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In this paper an new approach combining 2-bit and 3-bit BCH error correction with fast and simple error detection for errors of higher order is presented. Under the assumption that a 2-bit error or 3-bit error occurred, the corresponding correction bits are determined using the syndrome components \(s_1, s_3\) for 2-bit errors and \(s_1, s_3, s_5\) for 3-bit errors. These correction bits are used to calculate higher syndrome components up to \(s_{2T-1}\), which are compared to the actual corresponding syndrome components. If the syndrome components match, a 2-bit error or 3-bit error was detected. In the case of a syndrome mismatch, an error other than a 2-bit error or 3-bit error occurred and was detected. The proposed method provides a simple way to differentiate between 2-bit errors (3-bit errors) and errors of higher order.

In this paper, an error correction is combined with additional detection using a BCH code. It is shown that a fast 1-bit correction can be efficiently combined with fast BCH multibit detection for all up to $(2T-1)$-bits errors, where T can be specified. In the case of an error, the syndrome is calculated and both a speculative 1-bit correction and an error detection process are started in parallel. The proposed error detection process checks if the actual error syndrome components contradict the 1-bit error assumption. The corresponding determinants for 2-bit to T-bit errors are computed in ascending order up to the first determinant indicating an error larger than 1-bit. This differs from the classic approach where a sequence of corresponding determinants containing syndrome components in descending order from T to 2 is computed. For the classic approach, the first determinant not equal 0 in descending order indicates the number of errors. The presented approach allows to speed up the detection by simplifying the determinants using the results of previous iterations. Under the assumption of a 1-bit error, the determinants can be simplified to a constant size. The proposed approach speeds up the error detection considerably. This method is useful for error detection and error correction in safety critical applications where 100 percent of the multi-bit errors up to a certain multiplicity have to be detected.

Riboswitches are genetic regulatory elements mainly found in bacteria, which regulate gene expression based on the availability of a ligand. Purine-sensing riboswitches, including the guanine-sensing riboswitch (Gsw), possess tertiary interactions connecting the L2 and L3 loops. These interactions are important for ligand binding to the aptamer. However, atomic-level structural knowledge about the unbound state and how the tertiary interactions influence the conformational heterogeneity of the aptamer is still scarce. We performed replica exchange molecular dynamics simulations of the aptamer domain of wild-type Gsw and a G37A/C61U mutant, which exhibits destabilized tertiary interactions, at different Mg2+ concentrations with an aggregate simulation time of ∼16 μs, and subsequently obtained free-energy landscapes. Our data provide evidence that suggests that the unbound state of wild-type Gsw is conformationally rather homogeneous from a global viewpoint, yet the ligand binding site shows functionally ne...

This paper was originally published under standard Springer Nature copyright. As of the date of this correction, the Analysis is available online as an open-access paper with a CC-BY license. No other part of the paper has been changed.

Riboswitches are noncoding regulatory elements that control gene expression in response to the presence of metabolites, which bind to the aptamer domain. Metabolite binding appears to occur through a combination of conformational selection and induced fit mechanism. This demands to characterize the structural dynamics of the apo state of aptamer domains. In principle, molecular dynamics (MD) simulations can give insights at the atomistic level into the dynamics of the aptamer domain. However, it is unclear to what extent contemporary force fields can bias such insights. Here, we show that the Amber force field ff99 yields the best agreement with detailed experimental observations on differences in the structural dynamics of wild type and mutant aptamer domains of the guanine-sensing riboswitch (Gsw), including a pronounced influence of Mg2+. In contrast, applying ff99 with parmbsc0 and parmχOL modifications (denoted ff10) results in strongly damped motions and overly stable tertiary loop-loop interactions. These results are based on 58 MD simulations with an aggregate simulation time11 μs, careful modeling of Mg2+ ions, and thorough statistical testing. Our results suggest that the moderate stabilization of the χ-anti region in ff10 can have an unwanted damping effect on functionally relevant structural dynamics of marginally stable RNA systems. This suggestion is supported by crystal structure analyses of Gsw aptamer domains that reveal χ torsions with high-anti values in the most mobile regions. We expect that future RNA force field development will benefit from considering marginally stable RNA systems and optimization toward good representations of dynamics in addition to structural characteristics.

Riboswitches are noncoding regulatory elements that control gene expression in response to the presence of metabolites, which bind to the aptamer domain. Metabolite binding appears to occur through a combination of conformational selection and induced fit mechanism. This demands to characterize the structural dynamics of the apo state of aptamer domains. In principle, molecular dynamics (MD) simulations can give insights at the atomistic level into the dynamics of the aptamer domain. However, it is unclear to what extent contemporary force fields can bias such insights. Here, we show that the Amber force field ff99 yields the best agreement with detailed experimental observations on differences in the structural dynamics of wild type and mutant aptamer domains of the guanine-sensing riboswitch (Gsw), including a pronounced influence of Mg 2 + . In contrast, applying ff99 with parmbsc0 and parmχ OL modifications (denoted ff10) results in strongly damped motions and overly stable tertiary loop–loop interactions. These results are based on 58 MD simulations with an aggregate simulation time > 11 μs, careful modeling of Mg 2 + ions, and thorough statistical testing. Our results suggest that the moderate stabilization of the χ - anti region in ff10 can have an unwanted damping effect on functionally relevant structural dynamics of marginally stable RNA systems. This suggestion is supported by crystal structure analyses of Gsw aptamer domains that reveal χ torsions with high- anti values in the most mobile regions. We expect that future RNA force field development will benefit from considering marginally stable RNA systems and optimization toward good representations of dynamics in addition to structural characteristics.

Riboswitches are genetic regulatory elements that control gene expression depending on ligand binding. The guanine-sensing riboswitch (Gsw) binds ligands at a three-way junction formed by paired regions P1, P2, and P3. Loops L2 and L3 cap the P2 and P3 helices and form tertiary interactions. Part of P1 belongs to the switching sequence dictating the fate of the mRNA. Previous studies revealed an intricate relationship between ligand binding and presence of the tertiary interactions, and between ligand binding and influence on the P1 region. However, no information is available on the interplay among these three main regions in Gsw. Here we show that stabilization of the L2-L3 region by tertiary interactions, and the ligand binding site by ligand binding, cooperatively influences the structural stability of terminal base pairs in the P1 region in the presence of Mg2+ ions. The results are based on molecular dynamics simulations with an aggregate simulation time of ~10 μs across multiple systems of the unbound state of the Gsw aptamer and a G37A/C61U mutant, and rigidity analyses. The results could explain why the three-way junction is a central structural element also in other riboswitches and how the cooperative effect could become contextual with respect to intracellular Mg2+ concentration. The results suggest that the transmission of allosteric information to P1 can be entropy-dominated.

The mechanical heterogeneity of biomolecular structures is intimately linked to their diverse biological functions. Applying rigidity theory to biomolecules identifies this heterogeneous composition of flexible and rigid regions, which can aid in the understanding of biomolecular stability and long-ranged information transfer through biomolecules, and yield valuable information for rational drug design and protein engineering. We review fundamental concepts in rigidity theory, ways to represent biomolecules as constraint networks, and methodological and algorithmic developments for analyzing such networks and linking the results to biomolecular function. Software packages for performing rigidity analyses on biomolecules in an efficient, automated way are described, as are rigidity analyses on biomolecules including the ribosome, viruses, or transmembrane proteins. The analyses address questions of allosteric mechanisms, mutation effects on (thermo-)stability, protein (un-)folding, and coarse-graining of biomolecules. We advocate that the application of rigidity theory to biomolecules has matured in such a way that it could be broadly applied as a computational biophysical method to scrutinize biomolecular function from a structure-based point of view and to complement approaches focused on biomolecular dynamics. We discuss possibilities to improve constraint network representations and to perform large-scale and prospective studies. WIREs Comput Mol Sci 2017, 7:e1311. doi: 10.1002/wcms.1311 For further resources related to this article, please visit the WIREs website.

Non-protein coding RNAs perform essential functions in living organisms. They commonly exist as dynamic ensembles of conformational states. While many structurally known RNAs are trapped in one or a few conformations by interactions with proteins or tertiary contacts between stems, bulges, or loops the knowledge of equilibrium structures, conformational space, and tertiary conformational changes of large RNAs not being restrained by external or tertiary interactions is still very limited.Helical four-way and three-way junctions (4WJs and 3WJs) are an essential structural motif of the for functional RNA structures. Here we explore the topology of a set of a 4WJ and related 3WJs related to the hairpin ribozyme by measuring more than 250 different FRET-pairs using single-molecule multi-parameter fluorescence detection [1]. Using FRET restrained high-precision structural modeling combined with full atom MD simulations as a hybrid tool [2,3], we resolve the structures of three coexisting conformers of a fully Watson-Crick base paired RNA4WJ. By a suitable choice of the number of bases in the bulges the helices arrangements of the corresponding 3WJs can span a huge conformational space which is necessary for the stem communication in functional RNAs.[1] Sisamakis, E., et al.; Methods in Enzymology 475, 455-514 (2010).[2] Sindbert, S., et al.; J. Am. Chem. Soc. 133, 2463-2480 (2011).[3] Kalinin, S. et al. Nat. Methods 9, 1218-1225 (2012)

Forster-Resonance-Energy-Transfer (FRET) restrained high-precision structural modeling is a powerful tool for analyzing biomolecular structures. Here we apply multi-parameter fluorescence detection (MFD) of single molecules and ensemble Time-Correlated Single Photon Counting measurements to perform FRET study on RNA three- and four-way-junctions (4WJs and 3WJs) with a high level of precision in distance better than 1% of the Forster radius [1].We have generated a database of RNA 4WJs and six different RNA 3WJs with different bulges and sequences to study the influence of these factors on the junction conformations of RNA 3WJs. Overall 260 FRET pairs were measured with single-molecule MFD at 20 mM MgCl2 concentration and analyzed with the analysis toolkit [2] that includes probability distribution analysis (PDA) for FRET distance determination and FRET position and screening (FPS) toolkit for structural model generation.Monte Carlo simulations showed that sterically allowed conformational space for RNA junctions is large. However, FRET measurements detect the existence of three different static conformers for RNA 4WJ, whereas RNA 3WJs have only one predominant static conformation. terically allowed conformational space for RNA is large. Their junction geometry was described in terms of mutual and Euler angles between helices. The FRET-derived structures suggest that the sequence dictates a junction specific conformation within the large topology space. Furthermore we see that bulges in the junction region determine orientation and rotation of helices and induce coaxial stacking between two of them.[1] Antonik, M., et al., J.Phys.Chem.B, 110, 6970-6978 (2006)[2] Kalinin, S. et al, Nat. Meth., 9, 1218-1225 (2012)

Like for many other non-coding RNAs, helical four-way and three-way junctions (4WJs and 3WJs) are an essential structural motif of the for functional RNA structures. Using FRET restrained high-precision structural modeling as a hybrid tool we resolve the structures of three coexisting conformers of a fully Watson-Crick base paired RNA4WJ based on the hairpin ribozyme. 51 different FRET-pairs were measured using single-molecule multi-parameter fluorescence detection (smMFD). For each dataset, the single-molecule approach allowed for the simultaneous extraction of three distances (and their corresponding errors) belonging to one major FRET state and two minor states. Distinct Mg2+-affinities were used for the assignment of the two minor states to the corresponding conformers. Rigid body models for the major and both minor conformers were obtained by docking rigid ds A-RNA helices explicitly taking into account dye position distributions. The three rigid body models were refined by all-atom MD simulations and coarse-grained RNA folding using FRET-restraints. A cluster analysis gives confidence levels for the proposed ensemble of models, and the precision was assessed via bootstrapping. The achieved precisions are significantly better than the uncertainty of the dye position with respect to the macromolecule. The structure of the 4WJ was compared with FRET restrained structures of related RNA 3WJs, where one stem was removed. The types of 3WJs were studied: (I) without bulges, (II) with a small bulge (two unpaired nucleotides) and (III) with larger bulge (5 unpaired nucleotides). In conclusion the overall geometry of the RNA helices depends drastically on the junction type.[1] Sisamakis, E., et al.; Methods in Enzymology 475, 455-514 (2010)[2] Sindbert, S., et al.; J. Am. Chem. Soc. 133, 2463-2480 (2011)[3] Kalinin, S. et al. Nat. Methods in press

Forster-Resonance-Energy-Transfer (FRET) restrained high-precision structural modeling is a powerful tool for analyzing the biomolecular structure. We apply multi-parameter fluorescence detection (MFD) of single molecules and ensemble Time-Correlated Single Photon Counting measurements (eTCSPC) to perform FRET study on RNA three- and four-way-junctions (4WJs and 3WJs) which are derived from the hairpin ribozyme.Overall 283 FRET pairs were measured with single-molecule MFD and analyzed with the analysis toolkit [1] that includes probability distribution analysis (PDA) for FRET distance determination and FRET position and screening (FPS) toolkit for structural model generation.In order to study the influence of the junction on the RNA structure we studied the functional junction part with prolonged helices. Bulge and sequence variations were considered as dominant factors influencing junction conformations for RNA 3WJ. Six different RNA 3WJ with different sequences were studied, two of which have two and five unpaired nucleotides in the junction region.We found three different conformers for RNA 4WJ. However RNAs 3WJ have only one predominant conformer. Furthermore we report that bulges in the junction region determine orientation and rotation of helices, inducing coaxial stacking. Noteworthy the stacked helices are different for the 3WJs with different bulges. Our results show that small changes in the sequence make dramatic changes in RNA 3WJ tertiary structures which are expected to have significant impact on the functionality.[1] Kalinin, S. et al, Nature Methods, 9, 1218-1225 (2012).