Routes are trees: the parsing perspective on protein folding

Linguistics-based formalization of the antibody language as a basis for antibody language models

Apparent parallels between natural language and antibody sequences have led to a surge in deep language models applied to antibody sequences for predicting cognate antigen recognition. However, a linguistic formal definition of antibody language does not exist, and insight into how antibody language models capture antibody-specific binding features remains largely uninterpretable. Here we describe how a linguistic formalization of the antibody language, by characterizing its tokens and grammar, could address current challenges in antibody language model rule mining.

On Stable States in a Topologically Driven Protein Folding Model

Theoretical models of protein folding often make simplifying assumptions that allow analysis, yielding interesting theoretical results. In this article, we study models where folding dynamics is primarily driven by local topological features in an iterative manner. We illustrate the merit of the proposed approach through its ability to simulate realistic protein folding processes even when the sequence content information is reduced to just hydrophobic and polar. We then analyze our models and show that under our simple assumptions, certain structures are inherently unstable, and that determining whether structures can be stable is an [Formula: see text]-hard problem. Interestingly, we find that when our model has only two amino acids, the problem becomes solvable in polynomial time.

Determinants of Helix Formation for a Kv1.3 Transmembrane Segment inside the Ribosome Exit Tunnel

Proteins begin to fold in the ribosome, and misfolding has pathological consequences. Among the earliest folding events in biogenesis is the formation of a helix, an elementary structure that is ubiquitously present and required for correct protein folding in all proteomes. The determinants underlying helix formation in the confined space of the ribosome exit tunnel are relatively unknown. We chose the second transmembrane segment, S2, of a voltage-gated potassium channel, Kv1.3, as a model to probe this issue. Since the N terminus of S2 is initially in an extended conformation in the folding vestibule of the ribosome yet ultimately emerges at the exit port as a helix, S2 is ideally suited for delineating sequential events and folding determinants of helix formation inside the ribosome. We show that S2's extended N terminus inside the tunnel is converted into a helix by a single, distant mutation in the nascent peptide. This transition depends on nascent peptide sequence at specific tunnel locations. Co-translational secondary folding of nascent chains inside the ribosome has profound physiological consequences that bear on correct membrane insertion, tertiary folding, oligomerization, and biochemical modification of the newborn protein during biogenesis.

Network representation of conformational transitions between hidden intermediates of Rd-apocytochrome b562

The folding kinetics of Rd-apocytochrome b562 is two-state, but native-state hydrogen exchange experiments show that there are discrete partially unfolded (PUF) structures in equilibrium with the native state. These PUF structures are called hidden intermediates because they are not detected in kinetic experiments and they exist after the rate-limiting step. Structures of the mimics of hidden intermediates of Rd-apocytochrome b562 are resolved by NMR. Based upon their relative stability and structural features, the folding mechanism was proposed to follow a specific pathway (unfolded → rate-limiting transition state → PUF1 → PUF2 → native). Investigating the roles of equilibrium PUF structures in folding kinetics and their interrelationship not only deepens our understanding of the details of folding mechanism but also provides guides in protein design and prevention of misfolding. We performed molecular dynamics simulations starting from a hidden intermediate and the native state of Rd-apocytochrome b562 in explicit solvent, for a total of 37.18 μs mainly with Anton. We validated our simulations by detailed comparison with experimental data and other computations. We have verified that we sampled the post rate-limiting transition state region only. Markov state model was used to analyze the simulation results. We replace the specific pathway model with a network model. Transition-path theory was employed to calculate the net effective flux from the most unfolded state towards the most folded state in the network. The proposed sequential folding pathway via PUF1 then more stable, more native-like PUF2 is one of the routes in our network, but it is not dominant. The dominant path visits PUF2 without going through PUF1. There is also a route from PUF1 directly to the most folded state in the network without visiting PUF2. Our results indicate that the PUF states are not necessarily sequential in the folding. The major routes predicted in our network are testable by future experiments such as single molecule experiment.

Customised fragments libraries for protein structure prediction based on structural class annotations

Background

Since experimental techniques are time and cost consuming, in silico protein structure prediction is essential to produce conformations of protein targets. When homologous structures are not available, fragment-based protein structure prediction has become the approach of choice. However, it still has many issues including poor performance when targets’ lengths are above 100 residues, excessive running times and sub-optimal energy functions. Taking advantage of the reliable performance of structural class prediction software, we propose to address some of the limitations of fragment-based methods by integrating structural constraints in their fragment selection process.

Results

Using Rosetta, a state-of-the-art fragment-based protein structure prediction package, we evaluated our proposed pipeline on 70 former CASP targets containing up to 150 amino acids. Using either CATH or SCOP-based structural class annotations, enhancement of structure prediction performance is highly significant in terms of both GDT_TS (at least +2.6, p-values < 0.0005) and RMSD (−0.4, p-values < 0.005). Although CATH and SCOP classifications are different, they perform similarly. Moreover, proteins from all structural classes benefit from the proposed methodology. Further analysis also shows that methods relying on class-based fragments produce conformations which are more relevant to user and converge quicker towards the best model as estimated by GDT_TS (up to 10% in average). This substantiates our hypothesis that usage of structurally relevant templates conducts to not only reducing the size of the conformation space to be explored, but also focusing on a more relevant area.

Conclusions

Since our methodology produces models the quality of which is up to 7% higher in average than those generated by a standard fragment-based predictor, we believe it should be considered before conducting any fragment-based protein structure prediction. Despite such progress, ab initio prediction remains a challenging task, especially for proteins of average and large sizes. Apart from improving search strategies and energy functions, integration of additional constraints seems a promising route, especially if they can be accurately predicted from sequence alone.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0576-2) contains supplementary material, which is available to authorized users.

Atomic-accuracy prediction of protein loop structures through an RNA-inspired Ansatz

Consistently predicting biopolymer structure at atomic resolution from sequence alone remains a difficult problem, even for small sub-segments of large proteins. Such loop prediction challenges, which arise frequently in comparative modeling and protein design, can become intractable as loop lengths exceed 10 residues and if surrounding side-chain conformations are erased. Current approaches, such as the protein local optimization protocol or kinematic inversion closure (KIC) Monte Carlo, involve stages that coarse-grain proteins, simplifying modeling but precluding a systematic search of all-atom configurations. This article introduces an alternative modeling strategy based on a ‘stepwise ansatz’, recently developed for RNA modeling, which posits that any realistic all-atom molecular conformation can be built up by residue-by-residue stepwise enumeration. When harnessed to a dynamic-programming-like recursion in the Rosetta framework, the resulting stepwise assembly (SWA) protocol enables enumerative sampling of a 12 residue loop at a significant but achievable cost of thousands of CPU-hours. In a previously established benchmark, SWA recovers crystallographic conformations with sub-Angstrom accuracy for 19 of 20 loops, compared to 14 of 20 by KIC modeling with a comparable expenditure of computational power. Furthermore, SWA gives high accuracy results on an additional set of 15 loops highlighted in the biological literature for their irregularity or unusual length. Successes include cis-Pro touch turns, loops that pass through tunnels of other side-chains, and loops of lengths up to 24 residues. Remaining problem cases are traced to inaccuracies in the Rosetta all-atom energy function. In five additional blind tests, SWA achieves sub-Angstrom accuracy models, including the first such success in a protein/RNA binding interface, the YbxF/kink-turn interaction in the fourth ‘RNA-puzzle’ competition. These results establish all-atom enumeration as an unusually systematic approach to ab initio protein structure modeling that can leverage high performance computing and physically realistic energy functions to more consistently achieve atomic accuracy.

A primer in macromolecular linguistics

Polymeric macromolecules, when viewed abstractly as strings of symbols, can be treated in terms of formal language theory, providing a mathematical foundation for characterizing such strings both as collections and in terms of their individual structures. In addition this approach offers a framework for analysis of macromolecules by tools and conventions widely used in computational linguistics. This article introduces the ways that linguistics can be and has been applied to molecular biology, covering the relevant formal language theory at a relatively nontechnical level. Analogies between macromolecules and human natural language are used to provide intuitive insights into the relevance of grammars, parsing, and analysis of language complexity to biology.

Geofold: topology-based protein unfolding pathways capture the effects of engineered disulfides on kinetic stability

Protein unfolding is modeled as an ensemble of pathways, where each step in each pathway is the addition of one topologically possible conformational degree of freedom. Starting with a known protein structure, GeoFold hierarchically partitions (cuts) the native structure into substructures using revolute joints and translations. The energy of each cut and its activation barrier are calculated using buried solvent accessible surface area, side chain entropy, hydrogen bonding, buried cavities, and backbone degrees of freedom. A directed acyclic graph is constructed from the cuts, representing a network of simultaneous equilibria. Finite difference simulations on this graph simulate native unfolding pathways. Experimentally observed changes in the unfolding rates for disulfide mutants of barnase, T4 lysozyme, dihydrofolate reductase, and factor for inversion stimulation were qualitatively reproduced in these simulations. Detailed unfolding pathways for each case explain the effects of changes in the chain topology on the folding energy landscape. GeoFold is a useful tool for the inference of the effects of disulfide engineering on the energy landscape of protein unfolding.

An enumerative stepwise ansatz enables atomic-accuracy RNA loop modeling

Atomic-accuracy structure prediction of macromolecules should be achievable by optimizing a physically realistic energy function but is presently precluded by incomplete sampling of a biopolymer's many degrees of freedom. We present herein a working hypothesis, called the "stepwise ansatz," for recursively constructing well-packed atomic-detail models in small steps, enumerating several million conformations for each monomer, and covering all build-up paths. By making use of high-performance computing and the Rosetta framework, we provide first tests of this hypothesis on a benchmark of 15 RNA loop-modeling problems drawn from riboswitches, ribozymes, and the ribosome, including 10 cases that are not solvable by current knowledge-based modeling approaches. For each loop problem, this deterministic stepwise assembly method either reaches atomic accuracy or exposes flaws in Rosetta's all-atom energy function, indicating the resolution of the conformational sampling bottleneck. As a further rigorous test, we have carried out a blind all-atom prediction for a noncanonical RNA motif, the C7.2 tetraloop/receptor, and validated this model through nucleotide-resolution chemical mapping experiments. Stepwise assembly is an enumerative, ab initio build-up method that systematically outperforms existing Monte Carlo and knowledge-based methods for 3D structure prediction.

Constructing templates for protein structure prediction by simulation of protein folding pathways

How a one-dimensional protein sequence folds into a specific 3D structure remains a difficult challenge in structural biology. Many computational methods have been developed in an attempt to predict the tertiary structure of the protein; most of these employ approaches that are based on the accumulated knowledge of solved protein structures. Here we introduce a novel and fully automated approach for predicting the 3D structure of a protein that is based on the well accepted notion that protein folding is a hierarchical process. Our algorithm follows the hierarchical model by employing two stages: the first aims to find a match between the sequences of short independently-folding structural entities and parts of the target sequence and assigns the respective structures. The second assembles these local structural parts into a complete 3D structure, allowing for long-range interactions between them. We present the results of applying our method to a subset of the targets from CASP6 and CASP7. Our results indicate that for targets with a significant sequence similarity to known structures we are often able to provide predictions that are better than those achieved by two leading servers, and that the most significant improvements in comparison with these methods occur in regions of a gapped structural alignment between the native structure and the closest available structural template. We conclude that in addition to performing well for targets with known homologous structures, our method shows great promise for addressing the more general category of comparative modeling targets, which is our next goal.

Blind test of physics-based prediction of protein structures

We report here a multiprotein blind test of a computer method to predict native protein structures based solely on an all-atom physics-based force field. We use the AMBER 96 potential function with an implicit (GB/SA) model of solvation, combined with replica-exchange molecular-dynamics simulations. Coarse conformational sampling is performed using the zipping and assembly method (ZAM), an approach that is designed to mimic the putative physical routes of protein folding. ZAM was applied to the folding of six proteins, from 76 to 112 monomers in length, in CASP7, a community-wide blind test of protein structure prediction. Because these predictions have about the same level of accuracy as typical bioinformatics methods, and do not utilize information from databases of known native structures, this work opens up the possibility of predicting the structures of membrane proteins, synthetic peptides, or other foldable polymers, for which there is little prior knowledge of native structures. This approach may also be useful for predicting physical protein folding routes, non-native conformations, and other physical properties from amino acid sequences.

Modeling ensembles of transmembrane beta-barrel proteins

Transmembrane beta-barrel (TMB) proteins are embedded in the outer membrane of gram-negative bacteria, mitochondria, and chloroplasts. Despite their importance, very few nonhomologous TMB structures have been determined by X-ray diffraction because of the experimental difficulty encountered in crystallizing transmembrane proteins. We introduce the program partiFold to investigate the folding landscape of TMBs. By computing the Boltzmann partition function, partiFold estimates inter-beta-strand residue interaction probabilities, predicts contacts and per-residue X-ray crystal structure B-values, and samples conformations from the Boltzmann low energy ensemble. This broad range of predictive capabilities is achieved using a single, parameterizable grammatical model to describe potential beta-barrel supersecondary structures, combined with a novel energy function of stacked amino acid pair statistical potentials. PartiFold outperforms existing programs for inter-beta-strand residue contact prediction on TMB proteins, offering both higher average predictive accuracy as well as more consistent results. Moreover, the integration of these contact probabilities inside a stochastic contact map can be used to infer a more meaningful picture of the TMB folding landscape, which cannot be achieved with other methods. Partifold's predictions of B-values are competitive with recent methods specifically designed for this problem. Finally, we show that sampling TMBs from the Boltzmann ensemble matches the X-ray crystal structure better than single structure prediction methods. A webserver running partiFold is available at http://partiFold.csail.mit.edu/.

A comparative study of the reported performance of ab initio protein structure prediction algorithms

Protein structure prediction is one of the major challenges in bioinformatics today. Throughout the past five decades, many different algorithmic approaches have been attempted, and although progress has been made the problem remains unsolvable even for many small proteins. While the general objective is to predict the three-dimensional structure from primary sequence, our current knowledge and computational power are simply insufficient to solve a problem of such high complexity. Some prediction algorithms do, however, appear to perform better than others, although it is not always obvious which ones they are and it is perhaps even less obvious why that is. In this review, the reported performance results from 18 different recently published prediction algorithms are compared. Furthermore, the general algorithmic settings most likely responsible for the difference in the reported performance are identified, and the specific settings of each of the 18 prediction algorithms are also compared. The average normalized r.m.s.d. scores reported range from 11.17 to 3.48. With a performance measure including both r.m.s.d. scores and CPU time, the currently best-performing prediction algorithm is identified to be the I-TASSER algorithm. Two of the algorithmic settings--protein representation and fragment assembly--were found to have definite positive influence on the running time and the predicted structures, respectively. There thus appears to be a clear benefit from incorporating this knowledge in the design of new prediction algorithms.

The protein folding problem

The "protein folding problem" consists of three closely related puzzles: (a) What is the folding code? (b) What is the folding mechanism? (c) Can we predict the native structure of a protein from its amino acid sequence? Once regarded as a grand challenge, protein folding has seen great progress in recent years. Now, foldable proteins and nonbiological polymers are being designed routinely and moving toward successful applications. The structures of small proteins are now often well predicted by computer methods. And, there is now a testable explanation for how a protein can fold so quickly: A protein solves its large global optimization problem as a series of smaller local optimization problems, growing and assembling the native structure from peptide fragments, local structures first.

The protein folding problem: when will it be solved?

The protein folding problem can be viewed as three different problems: defining the thermodynamic folding code; devising a good computational structure prediction algorithm; and answering Levinthal's question regarding the kinetic mechanism of how proteins can fold so quickly. Once regarded as a grand challenge, protein folding has seen much progress in recent years. Folding codes are now being used to successfully design proteins and non-biological foldable polymers; aided by the Critical Assessment of Techniques for Structure Prediction (CASP) competition, protein structure prediction has now become quite good. Even the once-challenging Levinthal puzzle now seems to have an answer--a protein can avoid searching irrelevant conformations and fold quickly by making local independent decisions first, followed by non-local global decisions later.