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PubMed2001

A physical origin for functional domain structure in nucleic acids as evidenced by cross-linking entropy: I.

A global strategy for estimating the entropy of long sequences of RNA is proposed to help improve the predictive capacity of RNA secondary structure dynamic programming algorithm (DPA) free energy (FE) minimization methods. These DPA strategies only consider the effects that occur in the immediate (nearest neighbor) vicinity of a given base pair (bp) in a secondary structure plot. They are therefore defined as nearest-neighbor secondary structure (NNSS) strategies. The new approach utilizes the statistical properties of the Gaussian polymer chain model to introduce both local and global contributions to the entropy of a given secondary structure. These entropic contributions are primarily a function of the persistence length of the RNA. Limits on the domain size are strongly suggested by this model and these limits are a function of both the length and the percentage of bp enclosed within a given domain. The model generalizes the penalties found in the NNSS algorithms. The approach considers the importance of flexibility in the folding and stability of RNA by considering the role of the persistence length in a biopolymer structure. The theory also suggests that molecular machinery may also take advantage of this global entropic effect to bring about catalytic effects. The applications can also be extended to protein structure calculations with some additional considerations.

Algorithms↗

PubMed2001

Expression, purification, and crystallization of the RGS-like domain from the Rho nucleotide exchange factor, PDZ-RhoGEF, using the surface entropy reduction approach.

Lsc-homology domains are found in several eukaryotic nucleotide exchange factors which act on Rho-family GTPases. They show limited amino acid sequence similarity to RGS proteins, which down-regulate the cellular signaling by the alpha-subunits of trimeric G-proteins and have been shown to interact with Galpha12 and Galpha13. It is believed that the RGS-like (RGSL) domain constitutes the functional link between G-protein-coupled receptors and cytosolic Rho-GTPases. We report here the expression, purification, and crystallization of the RGSL domain from the PDZ-RhoGEF. To obtain X-ray-grade crystals we have used the recently proposed approach of crystallization by mutational surface entropy reduction, in which selected Lys --> Ala, Glu --> Ala, and/or combined point mutations are introduced into the target protein to reduce the cumulative conformational entropy of surface residues. Of the five mutants that were designed and prepared, the second one tried (K463A, E465A, E466A) yielded crystals suitable for further analysis and diffracted X-rays to 2.8 A resolution on a home source. The crystals exhibit hexagonal symmetry, space group P6(1) 22 or P6(5) 22, with unit cell parameters a = b = 63.1 A, c = 202.1 A, and contain one molecule in the asymmetric unit.

Amino Acid Sequence↗

PubMed2000

Evaluation of renormalised entropy for risk stratification using heart rate variability data.

Standard time and frequency parameters of heart rate variability (HRV) describe only linear and periodic behaviour, whereas more complex relationships cannot be recognised. A method that may be capable of assessing more complex properties is the non-linear measure of 'renormalised entropy.' A new concept of the method, RE(AR), has been developed, based on a non-linear renormalisation of autoregressive spectral distributions. To test the hypothesis that renormalised entropy may improve the result of high-risk stratification after myocardial infarction, it is applied to a clinical pilot study (41 subjects) and to prospective data of the St George's Hospital post-infarction database (572 patients). The study shows that the new RE(AR) method is more reproducible and more stable in time than a previously introduced method (p<0.001). Moreover, the results of the study confirm the hypothesis that on average, the survivors have negative values of RE(AR) (-0.11+/-0.18), whereas the non-survivors have positive values (0.03+/-0.22, p<0.01). Further, the study shows that the combination of an HRV triangular index and RE(AR) leads to a better prediction of sudden arrhythmic death than standard measurements of HRV. In summary, the new RE(AR) method is an independent measure in HRV analysis that may be suitable for risk stratification in patients after myocardial infarction.

Electrocardiography↗

PubMed2002

Enthalpy-entropy compensation: a phantom phenomenon.

Enthalpy-entropy compensation is the name given to the correlation sometimes observed between the estimates of the enthalpy and entropy of a reaction obtained from temperature-dependence data. Although the mainly artefactual nature of this correlation has been known for many years, the subject enjoys periodical revivals, in part because of the frequent excellence of the correlation. As with other cases of impossibly good correlation between two biological variables, the explanation is that what purports to be two variables are very largely the same variable looked at in two different ways.

Animals↗

PubMed2003

Maximum-entropy decomposition of fluorescence correlation spectroscopy data: application to liposome-human serum albumin association.

Fluorescence correlation spectroscopy was used to measure the diffusion behavior of a mixture of DMPC or DMPC/DMPG liposomes with human serum albumin (HSA) and mesoporphyrin (MP), which was used as the fluorescent label for liposomes and HSA as well. For decomposing the fluorescence intensity autocorrelation function (ACF) into components corresponding to a liposome population, HSA and MP, we used a maximum entropy procedure that computes a distribution of diffusion times consistent with the ACF data. We found that a simple parametric non-linear fit with a discrete set of decay components did not converge to a stable parameter set. The distribution calculated with the maximum entropy method was stable and the average size of the particles calculated from the effective diffusion time was in good agreement with the data determined using the discrete-component fit.

Biophysical Phenomena↗

PubMed2006

A comparative scale of autonomic function with age through the tone-entropy analysis on heart period variation.

Tremendous numbers of heart rate variability studies have aimed to elucidate age-associated alterations of autonomic function in the past decades. However, the studies, far from clarifying ageing mechanisms, fell into confusion by a lack of common scales. The purpose of this study is to show a possibility to establish a comparative scale of autonomic function through a method, tone-entropy (T-E) analysis on heart period variation, whose validity has been already examined on typical physiological cases (Oida et al. in J Appl Physiol 82:1794-1801, 1997; Oida et al. in J Gerontol 54A:M219-M224, 1999a; Oida et al. in Acta Physiol Scand 165:129-134, 1999b; Oida et al. in Acta Physiol Scand 165:421-422, 1999c; Amano et al. in Eur J Appl Physiol 94:602-610, 2005). In this study, 276 subjects from teens to seventies were examined at rest by T-E analysis together with conventional time and frequency domain analyses. The tone (negativity represents vagal predominance) became significantly high [-0.174 +/- 0.026 (teens) to -0.024 +/- 0.004 (seventies), P < 0.05 for one-way ANOVA], and the entropy (total autonomic activity), significantly low [4.40 +/- 0.12 (teens) to 2.90 +/- 0.09 bit (seventies), P < 0.05] with advancing age. The result, plotted in 2-D T-E space, showed that the ageing traced a curvi-linear relation from right-bottom to left-top, and was consistent with previously studied typical physiological cases. The conventional analyses showed almost the same autonomic reduction as T-E did, but failed in detecting delicate alteration of autonomic balance. The results, showing that autonomic activity reduced in both pathways impairing vagal predominance significantly with ageing, suggested a possibility to assess autonomic function in 2-D T-E space in a comparative way.

Adolescent↗

PubMed2001

Normalized entropy applied to the analysis of interindividual and gender-related differences in the cardiovascular effects of stress.

Nonlinear dynamic methods are considered to be a potential tool for studying the complex behavior of the cardiovascular system. In the present study, interindividual and gender-related differences in cardiovascular (CV) responses to various stress stimuli were studied using conventional CV variables such as heart rate (HR) and blood pressure (BP), as well as a recently introduced criterion of system complexity, normalized entropy (E/H, where E is entropy and H is system energy). A group of healthy students (n = 270) of both genders (17-20 years of age) were subjected to noise exposure, mental arithmetic, arithmetic against noise and examination stress. Results showed that CV reactivity depended upon the kind of stress imposed and the gender of the subject. HR and BP stress-induced responses did not differ between men and women. However, men had higher absolute BP levels at baseline and during exposure to stressors. Stress-induced pressor responses lasted longer in men than in women. Changes in the complexity degree of CV signals, as assessed by E/H, were more pronounced and prolonged than those of HR and BP. Unlike the latter, E/H changed significantly in all stress situations for each subject tested and could be divided into two types of stress-induced response. These results allow one to conclude that E/H can better quantitate individual differences in CV stress reactivity in comparison with HR and BP. These findings suggest that stress-induced changes in CV functioning are more varied than can be revealed by applying conventional CV measures.

Adolescent↗

PubMed2005

Physical entropy and the senses.

With reference to two specific modalities of sensation, the taste of saltiness of chloride salts, and the loudness of steady tones, it is shown that the laws of sensation (logarithmic and power laws) are expressions of the entropy per mole of the stimulus. That is, the laws of sensation are linear functions of molar entropy. In partial verification of this hypothesis, we are able to derive an approximate value for the gas constant, a fundamental physical constant, directly from psychophysical measurements. The significance of our observation lies in the linking of the phenomenon of "sensation" directly to a physical measure. It suggests that if the laws of physics are universal, the laws of sensation and perception are similarly universal. It also connects the sensation of a simple, steady physical signal with the molecular structure of the signal: the greater the number of microstates or complexions of the stimulus signal, the greater the magnitude of the sensation (saltiness or loudness). The hypothesis is currently tested on two sensory modalities.

Entropy↗

PubMed2006

Response entropy is more reactive than bispectral index during laparoscopic gastric banding.

OBJECTIVE: There is a potential use for spectral entropy or bispectral index (BIS) for controlling level of anesthesia, but it is not known how these EEG monitors relate during steady state anesthesia. We compared Response Entropy (RE) and BIS during anesthesia for laparoscopic gastric banding with RE targeted to 45. METHODS: Forty patients undergoing laparoscopic gastric banding were randomly assigned to receive either fentanyl or dexmedetomidine infusion, with desflurane concentration adjusted to maintain RE at 45. During anesthesia the average RE and BIS was determined in each patient and the RE-BIS difference plotted as a function of RE every 10 seconds. Fifteen of 40 patients showed activation of RE above 60 during surgery. In these patients RE, BIS and the electromyogram (EMG) were evaluated for the period 10 minutes before and including the peak change in RE. RESULTS: In fentanyl and dexmedetomidine treated patients the average RE was 44-47 with no statistical difference between anesthesia groups or between RE and BIS. In each patient there was a linear relationship between the RE-BIS difference and RE during anesthesia. RE and BIS were similar at a level of 41-44 and RE showed a greater range at higher and lower values compared to BIS. When RE activation was identified during surgery in 15 patients, it was associated with an increase in BIS and EMG. CONCLUSION: Within the range of 41-44, RE and BIS are equal but the gain of RE is 0.5 greater than BIS with deeper or lighter anesthesia. This is not likely due to increased smoothing with BIS. Identifying periods of RE activation show that BIS, EMG and RE increase together.

Adult↗

PubMed2006

JEDA: Joint entropy diversity analysis. An information-theoretic method for choosing diverse and representative subsets from combinatorial libraries.

The joint entropy-based diversity analysis (JEDA) program is a new method of selecting representative subsets of compounds from combinatorial libraries. Similar to other cell-based diversity analyses, a set of chemical descriptors is used to partition the chemical space of a library of compounds; however, unlike other metrics for choosing a compound from each partition, a Shannon-entropy based scoring function implemented in a probabilistic search algorithm determines a representative subset of compounds. This approach enables the selection of compounds that are not only diverse but that also represent the densities of chemical space occupied by the original chemical library. Additionally, JEDA permits the user to define the size of the subset that the chemist wishes to create so that restrictions on time and chemical reagents can be considered. Subsets created from a chemical library by JEDA are compared to subsets obtained using other partition-based diversity analyses, namely principal components analysis and median partitioning, on a combinatorial library derived from the Comprehensive Medical Chemistry Dataset.

Chemistry, Pharmaceutical↗

PubMed2006

Permutation entropy improves fetal behavioural state classification based on heart rate analysis from biomagnetic recordings in near term fetuses.

The relevance of the complexity of fetal heart rate fluctuations with regard to the classification of fetal behavioural states has not been satisfyingly clarified so far. Because of the short behavioural states, the permutation entropy provides an advantageous complexity estimation leading to the Kullback-Leibler entropy (KLE). We test the hypothesis that parameters derived from KLE can improve the classification of fetal behaviour states based on classical heart rate fluctuation parameters (SDNN, RMSSD, ln(LF), ln(HF)). From measured heartbeat sequences (35 healthy fetuses at a gestational age between 35 and 40 completed weeks) representative intervals of 256 heartbeats were visually preclassified into fetal behavioural states. Employing discriminant analysis to separate the states 1F, 2F and 4F, the best classification result by classical parameters was 80.0% (SDNN). After additionally considering KLE parameters it was improved significantly (p<0.0005) to 94.3% (ln(LF), KLE_Mean). It could be confirmed that KLE can improve the state classification. This might reflect the consideration of different physiological aspects by classical and complexity measures.

Cardiotocography↗

PubMed2003

Microvascular structural entropy: a novel approach to assess angiogenesis in pituitary tumors.

Entropy, a measure of the degree of disorder in a system, has recently been used in different morphologic studies to quantify regularity. Our aims were (a) to study the structural organization of the microvascular bed in prolactin (PRL)-producing adenomas and carcinomas, the most vascularized of pituitary tumors, by assessing microvascular structural entropy (MSE), and (b) to determine whether the degree of disorder of the capillary bed correlates with tumor cell proliferation as estimated by MIB-1 labeling, microvessel density (MVD), the most widely used method of quantifying blood vessel formation, and various clinicopathologic parameters (gender, age, tumor size and invasiveness). The morphometric study demonstrated statistically significant differences in MIB-1 labeling, MVD, and MSE between PRL-producing adenomas and carcinomas. Unlike MIB-1 labeling index (PRL-producing adenomas 1.5 +/- 0.27; carcinomas 15.0 +/- 4.04) and MVD (PRL-producing adenomas 2.7 +/- 0.34; carcinomas 4.2 +/- 0.72), the MSE values were significantly higher in adenomas (171.5 +/- 25.37) than in carcinomas (67.9 +/- 17.45). These results indicate that PRL-producing carcinomas have a less chaotic distribution of vessels than benign adenomas. In contrast to a lack of correlation between microvessel density and other morphometric parameters, a strong negative correlation was found between MSE and MIB-1 labeling index (r = 0.511, p = 0.003). It thus appears that regular, less chaotic microvascular geometry contributes to increased proliferative activity in PRL cell tumors. Analysis of MSE may provide an independent parameter of tumor behavior, and contributes to a better understanding of the role of microvasculature in pituitary tumor progression.

Adenoma↗

PubMed1995

Win some, lose some: enthalpy-entropy compensation in weak intermolecular interactions.

Enthalpy-entropy compensation is a general feature of many chemical reactions and processes in biological systems, but its origin has remained obscure. A simple thermodynamic argument suggests that enthalpy-entropy compensation is a general property of weak intermolecular interactions, and that the two contributions to the free energy should nearly balance out for a hydrogen bond at 300 K.

Biochemical Phenomena↗

PubMed2006

[Is entropy a monitor for the guidance of intraoperative analgesia?].

OBJECTIVE: Comparison between BIS (Bispectral Index) and state (SE) and response (RE) entropy during laparotomy for inflammatory bowel disease patients (IBD) and evaluation of the variations of RE and SE during nociceptive stimulation. STUDY DESIGN: Prospective, observational study. PATIENTS AND METHODS: Fourteen IBD's patients undergoing laparotomy were included. Anaesthesia aimed to maintain BIS between 40 and 60 by isoflurane and nitrous oxide. Analgesia was performed by sufentanil bolus administrated according to an increase of 20% of systolic blood pressure (SBP) and heart rate compared with the baseline values. BIS, RE and SE were measured at each nociceptive stimulation. A variance analysis (Anova) was used to assess BIS, RE and SE variations throughout surgery (p<0.05 as significant). Relationship between BIS, RE and SE was assessed by Pearson correlation (p<0.01 as significant). The ability for SE and RE to predict depth of anaesthesia and intraoperative analgesia was performed by calculating area under the receiver operated curves (AUC). RESULTS: BIS and entropy parameters had strictly the same evolution during anaesthesia. SBP increased significantly during nociceptive stimulation while no variation of RE was observed. A significant correlation was shown between BIS, RE and SE. The evaluation of anaesthesia depth was good for RE (AUC: 0.932+/-0.26) and SE (AUC: 0.926+/-0.27). There was however no difference between RE and SE to predict analgesic requirement. CONCLUSION: Because RE includes muscular frequency analysis, it does not allow analgesic requirement evaluation in paralyzed patients.

Adult↗

PubMed2005

Entropy-assisted stacking of thylakoid membranes.

Chloroplasts in plants and some green algae contain a continuous thylakoid membrane system that is structurally differentiated into stacked granal membranes interconnected by unstacked thylakoids, the stromal lamellae. Experiments were conducted to test the hypothesis that the thermodynamic tendency to increase entropy in chloroplasts contributes to thylakoid stacking to form grana. We show that the addition of bovine serum albumin or dextran, two very different water-soluble macromolecules, to a suspension of envelope-free chloroplasts with initially unstacked thylakoids induced thylakoid stacking. This novel restacking of thylakoids occurred spontaneously, accompanied by lateral segregation of PSII from PSI, thereby mimicking the natural situation. We suggest that such granal formation, induced by the macromolecules, is partly explained as a means of generating more volume for the diffusion of macromolecules in a crowded stromal environment, i.e., greater entropy overall. This mechanism may be relevant in vivo where the stroma has a very high concentration of enzymes of carbon metabolism, and where high metabolic fluxes are required.

Buffers↗

PubMed2006

Fear induced complexity loss in the electrocardiogram of flight phobics: a multiscale entropy analysis.

In this study we explored the changes in the variability and complexity of the electrocardiogram (ECG) of flight phobics (N=61) and a matched non-phobic control group (N=58) when they performed a paced breathing task and were exposed to flight related stimuli. Lower complexity/entropy values were expected in phobics as compared to controls. The phobic system complexity as well as the heart rate variability (HRV) were expected to be reduced by the exposure to fearful stimuli. The multiscale entropy (MSE) analysis revealed lower entropy values in phobics during paced breathing and exposure, and a complexity loss was observed in phobics during exposure to threatening situations. The expected HRV decreases were not found in this study. The discussion is focused on the distinction between variability and complexity measures of the cardiac output, and on the usefulness of the MSE analysis in the field of anxiety disorders.

Adult↗

PubMed2026

Quantifying the peripheral surface information entropy from conformational ensembles of globular protein-peptide complexes.

Predicting favorable protein-peptide binding events remains a central challenge in biophysics, with continued uncertainty surrounding how nonlocal effects shape the global energy landscape. Here, we introduce peripheral surface information entropy, SΨ, a quantitative measure of the statistical variability in apolar and charged non-interacting surface (NIS) proportions across conformational ensembles. Within the Gibbs free-energy relation ΔG = ΔH - TΔS, SΨ is proposed as a computationally tractable entropic proxy rather than a direct thermodynamic observable or stand-alone estimator of binding affinity. Using energy-directed molecular docking via HADDOCK3 and explicit-solvent molecular dynamics simulations, it is demonstrated that favorable binding partners exhibit emergent, low-entropy N-states (discrete macrostates in NIS state space) indicative of preferential apolar/charged surface configurations. Across dozens of peptides and multiple receptor systems (WW, PDZ, and MDM2 domains), dominant N-states persisted under varied docking parameters and initial conditions. A meta-ensemble of 657 complexes from 36 experiments over 15 years confirmed the presence of dominant NIS modes independent of in silico methodology, suggesting an evolutionary selection pressure toward specific NIS fingerprints. These findings establish SΨ as a thermoinformatic descriptor that encodes favorable binding constraints into unique statistical signatures of the NIS.

Entropy↗

PubMed2006

Time distribution of adsorption entropy of gases on heterogeneous surfaces by reversed-flow gas chromatography.

The reversed-flow gas chromatography (RF-GC) technique has been applied to measure the adsorption entropy over time, when gaseous pentane is adsorbed on the surface of two solids (gamma-alumina and a silica supported rhodium catalyst) at 393.15 and 413.15K, respectively. Utilizing experimental chromatographic data, this novel methodology also permits the simultaneous measurement of the local adsorption energy, epsilon, local equilibrium adsorbed concentration, c(s)(*), and local adsorption isotherm, theta(p, T, epsilon) in a time resolved way. In contrast with other inverse gas chromatographic methods, which determine the standard entropy at zero surface coverage, the present method operates over a wide range of surface coverage taking into account not only the adsorbate-adsorbent interaction, but also the adsorbate-adsorbate interaction. One of the most interesting observations of the present work is the fact that the interaction of n-pentane is spontaneous on the Rh/SiO(2) catalyst for a very short time interval compared to that on gamma-Al(2)O(3). This can explain the different kinetic behavior of each particular gas-solid system, and it can be attributed to the fact that large amounts of n-C(5)H(12) are present on the active sites of the Rh/SiO(2) catalyst compared to those on gamma-Al(2)O(3), as the local equilibrium adsorbed concentration values, c(s)(*), indicate.

Adsorption↗