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PubMed2003

Spectral pattern recognition of in situ FT-IR spectroscopic reaction data using minimization of entropy and spectral similarity (MESS): application to the homogeneous rhodium catalyzed hydroformylation of isoprene.

An improved algorithm using minimization of entropy and spectral similarity (MESS) was tested to recover pure component spectra from in situ experimental Fourier transform infrared (FT-IR) reaction spectral data, which were collected from a homogeneous rhodium catalyzed hydroformylation of isoprene. The experimental spectra are complicated and highly overlapping because of the presence of multiple intermediate products in this reaction system. The traditional entropy minimization method fails to resolve real reaction mixture spectra, but MESS can successfully reconstruct pure component spectra of unknown intermediate products for real reaction systems by the addition of minimization of spectral similarity. The quantitative measure of spectral similarity between two spectra was given by their inner products. The results indicate that MESS is a stable and useful algorithm for spectral pattern recognition of highly overlapped experimental reaction spectra. Comparison is also made between MESS, entropy minimization, simple-to-use interactive self-modeling mixture analysis (SIMPLISMA), interactive principle component analysis (IPCA), and orthogonal projection approach-alternating least squares (OPA-ALS).

Algorithms↗

PubMed1999

Estimates of the loss of main-chain conformational entropy of different residues on protein folding.

The average contribution of conformational entropy for individual amino acid residues towards the free energy of protein folding is not well understood. We have developed empirical scales for the loss of the main-chain (torsion angles, phi and psi) conformational entropy by taking its side-chain into account. The analysis shows that the main-chain component of the total conformational entropy loss for a residue is significant and reflects intrinsic characteristics associated with individual residues. The values have direct correlation with the hydrophobicity values and this has important bearing on the folding process. Proteins 1999;36:332-339.

Amino Acid Substitution↗

PubMed1992

Approximate entropy, a statistic of regularity, applied to fetal heart rate data before and during labor.

OBJECTIVE: To determine whether approximate entropy (ApEn), a new statistic of regularity, when applied to fetal heart rate (FHR) data antepartum or in labor, would offer an advantage over standard statistics of variation in predicting outcome. METHODS: A large data base of antepartum FHR records collected in clinical practice over 10 years was available. Two data sets in labor were stored on disk in small computers interfaced to fetal monitors on-line. Outcomes were assessed using blood gas values on delivery and Apgar scores. RESULTS: Antepartum, when the most favorable form of ApEn was used on 769 good-quality FHR records, the correlation with measurement of short-term variation was high. This was especially true when the fetal pulse interval variation fell below the normal range (less than 6 milliseconds short-term; r = 0.93) and in 20 other records with sinusoidal variation (r = 0.96). Approximate entropy varied with fetal sleep cycles and took longer to calculate than FHR variation. During the last hour of labor, in 319 records, there was no significant correlation between umbilical artery base deficit values on delivery and ApEn measurement. In 871 additional good-quality records of fetuses with normal outcome, the mean (+/- standard error [SE]) ApEn (0.95 +/- 0.005) was significantly greater than in 22 records (0.88 +/- 0.028) from fetuses with abnormal outcome (umbilical artery base deficit more than 12 mmol/L and Apgar score of 3 or less at 1 minute). However, consideration of the frequency distributions of these measurements showed that ApEn did not discriminate between normal and abnormal outcomes. The SD of fetal pulse intervals rose in labor whereas ApEn values fell, confirming that this new statistic of regularity differs from standard statistics of variation. CONCLUSION: Approximate entropy offered no advantage over measurement of short-term FHR variation antepartum, and neither measurement predicted outcome in labor.

Adult↗

PubMedDate not supplied

Recovery of postural control after cerebral concussion: new insights using approximate entropy.

CONTEXT: The return-to-play decision after sport-related cerebral concussion depends in part on knowing when an athlete has fully recovered postural control after injury. OBJECTIVE: To describe the postconcussion recovery of postural control using approximate entropy (ApEn), a regularity statistic from nonlinear dynamics. DESIGN: Retrospective case series analysis. SETTING: Sports medicine research laboratory. PATIENTS OR OTHER PARTICIPANTS: Collegiate athletes from whom center-of-pressure and symptom data were collected at preseason, less than 48 hours after injury, and 48 to 96 hours after injury. MAIN OUTCOME MEASURE(S): Approximate entropy values reflecting the amount of randomness contained in center-of-pressure oscillations were calculated for anterior-posterior (AP) and medial-lateral (ML) time series. Equilibrium scores reflecting the amplitude of center-of-pressure AP oscillations were used to indicate postural stability. The number and severity of symptoms were described. RESULTS: Compared with the healthy preseason state, ApEn values for the AP and ML time series generally declined immediately after injury in both steady and unsteady injured athletes. At 48 to 96 hours after injury, ApEn values for the ML time series remained significantly depressed (mean difference compared with preseason = -0.268, standard error = 0.072), even among athletes whose initial postural instability had resolved. We found few significant relationships between changes in ApEn values and changes in symptoms before and after injury. CONCLUSIONS: The effects of cerebral concussion on postural control appear to persist for longer than 3 to 4 days, even among athletes with no signs of unsteadiness. Our results may reflect changes in neurophysiologic or mechanical constraints on postural control. Approximate entropy provides a theoretically distinct, valuable measurement alternative that may prove useful for reducing uncertainty in the return-to-play decision.

Journal Article↗

PubMed1991

[Changes in the entropy of heart mass in dogs during inhalation of transuranic radionuclides].

Altogether 140 random-bred dogs of both sexes, aged 2 to 4 (body mass 14.5 +/- 0.1 kg) were examined. Age-related changes of heart mass entropy, resulting from disorder in the correlation of cardiac parts during aging, progress with age. During inhalation of acute, subacute and chronic effective amounts of nitrates of polymeric 239Pu and monomeric 241Am aerosol particles, measured in micron, dog heart mass entropy increases as compared to the age control, and during inhalation of transuranic radionuclides at small amounts, causing the animals' life prolongation, heart mass entropy decreases.

Administration, Inhalation↗

PubMed1983

[Clinical value of the study of cardiac rhythm entropy in patients with myocardial infarction].

Heart rhythm entropy was shown to decrease with age both in normal subjects and myocardial infarction patients. Yet in the latter it is smaller at all ages as compared to the former. It is also smaller in patients with severe course and unfavourable prognosis of myocardial infarction as compared to patients with favourable prognosis and uncomplicated course of the disease. In the course of infarction, heart rhythm entropy increases in cases with favourable prognosis, and remains small in those with unfavourable prognosis and severe clinical course. Rationed-exercise tests revealed a relationship between the prognosis of outcome, the severity of myocardial infarction and the magnitude of exercise-induced changes in heart rhythm entropy.

Adult↗

PubMed1980

Entropy and the contractile state.

Entropy production must accompany the utilization of free energy in any cellular process and is a measure of the degree of randomness or molecular disorder within a system. A highly entropized system approaches equilibrium, is incapable of performing work, and never unrandomizes spontaneously. Therefore, chemical reactions are reversible only if the entropy of the system can be reduced through the expenditure of free energy and at the expense of an increase in the entropy of the surroundings. This concept is discussed in terms of energy production and utilization by myocardial cells under normal and diseased states.

Animals↗

PubMed1977

Enthalpy-entropy compensation in dinitrophenyl--anti-dinitrophenyl antibody interaction(s).

The effect of varying the temperature over a wide range (-3 dergees -67 degrees) on the binding of xi-DNP-L-Lysine to bovine colostral anti-DNA IgG1, and also rabbit anti-DNP IgG revealed non-linear van't Hoff plots. The extent of the curvatures were found to be indicative of large positive heat capacity changes; and the thermodynamic parameters, calculated using a non-linear least-squares computer procedure for these anti-DNP antibody preparations, revealed an enthalpy-entropy compensation mechanism for hapten-antibody binding. The enthalpy factor was found to be the primary contributor for the binding process at low temperatures, but at increasing temperatures the entropy factor assumed greater importance. At physiological temperature (37 degrees), the entropy factor was the major contributor to the free energy of reaction for rabbit anti-DNP IgG, while for bovine colostral anti-DNP IgG it was predominant at temperatures higher than 37 degrees.

Animals↗

PubMed1998

Decreased Approximate Entropy of Heart Rate Variability in the Hypoxic Ovine Fetus

>Objective: Variability of the fetal heart rate (FHR) is used clinically to assess fetal well being. Approximate entropy (ApEn) is a statistic that quantifies the regularity of a time series. This study was designed to test whether ApEn changed in the FHR of the hypoxic ovine fetus.Methods: Five time-bred ewes at 130 days of gestation were surgically prepared with fetal arterial catheters, fetal electrodes, and a maternal common uterine artery snare occluder. After recovery, a continuous fetal electrocardiogram recording was started, and control blood gas measurements were made. The uterine blood flow was then reduced with the occluder, and blood gas measurements were repeated at fetal pH 7.20 and 7.00. The FHR tracing (1,000 beats) was extracted from the fetal electrocardiogram tracing at the time of each blood gas. For each heart rate tracing, the ApEn was calculated. The significance of changes was assessed using analysis of variance for repeated measures.Results: The snare occluder produced significant fetal hypoxia and acidosis. Although FHR variability was increased, approximate entropy was significantly decreased during periods of hypoxia in the ovine fetus.Conclusions: Approximate entropy of the ovine fetus is directly related to the degree of hypoxia. The decreased ApEn indicates increased regularity in the FHR during hypoxia in spite of the increased variability. ApEn may provide insight into the regulatory feedback mechanisms of the fetal heart rate during periods of hypoxia.

Journal Article↗

PubMed2026

Entropy-Driven Electrolyte Design for Lithium Metal Batteries: Achieving Interfacial Stability With Fluorinated Fullerene Nanoparticle Additives.

Lithium metal batteries are highly attractive for next-generation high-energy-density storage, and ether-based electrolytes such as LiFSI/DME are particularly promising for high-rate operation because of their low viscosity, high ionic conductivity, and favorable compatibility with Li metal. However, current electrolyte optimization strategies still rely mainly on small-molecule additives that regulate bulk solvation or the primary Li+ solvation sheath, whereas entropy-driven modulation of the interfacial solvation environment by large molecular additives remains largely unexplored. Herein, fluorinated fullerene C60F30 (FF) is introduced as a nanoparticle additive to create a dynamically disordered interface that enhances configurational entropy without sacrificing Li+ diffusivity, while accelerating Li+ desolvation and transport. Meanwhile, FF cooperates with FSI--derived species to build a robust fluorine-rich SEI, suppressing dendrite growth and parasitic reactions. As a result, Li||Li symmetric cells cycle stably for 1500 h, while high-loading Li||LiFePO4 cells retain 96.0% capacity after 500 cycles at 2C and 95.9% after 1000 cycles at 10C. Moreover, pouch cells and high-loading Li||NCM811 cells further verify the practical promise of the FF-enabled electrolyte for high-rate, long-cycling LMBs.

Li metal batteries↗

PubMed2007

Quantitative CARS spectroscopy using the maximum entropy method: the main lipid phase transition.

The maximum entropy method for phase retrieval of multiplex coherent anti-Stokes Raman scattering (CARS) spectra is described in detail and applied to the time-resolved measurement of the main lipid phase transition of small, unilamellar 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) vesicles subject to a 3 min temperature sweep. Since the--thus derived--imaginary part of the third-order CARS susceptibility can be directly related to the linear vibrational spectrum, the multiplex CARS spectral data can be analyzed quantitatively and without prior knowledge of the sample. It is shown that the maximum entropy model provides an exact description of the original data, including the noise, if all available autocorrelation functions are used. Our findings confirm the acyl-chain order-disorder phase-transition behavior of small, unilamellar lipid vesicles.

Computer Simulation↗

PubMed2002

Searching for quantitative entropy-enthalpy compensation among protein variants.

Entropy-enthalpy (SH) compensation occurs when a small change in DeltaG is caused by large, and nearly compensatory, changes in DeltaH and DeltaS. It is considered a ubiquitous property of reactions in water. Because water is intimately involved in protein stability, SH compensation among protein variants, if it exists, could lead to important knowledge about protein-water interactions. In light of recent theoretical work on SH compensation, we gathered thermodynamic data for >200 protein variants to seek evidence for the simplest quantitative model of SH compensation (i.e., The van't Hoff denaturation enthalpy divided by the van't Hoff denaturation entropy is a constant). We conclude that either the data are insufficient to support the idea that quantitative SH compensation is a general feature of variant proteins or that such compensation does not exist. This study reinforces the idea that DeltaH-versus-DeltaS plots should not be used to provide evidence for SH compensation.

Cytochrome c Group↗

PubMed2003

Identification of functionally conserved residues with the use of entropy-variability plots.

We introduce sequence entropy-variability plots as a method of analyzing families of protein sequences, and demonstrate this for three well-known sequence families: globins, ras-like proteins, and serine-proteases. The location of an aligned residue position in the entropy-variability plot correlates with structural characteristics, and with known facts about the roles of individual amino acids in the function of these proteins. The large numbers of known sequences in these families allowed us to introduce new filtering methods for variability patterns. The results are discussed in terms of a simple evolutionary model for functional proteins.

Algorithms↗

PubMed2004

A Shannon entropy-based filter detects high- quality profile-profile alignments in searches for remote homologues.

Detection of homologous proteins with low-sequence identity to a given target (remote homologues) is routinely performed with alignment algorithms that take advantage of sequence profile. In this article, we investigate the efficacy of different alignment procedures for the task at hand on a set of 185 protein pairs with similar structures but low-sequence similarity. Criteria based on the SCOP label detection and MaxSub scores are adopted to score the results. We investigate the efficacy of alignments based on sequence-sequence, sequence-profile, and profile-profile information. We confirm that with profile-profile alignments the results are better than with other procedures. In addition, we report, and this is novel, that the selection of the results of the profile-profile alignments can be improved by using Shannon entropy, indicating that this parameter is important to recognize good profile-profile alignments among a plethora of meaningless pairs. By this, we enhance the global search accuracy without losing sensitivity and filter out most of the erroneous alignments. We also show that when the entropy filtering is adopted, the quality of the resulting alignments is comparable to that computed for the target and template structures with CE, a structural alignment program.

Algorithms↗

PubMed2006

A two-entropies analysis to identify functional positions in the transmembrane region of class A G protein-coupled receptors.

Residues in the transmembrane region of G protein-coupled receptors (GPCRs) are important for ligand binding and activation, but the function of individual positions is poorly understood. Using a sequence alignment of class A GPCRs (grouped in subfamilies), we propose a so-called "two-entropies analysis" to determine the potential role of individual positions in the transmembrane region of class A GPCRs. In our approach, such positions appear scattered, while largely clustered according to their biological function. Our method appears superior when compared to other bioinformatics approaches, such as the evolutionary trace method, entropy-variability plot, and correlated mutation analysis, both qualitatively and quantitatively.

Amino Acid Sequence↗

PubMed1996

Dynamic contributions to the DNA binding entropy of the EcoRI and EcoRV restriction endonucleases.

Molecular Dynamics simulations on DNA-EcoRI and DNA-EcoRV complexes suggest that the DNA within these complexes is significantly more ordered than free DNA. Similarly, both the protein and the DNA are more ordered in the specific (cognate) DNA-EcoRV complex than they are in the non-cognate DNA-protein complex, consistent with recently proposed analogies between protein folding and sequence-specific DNA-protein recognition. Analysis of the trajectories shows that the net entropy gain upon specific binding to be the result of opposing contributions. Solvent release, which increases entropy versus configurational terms (as measured by the magnitude of the atomic fluctuations), and collective terms from tight coupling between the motions of the protein and the DNA.

Computer Simulation↗

PubMed1998

Backbone and methyl dynamics of the regulatory domain of troponin C: anisotropic rotational diffusion and contribution of conformational entropy to calcium affinity.

The N-terminal domain (residues 1 to 90) of chicken skeletal troponin C (NTnC) regulates muscle contraction upon the binding of a calcium ion to each of its two calcium binding loops. In order to characterize the backbone dynamics of NTnC in the apo state (NTnC-apo), we measured and carefully analyzed 15N NMR relaxation parameters T1, T2 and NOE at 1H NMR frequencies of 500 and 600 MHz. The overall rotational correlation time of NTnC-apo at 29.6 degrees C is 4.86 (+/-0.15) ns. The experimental data indicate that the rotational diffusion of NTnC-apo is anisotropic with a diffusion anisotropy, D parallel/D perpendicular, of 1.10. Additionally, the dynamic properties of side-chains having a methyl group were derived from 2H relaxation data of CH2D groups of a partially deuterated sample. Based on the dynamic characteristics of TnC, two different levels of "fine tuning" of the calcium affinity are presented. Significantly lower backbone order parameters (S2), were observed for calcium binding site I relative to site II and the contribution of the bond vector fluctuations to the conformational entropy of sites I and II was calculated. The conformational entropy loss due to calcium binding (DeltaDeltaSp) differs by 1 kcal/mol between sites I and II. This is consistent with the different dissociation constants previously measured for sites I and II of 16 microM and 1. 7 microM, respectively. In addition to the direct role of binding loop dynamics, the side-chain methyl group dynamics play an indirect role through the energetics of the calcium-induced structural change from a closed to an open state. Our results show that the side-chains which will be exposed upon calcium binding have reduced motion in the apo state, suggesting that conformational entropic contributions can be used to offset the free energy cost of exposing hydrophobic groups. It is clear from this work that a complete determination of their dynamic characteristics is necessary in order to fully understand how TnC and other proteins are fine tuned to appropriately carry out their function.

Animals↗

PubMed1997

Quantification of maximum-entropy spectrum reconstructions.

Maximum-entropy spectrum reconstruction derives much of its power from its nonlinearity. This nonlinearity causes difficulties in several contexts, however, including computation of multidimensional spectra and quantification of reconstructed spectra. We describe two methods for avoiding these difficulties: a "Constant-lambda" algorithm for performing row-wise reconstructions, which uses a fixed weighting of the entropy and the experimental constraint in the objective function, and in situ error analysis, for calibrating the nonlinearity. These methods are applied to data from quantitative J-correlation and relaxation experiments.

Algorithms↗