Folding Rules Research Articles

Construction and transformation method of 3D models based on the chain-type modular structure

This study proposes a method of constructing and transforming three-dimensional (3D) models that can convert a 3D model into a chain-type modular configuration and realize the mutual transformation between different configurations with a straight chain as the intermediate state through standard folding steps. A method for detailed representation of voxels is proposed. Based on detailed voxels, an accelerated generation algorithm for the connection forest, which can describe the possible chain configurations, is developed. The foldability verification of the configurations and the generation of the folding operations are realized according to the folding rules. A collision detection algorithm based on encoding and projection is also introduced to detect collisions in the process of folding sequence generation. In this work, an interactive platform is established for users to calculate the input model transformation through simple operations and obtain a simulation animation of the folding operations. The experimental cases prove the effectiveness of the method in constructing and transforming the chain-type modular configurations of the input 3D models.

Sampling of structure and sequence space of small protein folds

Nature only samples a small fraction of the sequence space that can fold into stable proteins. Furthermore, small structural variations in a single fold, sometimes only a few amino acids, can define a protein’s molecular function. Hence, to design proteins with novel functionalities, such as molecular recognition, methods to control and sample shape diversity are necessary. To explore this space, we developed and experimentally validated a computational platform that can design a wide variety of small protein folds while sampling shape diversity. We designed and evaluated stability of about 30,000 de novo protein designs of eight different folds. Among these designs, about 6,200 stable proteins were identified, including some predicted to have a first-of-its-kind minimalized thioredoxin fold. Obtained data revealed protein folding rules for structural features such as helix-connecting loops. Beyond serving as a resource for protein engineering, this massive and diverse dataset also provides training data for machine learning. We developed an accurate classifier to predict the stability of our designed proteins. The methods and the wide range of protein shapes provide a basis for designing new protein functions without compromising stability.

Structure and folding of four putative kink turns identified in structured RNA species in a test of structural prediction rules.

k-Turns are widespread key architectural elements that occur in many classes of RNA molecules. We have shown previously that their folding properties (whether or not they fold into their tightly kinked structure on addition of metal ions) and conformation depend on their local sequence, and we have elucidated a series of rules for prediction of these properties from sequence. In this work, we have expanded the rules for prediction of folding properties, and then applied the full set to predict the folding and conformation of four probable k-turns we have identified amongst 224 structured RNA species found in bacterial intergenenic regions by the Breaker lab (1). We have analyzed the ion-dependence of folding of the four k-turns using fluorescence resonance energy transfer, and determined the conformation of two of them using X-ray crystallography. We find that the experimental data fully conform to both the predicted folding and conformational properties. We conclude that our folding rules are robust, and can be applied to new k-turns of unknown characteristics with confidence.

The Roots of Genetic Coding in Aminoacyl-tRNA Synthetase Duality.

Codon-dependent translation underlies genetics and phylogenetic inferences, but its origins pose two challenges. Prevailing narratives cannot account for the fact that aminoacyl-tRNA synthetases (aaRSs), which translate the genetic code, must collectively enforce the rules used to assemble themselves. Nor can they explain how specific assignments arose from rudimentary differentiation between ancestral aaRSs and corresponding transfer RNAs (tRNAs). Experimental deconstruction of the two aaRS superfamilies created new experimental tools with which to analyze the emergence of the code. Amino acid and tRNA substrate recognition are linked to phase transfer free energies of amino acids and arise largely from aaRS class-specific differences in secondary structure. Sensitivity to protein folding rules endowed ancestral aaRS-tRNA pairs with the feedback necessary to rapidly compare alternative genetic codes and coding sequences. These and other experimental data suggest that the aaRS bidirectional genetic ancestry stabilized the differentiation and interdependence required to initiate and elaborate the genetic coding table.

Interpreting a black box predictor to gain insights into early folding mechanisms

Protein folding and function are closely connected, but the exact mechanisms by which proteins fold remain elusive. Early folding residues (EFRs) are amino acids within a particular protein that induce the very first stages of the folding process. High-resolution EFR data are only available for few proteins, which has previously enabled the training of a protein sequence-based machine learning 'black box' predictor (EFoldMine). Such a black box approach does not allow a direct extraction of the 'early folding rules' embedded in the protein sequence, whilst such interpretation is essential to improve our understanding of how the folding process works. We here apply and investigate a novel 'grey box' approach to the prediction of EFRs from protein sequence to gain mechanistic residue-level insights into the sequence determinants of EFRs in proteins. We interpret the rule set for three datasets, a default set comprised of natural proteins, a scrambled set comprised of the scrambled default set sequences, and a set of de novo designed proteins. Finally, we relate these data to the secondary structure adopted in the folded protein and provide all information online via http://xefoldmine.bio2byte.be/, as a resource to help understand and steer early protein folding.

Graphene gets bent

Graphene gets bent

Computational guided drug repurposing for targeting 2′-O-ribose methyltransferase of SARS-CoV-2

AimsThe recent outbreak of pandemic severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has led the world towards a global health emergency. Currently, no proper medicine or effective treatment strategies are available; therefore, repurposing of FDA approved drugs may play an important role in overcoming the situation. Materials and methodsThe SARS-CoV-2 genome encodes for 2-O-methyltransferase (2′OMTase), which plays a key role in methylation of viral RNA for evading host immune system. In the present study, the protein sequence of 2′OMTase of SARS-CoV-2 was analyzed, and its structure was modeled by a comparative modeling approach and validated. The library of 3000 drugs was screened against the active site of 2′OMTase followed by re-docking analysis. The apo and ligand-bound 2′OMTase were further validated and analyzed by using molecular dynamics simulation. Key findingsThe modeled structure displayed the conserved characteristic fold of class I MTase family. The quality assessment analysis by SAVES server reveals that the modeled structure follows protein folding rules and of excellent quality. The docking analysis displayed that the active site of 2′OMTase accommodates an array of drugs, which includes alkaloids, antivirals, cardiac glycosides, anticancer, steroids, and other drugs. The redocking and MD simulation analysis of the best 5 FDA approved drugs reveals that these drugs form a stable conformation with the 2′OMTase. SignificanceThe results suggested that these drugs may be used as potential inhibitors for 2′OMTase for combating the SARS-CoV-2 infection.

Research on folding diversity in statistical learning methods for RNA secondary structure prediction.

How to improve the prediction accuracy of RNA secondary structure is currently a hot topic. The existing prediction methods for a single sequence do not fully consider the folding diversity which may occur among RNAs with different functions or sources. This paper explores the relationship between folding diversity and prediction accuracy, and puts forward a new method to improve the prediction accuracy of RNA secondary structure. Our research investigates the following: 1. The folding feature based on stochastic context-free grammar is proposed. By using dimension reduction and clustering techniques, some public data sets are analyzed. The results show that there is significant folding diversity among different RNA families. 2. To assign folding rules to RNAs without structural information, a classification method based on production probability is proposed. The experimental results show that the classification method proposed in this paper can effectively classify the RNAs of unknown structure. 3. Based on the existing prediction methods of statistical learning models, an RNA secondary structure prediction framework is proposed, namely “Cluster - Training - Parameter Selection - Prediction”. The results show that, with information on folding diversity, prediction accuracy can be significantly improved.

Protein Engineering Approaches in the Post-Genomic Era.

Proteins are one of the most multifaceted macromolecules in living systems. Proteins have evolved to function under physiological conditions and, therefore, are not usually tolerant of harsh experimental and environmental conditions. The growing use of proteins in industrial processes as a greener alternative to chemical catalysts often demands constant innovation to improve their performance. Protein engineering aims to design new proteins or modify the sequence of a protein to create proteins with new or desirable functions. With the emergence of structural and functional genomics, protein engineering has been invigorated in the post-genomic era. The three-dimensional structures of proteins with known functions facilitate protein engineering approaches to design variants with desired properties. There are three major approaches of protein engineering research, namely, directed evolution, rational design, and de novo design. Rational design is an effective method of protein engineering when the threedimensional structure and mechanism of the protein is well known. In contrast, directed evolution does not require extensive information and a three-dimensional structure of the protein of interest. Instead, it involves random mutagenesis and selection to screen enzymes with desired properties. De novo design uses computational protein design algorithms to tailor synthetic proteins by using the three-dimensional structures of natural proteins and their folding rules. The present review highlights and summarizes recent protein engineering approaches, and their challenges and limitations in the post-genomic era.

Using sequence signatures and kink-turn motifs in knowledge-based statistical potentials for RNA structure prediction

Kink turns are widely occurring motifs in RNA, located in internal loops and associated with many biological functions including translation, regulation and splicing. The associated sequence pattern, a 3-nt bulge and G-A, A-G base-pairs, generates an angle of ∼50° along the helical axis due to A-minor interactions. The conserved sequence and distinct secondary structures of kink-turns (k-turn) suggest computational folding rules to predict k-turn-like topologies from sequence. Here, we annotate observed k-turn motifs within a non-redundant RNA dataset based on sequence signatures and geometrical features, analyze bending and torsion angles, and determine distinct knowledge-based potentials with and without k-turn motifs. We apply these scoring potentials to our RAGTOP (RNA-As-Graph-Topologies) graph sampling protocol to construct and sample coarse-grained graph representations of RNAs from a given secondary structure. We present graph-sampling results for 35 RNAs, including 12 k-turn and 23 non k-turn internal loops, and compare the results to solved structures and to RAGTOP results without special k-turn potentials. Significant improvements are observed with the updated scoring potentials compared to the k-turn-free potentials. Because k-turns represent a classic example of sequence/structure motif, our study suggests that other such motifs with sequence signatures and unique geometrical features can similarly be utilized for RNA structure prediction and design.

Origami acoustics: using principles of folding structural acoustics for simple and large focusing of sound energy

Fixed in spatial distribution, arrays of planar, electromechanical acoustic transducers cannot adapt their wave energy focusing abilities unless each transducer is externally controlled, creating challenges for the implementation and portability of such beamforming systems. Recently, planar, origami-based structural tessellations are found to facilitate great versatility in system function and properties through kinematic folding. In this research we bridge the physics of acoustics and origami-based design to discover that the simple topological reconfigurations of a Miura-ori-based acoustic array yield many orders of magnitude worth of reversible change in wave energy focusing: a potential for acoustic field morphing easily obtained through deployable, tessellated architectures. Our experimental and theoretical studies directly translate the roles of folding the tessellated array to the adaptations in spectral and spatial wave propagation sensitivities for far field energy transmission. It is shown that kinematic folding rules and flat-foldable tessellated arrays collectively provide novel solutions to the long-standing challenges of conventional, electronically-steered acoustic beamformers. While our examples consider sound radiation from the foldable array in air, linear acoustic reciprocity dictates that the findings may inspire new innovations for acoustic receivers, e.g. adaptive sound absorbers and microphone arrays, as well as concepts that include water-borne waves.

Characteristics of equipartition for RNA structure.

BackgroundWith the continuous discovery of novel RNA molecules with key cellular functions and of novel pathways and interaction networks, the need for structural information of RNA is still increasing. In order to predict structure of long RNA and understand its natural folding mechanism, exploring the characteristic of RNA structure is an important issue.MethodsThe real RNA secondary structures of all 480 sequences from the database of RNA strand, validated by nuclear magnetic resonance or x-ray are selected. For one sequence with multiple domains, the length ratios of these domains to the sequence are computed. For one sequence with one domain and multiple sub-domains, the length ratios of these sub-domains to the domain are computed. Then the ratios are compared and analyzed to seek the partition characteristic of domains and subdomains.ResultsFor most RNAs, the length ratios of multiple domains to its sequence are close to equal, and those of sub-domains to its domain are also nearly identical. Most RNAs with multiple domains have two domains, so the length ratios of the domains to its sequence are close to 0.5. For sequence with one domain and no sub-domain or one sub-domain, the centre of domain and sub-domain is close to that of the sequence.ConclusionsA novel finding is given that RNA folding accords with the characteristic of equipartition based on statistical analysis. The characteristic reflects the folding rules of RNA from a new angle, which maybe more close to natural folding.

Characteristics and prediction of RNA structure.

RNA secondary structures with pseudoknots are often predicted by minimizing free energy, which is NP-hard. Most RNAs fold during transcription from DNA into RNA through a hierarchical pathway wherein secondary structures form prior to tertiary structures. Real RNA secondary structures often have local instead of global optimization because of kinetic reasons. The performance of RNA structure prediction may be improved by considering dynamic and hierarchical folding mechanisms. This study is a novel report on RNA folding that accords with the golden mean characteristic based on the statistical analysis of the real RNA secondary structures of all 480 sequences from RNA STRAND, which are validated by NMR or X-ray. The length ratios of domains in these sequences are approximately 0.382L, 0.5L, 0.618L, and L, where L is the sequence length. These points are just the important golden sections of sequence. With this characteristic, an algorithm is designed to predict RNA hierarchical structures and simulate RNA folding by dynamically folding RNA structures according to the above golden section points. The sensitivity and number of predicted pseudoknots of our algorithm are better than those of the Mfold, HotKnots, McQfold, ProbKnot, and Lhw-Zhu algorithms. Experimental results reflect the folding rules of RNA from a new angle that is close to natural folding.

Proving Theorems by Program Transformation

In this paper we present an overview of the unfold/fold proof method, a method for proving theorems about programs, based on program transformation. As a metalanguage for specifying programs and program properties we adopt constraint logic programming CLP, and we present a set of transformation rules including the familiar unfolding and folding rules which preserve the semantics of CLP programs. Then, we show how program transformation strategies can be used, similarly to theorem proving tactics, for guiding the application of the transformation rules and inferring the properties to be proved. We work out three examples: i the proof of predicate equivalences, applied to the verification of equality between CCS processes, ii the proof of first order formulas via an extension of the quantifier elimination method, and iii the proof of temporal properties of infinite state concurrent systems, by using a transformation strategy that performs program specialization.

Resistance to Wheat streak mosaic virus generated by expression of an artificial polycistronic microRNA in wheat

Wheat streak mosaic virus (WSMV) is a persistent threat to wheat production, necessitating novel approaches for protection. We developed an artificial miRNA strategy against WSMV, incorporating five amiRNAs within one polycistronic amiRNA precursor. Using miRNA sequence and folding rules, we chose five amiRNAs targeting conserved regions of WSMV but avoiding off-targets in wheat. These replaced the natural miRNA in each of five arms of the polycistronic rice miR395, producing amiRNA precursor, FanGuard (FGmiR395), which was transformed into wheat behind a constitutive promoter. Splinted ligation detected all five amiRNAs being processed in transgenic leaves. Resistance was assessed over two generations. Three types of response were observed in T(1) plants of different transgenic families: completely immune; initially resistant with resistance breaking down over time; and initially susceptible followed by plant recovery. Deep sequencing of small RNAs from inoculated leaves allowed the virus sequence to be assembled from an immune transgenic, susceptible transgenic, and susceptible non-transgenic plant; the amiRNA targets were fully conserved in all three isolates, indicating virus replication on some transgenics was not a result of mutational escape by the virus. For resistant families, the resistance segregated with the transgene. Analysis in the T(2) generation confirmed the inheritance of immunity and gave further insights into the other phenotypes. Stable resistant lines developed no symptoms and no virus by ELISA; this resistance was classified as immunity when extracts failed to transmit from inoculated leaves to test plants. This study demonstrates the utility of a polycistronic amiRNA strategy in wheat against WSMV.

Natural and artificial RNAs occupy the same restricted region of sequence space

Different chemical and mutational processes within genomes give rise to sequences with different compositions and perhaps different capacities for evolution. The evolution of functional RNAs may occur on a "neutral network" in which sequences with any given function can easily mutate to sequences with any other. This neutral network hypothesis is more likely if there is a particular region of composition that contains sequences that are functional in general, and if many different functions are possible within this preferred region of composition. We show that sequence preferences in active sites recovered by in vitro selection combine with biophysical folding rules to support the neutral network hypothesis. These simple active-site specifications and folding preferences obtained by artificial selection experiments recapture the previously observed purine bias and specific spread along the GC axis of naturally occurring aptamers and ribozymes isolated from organisms, although other types of RNAs, such as miRNA precursors and spliceosomal RNAs, that act primarily through complementarity to other amino acids do not share these preferences. These universal evolved sequence features are therefore intrinsic in RNA molecules that bind small-molecule targets or catalyze reactions.

Totally correct logic program transformations via well-founded annotations

We address the problem of proving the total correctness of transformations of definite logic programs. We consider a general transformation rule, called clause replacement, which consists in transforming a program P into a new program Q by replacing a set Γ 1 of clauses occurring in P by a new set Γ 2 of clauses, provided that Γ 1 and Γ 2 are equivalent in the least Herbrand model M(P) of the program P. We propose a general method for proving that transformations based on clause replacement are totally correct, that is, M(P)=M(Q). Our method consists in showing that the transformation of P into Q can be performed by: (i) adding extra arguments to predicates, thereby deriving from the given program P an annotated program $\overline{P}$ , (ii) applying a variant of the clause replacement rule and transforming the annotated program $\overline{P}$ into a terminating annotated program $\overline{Q}$ , and (iii) erasing the annotations from $\overline{Q}$ , thereby getting Q. Our method does not require that either P or Q are terminating and it is parametric with respect to the annotations. By providing different annotations we can easily prove the total correctness of program transformations based on various versions of the popular unfolding, folding, and goal replacement rules, which can all be viewed as particular cases of our clause replacement rule.

Totally correct logic program transformations via well-founded annotations

We address the problem of proving the total correctness of transformations of definite logic programs. We consider a general transformation rule, called clause replacement, which consists in transforming a program P into a new program Q by replacing a set Γ 1 of clauses occurring in P by a new set Γ 2 of clauses, provided that Γ 1 and Γ 2 are equivalent in the least Herbrand model M(P) of the program P.We propose a general method for proving that transformations based on clause replacement are totally correct, that is, M(P)=M(Q). Our method consists in showing that the transformation of P into Q can be performed by: (i) adding extra arguments to predicates, thereby deriving from the given program P an annotated program \(\overline{P}\) , (ii) applying a variant of the clause replacement rule and transforming the annotated program \(\overline{P}\) into a terminating annotated program \(\overline{Q}\) , and (iii) erasing the annotations from \(\overline{Q}\) , thereby getting Q.Our method does not require that either P or Q are terminating and it is parametric with respect to the annotations. By providing different annotations we can easily prove the total correctness of program transformations based on various versions of the popular unfolding, folding, and goal replacement rules, which can all be viewed as particular cases of our clause replacement rule.

Chaperoning Anfinsen: the steric foldases

Some proteins are so much resistant to proteolysis and unfolding that they violate folding rules shared by the vast majority of proteins. These unusual proteins manage to fold into an active native conformation that is thermodynamically at best marginally, but often even less stable than the unfolded state. A huge energetic barrier traps these proteins kinetically in the folded state. The drawback of this situation is the need for a specialized chaperone that adds steric information to the proteins to cross this barrier on the folding pathway. Until now, our knowledge of these intriguing chaperones was restricted to the prodomains of secreted proteases, which function intramolecularly. Recent research has added more examples, which now include the membrane-anchored lipase-specific foldase and the pilus subunit specific chaperone, both acting intermolecularly. The case of the pilin chaperone is somewhat deviant in that steric information is definitely provided, but the pilus subunit adopts a thermodynamically favourable stable conformation.

Transformations of logic programs with goals as arguments

We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by exploiting this capability when transforming programs, we can improve program efficiency. We propose a set of program transformation rules which extend the familiar unfolding and folding rules and allow us to manipulate clauses with goals which occur as arguments of predicates. In order to prove the correctness of these transformation rules, we formally define the operational semantics of our extended logic programming language. This semantics is a simple variant of LD-resolution. When suitable conditions are satisfied this semantics agrees with LD-resolution and, thus, the programs written in our extended language can be run by ordinary Prolog systems. Our transformation rules are shown to preserve the operational semantics and termination.