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PubMed2002

Solvent entropy contribution to the free energy of protein crystallization.

We show with three proteins that trapping and release of the water molecules upon crystallization is a determinant of the crystallization thermodynamics. With HbC, a strong retrograde solubility dependence on temperature yields a high positive enthalpy of 155 kJ mol(-1), i.e., crystallization is only possible because of the huge entropy gain of 610 J mol(-1) x K(-1), stemming from the release of up to 10 water molecules per protein intermolecular contact. With apoferritin, the enthalpy of crystallization is close to zero. The main component in the crystallization driving force is the entropy gain due to the release upon crystallization of two water molecules bound to one protein molecules in solution. With both proteins, the density of the growth sites imaged by AFM is in excellent agreement with a calculation using the crystallization free energy. With lysozyme, the entropy effect due to the restructuring of the water molecules is negative. This leads to higher solubility.

Animals↗

PubMed2006

A robust method for estimating respiratory flow using tracheal sounds entropy.

The relationship between respiratory sounds and flow is of great interest for researchers and physicians due to its diagnostic potentials. Due to difficulties and inaccuracy of most of the flow measurement techniques, several researchers have attempted to estimate flow from respiratory sounds. However, all of the proposed methods heavily depend on the availability of different rates of flow for calibrating the model, which makes their use limited by a large degree. In this paper, a robust and novel method for estimating flow using entropy of the band pass filtered tracheal sounds is proposed. The proposed method is novel in terms of being independent of the flow rate chosen for calibration; it requires only one breath for calibration and can estimate any flow rate even out of the range of calibration flow. After removing the effects of heart sounds (which distort the low-frequency components of tracheal sounds) on the calculated entropy of the tracheal sounds, the performance of the method at different frequency ranges were investigated. Also, the performance of the proposed method was tested using 6 different segment sizes for entropy calculation and the best segment sizes during inspiration and expiration were found. The method was tested on data of 10 healthy subjects at five different flow rates. The overall estimation error was found to be 8.3 +/- 2.8% and 9.6 +/- 2.8% for inspiration and expiration phases, respectively.

Adult↗

PubMed2004

Entropy-based kernel mixture modeling for topographic map formation.

A new information-theoretic learning algorithm for kernel-based topographic map formation is introduced. In the one-dimensional case, the algorithm is aimed at uniformizing the cumulative distribution of the kernel mixture densities by maximizing its differential entropy. A nonparametric differential entropy estimator is used on which normalized gradient ascent is performed. Both differentiable and nondifferentiable kernels are in principle supported, such as Gaussian and rectangular (on/off) kernels. The relation is shown with joint entropy maximization of the kernel outputs. The learning algorithm's performance is assessed and compared with the theoretically optimal performance. A fixed-point rule is derived for the case of heterogeneous kernel mixtures. Finally, an extension of the algorithm to the multidimensional case is suggested.

Algorithms↗

PubMed2007

Skin conductance or entropy for detection of non-noxious stimulation during different clinical levels of sedation.

BACKGROUND: State entropy (SE) measures electroencephalographic signals, whereas response entropy (RE) also includes frontal electromyographic activity. In the presence of electromyographic activity, the RE index is larger than the SE index, the difference being denoted as RE-Delta (RE-Delta= RE - SE). Skin conductance (SC) may be expressed by a slow reacting variable, the mean SC level, the derivate of the mean SC level (D-SC), the number of SC fluctuations (NSCF) or the amplitude of the SC fluctuations (ASCF), which directly shows skin sympathetic nerve activity. The goal of this study was to evaluate whether these SC and entropy variables could differentiate between the responses obtained to load sound stimuli at different sedation levels before the induction of general anaesthesia. METHODS: Twenty women scheduled for gynaecological laparotomy were studied. The modified observer's assessment of alertness sedation (OAAS) was used to classify the patients' hypnotic levels. White sounds (98 dB) were given at OAAS level 5 without propofol, at OAAS levels 4-3 and 3-2 with propofol and at OAAS levels 3-2 and < 2 with propofol and remifentanil. RESULTS: RE and SE showed a steady decline from OAAS level 5 to level < 2 (P < 0.01). RE-Delta did not discriminate between any of the OAAS levels (P= NS). The mean SC level discriminated between OAAS levels 4-3 to < 2 (P < 0.01). D-SC discriminated between all the different OAAS levels (P < 0.01). NSCF discriminated between OAAS levels 5 to 3-2 (P < 0.05), but did not discriminate at OAAS level 3-2 between propofol alone or combined with remifentanil, or between OAAS level 3-2 and < 2. ASCF differentiated between OAAS levels 5 and 4 (P < 0.001) and OAAS levels 3-2 and < 2 (P < 0.05) only. CONCLUSION: RE, SE and D-SC showed a similar discrimination between sound responses at the different sedation levels.

Acoustic Stimulation↗

PubMed2001

A maximum-entropy method for the planning of conformal radiotherapy.

The maximum entropy method (MEM) is a powerful inverse analysis technique that is used in many fields of science and engineering to perform tasks such as image reconstruction and processing of nuclear magnetic resonance signals. Unlike other methods, MEM naturally incorporates a priori knowledge of the problem into the optimized cost function. This feature is especially important in radiotherapy planning, because some knowledge is usually available about the stage of tumor development and about the prescription doses, including some dose constraints to the surrounding normal organs. Inverse planning is inherently consistent with the ability of MEM to estimate parameters inversely. In this investigation, an entropy function determines the homogeneity of dose distribution in the planning target volume; a least-squares function is added to the maximum entropy function as a constraint to measure the quality of reconstructed doses in organs at risk; and an iterative Newton-Ralphson algorithm searches for the optimization solution. Here we provide two examples that validate this application of MEM and the results were compared with manual plans. Although the examples involve conformal radiotherapy, we think MEM can be adopted to optimize intensity-modulated radiation therapy.

Algorithms↗

PubMed2006

Information entropy of humpback whale songs.

The structure of humpback whale (Megaptera novaeangliae) songs was examined using information theory techniques. The song is an ordered sequence of individual sound elements separated by gaps of silence. Song samples were converted into sequences of discrete symbols by both human and automated classifiers. This paper analyzes the song structure in these symbol sequences using information entropy estimators and autocorrelation estimators. Both parametric and nonparametric entropy estimators are applied to the symbol sequences representing the songs. The results provide quantitative evidence consistent with the hierarchical structure proposed for these songs by Payne and McVay [Science 173, 587-597 (1971)]. Specifically, this analysis demonstrates that: (1) There is a strong structural constraint, or syntax, in the generation of the songs, and (2) the structural constraints exhibit periodicities with periods of 6-8 and 180-400 units. This implies that no empirical Markov model is capable of representing the songs' structure. The results are robust to the choice of either human or automated song-to-symbol classifiers. In addition, the entropy estimates indicate that the maximum amount of information that could be communicated by the sequence of sounds made is less than 1 bit per second.

Acoustics↗

PubMed2000

Entropies of short binary sequences in heart period dynamics.

Dynamic aspects of R-R intervals have often been analyzed by means of linear and nonlinear measures. The goal of this study was to analyze binary sequences, in which only the dynamic information is retained, by means of two different aspects of regularity. R-R interval sequences derived from 24-h electrocardiogram (ECG) recordings of 118 healthy subjects were converted to symbolic binary sequences that coded the beat-to-beat increase or decrease in the R-R interval. Shannon entropy was used to quantify the occurrence of short binary patterns (length N = 5) in binary sequences derived from 10-min intervals. The regularity of the short binary patterns was analyzed on the basis of approximate entropy (ApEn). ApEn had a linear dependence on mean R-R interval length, with increasing irregularity occurring at longer R-R interval length. Shannon entropy of the same sequences showed that the increase in irregularity is accompanied by a decrease in occurrence of some patterns. Taken together, these data indicate that irregular binary patterns are more probable when the mean R-R interval increases. The use of surrogate data confirmed a nonlinear component in the binary sequence. Analysis of two consecutive 24-h ECG recordings for each subject demonstrated good intraindividual reproducibility of the results. In conclusion, quantification of binary sequences derived from ECG recordings reveals properties that cannot be found using the full information of R-R interval sequences.

Electrocardiography, Ambulatory↗

PubMed1997

Tone-entropy analysis on cardiac recovery after dynamic exercise.

Autonomic controls on heart rate variability have been investigated; however, sympathovagal interactive modulations remain unexplored. The purpose of this study is to present a new method, tone-entropy analysis (T-E analysis) of heart period fluctuations, and to make clear an intensive cooperation of autonomic networks in heart recovery. On the basis of evidence obtained in animal experiments, we hypothesized that heart periods are lengthened or shortened beat to beat by assumed physiological mediators: accelerator and inhibitor. Their operations were evaluated through a normalized successive variation of the period, that is, the percentage index (PI). The process was described through PI distributions by using two indexes, tone and entropy, standard values of which were obtained through pharmacological autonomic blockade experiment. T-E analysis was applied to heart recovery (70 min) after dynamic exercise by 12 female athletes. Interactive autonomic modulations were expressed by a curved path in tone-entropy space. Results suggested that heart rate decay proceeds not by withdrawal of one pathway but by increasing activity of both pathways as vagosympathetic balance inclines slightly but significantly to the vagus division in the course of recovery. The process was examined through Fourier spectral analysis as well.

Adult↗

PubMed2004

Estimating the entropy rate of spike trains via Lempel-Ziv complexity.

Normalized Lempel-Ziv complexity, which measures the generation rate of new patterns along a digital sequence, is closely related to such important source properties as entropy and compression ratio, but, in contrast to these, it is a property of individual sequences. In this article, we propose to exploit this concept to estimate (or, at least, to bound from below) the entropy of neural discharges (spike trains). The main advantages of this method include fast convergence of the estimator (as supported by numerical simulation) and the fact that there is no need to know the probability law of the process generating the signal. Furthermore, we present numerical and experimental comparisons of the new method against the standard method based on word frequencies, providing evidence that this new approach is an alternative entropy estimator for binned spike trains.

Action Potentials↗

PubMed2005

Estimating entropy rates with Bayesian confidence intervals.

The entropy rate quantifies the amount of uncertainty or disorder produced by any dynamical system. In a spiking neuron, this uncertainty translates into the amount of information potentially encoded and thus the subject of intense theoretical and experimental investigation. Estimating this quantity in observed, experimental data is difficult and requires a judicious selection of probabilistic models, balancing between two opposing biases. We use a model weighting principle originally developed for lossless data compression, following the minimum description length principle. This weighting yields a direct estimator of the entropy rate, which, compared to existing methods, exhibits significantly less bias and converges faster in simulation. With Monte Carlo techinques, we estimate a Bayesian confidence interval for the entropy rate. In related work, we apply these ideas to estimate the information rates between sensory stimuli and neural responses in experimental data (Shlens, Kennel, Abarbanel, & Chichilnisky, in preparation).

Bayes Theorem↗

PubMed2005

Detection of nuclei in 4D Nomarski DIC microscope images of early Caenorhabditis elegans embryos using local image entropy and object tracking.

BACKGROUND: The ability to detect nuclei in embryos is essential for studying the development of multicellular organisms. A system of automated nuclear detection has already been tested on a set of four-dimensional (4D) Nomarski differential interference contrast (DIC) microscope images of Caenorhabditis elegans embryos. However, the system needed laborious hand-tuning of its parameters every time a new image set was used. It could not detect nuclei in the process of cell division, and could detect nuclei only from the two- to eight-cell stages. RESULTS: We developed a system that automates the detection of nuclei in a set of 4D DIC microscope images of C. elegans embryos. Local image entropy is used to produce regions of the images that have the image texture of the nucleus. From these regions, those that actually detect nuclei are manually selected at the first and last time points of the image set, and an object-tracking algorithm then selects regions that detect nuclei in between the first and last time points. The use of local image entropy makes the system applicable to multiple image sets without the need to change its parameter values. The use of an object-tracking algorithm enables the system to detect nuclei in the process of cell division. The system detected nuclei with high sensitivity and specificity from the one- to 24-cell stages. CONCLUSION: A combination of local image entropy and an object-tracking algorithm enabled highly objective and productive detection of nuclei in a set of 4D DIC microscope images of C. elegans embryos. The system will facilitate genomic and computational analyses of C. elegans embryos.

Algorithms↗

PubMed2006

Incorporating background frequency improves entropy-based residue conservation measures.

BACKGROUND: Several entropy-based methods have been developed for scoring sequence conservation in protein multiple sequence alignments. High scoring amino acid positions may correlate with structurally or functionally important residues. However, amino acid background frequencies are usually not taken into account in these entropy-based scoring schemes. RESULTS: We demonstrate that using a relative entropy measure that incorporates amino acid background frequency results in improved performance in identifying functional sites from protein multiple sequence alignments. CONCLUSION: Our results suggest that the application of appropriate background frequency information may lead to more biologically relevant results in many areas of bioinformatics.

Amino Acid Sequence↗

PubMed2000

Short-term fasting selectively suppresses leptin pulse mass and 24-hour rhythmic leptin release in healthy midluteal phase women without disturbing leptin pulse frequency or its entropy control (pattern orderliness).

Nutritional signals strongly regulate neuroendocrine axes, such as those subserving release of LH, GH, and TSH, presumptively in part via the adipocyte-derived neuroactive peptide leptin. In turn, leptin release is controlled by both acute (fasting) and long-term (adipose store) nutrient status. Here, we investigate the neuroendocrine impact of short-term (2.5-day) fasting on leptin release in healthy young women studied in the steroid-replete midluteal phase of the normal menstrual cycle. Eight women each underwent 24-h blood sampling at 10-min intervals during a randomly ordered 2.5-day fasting vs. fed session in separate menstrual cycles. Pulsatile leptin release was quantified by model-free Cluster analysis, the orderliness of leptin patterns by the approximate entropy statistic, and nyctohemeral leptin rhythmicity by cosinor analysis. Mean (24-h) serum leptin concentrations fell by 4.6-fold during fasting; namely, from 15.2+/-2.3 to 3.4+/-0.6 microg/L (P = 0.0007). Cluster analysis identified 13.9+/-1.1 and 14.3+/-1.1 leptin peaks per 24 h in the fed and fasting states (P = NS), and unchanging leptin interpeak intervals (89+/-5.4 vs. 92+/-5.3 min). Leptin peak area declined by 4.2-fold (155+/-21 vs. 37+/-7 area units, P = 0.004), due to a reduction in incremental leptin pulse amplitude (4.4+/-0.7 vs. 1.0+/-0.13 microg/L, P = 0.0011). The cosine amplitude and mesor (mean) of the 24-h leptin rhythm decreased by 4-fold, whereas the acrophase (timing of the nyctohemeral leptin peak) remained fixed. The approximate entropy of leptin release was stable, thus indicating preserved orderliness of leptin release patterns in fasting. Cross-correlation analysis revealed both positive (fed) and negative (fasting) leptin-GH relationships, but no leptin-LH correlations. In summary, short-term (2.5-day) fasting profoundly suppresses 24-h serum leptin concentrations and pulsatile leptin release in the sex steroid-sufficient midluteal phase of healthy women via mechanisms that selectively attenuate leptin pulse area and incremental amplitude. In contrast, the pulse-generating, nyctohemeral phase-determining, and entropy-control mechanisms that govern 24-h leptin release are not altered by acute nutrient restriction at this menstrual phase. Leptin-GH (but not leptin-LH) showed nutrient-dependent positive (fed) and negative (fasting) cross-correlations. Whether similar neuroendocrine mechanisms supervise altered leptin signaling during short-term nutrient restriction in men, children, or postmenopausal women is not known.

Adult↗

PubMed2002

[Approximate entropy of anesthesia EEG: compromise between calculation time and clinical validity].

Approximate entropy, a measure of regularity, can be used to analyze the electroencephalogram of patients in general anesthesia to discriminate between different states of consciousness. EEG burst suppression patterns reflect a state of deep anesthesia. Due to the instationary character of this EEG pattern approximate entropy values do not correctly classify the patient state. Possible solutions to this problem may be limited by the demand of computing power for entropy calculation and the reaction time following changes in patient state. Different approaches for an online monitoring application are examined.

Algorithms↗

PubMed2006

Dihedral-angle information entropy as a gauge of secondary structure propensity.

Protein structural information can be uncovered using an information-theory-based entropy and auxiliary functions by taking advantage of high-quality correlation plots between the dihedral angles around a residue and those between sequential residues. A standard information entropy for a primary sequence has been defined using the values of the probabilities of the most likely dihedral angles along the sequence. The distribution of entropy differences relative to the standard for each protein in a reference set--a sublibrary of the Protein Data Bank at the 90% sequence redundancy level--appears to be nearly Gaussian. It gives rise to an auxiliary checking function whose value signals the extent to which the dihedral angle propensities differ from typical structures. Such deviations can arise either because of incorrect dihedral angle assignments or secondary structural propensities that are atypical of the structures in the reference set. This auxiliary checking function can be readily calculated at the public website, (http://www.d2check.gatech.edu). Its utility is demonstrated here in an analysis displaying differences between experimentally and theoretically derived structures, and in the analysis of structures derived by homology modeling. A comparison of the new measure, D(2)Check, to other checking functions based on backbone conformation-namely, PROCHECK and WHAT_CHECK--is also provided.

Algorithms↗

PubMedDate not supplied

Entropy changes drive the electron transfer reaction of triplet flavin mononucleotide from aromatic amino acids in cation-organized aqueous media. A laser-induced optoacoustic study.

The thermodynamic parameters for the formation of the free radicals upon electron transfer quenching of the flavin triplet state (3FMN) by tryptophan and tyrosine, Delta(FR)H and Delta(FR)V, were obtained in aqueous solution by the application of laser-induced optoacoustic spectroscopy at various temperatures. The Delta(FR)H and Delta(FR)V values include the electron transfer and charge separation steps plus the protonation of the FMN anion radical and the deprotonation of the amino-acid cation radical. A linear correlation was found between the Delta(FR)H and Delta(FR)V values for each of the amino acids in phosphate buffers of [CH3(CH2)3]4N+, Li+, NH4+, K+ and Cs+. The compensation between Delta(FR)H and Delta(FR)V within the salt series, and the independent evaluation of the Gibbs energy for electron transfer Delta(ET)G(o) afforded the entropy change, Delta(FR)S, for the reaction, different for the two amino acids. The values of Delta(FR)H, Delta(FR)V and Delta(FR)S in each buffer are mainly determined by the changes in strength and probably number of hydrogen bonds between the reacting partners and water produced along all steps leading to the radicals FMNH* and A*. The Delta(FR)V values linearly correlate with the tabulated entropy of organization of the water structure for the five cations, DeltaS(o)(cat). The entropy change upon formation of the free radicals, Delta(FR)S, quantitatively correlated to the Delta(FR)V value, drives the separation of the ion pair after the electron transfer reaction in the case of highly organizing cations. The ratio X = T Delta(FR)S/Delta(FR)V = (55 +/- 9) kJ cm(-3) for Trp as 3FMN quencher is smaller than X = (83 +/- 9) kJ cm(-3) for Tyr as quencher. These values are discussed in conjunction with the Marcus reorganization energy, as calculated from the Gibbs activation energy of the electron transfer process, which is independent of the salt present but different for each of the two quenchers.

Cations↗

PubMed2001

Entropy and variability discrimination.

Two experiments examined college students' discrimination of complex visual displays that involved different degrees of variability or "entropy." Displays depicted 16 black and white line drawings of various types (e.g., a brain, a clock, a hand); the participants were required to classify a display in terms of its variability (e.g., a low-variability display contains many identical items, whereas a high-variability display contains few identical items). The participants' accuracy and reaction time scores on a 2-alternative forced-choice discrimination disclosed that people can and do use entropy to classify different levels of visual display variability. Individuals differed in their use of absolute rather than relative entropy.

Adult↗

PubMed2003

[Application of power spectral entropy to the noninvasive detection of focal ischemic cerebral injury].

A model of SD rat focal ischemic cerebral injury is presented for use in noninvasively detecting both the extent and the location of focal ischemic cerebral injury. EEG signals of ischemic region and normal region are recorded from the moment before ischemia to 30 minutes after ischemia. Then the Power Spectral Entropy(PSE) analysis of EEG is performed. Results show that the PSE of EEG signals changes greatly as a result of focal ischemic cerebral injury. The PSE of EEG signal of ischemic region is less than that before ischemia as the ischemia lasts 15 minutes. The PSE of EEG signals of ischemic region is much less than that of normal region. These indicate that the power spectral entropy of EEG signal is a good index of focal ischemic cerebral injury and the method of power spectral entropy analysis is simple and effective.

Animals↗