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PubMed2003

Entropy evaluation using the kinetic method: is it feasible?

The kinetic method is one of the most widely used experimental techniques for the measurement of thermochemical parameters by mass spectrometry. Recently it has been realized that it can also be used to determine reaction entropies, but the validity of this approach has not been established. This Perspective evaluates kinetic method plots in cases where there is a significant entropy difference between the competing fragmentation channels (i.e. between sample and reference compounds in the dissociating cluster ion). The concept underlying this study is to calculate mass spectra theoretically, based on known thermochemical parameters and as a function of experimental conditions. This can be done accurately using the RRKM-based MassKinetics software. The resulting mass spectra are then interpreted by the kinetic method, yielding DeltaH and DeltaS values. These values are, in turn, compared with the true values used to generate the calculated mass spectra. The results show that the reaction entropy difference between sample and reference has a very large influence on kinetic method plots. This should always be considered when studying energy-dependent mass spectra (using metastable ions or low- or high-energy collision-induced dissociation (CID)), even if only DeltaH is to be determined. Kinetic method plots are not strictly linear and this becomes a serious issue in the case of small molecules showing a large entropy effect. In such cases, results obtained at a low degree of excitation are more accurate. Energy and entropy effects can be evaluated in a relatively straightforward manner: first, the apparent Gibbs energy (DeltaG(app)) and effective temperature (T(eff)) are determined from kinetic method plots (intercept and slope, respectively), obtained from experiments using various degrees of excitation. Second, the resulting DeltaG(app) is plotted against T(eff), the slope yielding DeltaS while the intercept (extrapolation to zero temperature) yields DeltaH. This data evaluation yields more accurate results than alternative methods used in the literature. The resulting DeltaH values are fairly accurate, with errors, in most cases, <4 kJ mol(-1). On the other hand, DeltaS is systematically underestimated by 20-40%. Empirically scaling DeltaS values determined by the kinetic method by 1.35 results in a DeltaS value within 20% (or 10 J mol(-1) K(-1)) of the theoretical value.

Journal Article↗

PubMed2006

Comparison of atomic-level and coarse-grained models for liquid hydrocarbons from molecular dynamics configurational entropy estimates.

Molecular liquids can be modeled at different levels of spatial resolution. In atomic-level (AL) models, all (heavy) atoms can be explicitly simulated. In coarse-grained (CG) models, particles (beads) that represent groups of covalently bound atoms are used as elementary units. Ideally, a CG model should reproduce the thermodynamic and structural properties of the corresponding AL model after mapping to the lower-resolution scale. In the present work, two such models are investigated: (i) the classical GROMOS atomic-level model; (ii) a CG model recently proposed by Marrink et al., which maps approximately four non-hydrogen atoms to one bead [J. Phys. Chem. B 2004, 108, 750]. The study is restricted to n-alkanes whose aliphatic fragments are abundantly found in lipids of biological interest. Additionally, cis-9-octadecene is included, as a template chain of the lipid dioleoylphosphatidylcholine (DOPC). The two representations of molecules in the liquid phase are compared in terms of average molecular structures, extent of configurational space sampled, and single-molecule entropies. An approximate method is used to estimate the rotational contributions to the absolute configurational entropy. Good correspondence between the AL and CG representations is found. The loss in configurational entropy due to the reduction in degrees of freedom upon coarse-graining of the model is estimated.

Algorithms↗

PubMed2002

Effect of angular momentum on equilibrium properties of a self-gravitating system.

The microcanonical properties of a two-dimensional system of N classical particles interacting via a smoothed Newtonian potential, as a function of the total energy E and the total angular momentum L, are discussed. The two first moments of the distribution of the linear momentum of a given particle at a fixed position show that (a) on average the system rotates like a solid body and (b) the velocity dispersion is a function of the distance from the center. In order to estimate suitable observables, a numerical method based on an importance sampling algorithm is presented. The entropy surface S shows a negative specific heat capacity region at fixed L for all L. Observables probing the average mass distribution are used to understand the link between thermostatistical properties and the spatial distribution of particles. In order to define a phase in a nonextensive system, we introduce a more general observable than that proposed by Gross and Votyakov [Eur. Phys. J. B 15, 115 (2000)]. This observable is the sign of the largest eigenvalue of the Hessian matrix of the entropy surface. If it is negative then the system is in a pure (single) phase; if it is positive then the system undergoes a first order phase transition. At large E the gravitational system is in a homogeneous gas phase. At low E there are several collapse phases. At L=0 there is a single-cluster phase and for L not equal 0 there are several phases with two clusters. The relative size of the clusters depends on L. All these pure phases are separated by a first order phase transition region. Signals of critical behavior emerge at several points of the parameter space (E,L). We also show that a huge loss of information appears if we treat the system as a function of the intensive parameters. Besides the known nonequivalence at first order phase transitions, the pure phases with two clusters of different sizes are not accessible to the canonical ensemble. Moreover, for a particular choice of intensive parameters introduced in this paper, there exist in the microcanonical ensemble some values of those intensive parameters for which the corresponding canonical ensemble does not exist, i.e., the partition sum diverges.

Journal Article↗

PubMed2005

Application of Maximum Entropy reconstruction to PISEMA spectra.

Maximum Entropy reconstruction is applied to two-dimensional PISEMA spectra of stationary samples of peptide crystals and proteins in magnetically aligned virus particles and membrane bilayers. Improvements in signal-to-noise ratios were observed with minimal distortion of the spectra when Maximum Entropy reconstruction was applied to non-linearly sampled data in the indirect dimension. Maximum Entropy reconstruction was also applied in the direct dimension by selecting sub-sets of data from the free induction decays. Because the noise is uncorrelated in the spectra obtained by Maximum Entropy reconstruction of data with different non-linear sampling schedules, it is possible to improve the signal-to-noise ratios by co-addition of multiple spectra derived from one experimental data set. The combined application of Maximum Entropy to data in the indirect and direct dimensions has the potential to lead to substantial reductions in the total amount of experimental time required for acquisition of data in multidimensional NMR experiments.

Bacteriophages↗

PubMed2005

The influence of lipids on the energetics of uptake of polycyclic aromatic hydrocarbons by natural organic matter.

Although most of the organic carbon in soils and sediments may be composed of humic substances, their interaction with other compounds, especially their sorption interactions, may be significantly affected by the presence of small amounts of the other components of natural organic matter (NOM). In this investigation, the influence of the lipid fraction of NOM on the sorption thermodynamics of fluorene, phenanthrene, and pyrene to several geosorbent samples was examined before and after extraction of lipids. Batch experiments were performed at the same concentration for all polycyclic aromatic hydrocarbons (PAHs) (0.025 x their solubility in water) at different temperatures (10, 20, 30, and 40 degrees C), and the thermodynamic parameters were calculated. Removal of the lipids increases the sorption capacity of the samples as well as the exothermicity of the process. The free energy change was negative for all the samples and no significant differences were noticed on lipid removal. The entropy changes were small and positive for the whole geosorbent samples, but even smaller or more negative when the lipids were removed. This indicates that the interaction of PAHs with soils and sediments in the absence of extractable lipids is stronger and the mechanisms involved may be different, changing from a partitioning-like mechanism to specific adsorption. Because of the competition between lipids and PAHs for the same sorption sites, the lipids can be viewed as an "implicit sorbate."

Adsorption↗

PubMed1989

Adolescent psychic entropy: a response to unacknowledged fears.

The purpose of this study was to explore the feasibility of measuring psychic entropy in adolescents and to note the predictability of two variables--gender and grade. The subjects were 22 male and female junior and senior high school Caucasians in a central Kentucky church youth choir. They were given the 20-item Psychic Entropy Measure for Adolescents, which is a list of 20 negatively presented statements rated on a five-point scale. The five highest scoring items specifically reflect the phenomenon of psychic entropy. The findings suggest that unacknowledged adolescent fears may be developmental. The limited sample demonstrated that a revised instrument of the Psychic Entropy Measure for Adolescents could be an effective instrument in therapy.

Adaptation, Psychological↗

PubMed2002

[Effects of sampling parameter variation on the complexity analysis of EEG].

The algorithmic complexity and the approximate entropy of EEG were calculated and analyzed with different data points, different sample frequencies and different sample time duration. The results showed that under fixed sample frequency, the longer the data was, the more stable the complexity values were. With fixed sample time duration or fixed data point, lower sample frequency would be better both for EEG distinguishing and for computing time saving.

Algorithms↗

PubMed2004

Systematic and random errors in ion affinities and activation entropies from the extended kinetic method.

An evaluation of the extended kinetic method with full entropy analysis was conducted using RRKM theory to simulate data for collision-induced dissociation under single-collision conditions. A rigorous method for analyzing kinetic method data, orthogonal distance regression, is introduced and compared with previous methods in the literature. The results demonstrate that the use of the extended kinetic method is definitely superior to the standard kinetic method, but final ion affinities and activation entropies differ intrinsically from the correct values. Considering the effects of both systematic and random error in Monte Carlo simulations of the full entropy analysis, error distributions of +/-4 to +/-12 kJ mol(-1) for ion affinities and of +/-9 to +/-30 J mol(-1) K(-1) for activation entropy differences are found (+/-2 standard deviations of the sample populations). The systematic errors in ion affinities are larger for systems with large activation entropy differences. These uncertainties do not include any error in the absolute calibration of the reference ion affinity scale. We argue that application of an empirical correction factor is inadvisable.

Journal Article↗

PubMed2006

Calculation of the entropy and free energy of peptides by molecular dynamics simulations using the hypothetical scanning molecular dynamics method.

Hypothetical scanning (HS) is a method for calculating the absolute entropy S and free energy F from a sample generated by any simulation technique. With this approach each sample configuration is reconstructed with the help of transition probabilities (TPs) and their product leads to the configuration's probability, hence to the entropy. Recently a new way for calculating the TPs by Monte Carlo (MC) simulations has been suggested, where all system interactions are taken into account. Therefore, this method--called HSMC--is in principle exact where the only approximation is due to insufficient sampling. HSMC has been applied very successfully to liquid argon, TIP3P water, self-avoiding walks on a lattice, and peptides. Because molecular dynamics (MD) is considered to be significantly more efficient than MC for a compact polymer chain, in this paper HSMC is extended to MD simulations as applied to peptides. Like before, we study decaglycine in vacuum but for the first time also a peptide with side chains, (Val)(2)(Gly)(6)(Val)(2). The transition from MC to MD requires implementing essential changes in the reconstruction process of HSMD. Results are calculated for three microstates, helix, extended, and hairpin. HSMD leads to very stable differences in entropy TDeltaS between these microstates with small errors of 0.1-0.2 kcal/mol (T=100 K) for a wide range of calculation parameters with extremely high efficiency. Various aspects of HSMD and plans for future work are discussed.

Chemistry, Physical↗

PubMed1988

Double-stranded structure for hyaluronic acid in ethanol-aqueous solution as revealed by circular dichroism of oligomers.

The sigmoidal nature of circular dichroism (CD) changes for hyaluronic acid solutions as a function of solvent composition or temperature is studied as a function of chain length by using oligomers. We find a chain length effect with approximately nine disaccharides required for the structural transition as a function of organic solvent, which proves that the transition is cooperative with large transition enthalpy and entropy. The transition also depends on sample concentration as expected for strand association, and this was investigated in detail for oligomers 12 and 16 disaccharides long. Indeed, it was possible to prevent completely the transition in mixed solvent with sufficient dilution of these oligomers, which demonstrates strand association. The CD data in mixed solvent as a function of oligomer concentration were fit with various models for association of two and more strands. Simplex methods were used to investigate the vector space of unknowns for the models, and two-strand models were shown to consistently give a better fit. A cooperative two-strand zipper model which allows relative sliding of the chains had the smallest fitting error and produced the following thermodynamic parameters (in terms of a duplex of disaccharide units) for the ordered structure in an aqueous solution containing 45% v/v ethanol, 12.5 mM NaH2PO4, and 7.5 mM H3PO4: enthalpy of growth, -1.0 +/- 0.3 kcal mol-1; entropy of growth, -2.3 +/- 1.3 eu mol-1; enthalpy of initiation, -20 +/- 3 kcal mol-1; entropy of initiation, -71 +/- 15 eu mol-1. The results are consistent with a double-stranded and helical structure for hyaluronic acid in solutions of reduced dielectric constant.

Carbohydrate Conformation↗

PubMed2005

Alkyl group as entropy reservoir in an MMX chain complex, Pt2(n-PenCS2)4I.

Heat capacity of halogen-bridged one-dimensional binuclear metal complex (so-called MMX chain) having four n-pentyl groups, Pt2(n-PenCS2)4I, was measured by adiabatic calorimetry. A first-order phase transition was observed at 207.4 K when measurement was made after cooling from room temperature. The enthalpy and entropy of transition were determined to be 10.19 kJ mol(-1) and 49.1 J K(-1) mol(-1), respectively. A monotropic phase transition was observed at 324 K on heating, and the entropy of transition was essentially null. The sample once heated above 324 K never returned to the initial phase at room temperature and underwent a higher-order phase transition at 173 K and a first-order phase transition at 220.5 K. The enthalpy and entropy of the first-order phase transition were estimated to be 11.6 kJ mol(-1) and 52.4 J K(-1) mol(-1), respectively. The magnitude of the entropy gain at the phase transition from the initial room-temperature phase to the high-temperature phase at 324 K shows that in Pt2(n-PenCS2)4I a large amount of entropy reserved in alkyl chain is transferred to dithiocarboxylato groups upon the phase transition, as in the cases of Pt2(n-PrCS2)4I and Pt2(n-BuCS2)4I.

Journal Article↗

PubMed1997

Empirical free energy calculations: a blind test and further improvements to the method.

Empirical Gibbs functions estimate free energies of non-covalent reactions (deltaG) from atomic coordinates of reaction products (e.g. antibody-antigen complexes). The function previously developed by us has four terms that quantify the effects of hydrophobic, electrostatic and entropy changes (conformational, association) upon complexation. The function was used to calculate delta deltaG of ten lysozyme mutants affecting the stability of the HyHEL-10 antibody-lysozyme complex. The mutants were computer-modeled from the X-ray structure of the wild-type, and free energy calculations produced a correlation coefficient of 0.5 with the experimental delta deltaG data (average absolute error +/-3 kcal). The following changes were then introduced into the Gibbs function: (1) the hydrophobic force was made proportional to the molecular surface, as calculated by the GEPOL93 algorithm, with the scaling constant of 70 cal/mol/A2; (2) calculation of the electrostatics of binding was carried out by the finite difference Poisson-Boltzmann algorithm, which employed uniform grid charging, dielectric boundary smoothing and charge anti-aliasing; and (3) side-chain conformational entropy was estimated from the CONGEN sampling of torsional degrees of freedom. In the new calculations, correlation with experimental data improved to 0.6 or 0.8 if a single outlying mutant, K96M, was neglected. Analysis of the errors remaining in our calculations indicated that molecular mechanics-based modeling of the mutants, rather than the form of our amended Gibbs function, was the main factor limiting the accuracy of the free energy estimates.

Animals↗

PubMed2000

Genetic heterogeneity of hypervariable region 1 of the hepatitis C virus (HCV) genome and sensitivity of HCV to alpha interferon therapy.

Hepatitis C virus (HCV) populations persist in vivo as a mixture of heterogeneous viruses called quasispecies. The relationship between the genetic heterogeneity of these variants and their responses to antiviral treatment remains to be elucidated. We have studied 26 virus strains to determine the influence of hypervariable region 1 (HVR-1) of the HCV genome on the effectiveness of alpha interferon (IFN-alpha) therapy. Following PCR amplification, we cloned and sequenced HVR-1. Pretreatment serum samples from 13 individuals with chronic hepatitis C whose virus was subsequently eradicated by treatment were compared with samples from 13 nonresponders matched according to the major factors known to influence the response, i.e., sex, genotype, and pretreatment serum HCV RNA concentration. The degree of virus variation was assessed by analyzing 20 clones per sample and by calculating nucleotide sequence entropy (complexity) and genetic distances (diversity). Types of mutational changes were also determined by calculating nonsynonymous substitutions per nonsynonymous site (K(a)) and synonymous substitutions per synonymous site (K(s)). The paired-comparison analysis of the nucleotide sequence entropy and genetic distance showed no statistical differences between responders and nonresponders. By contrast, nonsynonymous substitutions were more frequent than synonymous substitutions (P </= 0.05) in responders, but there was no significant difference in nonresponders. Nonsynonymous substitutions tended to be more frequent than synonymous substitutions in women (P = 0.06) but not in men. Nucleotide entropy and genetic distances were significantly related to serum RNA concentration (P </= 0.01). Our findings suggest that after controlling for the major determinants of interferon response, neither complexity nor diversity of the HVR-1 region is associated per se with virus eradication. Because a higher proportion of nonsynonymous substitutions than synonymous substitutions was found only in responders, host anti-HCV-specific immune response rather than viral factors may be playing an important role in the interferon response.

Adult↗

PubMed1998

Conformational features of a peptide model Ac-DTVKLMYKGQPMTFR-NH2, corresponding to an early folding beta hairpin region of staphylococcal nuclease.

Recent H-D exchange 1H NMR studies of the refolding of Staphylococcal nuclease (P117G) variant suggest that, a region of the protein corresponding to a beta hairpin in the native structure folded early in the refolding process. In order to investigate whether the formation of beta hairpin is an early folding event, we investigated the conformational features of the beta hairpin peptide model Ac-DTVKLMYKGQPMTFR-NH2 from Staphylococcal nuclease with 1H NMR techniques. It appears that the peptide aggregates even at a low concentration. However, based on the observation of weak dnn(i, i + 1) NOEs between K8-G9, G9-Q10, an upfield shift of Gly9 NH and a low temperature coefficient (-d delta/dT) for Gly9 NH, we suggest that the sequence YKGQP as part of the beta hairpin peptide model samples conformational forms with reduced conformational entropy and turn potential. The presence of aggregation could be restricting the population of folded conformational forms and formation of beta hairpin at detectable concentrations. We suggest that, formation of beta hairpin could be an early event in the folding of Staphylococcal nuclease and this observation correlates with H-D exchange 1H NMR results and also with the prediction of a protein folding model proposed in literature.

Amino Acid Sequence↗

PubMed2006

Application of band-target entropy minimization to infrared emission spectroscopy and the reconstruction of pure component emissivities from thin films and liquid samples.

Thermal emission spectral data sets were collected for a thin solid film (parafilm) and a thin liquid film (isopropanol) on the interval of 298-348 K. The measurements were performed using a conventional Fourier transform infrared (FT-IR) spectrometer with external optical bench and in-house-designed emission cell. Both DTGS and MCT detectors were used. The data sets were analyzed with band-target entropy minimization (BTEM), which is a pure component spectral reconstruction program. Pure component emissivities of the parafilm, isopropanol, and thermal background were all recovered without any a priori information. Furthermore, the emissivities were obtained with increased signal-to-noise ratios, and the signals due to absorbance of thermal radiation by gas-phase moisture and CO2 were significantly reduced. As expected, the MCT results displayed better signal-to-noise ratios than the DTGS results, but the latter results were still rather impressive given the low temperatures used in this study. Comparison is made with spectral reconstruction using the orthogonal projection approach-alternating least squares (OPA-ALS) technique. This contribution introduces the primary equation for emission spectral reconstruction using BTEM and discusses some of the unusual characteristics of thermal emission and their impact on the analysis.

Algorithms↗

PubMed2026

Tissue-Level Transcriptomic Entropy Reveals Organ-Specific Aging Patterns and Predicts Cancer Progression.

Although aging and cancer share complex molecular mechanisms, distinguishing causative factors from byproducts remains challenging. Here, we investigated the role of tissue transcriptomic entropy-a measure of transcriptional disorder-in aging and cancer processes by analyzing RNA-sequencing data from over 25,000 samples from human and mouse tissues. We found that entropy changes during aging are highly tissue-specific, with some tissues showing increased entropy while others exhibit decreased or stable entropy levels. Moreover, transcriptomic entropy strongly correlates with age-related processes, showing positive associations with proliferation, cellular senescence, somatic mutation burden, and cellular reprogramming, whereas it negatively correlates with stemness. In cancer, we observed that primary tumors generally display higher entropy than normal tissue, with its levels further increasing in metastatic stages. Cancer treatment modulated entropy patterns in multiple contexts, with changes suggesting a role for transcriptional complexity in tumor plasticity and therapy resistance. Elevated entropy levels predicted poor survival outcomes in multiple cancer types, suggesting its potential as a prognostic marker. Furthermore, differential expression analysis revealed that entropy-associated genes are enriched in developmental processes and depleted in metabolic pathways, indicating a possible link to cellular dedifferentiation. Finally, we found increased entropy in various age-related disorders beyond cancer, suggesting that transcriptomic entropy may be a common feature in age-related diseases. Our findings establish transcriptomic entropy as a fundamental parameter in aging and cancer progression, offering new insights into disease mechanisms.

Humans↗

PubMed2006

Protein design simulations suggest that side-chain conformational entropy is not a strong determinant of amino acid environmental preferences.

Loss of side-chain conformational entropy is an important force opposing protein folding and the relative preferences of the amino acids for being buried or solvent exposed may be partially determined by which amino acids lose more side-chain entropy when placed in the core of a protein. To investigate these preferences, we have incorporated explicit modeling of side-chain entropy into the protein design algorithm, RosettaDesign. In the standard version of the program, the energy of a particular sequence for a fixed backbone depends only on the lowest energy side-chain conformations that can be identified for that sequence. In the new model, the free energy of a single amino acid sequence is calculated by evaluating the average energy and entropy of an ensemble of structures generated by Monte Carlo sampling of amino acid side-chain conformations. To evaluate the impact of including explicit side-chain entropy, sequences were designed for 110 native protein backbones with and without the entropy model. In general, the differences between the two sets of sequences are modest, with the largest changes being observed for the longer amino acids: methionine and arginine. Overall, the identity between the designed sequences and the native sequences does not increase with the addition of entropy, unlike what is observed when other key terms are added to the model (hydrogen bonding, Lennard-Jones energies, and solvation energies). These results suggest that side-chain conformational entropy has a relatively small role in determining the preferred amino acid at each residue position in a protein.

Amino Acid Sequence↗

PubMed1996

Enlarged scaling ranges for the KS-entropy and the information dimension.

Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample where these rates are uncomputable because of the lack of neighbours, yields improved entropy estimates. In the same way, the scaling range for estimates of the information dimension can be extended considerably. The improvement is demonstrated for experimental data. (c) 1996 American Institute of Physics.

Journal Article↗