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At least 19 recordsLinked to original sources
PubMed2005

Recovery from paralysis with succinylcholine increased Response entropy and EMG but not State entropy.

OBJECTIVE: It is reported that the electromyogram is an indicator of patient arousal during pain stimulation if anesthesia is inadequate. This may not be true during recovery from succinylcholine induced paralysis. We evaluated State entropy of the electroencephalogram (EEG, 0.8-32 Hz) and Response entropy, a combined measure of the electromyogram (EMG) and EEG (0.8-47 Hz), during recovery from paralysis with succinylcholine. METHODS: Twenty patients were randomized to receive either 0.8% (n = 10) or 1.4% isoflurane (n = 10), with 2 mg/kg succinylcholine administered for paralysis in all patients. State entropy and Response entropy were evaluated using a Datex-Ohmeda Entropy module. Frontal EMG was measured separately by an EEG module. State entropy, Response entropy, and EMG were measured in awake patients, during isoflurane anesthesia and paralysis, and after 100% recovery to train of four stimulation. RESULTS: Response entropy and State entropy decreased from awake levels in a dose related manner during 0.8% or 1.4% isoflurane and succinylcholine. Recovery from succinylcholine significantly increased Response entropy and EMG in 5 of 10 patients with 0.8% isoflurane and 8 of 10 with 1.4% isoflurane without a change in State entropy. CONCLUSION: Although RE and EMG increased during recovery from paralysis with succinylcholine, SE, an indicator of EEG, was not stimulated. EMG activity may not be an indicator of patient arousal after succinylcholine treatment.

Anesthetics, Inhalation↗
PubMed1989

Entropy flow and entropy production in the human body in basal conditions.

Entropy inflow and outflow for the naked human body in basal conditions in the respiration calorimeter due to infrared radiation, convection, evaporation of water and mass-flow are calculated by use of the energetic data obtained by Hardy & Du Bois. Also, the change of entropy content in the body is estimated. The entropy production in the human body is obtained as the change of entropy content minus the net entropy flow into the body. The entropy production thus calculated becomes positive. The magnitude of entropy production per effective radiating surface area does not show any significant variation with subjects. The entropy production is nearly constant at the calorimeter temperatures of 26-32 degrees C; the average in this temperature range is 0.172 J m-2 sec-1 K-1. The forced air currents around the human body and also clothing have almost no effect in changing the entropy production. Thus, the entropy production of the naked human body in basal conditions does not depend on its environmental factors.

Body Temperature Regulation↗
PubMed2002

Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: a basis for q-exponential distributions.

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.

Journal Article↗
PubMed2006

Temporal extensivity of Tsallis' entropy and the bound on entropy production rate.

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis entropy indexed by q is temporally extensive: linear growth in time, i.e., finite entropy production rate. Then, the universal bound on the entropy production rate is shown to be 1/ absolute value (1-q). The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.

Journal Article↗
PubMed2002

Entropy calculations on the molten globule state of a protein: side-chain entropies of alpha-lactalbumin.

We present entropy estimates based on molecular dynamics simulations of models of the molten globule state of the protein alpha-lactalbumin at low pH. The entropy calculations use the covariance matrix of atom-positional fluctuations and yield the complete configurational entropy. The configurational entropy of the entire protein and of each of its side chains is calculated. Exposed side chains show a larger entropy compared to buried side chains. A comparison to data from rotamer counting is made and significant differences are found.

Entropy↗
PubMed2000

Physiological time-series analysis using approximate entropy and sample entropy.

Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.

Entropy↗
PubMed1992

Structural fluctuations and conformational entropy in proteins: entropy balance in an intramolecular reaction in methemoglobin.

The reversible intramolecular binding of the distal histidine side chain to the heme iron in methemoglobin is of special interest due to the very large negative reaction entropy which overcompensates the large reaction enthalpy. It may be considered as a prominent example of the ability of proteins (including enzymes) to provide global entropy in a local process. In this work new experiments and model calculations are reported which aim at finding the structural elements contributing to the reaction entropy. Geometrical studies prove the implication of the 20 residue E-helix being shifted by more than 2 A. Vibrational entropies are calculated by a procedure derived from the method of Karplus and Kushik. It turns out that neither the histidine alone nor the complete E-helix contribute more than 15 per cent of the required entropy.

Amino Acid Sequence↗
PubMed2002

Nonequilibrium stochastic processes: time dependence of entropy flux and entropy production.

Based on the Fokker-Planck and the entropy balance equations we have studied the relaxation of a dissipative dynamical system driven by external Ornstein-Uhlenbeck noise processes in the absence and presence of nonequilibrium constraint in terms of the thermodynamically inspired quantities such as entropy flux and entropy production. The interplay of nonequilibrium constraint, dissipation, and noise reveals some interesting extremal nature in the time dependence of entropy flux and entropy production.

Journal Article↗
PubMed1994

Entropy in biological binding processes: estimation of translational entropy loss.

The loss of translational degrees of freedom makes an important, unfavorable contribution to the free energy of binding. Examination of experimental values suggest that calculation of this entropy using the Sackur-Tetrode equation produces largely overestimated values. Better agreement is obtained using the cratic entropy. Theoretical considerations suggest that the volumes available for the movement of a ligand in solution and in a complex are rather similar, suggesting also that the cratic entropy provides the best estimate of the loss of translational entropy.

Angiotensin II↗
PubMed2003

Structural information in two-dimensional patterns: entropy convergence and excess entropy.

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.

Journal Article↗
PubMed1994

[DNA and MST entropy and current of entropy. New parameters of tumor biological characterization].

The clinical significance of the entropy of the integrated optical density E (IOD) and the corresponding entropiefluss EF (IOD) is discussed as well as the structural entropy E (MST) and its entropiefluss EF (MST). The E (IOD) is based upon the formula given by Stenkvist and Strande. It describes the statistical entropy of the DNA distribution of tumor cell nuclei; the E (MST) is based upon differences in IOD and distance between neighboring tumor cell nuclei and describes the deviation of tumor structure from a "biological constant" structure. The entropiefluss measures the current of entropy or irreversibly created heat which has to be removed through the surface of the tumor. It is a universally valid description of a thermodynamically open system and measures the distance of such a system from its equilibrium stage. The clinical significance of these parameters is tested on 241 specimens of human lung carcinomas and intrapulmonary metastases of extrapulmonary malignancies. The surgical specimens were fixed with buffered formalin. Histological sections cut from paraffin-embedded tissue were FEULGEN stained. The nuclei of the histomorphological images were segmented using an automated image analyzing system, and the attributed minimum spanning trees (MST) were calculated. The following results were obtained: The measured E (IOD) and E (MST) showed significant differences in the primary carcinomas compared to those measured in intrapulmonary lymph node metastases or intrapulmonary metastases. The survival of patients was remarkably improved if the carcinomas displayed a low E (MST), EF (IOD), and EF (MST).

Adenocarcinoma↗
PubMed2001

Entropy, entropy rate, and pattern classification as tools to typify complexity in short heart period variability series.

An integrated approach to the complexity analysis of short heart period variability series (approximately 300 cardiac beats) is proposed and applied to healthy subjects during the sympathetic activation induced by head-up tilt and during the driving action produced by controlled respiration (10, 15, and 20 breaths/min, CR10, CR15, and CR20 respectively). The approach relies on: 1) the calculation of Shannon entropy (SE) of the distribution of patterns lasting three beats; 2) the calculation of a regularity index based on an entropy rate (i.e., the conditional entropy); 3) the classification of frequent deterministic patterns (FDPs) lasting three beats. A redundancy reduction criterion is proposed to group FDPs in four categories according to the number and type or of heart period changes: a) no variation (0V); b) one variation (1V); and c) two like variations (2LV); 4) two unlike variations (2UV). We found that: 1) the SE decreased during tilt due to the increased percentage of missing patterns; 2) the regularity index increased during tilt and CR10 as patterns followed each other according to a more repetitive scheme; and 3) during CR10, SE and regularity index were not redundant as the regularity index significantly decreased while SE remained unchanged. Concerning pattern analysis we found that: a) at rest mainly three classes (0V, 1V, and 2LV) were detected; b) 0V patterns were more likely during tilt; c) 1V and 2LV patterns were more frequent during CR10; and d) 2UV patterns were more likely during CR20. The proposed approach based on quantification of complexity allows a full characterization of heart period dynamics and the identification of experimental conditions known to differently perturb cardiovascular regulation.

Analysis of Variance↗
PubMed2004

Entropy calculation of HIV-1 Env gp120, its receptor CD4, and their complex: an analysis of configurational entropy changes upon complexation.

The HIV-1 gp120/CD4 interaction shows a large, unprecedented entropy/enthalpy compensation, with the capacity to fine-tune recognition over a broad range of affinity. The intermolecular interaction involves stable hydrophobic contacts with a unique protruding CD4-Phe43 structure surrounded by an intermolecular hydrogen-bond network that covers the hemisphere of the CD4 D1 domain. We have applied a heuristic formula based on the covariance matrix of atom-positional fluctuations to assess the configurational entropy of the gp120/CD4 complex at different levels. The system was dissected into various subsets of atoms to evaluate the entropic contributions of different functional elements. By combining the trajectories of the free and complex forms, further insight into the conformational sampling was extracted. Despite the limited sampling time of 10 ns, the theoretically derived changes in configurational entropy are in fair agreement with the experimentally determined data. The simultaneous evaluation of different interaction modes through a decomposition approach is only feasible with the knowledge of the atomic trajectory of the system. The configurational entropy analysis in terms of combined trajectories presented here shall potentially provide accurate estimations of thermodynamic properties of biomolecules given sufficient sampling of conformational space.

Biophysics↗
PubMed1996

Two-dimensional distributions of activation enthalpy and entropy from kinetics by the maximum entropy method.

The maximum entropy method (MEM) is used to numerically invert the kinetics of ligand rebinding at low temperatures to obtain the underlying two-dimensional distribution of activation enthalpies and entropies, g(H,S). A global analysis of the rebinding of carbon monoxide (CO) to myoglobin (Mb), monitored in the Soret band at temperatures from 60 to 150 K, is performed using a Newton-Raphson optimization algorithm. The MEM approach describes the data much better than traditional least-squares analyses, reducing chi 2 by an order of magnitude. The MEM resolves two barrier distributions suggestive of rebinding to different bound conformations of MbCO, the so-called A1 and A3 substates, whose activation barriers have been independently estimated from kinetics monitored in the infrared. The distribution corresponding to A3 possesses higher activation entropies, also consistent with infrared measurements. Within an A substate, correlations of S and H are recovered qualitatively from simulated data but can be difficult to obtain from experimental data. When the rebinding measured at 60 K is excluded from the inversion, two peaks are no longer clearly resolved. Thus, data of very high quality are required to unambiguously determine the kinetic resolvability of subpopulations and the shape of the barrier distribution for a single A substate.

Algorithms↗
PubMed1996

Persistent confusion of total entropy and chemical system entropy in chemical thermodynamics.

The change in free energy with temperature at constant pressure of a chemical reaction is determined by the sum (dS) of changes in entropy of the system of reagents, dS(i), and the additional entropy change of the surroundings, dS(H), that results from the enthalpy change, W. A faulty identification of the total entropy change on reaction with dS(i) has been responsible for the attribution of general validity to the expressions (d deltaG/dT)p = -deltaS(i) and d(deltaG/T)/d(1/T)= deltaH, which are found in most textbooks and in innumerable papers.

Kinetics↗
PubMed2002

Average entropy of a subsystem from its average Tsallis entropy.

In the non-extensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem [Phys. Rev. Lett. 71, 1291 (1993)] as well as its demonstration are generalized, i.e., when a pure quantum system, whose Hilbert space dimension is mn, is considered, the average Tsallis entropy of an m-dimensional subsystem is obtained. This demonstration is expected to be useful to study systems where the usual entropy does not give satisfactory results.

Journal Article↗
PubMed1975

Thermodynamical studies of oxygen equilibrium of hemoglobin. Nonuniform heats and entropy changes for the individual oxygenation steps and enthalpy-entropy compensation.

Precise oxygen equilibrium curves of human adult hemoglobin were determined by the automatic recording method at several temperatures in the presence and absence of 2,3-diphosphoglycerate (DPG) or inositol hexaphosphate (IHP) with 0.05 M 2,2-bis(hydroxymethyl)-2,2',2''-nitrolotriethanol (bis-tris) buffers (pH 7.4) containing 0.1 M Cl-. The equilibrium data were analyzed according to the Adair scheme, and the heats, deltaHi (i = 1,2,3,4) and the entropy changes, deltaSi (i = 1,2,3,4), for the individual oxygenation steps were obtained. The shape of the equilibrium curve varies on temperature changes whether DPG or IHP is present or absent. In consequence, the deltaHi value depends on i and on the presence of DPG and IHP. Behavior of deltaSi is similar to that of deltaHi. The similar behavior of deltaHi and deltaSi resulted in a compensation phenomenon. The contribution of T cdeltaSi to the free energy change is compensated by the contribution of deltaHi at the first three oxygenation steps but not at the fourth step, and for i = 1,2, and 3 changes of T cdeltaSi value upon the addition of DPG and IHP are compensated by accompanied changes of deltaHi value, where T c (= 260 K) is the compensation temperature. A major part of both the enthalpy-entropy compensation and nonuniformity of deltaHi and deltaSi appears to be attributable to contributions of the oxygen-linked binding of Cl-, DPG and IHP, by hemoglobin. The present results do not necessarily support the earlier idea of Wyman that the cooperative oxygenbinding is essentially an entropy effect.

Adult↗
PubMed2005

Maximum entropy deconvolution of infrared spectra: use of a novel entropy expression without sign restriction.

Absorbance and difference infrared spectra are often acquired aiming to characterize protein structure and structural changes of proteins upon ligand binding, as well as for many other chemical and biochemical studies. Their analysis requires as a first step the identification of the component bands (number, position, and area) and as a second step their assignment. The first step of the analysis is challenged by the habitually strong band overlap in infrared spectra. Therefore, it is useful to make use of a mathematical method able to narrow the component bands to the extent to eliminate, or at least reduce, the band overlap. Additionally, to be of general applicability this method should permit negative values for the solution. We present a maximum entropy deconvolution approach for the band-narrowing of absorbance and difference spectra showing the required characteristics, which uses the generalized negative Burg-entropy (Itakura-Saito discrepancy) generalized for difference spectra. We present results on synthetic noisy absorbance and difference spectra, as well as on experimental infrared spectra from the membrane protein bacteriorhodopsin.

Algorithms↗