRIEF: WHAT WE DID
Using X-ray crystallography and a range of biophysical techniques, we have determined the molecular architecture of SAS-5. We show that SAS-5 forms a complex oligomeric structure, mediated by two self-associating domains: a trimeric coiled coil and a novel globular dimeric Implico domain. Disruption of either domain leads to centriole duplication failure in worm embryos, indicating that large SAS-5 assemblies are necessary for function. We propose that SAS-5 provides multivalent attachment sites that are critical for promoting assembly of SAS-6 into a cartwheel, and thus centriole formation.

For details, check out our latest paper 10.7554/eLife.07410!

@kbrogala

Top panel: cartoon overview of the proposed mechanism of centriole formation. In cytoplasm, SAS-5 exists at low concentrations as a dimer, and each of those dimers can stochastically bind two molecules of SAS-6. Once SAS-5 / SAS-6 complex is targeted to the centrioles, it starts to self-oligomerise. Such self-oligomerisation of SAS-5 allows for the attached molecules of SAS-6 to form a cartwheel. Bottom panel: detailed overview of the proposed process of centriole formation. In cytoplasm, where concentration of SAS-5 is low, the strong Implico domain (SAS-5 Imp, ZZ shape) of SAS-5 holds the molecule in a dimeric form. Each SAS-5 protomer can bind (through the disordered linker) to the coiled coil of dimeric SAS-6. Once SAS-5 / SAS-6 complex is targeted to the site where a daughter centriole is to be created, SAS-5 forms higher-order oligomers through self-oligomerisation of its coiled coil domain (SAS-5 CC – triple horizontal bar). Such large oligomer of SAS-5 provides multiple attachments sites for SAS-6 dimers in a very confied space. This results in a burst of local concentration of SAS-6 through the avidity effect, allowing an otherwise weak oligomer of SAS-6 to also form larger species. Effectively, this seeds the growth of a cartwheel (or a spiral in C. elegans), which in turn serves as a template for a new centriole.

 

Natural Move Monte Carlo: Sampling Collective Motions in Proteins

Protein and RNA structures are built up in a hierarchical fashion: from linear chains and random coils (primary) to local substructures (secondary) that make up a subunit’s 3D geometry (tertiary) which in turn can interact with additional subunits to form homomeric or heteromeric multimers (quaternary). The metastable nature of the folded polymer enables it to carry out its function repeatedly while avoiding aggregation and degradation. These functions often rely on structural motions that involve multiple scales of conformational changes by moving residues, secondary structure elements, protein domains or even whole subunits collectively around a small set of degrees of freedom.

The modular architecture of antibodies, makes them amenable to act as an example for this phenomenon. Using MD simulations and fluorescence anisotropy experiments Kortkhonjia et al. observed that Ig domain motions in their antibody of interest were shown to correlate on two levels: 1) with laterally neighbouring Ig domains (i.e. VH with VL and CH1 with CL) and 2) with their respective Fab and Fc regions.

Correlated Motion

Correlated motion between all residue pairs of an antibody during an MD simulation. The axes identify the residues whereas the colours light up as the correlation in motion increases. The individual Ig domains as well as the two Fabs and the Fc can be easily identified. ref: Kortkhonjia, et al., MAbs. Vol. 5. No. 2. Landes Bioscience, 2013.

This begs the question: Can we exploit these molecular properties to reduce dimensionality and overcome energy barriers when sampling the functional motions of metastable proteins?

In 2012 Sim et al. have published an approach that allows for the incorporation of these collective motions (they call them “Natural Moves”) into simulation. Using simple RNA model structures they have shown that explicitly sampling large structural moves can significantly accelerate the sampling process in their Monte Carlo simulation. By gradually introducing DOFs that propagate increasingly large substructures of the molecule they managed to reduce the convergence time by several orders of magnitude. This can be ascribed to the resulting reduction of the search space that narrows down the sampling window. Instead of sampling all possible conformations that a given polynucleotide chain may take, structural states that differ from the native state predominantly in tertiary structure are explored.

Reduced Dimensionality

Reducing the conformational search space by introducing Natural Moves. A) Ω1 (residue-level flexibility) represents the cube, Ω2 (collective motions of helices) spans the plane and Ω3 (collective motions of Ω2 bodies) is shown as a line. B) By integrating multiple layers of Natural Moves the dimensionality is reduced. ref: Sim et al. (2012). PNAS 109(8), 2890–5. doi:10.1073/pnas.1119918109

It is important to stress, however, that in addition to these rigid body moves local flexibility is maintained by preserving residue level flexibility. Consequently, the authors argue, high energy barriers resulting from large structural rearrangements are reduced and the resulting energy landscape is smoothened. Therefore, entrapment in local energy minima becomes less likely and the acceptance rate of the Monte Carlo simulation is improved.

Although benchmarking of this method has mostly relied on case studies involving model RNA structures with near perfect symmetry, this method has a natural link to near-native protein structure sampling. Similarly to RNA, proteins can be decomposed into local substructures that may be responsible for the main functional motions in a given protein. However, due to the complexity of protein motion and limited experimental data we have a limited understanding of protein dynamics. This makes it a challenging task to identify suitable decompositions. As more dynamic data emerges from biophysical methods such as NMR spectroscopy and databases such as www.dynameomics.org are extended we will be able to better approximate protein motions with Natural Moves.

In conclusion, when applied to suitable systems and when used with care, there is an opportunity to breathe life into the static macromolecules of the pdb, which may help to improve our understanding of the heterogeneous structural landscape and the functional motions of metastable proteins and nanomachines.

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.

[1] Kinetic modelling indicates that fast-translating codons can coordinate cotranslational protein folding by avoiding misfolded intermediates.

A very long introductory post about protein structure prediction

If you are a protein informatician, bioinformatician, biochemist, biologist or simply a person well informed about science, you probably heard about protein structure prediction. If that is the case, you might be wondering what all the fuss is about, right? If you never heard those terms before, don’t panic! You are about to find out what protein structure prediction is all about!

Based on my group meeting’s presentation last Wednesday, this blog entry will discuss why protein structure prediction is important and the potential limitations of existing methods. I will also discuss how the quality of input may be a potential source for lack of accuracy in existing software.

First, let us remember a little biology: our genetic code encrypts the inner-works of a complicated cellular machinery tightly regulated by other (macro)molecules such as proteins and RNAs. These two types of macromolecules are agents that perform the set of instructions codified by DNA. Basically, RNAs and proteins are involved in a series of processes that regulate cellular function and control how the genetic code is accessed and used.

For that reason, a huge chunk of genomic data can be pretty useless not that useful if considered on their own. Scientists around the globe have invested millions of moneys and a huge chunk of time in order to amass piles and piles of genome sequencing data. To be fair, this whole “gotta sequence ’em all” mania did not provide us with the fundamental answers everybody was hoping for. Cracking the genetic code was like watching an episode of Lost, in which we were left with more questions than answers. We got a very complicated map that we can’t really understand just yet.

For that reason, I feel obliged to justify myself: protein structures ARE useful. If we know a protein structure, we can formulate a very educated guess about that protein’s function. Combine that with empirical data (e.g. where and when the protein is expressed) and it can help us unveil a lot of info about the protein’s role in cellular processes. Basically, it can answer some of the questions about the (genomic) map. If only we could do that with Lost…

There is also evidence that knowing a protein’s structure can help us design specific drugs to target and inhibit that protein. Although the evidence of such biomedical application is sparse, I believe that with development of the field, there is a trend for protein structures to become more and more important in drug discovery protocols.

Still, if we look at the number of known genome sequences and known protein structures and at the growth of those figures over the past decade, we look at a drastic scenario:

Growth of Sequences vs Structures


There is a tendency for the gap between the number of protein sequences and protein structures to increase. Hence, we are getting more and more questions and little to no answers. Observe how the green line (the protein sequences associated with a known or predicted function) is very close to the red line (the number of known protein structures). However, there is a growing gap between the red and the blue line (the number of protein sequences). Source: http://gorbi.irb.hr/en/method/growth-of-sequence-databases/

Well, gathering protein structure data is just as important, if not more important, than gathering sequence data. This motivated the creation of Structural Genomics Consortiums (SGC), facilities that specialize in solving protein structures.

I am sorry to tell you that this is all old news. We have known this for years. Nonetheless, the graph above hasn’t changed. Why? The cost limitations and the experimental difficulties associated with protein structure determination are holding us back. Solving protein structures in the lab is hard and time consuming and we are far from being as efficient at structure determination as we are at genome sequencing.

There is a possible solution to the problem: you start with a protein sequence (a sequential aminoacid list) and you try to predict its structure. This is known as protein structure prediction or protein structure modelling. Well, we have a limited number of building blocks (20) and a good understanding of their physicochemical properties, it shouldn’t be that hard right?

Unfortunately, modelling protein structure is not as simple as calculating how fast a block slides on an inclined plane. Predicting protein structure from sequence is a very hard problem indeed! It has troubled a plethora of minds throughout the past decades, making people lose many nights of sleep (I can vouch for that).

We can attribute that to two major limitations:

1- There are so many possible ways one can combine 20 “blocks” in a sequence of hundreds of aminoacids. Each aminoacid can also assume a limited range of conformations. We are looking at a massive combinatorial problem. The conformational space (the space of valid conformations a protein with a given sequence can assume) is so large that if you could check a single conformation every nanosecond, it would still take longer than the age of the universe to probe all possible conformations.

2- Our physics (and our statistics) are inaccurate. We perform so many approximations in order to make the calculations feasible with current computers that we end up with very inaccurate models.

Ok! So now you should know what protein structure prediction is, why it is important and, more importantly, why it is such a hard problem to solve. I am going to finish off by giving you a brief overview of the two most commons approaches to perform protein structure prediction: template-based modelling (also known as homology modelling) and de novo structure prediction.

There is a general understanding that if two proteins have very similar sequences (namely, if they are homologs), than they will have similar structures. So, we can use known structures of homologs as templates to predict other structures. This is known as homology modelling.

One can do a lot of fancy talk to justify why this works. There is the evolutionary argument: “selective pressure acts on the phenotype level (which can encompass a protein structure) rather than the genotype level. Hence protein structures tend to be more conserved than sequence. For that reason and considering that sequence alone is enough to determine structure, similar sequences will have even more similar structures.”

One can also formulate some sort of physics argument: “a similar aminoacid composition will lead to a similar behaviour of the interacting forces that keep the protein structure packed together. Furthermore, the energy minimum where a certain protein structure sits is so stable that it would take quite a lot of changes in the sequence to disturb that minimum energy conformation drastically.”

Probably the best argument in favour of homology modelling is that it works somewhat well. Of course, the accuracy of the models has a strong dependency on the sequence similarity, but for proteins with more than 40% identity, we can use this method in order to obtain good results.

This raises another issue: what if we can’t find a homolog with known structure? How can we model our templateless protein sequence then? Well, turns out that if we group proteins together into families based on their sequence similarity, more than half of the families would not have a member with known structure. [This data was obtained by looking at the representativeness of the Pfam (a protein family database) on the PDB (a protein structure database).]

Ergo, for a majority of cases we have to perform predictions from scratch (known as free modelling or de novo modelling).

Well, not necessarily from scratch. There is a specific approach to free modelling where we can build our models using existing knowledge. We can use chunks of protein, contiguous fragments extracted from known structures, to generate models. This is known as a fragment-based approach to de novo protein structure prediction. And that is one big name!

One can think of this as a small scale homology modelling, where both the physics and evolutionary arguments should still hold true to some degree. And how do we do? Can we generate good models? We perform appallingly! Accuracies are too low to generate any useful knowledge in a majority of cases. The problem with the rare cases when you get it right is that you have no means to know if you actually got the right answer.

The poor quality of the results can be justified by the 2 biggest limitations discussed above. Yet  something else might be in play. In homology modelling, if you use a bad template, you will most certainly get a bad model. In a similar way, using a bad set of fragments will lead you to a very poor final model.

Considering we already have the other two big issues (size of conformational space and accuracy of current potentials) to worry about, we should aim to use the best fragment library we possibly can. This has been the recent focus of my work. An attempt to make a small contribution to solve such a hard problem.

I would love to detail my work on finding better fragments here, but I believe this post is already far too long for anyone to actually endure it and read it until the end. So, congratulations if you made it through!