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[Change in entropy of the free polypeptide chain during formation of hydrogen bonds].

Formation probabilities of different hydrogen bonds between carbonyl oxygen and amide hydrogen were determined by Monte Carlo simulations using a computer model in the space of sterically allowable conformations of alanine and glycine oligopeptides, and the corresponding entropy losses for the peptide backbone, T delta S, were calculated. The model was studied at different criteria of steric interactions. Comparison with the data of other authors showed the values of T delta S to be mainly determined by overall extent and type of the state space and to be only slightly dependent on its energy profile. Both short-range and long-range steric interactions were shown to prevent hydrogen bonding, especially in alanine peptides. In the model studied, the initiation of alpha(R)-helices is associated with T delta S = 8-10 kT, and prior formation of a 3/10-turn or one three-center H-bond does not appreciably decrease this entropy barrier. Elongation of the alpha(R)-helix by one residue leads to T delta S = 3.0-3.7 kT, the helices begin to stabilize after at least three sequential H-bonds are formed. The difference in the probability of insertion of Ala and Gly into the helix is lower than it follows from comparison of their mobility. The results could be explained assuming that factors different from helical H-bonds take part in the stabilization of the helices. One may suppose upon modeling of folding that even three sequential H-bonds are unable to fix the structure of a flexible peptide loop, while the elongation of alpha(R)-helices in the supersecondary helix-loop-helix structure is favorable as long as the loop conformation remains nearly optimal.

Computer Simulation↗

Forecasting of life threatening arrhythmias using the compression entropy of heart rate.

OBJECTIVES: Ventricular tachycardia (VT) provoking sudden cardiac death (SCD) are a major cause of mortality in the developed countries. The most efficient therapy for SCD prevention are implantable cardioverter defibrillators (ICD). In this study heart rate variability (HRV) measures were analyzed for short-term forecasting of VT in order to improve VT sensing and to enable a patient warning of forth-coming shocks. METHODS: The last 1000 normal beat-to-beat intervals before 50 VT episodes stored by the ICD were analyzed and compared to individually acquired control time series (CON). HRV analysis was performed with standard parameters of time and frequency domain as suggested by the HRV Task Force and furthermore with a newly developed and optimized nonlinear parameter that assesses the compression entropy of heart rate (Hc). RESULTS: Except of meanNN (p = 0.02) we found no significant differences in standard HRV parameters. In contrast, Hc revealed highly significant (p = 0.007) alterations in VT compared with CON suggesting a decreased complexity before the onset of VT. CONCLUSION: Compression entropy might be a suitable parameter for short-term forecasting of life-threatening tachycardia in ICD.

Arrhythmias, Cardiac↗

[The use of enthalpy-entropy compensation in the study of retention mechanism of aromatic positional isomers].

In this paper, the thermodynamic parameters of the separation process of six groups of aromatic positional isomers on nine crown ether polysiloxane, OV-1701 and Carbowax-20M capillary chromatographic columns have been investigated systematically. The Gibbs free energies for every compound at harmonic mean temperature, calculated were given. The enthalpy-entropy compensation effect of these chromatographic process was examined by using of Krug's ANOVA method. In the light of the axiom of extrathermodynamic relationship, the retention mechanisms of these aromatic compounds on each crown ether stationary phase have been expounded. We come to conclusion that, as a whole, the separation of various aromatic isomers on crown ether stationary phase is governed by multiple retention mechanisms, but the separation of some groups of aromatic isomer on the same crown ether phase can be led to single interaction mechanism since the phenomena of enthalpy-entropy compensation is observed. It may be that a kind of interaction parameter, which varies with the configuration of solutes, plays the main role in retention process of these isomers.

English Abstract↗

[Inverse iterative correction for translational motion artifact of magnetic resonance imaging based on histogram entropy minimization].

During the acquisition of a magnetic resonance images (MRI), blurring and ghosting artifacts caused by the patient's motion can seriously affect the result of diagnosis. A novel automatic post-processing strategy, inverse iterative correction (IIC), has been developed to suppress MRI artifacts due to the object's in-plane rigid-body motion. By means of the proposed histogram-based entropy function, IIC method uses two successive steps to reduce the simulated motion artifacts: first, the inverse phase errors are added to all possible simulated patient's motion directions, and in the second step, the actual directions and displacement from the patient's motion are estimated to properly correct the phase, hence remove the artifacts after searching all the trial directions. To verify its feasibility, the proposed method was used to reduce rigid-motion artifacts due to simulated motion in MRI images. The experimental results showed that the new algorithm significantly outperforms over the entropy auto-focus compensation algorithm on the quality of corrections for the motion artifacts and computational cost.

Algorithms↗

A soft decision algorithm for obstructive sleep apnea patient classification based on fast estimation of wavelet entropy of RRI data.

A soft decision algorithm for Obstructive Sleep Apnea (OSA) patient classification using R-R interval (RRI) data is investigated. This algorithm is based on fast and approximate estimation of the entropy of the wavelet-decomposed bands of the RRI data. The classification is done on the whole record as OSA patient or non-patient (normal). The ratio of the estimated entropy of the low-frequency (LF) band to that of the very-low frequency (VLF) band is used as a classification factor. RRI data used in this work are drawn from MIT database. The MIT trial records are used to set the threshold value of the classification factor using the Receiver Operating Characteristics (ROC). This threshold value is used then to classify the MIT challenge (test) records to obtain the efficiency of classification. The new algorithm classifies correctly 30/30 of MIT-test data using different wavelet filters. Comparison of the results of different wavelet filters is done in terms of complexity and distance parameters. The method is also compared with other two techniques using wavelets in their analysis. The consistency of the results is examined using the leave-one-out technique.

Adult↗

[Analysis of HRV from brain injury by use of nonextensive relative entropy].

Due to its great clinical significance, brain injury following cardiac arrest (CA) has attracted more attention now. Meanwhile, there are currently no approved real time objective methods used to monitor brain injury following CA. In this study, we adopt the method of nonextensive Kullback-Leibler Entropy in investigating the HRV signals from brain injury and compare the result with that of corresponding EEG analysis. The comparative analysis shows that Kullback-Leibler Entropy can reveal the injury level of brain following CA. And we propose a novel quantitative approach for monitoring brain injury.

Algorithms↗

[Quantitative relationship between molecular structure of polychlorinated biphenyls (PCBs) and enthalpy change (deltaH), entropy change (deltaS') in chromatographic process].

The relationship between the rule of chromatographic retention value and molecular structure is an important part in the research of chromatographic thermodynamics. The topological index structural parameter JG and the topological index adjoining parameter LJ are put forward. Parameter J(G) describes the correlation of quantity and position of chlorine atoms in polychlorinated biphenyl (PCB) molecules. Parameter L(J) describes the ortho-position correlation of chlorine atoms in PCB molecules. The relational expression between the PCB molecular structures and their enthalpy change (deltaH), entropy change (deltaS') in chromatographic process was discovered. The values of enthalpy change and entropy change for about 140 kinds of polychlorinated biphenyls in chromatographic process on three stationary phases, DB-1, DB-5 and DB-1701, were determined. In comparison with deltaH and deltaS' of the experimental data those calculated from the relational expression had the average relative deviations for deltaH and deltaS' are 0.56% -0.97% and 0.55% - 1.06%, respectively.

Chromatography↗

[Application of entropy weight and fuzzy synthetic evaluation in urban ecological security assessment].

Ecological security is one of the foundations of regional security, and the basis of sustainable development. Urban ecological security refers to the ecological support and main ecological issues of a city, which do not threaten its survival and development. To develop the research method on the ecological security of urban social-economic-natural complex ecosystem, an assessment indicator system of urban ecological security was set up based on Pressure - State - Response Model, which included 3 key factors and 33 concrete items. The five most developed cities of China were taken as the cases to assess their ecological security situation by using entropy weight and fuzzy synthetic evaluation method. The results showed that the urban ecological security of Suzhou and Beijing was at relatively safe level, while that of Shenzhen, Shanghai and Guangzhou was critical safe in the year of 2003. The urban ecosystem of Shenzhen was under heavy press, while that of Suzhou behaved best both in system status and system response. Comparing with other assessment methods, this evaluation method was easier and more reasonable. The results were basically consistent to the fact of these cities, suggesting that the urban ecological security indicator system and the entropy weight and fuzzy synthetic evaluation approach were feasible to some extent.

Ecology↗

Entropy as an algorithm for the statistical description of DNA cytometric data obtained by image analysis microscopy.

In an effort to obtain an additional statistical descriptor of DNA histograms we analysed a concept from mathematical information theory, called entropy, which describes the information content of histograms irrespective of parametric or non-parametric distributions. For this study, 32 fine-needle biopsies were analysed. It seems that the entropy of the DNA histogram is an extremely useful descriptor for the separation of distributions obtained from malignant tumours when compared with non-malignant lesions or normal controls.

Algorithms↗

Phosphorylation of solubilized sarcoplasmic reticulum by orthophosphate and its thermodynamic characteristics. The dominant role of entropy in the phosphorylation.

A large fraction of the Ca-2plus- and Mg-2plus-dependent ATPase (EC 3.6.1.3) in sarcoplasmic reticulum membranes solubilized with Triton X-100 was phosphorylated with Pi. The phosphorylation required Mg-2plus but was strongly inhibited by low concentrations of Ca-2plus. A Ca-2plus ion concentration of 30 muM caused half-maximum inhibition in the presence of 50 mM MgCl2. The phosphorylated enzyme showed a rapid turnover and was in dynamic equilibrium with Pi in the medium. At equilibrium the amount of the phosphorylated enzyme increased markedly with increased in the reaction temperature. The apparent standard free energy change, the apparent standard enthalpy change, and the apparent standard entropy change in the formation of the phosphorylated enzyme from the enzyme-phosphate complex in the presence of excess Mg-2plus at 37 degrees and pH 7.0 were, respectively, 0.35 Cal per mol, 15.9 Cal per mol, and 50.2 e.u. per mol. The susceptibility of the acid-denatured phosphorylated enzyme to hydroxylamine showed that the phosphorylated enzyme is of an acyl phosphate type. The present results are consistent with the probability that the phosphorylation results from reversal of late steps in the Ca-2plus transport process. The results clearly show that the phosphorylated enzyme is stabilized by a great increase in entropy upon its formation from the enzyme-phosphate complex.

Adenosine Triphosphatases↗

Maximum entropy methods in dark field electron micrographs and elemental maps.

A maximum entropy algorithm is described which not only fits a model to the data consistent with the size of the noise and the maximum entropy principle but also distributes the residuals between the data and the model in a way consistent with the noise in the data having been generated by a random gaussian process. The results of applying the algorithm to profiles of electron micrographs, electron micrographs and model data is presented. The algorithm is found to achieve various degrees of signal to noise ratio enhancement. Preliminary results show that the spatial resolution is not suppressed. A biassing artifact is described.

Algorithms↗

Assembly of collagen fibrils de novo by cleavage of the type I pC-collagen with procollagen C-proteinase. Assay of critical concentration demonstrates that collagen self-assembly is a classical example of an entropy-driven process.

Type I procollagen was purified from the medium of cultured human fibroblasts incubated with 14C-labeled amino acids, the NH2-terminal propeptides were cleaved with procollagen N-proteinase, and the resulting pC-collagen was isolated by gel filtration chromatography. pC-collagen did not assemble into fibrils or large aggregates even at concentrations of 0.5 mg.ml-1 at 34 degrees C in a physiological buffer. However, cleavage of pC-collagen to collagen with purified C-proteinase (Hojima, Y., (1985) J. Biol. Chem. 260, 15996-16003) generated fibrils that were visible by eye and that were large enough to be separated from solution by centrifugation at 13,000 x g for 4 min. With high concentrations of enzyme, the pC-collagen was completely cleaved in 1 h, and turbidity was near maximal in 3 h, but collagen continued to be incorporated in fibrils for over 10 h. Because the pC-collagen was uniformly labeled with 14C-aminoacids, the concentration of soluble collagen and, therefore, the critical concentration of polymerization were determined directly. The critical concentration was independent of the initial pC-collagen concentration and of the rate of cleavage. The critical concentration decreased with temperature between 29 and 41 degrees C and was 0.12 +/- 0.06 (S.E.) microgram.ml-1 at 41 degrees C. The thermodynamic parameters of assembly were essentially independent of temperature in the range 29 to 41 degrees C. The process was endothermic with a delta H value of +56 kcal.mol-1, but entropy driven with a delta S value of +220 cal.K-1.mol-1. The Gibbs energy change for polymerization was -13 kcal.mol-1 at 37 degrees C. The data demonstrate, for the first time, that type I collagen fibril formation de novo is a classical example of an entropy-driven self-assembly process similar to the polymerization of actin, flagella, and tobacco mosaic virus protein.

Amino Acids↗

[Radiation entropy and its role in the process of photosynthesis].

The paper deals with the following problems: 1) radiation entropy and the value of maximum performance coefficient of photosynthesizing systems eta m; 2) problem of physical meaning of eta m and on its association with real processes in photosynthesis. It has been shown that for calculating entropy of nonequilibrium radiation its origin should be known and that the value eta m does not practically limit the processes which proceed in photosynthesis.

Mathematics↗

Entropy in the hierarchical cluster analysis of hospitals.

A new technique integrating concepts from cluster analysis and information theory was applied to the classification of Michigan hospitals. First, a number of cost-related variables that describe the hospitals and their surroundings were used in a cluster analysis to produce a hierarchy of classifications. Then for each classification, the within-group entropy was computed for each group of hospitals and averaged over the classification. Finally, this average entropy was used as an aid to judgment in deciding which of the many classifications in the hierarchy yields the most reasonable groupings of hospitals.

Blue Cross Blue Shield Insurance Plans↗

Coupling thermodynamics applied in chemical morphogenesis; influence of environmentally organized space-time structures upon nonequilibrium entropy functions of multivariate biosystems.

In this paper is proposed the so-called coupling thermodynamics which deals with coupled variables or elementary units which are influenced by input-output relations. In contrast to the usual definition of nonequilibrium entropy, external influences are considered directly in the entropy function dependent on space and time. The employment in morphology leads to a model of organized growth.

Biomedical Engineering↗

Maximum entropy weighting of aligned sequences of proteins or DNA.

In a family of proteins or other biological sequences like DNA the various subfamilies are often very unevenly represented. For this reason a scheme for assigning weights to each sequence can greatly improve performance at tasks such as database searching with profiles or other consensus models based on multiple alignments. A new weighting scheme for this type of database search is proposed. In a statistical description of the searching problem it is derived from the maximum entropy principle. It can be proved that, in a certain sense, it corrects for uneven representation. It is shown that finding the maximum entropy weights is an easy optimization problem for which standard techniques are applicable.

Amino Acid Sequence↗

Integrated optical density and entropiefluss (current of entropy) in bronchial carcinoma.

Histological sections of formalin-fixed, paraffin-embedded bronchial carcinomas comprising 241 surgical specimens (lobes and lungs) were Feulgen stained. The integrated optical density of the nuclei (IOD) and the minimum distance between their centers of gravity (DG) was measured with an automated image analyzing system consisting of a TV camera connected to a personal computer via a frame grapper. Intratumorous lymphocytes served as DNA standard (2C peak), and 300 nuclei were measured at minimum. The entropy of the IOD, the percentage of S-phases (PS) of tumor cells with an IOD > 3C and > 5C, and the 2CV mean standard deviation were measured. According the theory of thermodynamically open systems, the entropiefluss (current of entropy) was defined by the gradient IOD/time through the surface of the tumors which can be approximated by the formula IOD*PS*DG/tumor volume. The following results were obtained: a) IOD of bronchial carcinoma is not associated with tumor size or lymph node infiltration (pT and pN stage). b) The minimum distance between tumor cells decreases with increasing tumor stage and increasing lymph node stage (pT, pN stage). c) The entropiefluss is low in limited and advanced tumor stages, and highest in tumors at moderately progressive tumor stages (pT2, pT3, pN1, pN2). Thus, in accordance with the theory of thermodynamically open systems, the entropiefluss reflects the "biological activity" of bronchial carcinoma.

Bronchial Neoplasms↗

A calorimetric study of Ca2+ binding by wheat germ calmodulin. Regulatory steps driven by entropy.

A hypothesis has been proposed for Ca(2+)-binding proteins that a regulatory Ca2+ binding step is endothermic and is driven solely by entropy in the absence of Mg2+ (Imaizumi, M., Tanokura, M., and Yamada, K. (1987) J. Biol. Chem. 262, 7963-7966). To confirm this idea, microcalorimetric titrations of wheat germ calmodulin, with Ca2+ in the presence and absence of Mg2+ and with Mg2+ in the absence of Ca2+, have been carried out at 25 degrees C and at pH 7.0. The results indicate that the four binding sites in each molecule are thermodynamically equivalent to one another for both Ca2+ and Mg2+ binding and that the reaction is endothermic for Ca2+ binding in the absence of Mg2+. As compared with bovine brain calmodulin on Ca2+ binding in the absence of Mg2+, Ca2+ binding in both proteins is driven solely by a large favorable entropy change despite unfavorable enthalpy change. Therefore, the above idea seems plausible.

Calcium↗