DNA Word Set Design Based on Minimum Free Energy

The minimum free energy (MFE) of ribonucleic acids (RNAs) increases at an apparent linear rate with sequence length. Simple indices, obtained by dividing the MFE by the number of nucleotides, have been used for a direct comparison of the folding stability of RNAs of various sizes. Although this normalization procedure has been used in several studies, the relationship between normalized MFE and length has not yet been investigated in detail. Here, we demonstrate that the variation of MFE with sequence length is not linear and is significantly biased by the mathematical formula used for the normalization procedure. For this reason, the normalized MFEs strongly decrease as hyperbolic functions of length and produce unreliable results when applied for the comparison of sequences with different sizes. We also propose a simple modification of the normalization formula that corrects the bias enabling the use of the normalized MFE for RNAs longer than 40 nt. Using the new corrected normalized index, we analyzed the folding free energies of different human RNA families showing that most of them present an average MFE density more negative than expected for a typical genomic sequence. Furthermore, we found that a well-defined and restricted range of MFE density characterizes each RNA family, suggesting the use of our corrected normalized index to improve RNA prediction algorithms. Finally, in coding and functional human RNAs the MFE density appears scarcely correlated with sequence length, consistent with a negligible role of thermodynamic stability demands in determining RNA size.

In an attempt to improve automated gene prediction in the untranslated region of a gene, we completed an in-depth analysis of the minimum free energy for 8,689 sub-genetic DNA sequences. We expanded Zhang's classification model and classified each sub-genetic sequence into one of 27 possible motifs. We calculated the minimum free energy for each motif to explore statistical features that correlate to biologically relevant sub-genetic sequences. If biologically relevant sub-genetic sequences fall into distinct free energy quanta it may be possible to characterize a motif based on its minimum free energy. Proper characterization of motifs can lead to greater understanding in automated genefinding, gene variability and the role DNA structure plays in gene network regulation. Our analysis determined: (1) the average free energy value for exons, introns and other biologically relevant sub-genetic sequences, (2) that these subsequences do not exist in distinct energy quanta, (3) that introns exist however in a tightly coupled average minimum free energy quantum compared to all other biologically relevant sub-genetic sequence types, (4) that single exon genes demonstrate a higher stability than exons which span the entire coding sequence as part of a multi-exon gene and (5) that all motif types contain a free energy global minimum at approximately nucleotide position 1,000 before reaching a plateau. These results should be relevant to the biochemist and bioinformatician seeking to understand the relationship between sub-genetic sequences and the information behind them.

In our recent efforts to map protein surfaces using mixed-solvent molecular dynamics (MixMD) (Ghanakota, P.; Carlson, H. A. Moving Beyond Active-Site Detection: MixMD Applied to Allosteric Systems. J. Phys. Chem. B 2016, 120, 8685-8695), we were able to successfully capture active sites and allosteric sites within the top-four most occupied hotspots. In this study, we describe our approach for estimating the thermodynamic profile of the binding sites identified by MixMD. First, we establish a framework for calculating free energies from MixMD simulations, and we compare our approach to alternative methods. Second, we present a means to obtain a relative ranking of the binding sites by their configurational entropy. The theoretical maximum and minimum free energy and entropy values achievable under such a framework along with the limitations of the techniques are discussed. Using this approach, the free energy and relative entropy ranking of the top-four MixMD binding sites were computed and analyzed across our allosteric protein targets: Abl Kinase, Androgen Receptor, Pdk1 Kinase, Farnesyl Pyrophosphate Synthase, Chk1 Kinase, Glucokinase, and Protein Tyrosine Phosphatase 1B.

Identification of non-protein-coding RNAs (ncRNAs) in genomes is a crucial task for not only molecular cell biology but also bioinformatics. Secondary structures of ncRNAs are employed as a key feature of ncRNA analysis since biological functions of ncRNAs are deeply related to their secondary structures. Although the minimum free energy (MFE) structure of an RNA sequence is regarded as the most stable structure, MFE alone could not be an appropriate measure for identifying ncRNAs since the free energy is heavily biased by the nucleotide composition. Therefore, instead of MFE itself, several alternative measures for identifying ncRNAs have been proposed such as the structure conservation index (SCI) and the base pair distance (BPD), both of which employ MFE structures. However, these measurements are unfortunately not suitable for identifying ncRNAs in some cases including the genome-wide search and incur high false discovery rate. In this study, we propose improved measurements based on SCI and BPD, applying generalized centroid estimators to incorporate the robustness against low quality multiple alignments. Our experiments show that our proposed methods achieve higher accuracy than the original SCI and BPD for not only human-curated structural alignments but also low quality alignments produced by CLUSTAL W. Furthermore, the centroid-based SCI on CLUSTAL W alignments is more accurate than or comparable with that of the original SCI on structural alignments generated with RAF, a high quality structural aligner, for which twofold expensive computational time is required on average. We conclude that our methods are more suitable for genome-wide alignments which are of low quality from the point of view on secondary structures than the original SCI and BPD.

A computer method for construction of secondary structure from polynucleotide sequence. Possible structure of the bacterial replication origin

Over the last few years, many optimization algorithms have been developed to predict the optimal secondary structure of ribonucleic acid (RNA) with “minimum free energy” (MFE). These algorithms are either inspired by dynamic programming or by meta-heuristic techniques. RNA participates in several biological activities in the organism. These activities involve protein synthesis, understanding the functional behavior of RNA molecules, coding, decoding and gene expression, carrier of transferring genetic information, formation of protein, catalyst in biomedical reactions and structural molecule in cellular organelles, transcription, etc. Beside the said activities, the major role of RNA is in developing new drugs and understanding several diseases occurred due to genetic disorder and viruses. For the above said activities, it is required to predict the correct RNA secondary structure having minimum free energy with desired prediction accuracy. This paper presents a meta-heuristic optimization algorithm to obtain the optimal secondary structure of RNA with required functionality and requires less time than the others in the literature. The performance of the proposed algorithm is checked with different existing state-of-the-art techniques. It is found that the proposed algorithm gives better results against the other techniques.

In recent years, obtaining RNA secondary structure information has played an important role in RNA and gene function research. Although some RNA secondary structures can be gained experimentally, in most cases, efficient, and accurate computational methods are still needed to predict RNA secondary structure. Current RNA secondary structure prediction methods are mainly based on the minimum free energy algorithm, which finds the optimal folding state of RNA in vivo using an iterative method to meet the minimum energy or other constraints. However, due to the complexity of biotic environment, a true RNA structure always keeps the balance of biological potential energy status, rather than the optimal folding status that meets the minimum energy. For short sequence RNA its equilibrium energy status for the RNA folding organism is close to the minimum free energy status; therefore, the minimum free energy algorithm for predicting RNA secondary structure has higher accuracy. Nevertheless, in a longer sequence RNA, constant folding causes its biopotential energy balance to deviate far from the minimum free energy status. This deviation is because of its complex structure and results in a serious decline in the prediction accuracy of its secondary structure. In this paper, we propose a novel RNA secondary structure prediction algorithm using a convolutional neural network model combined with a dynamic programming method to improve the accuracy with large-scale RNA sequence and structure data. We analyze current experimental RNA sequences and structure data to construct a deep convolutional network model, and then we extract implicit features of an effective classification from large-scale data to predict the pairing probability of each base in an RNA sequence. For the obtained probabilities of RNA sequence base pairing, an enhanced dynamic programming method is applied to obtain the optimal RNA secondary structure. Results indicate that our proposed method is superior to the common RNA secondary structure prediction algorithms in predicting three benchmark RNA families. Based on the characteristics of deep learning algorithm, it can be inferred that the method proposed in this paper has a 30% higher prediction success rate when compared with other algorithms, which will be needed as the amount of real RNA structure data increases in the future.

Genomic studies have become noncoding RNA (ncRNA) centric after the study of different genomes provided enormous information on ncRNA over the past decades. The function of ncRNA is decided by its secondary structure, and across organisms, the secondary structure is more conserved than the sequence itself. In this study, the optimal secondary structure or the minimum free energy (MFE) structure of ncRNA was found based on the thermodynamic nearest neighbor model. MFE of over 2600 ncRNA sequences was analyzed in view of its signal properties. Mathematical models linking MFE to the signal properties were found for each of the four classes of ncRNA analyzed. MFE values computed with the proposed models were in concordance with those obtained with the standard web servers. A total of 95% of the sequences analyzed had deviation of MFE values within ±15% relative to those obtained from standard web servers.

Accurate prediction of RNA secondary structure from the base sequence is an unsolved computational challenge. The accuracy of predictions made by free energy minimization is limited by the quality of the energy parameters in the underlying free energy model. The most widely used model, the Turner99 model, has hundreds of parameters, and so a robust parameter estimation scheme should efficiently handle large data sets with thousands of structures. Moreover, the estimation scheme should also be trained using available experimental free energy data in addition to structural data. In this work, we present constraint generation (CG), the first computational approach to RNA free energy parameter estimation that can be efficiently trained on large sets of structural as well as thermodynamic data. Our CG approach employs a novel iterative scheme, whereby the energy values are first computed as the solution to a constrained optimization problem. Then the newly computed energy parameters are used to update the constraints on the optimization function, so as to better optimize the energy parameters in the next iteration. Using our method on biologically sound data, we obtain revised parameters for the Turner99 energy model. We show that by using our new parameters, we obtain significant improvements in prediction accuracy over current state of-the-art methods. Our CG implementation is available at http://www.rnasoft.ca/CG/.

We revise the classical Daoud-Cotton (DC) model to describe conformations of polymer and polyelectrolyte chains end-grafted to convex spherical and cylindrical surfaces. In the framework of the DC model, local stretching of chains in the brush does not depend on the degree of polymerization of grafted chains, and the polymer density profile follows a single-exponent power law. This model, however, does not correspond to a minimum in free energy of the curved brush. The nonlocal (NL) approximation exploited in the present paper implies the minimization of the overall free energy of the brush and predicts that the polymer density profile does not follow a single-exponent power law. In the limit of large surface curvature the NL approximation provides the same scaling laws for brush thickness and free energy as the local DC model. Numerical prefactors are however different. Extra extension of chains in the brush interior region leads to larger equilibrium brush thickness and lower free energy per chain. A significant difference between outcomes of the two models is found for brushes formed by ionic polymers, particularly for weakly dissociating (p H-sensitive) polyelectrolytes at low solution salinity.

Expanding on an earlier work that relied on linear force-free magnetic fields, we self-consistently derive the instantaneous free magnetic energy and relative magnetic helicity budgets of an unknown three-dimensional nonlinear force-free magnetic structure extending above a single, known lower-boundary magnetic field vector. The proposed method does not rely on the detailed knowledge of the three-dimensional field configuration but is general enough to employ only a magnetic connectivity matrix on the lower boundary. The calculation yields a minimum free magnetic energy and a relative magnetic helicity consistent with this free magnetic energy. The method is directly applicable to photospheric or chromospheric vector magnetograms of solar active regions. Upon validation, it basically reproduces magnetic energies and helicities obtained by well-known, but computationally more intensive and non-unique, methods relying on the extrapolated three-dimensional magnetic field vector. We apply the method to three active regions, calculating the photospheric connectivity matrices by means of simulated annealing, rather than a model-dependent nonlinear force-free extrapolation. For two of these regions we correct for the inherent linear force-free overestimation in free energy and relative helicity that is larger for larger, more eruptive, active regions. In the third studied region, our calculation can lead to a physical interpretation of observed eruptive manifestations. We conclude that the proposed method, including the proposed inference of the magnetic connectivity matrix, is practical enough to contribute to a physical interpretation of the dynamical evolution of solar active regions.

The problem of art culture's means special features is considered in this article. Condition of art relations' originality, art relations' character of development and its functioning mechanism are highlighted here. Classification of art culture's means and special features of art culture's use are considered in this article.

Silicone/ZnO nanorod composite coating as a marine antifouling surface

The aim of this work is to determine what free energy functionals are expressible as quadratic forms of the state functional \(I^t\) which is discussed in earlier papers. The single integral form is shown to include the functional \(\psi _F\) proposed a few years ago, and also a further category of functionals which are easily described but more complicated to construct. These latter examples exist only for certain types of materials. The double integral case is examined in detail, against the background of a new systematic approach developed recently for double integral quadratic forms in terms of strain history, which was used to uncover new free energy functionals. However, while, in principle, the same method should apply to free energies which can be given by quadratic forms in terms of \(I^t\), it emerges that this requirement is very restrictive; indeed, only the minimum free energy can be expressed in such a manner.

ABSTRACTThe shape of a liquid drop on a flat solid surface is examined by using the minimization of free energy. This free energy consists of the contributions from the gravitational potential energy of the drop mass and the energy of the interfacial surfaces. The minimization of free energy is solved by the Lagrange multipliers method keeping the drop volume constant. The generic differential equation for the shape of the drop and a relation among the contact angles (Young equation) are determined as a result of the minimization via the variation of a functional and by imposing the condition for equilibrium of the drop. The differential equation is solved analytically around the origin of the selected coordinate axis and for two special cases. For the general solution, the differential equation is solved numerically to obtain the general shape of the sessile drop. Furthermore, a new Axisymmetric Drop Shape Analysis method is proposed for non–wetting sessile drop.