Non-quantized minimum free energy in untranslated region exons

The distribution function of orientations of a segment, which interacts with the orienting field and is within the chain with given the end-to-end distance-vector, is calculated. The number of segments per chain is finite. The Lagrange method of conditional minimization of the chain free energy (the Helmholtz function) functional is used. Constraints for the segment orientations stem from fixed the chain end-to-end distance-vector. Hence, Lagrange multipliers, energy, free energy, and entropy, for the chain with given the end-to-end distance-vector, are calculated. Then, the distribution function of values of that vector is obtained. Furthermore, an average free energy per chain inside the polymer network with given a topological structure, the system self-deformation, and modulus of elasticity are calculated and discussed in Gaussian limit, that is, for the number of segments per chain tending to infinity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 138–144, 2010

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field–consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.

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.

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.

Guanine quadruplex (G-quadruplex) structures play a vital role in stabilizing the DNA genome and in protecting healthy cells from transforming into cancer cells. The structural stability of G-quadruplexes is greatly enhanced by the binding of monovalent cations such as Na+ or K+ into the interior axial channel. We computationally study the free energy of binding of Na+ and K+ ions to two intramolecular G-quadruplexes that differ considerably in their degree of rigidity and the presence or absence of terminal nucleotides. The goal of our study is two-fold. On the one hand, we study the free energy of binding every ion, which complements the experimental findings that report the average free energy for replacing Na+ with K+ ions. On the other hand, we examine the role of the G-quadruplex structure in the binding free energy. In the study, we employ all-atom molecular dynamics simulations and the alchemical transformation method for the computation of the free energies. To compare the cation-dependent contribution to the structural stability of G-quadruplexes, we use a two-step approach to calculate the individual free energy difference ΔG of binding two Na+ and two K+ to two G-quadruplexes: the unimolecular DNA d[T2GT2(G3T)3] (Protein Data Bank ID 2M4P) and the human telomeric DNA d[AGGG(TTAGGG)3] (PDB ID 1KF1). In contrast to the experimental studies that estimate the average free energy of binding, we find a varying difference of approximately 2-9 kcal/mol between the free energy contribution of binding the first and second cation, Na+ or K+. Furthermore, we found that the free energy of binding K+ is not affected by the chemical nature of the two quadruplexes. By contrast, Na+ showed dependency on the G-quadruplex structure; the relatively small size allows Na+ to explore larger configurational space than K+. Numerical results presented here may offer reference values for future design of cationic drug-like ligands that replace the metal ions in G-quadruplexes.

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.

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.

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.

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.

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.

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.

The problem of data and information encoding on DNA bears an increasing interest for both biological and nonbiological applications of biomolecular computing. Recent experimental and theoretical advances have produced and tested to obtain large code sets of oligonucleotides to support virtually any kind of application. In this paper, we have developed an algorithm to design DNA short-word sets based on minimum free energy (MFE) criteria. The MFE constraint is the minimum value among free energies of all the possible structures and the effective approach to control the generation of unexpected secondary structure of DNA sequences may cause error. The algorithm is constructive and directly produces the actual DNA words of the sets, unlike other academic and statistical numbers. According to the previous values, our experimental results can succeed in generating better DNA word sets based on MFE constraint. More importantly, using our results could decrease the emergence of false hybridization reaction, and improve the reliability and the scale of DNA computing.

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.