On combinatorial DNA word design.

In this paper, we give a matrix construction method for designing DNA codes that come from group matrix rings. We show that with our construction one can obtain reversible \(G^k\)-codes of length kn, where \(k, n \in \mathbb {N},\) over the finite commutative Frobenius ring R. We employ our construction method to obtain many DNA codes over \(\mathbb {F}_4\) that satisfy the Hamming distance, the reverse, the reverse-complement and the fixed GC-content constraints. Moreover, we improve many lower bounds on the sizes of some known DNA codes and we also give new lower bounds on the sizes of DNA codes of lengths 48, 56, 60, 64 and 72 for some fixed values of the Hamming distance d.

DNA codes consisting of DNA sequences are necessary for DNA computing. The minimum distance parameter of such codes is a measure of how dissimilar the codewords are, and thus is indirectly a measure of the likelihood of undetectedable or uncorrectable errors occurring during hybridization. To compute distance, an abstract metric, for example, longest common subsequence, must be used to model the actual bonding energies of DNA strands. In this paper we continue the development [1,2,3] of similarity functions for q-ary n-sequences The theoretical lower bound on the maximal possible size of codes, built on the space endowed with this metric, is obtained. that can be used (for q = 4) to model a thermodynamic similarity on DNA sequences. We introduce the concept of a stem similarity function and discuss DNA codes [2] based on the stem similarity. We suggest an optimal construction [2] and obtain random coding bounds on the maximum size and rate for such codes.KeywordsArbitrary IntegerRandom CodeUnique RootReverse ComplementLonge Common SubsequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

BackgroundEstimation of DNA duplex hybridization free energy is widely used for predicting cross-hybridizations in DNA computing and microarray experiments. A number of software programs based on different methods and parametrizations are available for the theoretical estimation of duplex free energies. However, significant differences in free energy values are sometimes observed among estimations obtained with various methods, thus being difficult to decide what value is the accurate one.ResultsWe present in this study a quantitative comparison of the similarities and differences among four published DNA/DNA duplex free energy calculation methods and an extended Nearest-Neighbour Model for perfect matches based on triplet interactions. The comparison was performed on a benchmark data set with 695 pairs of short oligos that we collected and manually curated from 29 publications. Sequence lengths range from 4 to 30 nucleotides and span a large GC-content percentage range. For perfect matches, we propose an extension of the Nearest-Neighbour Model that matches or exceeds the performance of the existing ones, both in terms of correlations and root mean squared errors. The proposed model was trained on experimental data with temperature, sodium and sequence concentration characteristics that span a wide range of values, thus conferring the model a higher power of generalization when used for free energy estimations of DNA duplexes under non-standard experimental conditions.ConclusionsBased on our preliminary results, we conclude that no statistically significant differences exist among free energy approximations obtained with 4 publicly available and widely used programs, when benchmarked against a collection of 695 pairs of short oligos collected and curated by the authors of this work based on 29 publications. The extended Nearest-Neighbour Model based on triplet interactions presented in this work is capable of performing accurate estimations of free energies for perfect match duplexes under both standard and non-standard experimental conditions and may serve as a baseline for further developments in this area of research.

The thermodynamic study of protein folding shows the generation of a narrow range of ΔG° values, as a net result of large changes in the ΔH° and TΔS° values of the folding process. The obvious consequence of this narrow range of values is that a linear enthalpy–entropy relationship, showing apparent enthalpy–entropy compensation (EEC), is clearly observed to be associated with the study of protein folding. Herein, we show the ΔH°, TΔS°, and ΔG° values for a set of 583 data from protein folding processes, at various temperatures, as calculated by using the Gibbs–Helmholtz equations. This set of thermodynamic data was calculated from the melting temperature (Tm), the melting enthalpy (ΔHm), and the change in heat capacity (ΔCp°) values, all of them associated with the heat-induced protein unfolding processes and included in the ProTherm Data Base. The average values of enthalpy (ΔH°av), entropy (TΔS°av), and free energy (ΔG°av) for the folding process were calculated within the range of temperature from 0 °C to the average value of Tm. The values and temperature dependency of TΔS°av within this temperature range are practically equal to those corresponding to ΔH°av, while ΔG°av remains small and displaying a curve with a minimum at about 10 °C and a value of ΔG° = −30.9 kJ/mol at the particular temperature of 25 °C. The large negative value of TΔS°av, together with the also large and negative value of ΔCp°av, suggests large conformational changes and important EEC, thus causing the small average value of ΔG° for protein folding, which is enough to guarantee both protein stability and molecular flexibility to allow for adaptation to the chemical potentials of the environment. Our analysis suggests that EEC may be the quantum-mechanical evolutive mechanism to make functional proteins adaptative to environmental temperature and metabolite concentrations. The analysis of protein folding data, compared with those of protein–ligand interaction, allows us to suggest strategies to overcome EEC in the design of new drugs.

DNA nanotechnology often requires collections of oligonucleotides called "DNA free energy gap codes" that do not produce erroneous crosshybridizations in a competitive muliplexing environment. This paper addresses the question of how to design these codes to accomplish a desired amount of work within an acceptable error rate. Using a statistical thermodynamic and probabilistic model of DNA code fidelity and mathematical random coding theory methods, theoretical lower bounds on the size of DNA codes are given. More importantly, DNA code design parameters (e.g., strand number, strand length and sequence composition) needed to achieve experimental goals are identified.

Summary Density functional theory (DFT) trends in Gibbs free energies and enthalpies were thoroughly studied in calcite. Different coordination was applied for ionic species that exist in seawater and smartwater as well as for carboxylic acids presented in crude oil at distinct two primary hydration sites: >CO3H, >CaOH. The studied hydration sites were proposed based on electro-kinetics besides surface titration experimental studies.17, 18 Interfacial energy runs using the Gaussian 09 suits of program21, with Becke’s three parameter exchange and Lee Yang Parr corrected correlation functional (B3LYP) and 3-21G basis set, based on previous surface sites were performed to account for stability, reactivity and wettability alteration. The calculations predict the most stable complexes for calcite are, CO3H, CaO-, CO3Ca, CO3Mg , CaCO3-, CaHCO , CaH2O+ and CaSO4-. We also demonstrate that free ion species are having a higher free energy in seawater than in case of a complex and thus indicates a more reactivity of complex species to interact with rock sites. Furthermore, corresponding values of free energy and enthalpy change of ions association with calcite surface provided insights about complexes that are most favorable at the surface. This study proposes a mathematical correlation between thermochemistry profiles and wettability alteration, which expresses to us how the surface affinity for a certain organic compound compares with its affinity for water. The calculations agrees with previous experiment findings especially in case of Ca+2, Mg+2, SO4-2,MgOH+1 ,OH-1, and NaCl. Some reversed trend can be explained by the smaller size of the basis set used in the calculations. The results of this insights help in understating the interaction mechanism of this unique systems in order to modify reactivity for enhancing oil recovery (EOR) purposes, and to use the outcomes of this study to pose questions and directions for continuing theoretical efforts destined at linking macroscopic reactivity in case of altering wettability with molecular-level understanding.

Neurodegenerative diseases are a global priority disease. According to the World Health Organization (WHO), it is estimated that by 2050, there will be 152 million people with neurodegenerative diseases. Currently, the method used for brain imaging is PET/CT, with the most widely used radiopharmaceutical being 18F-FDG [7,8]. 18F-FDG is used to determine brain glucose metabolism, however the 18F-FDG does not have a specific receptor. Pramipexole compounds can cross the blood-brain barrier and have high specificity for dopamine receptors. By modifying and labelling the structure of pramipexole derivatives, it is expected to obtain pramipexole derivatives with a good affinity to the dopamine receptor. In order to reduce the risk of failure, radiation hazard, and research funds, in this research, a molecular docking study was carried out using the targeted docking method between dopamine receptor proteins and 22 pramipexole derivatives using AutoDock 4, GaussView software for structure preparation, Gaussian software for energy calculation, and Biovia Discovery Studio for structure visualization. The experimental results showed that the free binding energy of pramipexole derivatives for the dopamine receptor was obtained in the range of -2.81 to -5.84 kcal/mol. The best free binding energy value was obtained for compound PD-7, with a free binding energy value of -5.84 kcal/mol, while the RMSD value obtained was 0.6 A°, and amino acid residues that interacted with compound PD-7 among others: Leu347, Leu343, Tyr198, Leu199, Glu202, Phe201, and Val203 with hydrophobic and hydrogen bond interactions. The PD-7 compound was labeled using the radioisotope iodine-131 based on the free binding energy value. From the experimental results, compound 131I-PD-7 showed a free binding energy value of -4.66 kcal/mol and interacts with the similar amino acid residues as compound PD-7. These results indicate that the compound131I-PD-7 is a potential candidate to be studied further as a radiopharmaceutical candidate for brain imaging.

Polyacid cascade dendrimers (generations 1−4) are used as a pseudostationary phase for electrokinetic capillary chromatography to separate mixtures of neutral species. Separation of a homologous series of molecules allow the capacity factors and distribution coefficients to be calculated, which in turn allow the standard enthalpy, entropy, and Gibbs free energy for solubilization to be evaluated by van't Hoff analysis. Comparison of these values to analogous values measured for sodium dodecyl sulfate (SDS) micelles suggests fundamental differences in the thermodynamic quantities associated with solubilization. As the size of the polyacid dendrimer increases, entropy becomes the driving force for solubilization, and enthalpy is disfavored. Gibb's free energy values are negative for all of the dendrimer/analyte interactions investigated. The capacity factor is found to increase linearly with increasing concentrations of dendrimer. Thermodynamic parameters are evaluated for several small molecules to show th...

The Widom particle insertion (WPI) method is used to compute the free energy, enthalpy, and entropy associated with the creation of empty cavities of different sizes in water and n-hexane. These thermodynamic parameters are computed from the likelihood of encountering such cavities in thermally equilibrated configurations from 4 ns (1 ns=10−9 s) molecular dynamics trajectories of the neat liquids. The obtained free energy values are in excellent agreement with those computed previously, using the same or other methods. We find that the entropy term is large and unfavorable in both liquids, but more so in water than in hexane. The change in internal energy is, on the other hand, virtually zero in hexane and slightly favorable in water. Comparison with scaled particle theory (SPT) predictions shows good agreement for the free energy values for small cavities, but the theory systematically underestimates these values for large cavities. In contrast, the free energy components obtained by the two methods show several significant differences. With WPI, the entropy of cavity formation is unfavorable in both liquids for all cavity sizes. SPT yields an unfavorable entropy only for water. In hexane, however, the predicted entropy is negative for small cavities, but changes sign for cavity radii >1.1 Å. In addition, SPT yields an unfavorable enthalpy of cavity formation in water, whereas with WPI this term is small but favorable. Taking n-hexane as a model for organic solvents, our calculations thus suggest that the process of cavity formation is similar in water and these solvents, a conclusion which seems to make good physical sense. SPT reaches an opposite conclusion, which seems harder to rationalize, and probably arises from the highly simplified solvent model used by this theory.

Free energy perturbation Monte Carlo (FEP/MC) simulations are performed for both the liquid and solid phases of water to determine the melting temperature of several popular three and four-site water models. Gibbs free energy vs. temperature plots are constructed from the simulations to determine the melting temperature. For the liquid phase, standard FEP/MC simulations are used to calculate the free energy relative to the gas phase at multiple temperatures. The free energy of the solid phase relative to the gas phase is calculated at multiple temperatures using the lattice-coupling method. The intersection of the free energy regression lines determines the estimate of the melting temperature. Additionally, simulations were carried out for simple salt solutions to determine the freezing point depressions (FPD). The simulations reproduce the FPD as a function of salt concentration for solutions of NaCl, KCl, CaCl2, and MgCl2.

pKa's, proton affinities, and proton dissociation free energies characterize numerous properties of drugs and the antioxidant activity of some chemical compounds. Even with a higher computational level of theory, the uncertainty in the proton solvation free energy limits the accuracy of these parameters. We investigated the thermochemistry of the solvation of the proton in methanol within the cluster-continuum model. The scheme used involves up to nine explicit methanol molecules, using the IEF-PCM and the strategy based on thermodynamic cycles. All computations were performed at B3LYP/6-31++G(dp) and M062X/6-31++G(dp) levels of theory. It comes out from our calculations that the functional M062X is better than B3LYP, on the evaluation of gas phase clustering energies of protonated methanol clusters, per methanol stabilization of neutral methanol clusters and solvation energies of the proton in methanol. The solvation free energy and enthalpy of the proton in methanol were obtained after converging the partial solvation free energy of the proton in methanol and the clustering free energy of protonated methanol clusters, as the cluster size increases. Finally, the recommended values for the solvation free energy and enthalpy of the proton in methanol are -257 and -252 kcal/mol, respectively.

Ionization constants of chloro, iodo and nitro substituted 4-methyl-thioanilines were determined over the range 30° to 50° using a spectro-photometric method. The results were analyzed in terms of the Harned-Robinson equation and values of heat, free energy and entropy of ionization were calculated. The free energies are additive, except in the case of 3, 5-diiodo-4-methylthioaniline, while the heats and the entropies are not.

An improved cluster pair correlation method that is based on the method originally introduced by Tuttle et al. ( Tuttle et al. J. Phys. Chem. A 2002 , 106 , 925 - 932 ) was developed and evaluated using a significantly larger data set than used previously. With this larger data set, values for the absolute proton hydration free energy of -259.3 and -265.0 kcal/mol were obtained using the original and improved method, respectively. The former value is ∼4.5 kcal/mol less negative than previously reported values obtained with the same method but with smaller data sets. The dependence of this value on data set size indicates that the uncertainty in the original method may be greater than previously realized. The improved method has the advantages of higher precision, and the effects of cluster size on the proton hydration free energy and enthalpy values can be more readily evaluated. Data for ions with extreme pK(a)s, many of which were included in previous estimates of the proton hydration free energy, were found to be unreliable and were eliminated from the extended data set. There is only a subtle effect of cluster size on the Gibbs free energy values, and within the limits of the approximation inherent in the cluster pair correlation method, the "best" value for the standard absolute proton hydration free energy obtained with this new method and larger data set is -263.4 kcal/mol (average for clusters with 4-6 water molecules). The absolute proton hydration enthalpy values decrease from -273.1 to -275.3 kcal/mol with increasing cluster size (one to six water molecules, respectively). This trend, along with an anomalously high value for the absolute proton hydration entropy, indicates that the enthalpy obtained with this method may not have converged for these relatively small clusters.

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