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PubMed2006

Temperature dependence of the Kováts retention index. The entropy index.

According to a novel equation, the temperature dependence of the Kováts retention index, dI/dT is proportional to the difference of the Kováts retention index, I, and the new entropy index, I(S), defined similarly as the retention index, but based on solvation entropy instead of the free energy of solvations. The new relationship was tested with the experimental retention and thermodynamic data published by Kováts and coworkers for 32 compounds on 6 different stationary phases. Very good correlations (r>0.99) were observed for dI/dT versus (I-I(S)) and dI/dT versus deltaDeltaC(p), the molar heat capacity difference of the solute and the hypothetical n-alkane, which has the same retention index as the solute. Deviations in the dI/dT versus deltaDeltaC(p) relationship were observed only for alcohols, suggesting a different solvation mechanism for alcohols as compared with other compounds.

Chromatography, Gas↗

PubMed2005

Maximum entropy: a complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR.

Tikhonov regularization (TIKR) has been demonstrated as a powerful and valuable method for the determination of distance distributions of spin-pairs in bi-labeled biomolecules directly from pulsed ESR signals. TIKR is a direct method, which requires no iteration, and, therefore, provides a rapid and unique solution. However, the distribution obtained tends to exhibit oscillatory excursions with negative portions in the presence of finite noise, especially in the peripheral regions of the distribution. The Shannon-Jaynes entropy of a probability distribution provides an intrinsic non-negativity constraint on the probability distribution and an unbiased way of obtaining information from incomplete data. We describe how the maximum entropy regularization method (MEM) may be applied to solve the ill-posed nature of the dipolar signal in pulsed ESR. We make use of it to suppress the negative excursions of the distance distribution and to increase the tolerance to noise in the dipolar signal. Model studies and experimental data are investigated, and they show that, with the initial or "seed" probability distribution that is required for MEM taken as the TIKR result, then MEM is able to provide a regularized solution, subject to the non-negativity constraint, and it is effective in dealing with noise that is problematic for TIKR. In addition we have incorporated into our MEM method the ability to extract the intermolecular dipolar component, which is embedded in the raw experimental data. We find that MEM minimization, which is implemented iteratively, is greatly accelerated using the TIKR result as the seed, and it converges more successfully. Thus we regard the MEM method as a complement to TIKR by securing a positive pair distance distribution and enhancing the accuracy of TIKR.

Cytochromes c↗

PubMed2004

Positional entropy during pigeon homing I: application of Bayesian latent state modelling.

In these two companion papers, we introduce a new approach to the analysis of bird navigation which brings together several novel mathematical and technical applications. Miniaturized GPS logging devices provide track data of sufficiently high spatial and temporal resolution that considerable variation in flight behaviour can be observed remotely from the form of the track alone. We analyse a fundamental measure of bird flight track complexity, spatio-temporal entropy, and explore its state-like structure using a probabilistic hidden Markov model. The emergence of a robust three-state structure proves that the technique has analytical power, since this structure was not obvious in the tracks alone. We propose the hypothesis that positional entropy is indicative of underlying navigational uncertainty, and that familiar area navigation may break down into three states of navigational confidence. By interpreting the relationship between these putative states and features on the map, we are able to propose a number of hypothetical navigational strategies feeding into these states. The first of these two papers details the novel technical developments associated with this work and the second paper contains a navigational interpretation of the results particularly with respect to visual features of the landscape.

Animals↗

PubMed2004

Positional entropy during pigeon homing II: navigational interpretation of Bayesian latent state models.

In these two companion papers we introduce a new approach to the analysis of bird navigation which brings together several novel mathematical and technical applications. Miniaturized GPS logging devices provide track data of sufficiently high spatial and temporal resolution that considerable variation in flight behaviour can be observed remotely from the form of the track alone. We analyse a fundamental measure of bird flight track complexity, spatio-temporal entropy, and explore its state-like structure using a probabilistic hidden Markov model. The emergence of a robust three-state structure proves that the technique has analytical power, since this structure was not obvious in the tracks alone. We propose the hypothesis that positional entropy is indicative of underlying navigational uncertainty, and that familiar area navigation may break down into three states of navigational confidence. By interpreting the relationship between these putative states and features on the map, we are able to propose a number of hypothetical navigational strategies feeding into these states. The first of these two papers details the novel technical developments associated with this work and the second paper contains a navigational interpretation of the results particularly with respect to visual features of the landscape.

Animals↗

PubMed2005

Detecting differentially expressed genes by relative entropy.

DNA microarray experiments have generated large amount of gene expression measurements across different conditions. One crucial step in the analysis of these data is to detect differentially expressed genes. Some parametric methods, including the two-sample t-test (T-test) and variations of it, have been used. Alternatively, a class of non-parametric algorithms, such as the Wilcoxon rank sum test (WRST), significance analysis of microarrays (SAM) of Tusher et al. (2001), the empirical Bayesian (EB) method of Efron et al. (2001), etc., have been proposed. Most available popular methods are based on t-statistic. Due to the quality of the statistic that they used to describe the difference between groups of data, there are situations when these methods are inefficient, especially when the data follows multi-modal distributions. For example, some genes may display different expression patterns in the same cell type, say, tumor or normal, to form some subtypes. Most available methods are likely to miss these genes. We developed a new non-parametric method for selecting differentially expressed genes by relative entropy, called SDEGRE, to detect differentially expressed genes by combining relative entropy and kernel density estimation, which can detect all types of differences between two groups of samples. The significance of whether a gene is differentially expressed or not can be estimated by resampling-based permutations. We illustrate our method on two data sets from Golub et al. (1999) and Alon et al. (1999). Comparing the results with those of the T-test, the WRST and the SAM, we identified novel differentially expressed genes which are of biological significance through previous biological studies while they were not detected by the other three methods. The results also show that the genes selected by SDEGRE have a better capability to distinguish the two cell types.

Acute Disease↗

PubMedDate not supplied

Cross-entropy embedding of high-dimensional data using the neural gas model.

A cross-entropy approach to mapping high-dimensional data into a low-dimensional space embedding is presented. The method allows to project simultaneously the input data and the codebook vectors, obtained with the Neural Gas (NG) quantizer algorithm, into a low-dimensional output space. The aim of this approach is to preserve the relationship defined by the NG neighborhood function for each pair of input and codebook vectors. A cost function based on the cross-entropy between input and output probabilities is minimized by using a Newton-Raphson method. The new approach is compared with Sammon's non-linear mapping (NLM) and the hierarchical approach of combining a vector quantizer such as the self-organizing feature map (SOM) or NG with the NLM recall algorithm. In comparison with these techniques, our method delivers a clear visualization of both data points and codebooks, and it achieves a better mapping quality in terms of the topology preservation measure q(m).

Algorithms↗

PubMed2004

Efficiency, power, and entropy in event-related FMRI with multiple trial types. Part I: theory.

Experimental designs for functional magnetic resonance imaging (fMRI) experiments can be characterized by their estimation efficiency, which is a measure of the variance in the estimate of the hemodynamic response function (HRF), and their detection power, which is a measure of the variance in the estimate of the amplitude of functional activity. Previous studies have shown that there exists a fundamental trade-off between efficiency and power for experiments with a single trial type of interest. This paper extends the prior work by presenting a theoretical model for the relation between detection power and estimation efficiency in experiments with multiple trial types. It is shown that the trade-off between efficiency and power present in multiple-trial-type experiments is identical in form to that observed for single-trial-type experiments. Departures from the predicted trade-off due to the inclusion of basis function expansions and the assumption of correlated noise are examined. Finally, conditional entropy is introduced as measure for the randomness of a design, and an empirical relation between entropy and estimation efficiency is presented.

Artifacts↗

PubMed2003

DNA binding of a non-sequence-specific HMG-D protein is entropy driven with a substantial non-electrostatic contribution.

The thermal properties of two forms of the Drosophila melanogaster HMG-D protein, with and without its highly basic 26 residue C-terminal tail (D100 and D74) and the thermodynamics of their non-sequence-specific interaction with linear DNA duplexes were studied using scanning and titration microcalorimetry, spectropolarimetry, fluorescence anisotropy and FRET techniques at different temperatures and salt concentrations. It was shown that the C-terminal tail of D100 is unfolded at all temperatures, whilst the state of the globular part depends on temperature in a rather complex way, being completely folded only at temperatures close to 0 degrees C and unfolding with significant heat absorption at temperatures below those of the gross denaturational changes. The association constant and thus Gibbs energy of binding for D100 is much greater than for D74 but the enthalpies of their association are similar and are large and positive, i.e. DNA binding is a completely entropy-driven process. The positive entropy of association is due to release of counterions and dehydration upon forming the protein/DNA complex. Ionic strength variation showed that electrostatic interactions play an important but not exclusive role in the DNA binding of the globular part of this non-sequence-specific protein, whilst binding of the positively charged C-terminal tail of D100 is almost completely electrostatic in origin. This interaction with the negative charges of the DNA phosphate groups significantly enhances the DNA bending. An important feature of the non-sequence-specific association of these HMG boxes with DNA is that the binding enthalpy is significantly more positive than for the sequence-specific association of the HMG box from Sox-5, despite the fact that these proteins bend the DNA duplex to a similar extent. This difference shows that the enthalpy of dehydration of apolar groups at the HMG-D/DNA interface is not fully compensated by the energy of van der Waals interactions between these groups, i.e. the packing density at the interface must be lower than for the sequence-specific Sox-5 HMG box.

Amino Acid Sequence↗

PubMed1999

Zones of low entropy in genomic sequences.

We consider the problem of detecting regions having low entropy in DNA sequences, which is a particular case of searching for dos-DNA zones. The entropy is measured in linear time as the number of distinct segments occurring in the regions. As a consequence, we are able to determine regions containing a small number of repetitions of long segments or a large number of repetitions of short segments. The method provides an index on sequences that is applied to compare them without any alignment. Comparisons extract regions having similar combinatorial features that would not have been found by standard alignment methods. The present methodology is applied to Saccharomyces cerevisiae yeast chromosomes to show what the approach is able to produce.

Base Sequence↗

PubMed2001

Wavelet entropy: a new tool for analysis of short duration brain electrical signals.

Since traditional electrical brain signal analysis is mostly qualitative, the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals. These methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of brain dynamics. Here, new method based on orthogonal discrete wavelet transform (ODWT) is applied. It takes as a basic element the ODWT of the EEG signal, and defines the relative wavelet energy, the wavelet entropy (WE) and the relative wavelet entropy (RWE). The relative wavelet energy provides information about the relative energy associated with different frequency bands present in the EEG and their corresponding degree of importance. The WE carries information about the degree of order/disorder associated with a multi-frequency signal response, and the RWE measures the degree of similarity between different segments of the signal. In addition, the time evolution of the WE is calculated to give information about the dynamics in the EEG records. Within this framework, the major objective of the present work was to characterize in a quantitative way functional dynamics of order/disorder microstates in short duration EEG signals. For that aim, spontaneous EEG signals under different physiological conditions were analyzed. Further, specific quantifiers were derived to characterize how stimulus affects electrical events in terms of frequency synchronization (tuning) in the event related potentials.

Adult↗

PubMed2002

Wavelet entropy analysis of event-related potentials indicates modality-independent theta dominance.

Sensory/cognitive stimulation elicits multiple electroencephalogram (EEG)-oscillations that may be partly or fully overlapping over the time axis. To evaluate co-existent multi-frequency oscillations, EEG responses to unimodal (auditory or visual) and bimodal (combined auditory and visual) stimuli were analyzed by applying a new method called wavelet entropy (WE). The method is based on the wavelet transform (WT) and quantifies entropy of short segments of the event-related brain potentials (ERPs). For each modality, a significant transient decrease of WE emerged in the post-stimulus EEG epoch indicating a highly-ordered state in the ERP. WE minimum was always determined by a prominent dominance of theta (4-8 Hz) ERP components over other frequency bands. Event-related 'transition to order' was most pronounced and stable at anterior electrodes, and after bimodal stimulation. Being consistently observed across different modalities, a transient theta-dominated state may reflect a processing stage that is obligatory for stimulus evaluation, during which interfering activations from other frequency networks are minimized.

Acoustic Stimulation↗

PubMed2003

Extensions to minimum relative entropy inversion for noisy data.

Minimum relative entropy (MRE) and Tikhonov regularization (TR) were compared by Neupauer et al. [Water Resour. Res. 36 (2000) 2469] on the basis of an example plume source reconstruction problem originally proposed by Skaggs and Kabala [Water Resour. Res. 30 (1994) 71] and a boxcar-like function. Although Neupauer et al. [Water Resour. Res. 36 (2000) 2469] were careful in their conclusions to note the basis of these comparisons, we show that TR does not perform well on problems in which delta-like sources are convolved with diffuse-groundwater contamination response functions, particularly in the presence of noise. We also show that it is relatively easy to estimate an appropriate value for epsilon, the hyperparameter needed in the minimum relative entropy solution for the inverse problem in the presence of noise. This can be estimated in a variety of ways, including estimation from the data themselves, analysis of data residuals, and a rigorous approach using the real cepstrum and the Akaike Information Criterion (AIC). Regardless of the approach chosen, for the sample problem reported herein, excellent resolution of multiple delta-like spikes is produced from MRE from noisy, diffuse data. The usefulness of MRE for noisy inverse problems has been demonstrated.

Entropy↗

PubMed2001

Minimum entropy production in photosynthesis.

In this paper a flux-coupling model of photosynthesis is presented. By requiring minimum entropy production, it is found that the photosynthetic efficiency is essentially given by the square root of D/lambda. D and lambda are the diffusion coefficient and thermal conductivity of the rate-limiting processes in the chloroplast, respectively. For experimental values of D and lambda, the efficiency is found to be 2.4-7.5%, with a likely value of 6.1%, whereas C4-plants are known to have an efficiency of 6.2%. We conclude that the process of photosynthesis is in quantitative agreement with the principle of minimum entropy production.

Diffusion↗

PubMed2002

Biological adaptabilities and quantum entropies.

The entropy-based theory of adaptability set forth by Michael Conrad in the early 1970s continued to appear in his work for over two decades, and was the subject of the only book he published in his lifetime. He applied this theory to a host of subjects ranging from enzyme dynamics to sociology. This paper reviews the formalism of adaptability theory, clarifying some of its mathematical and interpretive difficulties. The theory frames the computational tradeoff principle, a thesis that was the most frequently recurring claim in his work. The formulation of adaptability theory presented here allows the introduction of quantum entropy functions into the theory, revealing an interesting relationship between adaptability and another one of Conrad's deep preoccupations, the role of quantum processes in life.

Adaptation, Physiological↗

PubMed1998

Entropy and predictability of information carriers.

The structure of linear strings carrying information is investigated by means of entropy concepts. First conditional entropy and transinformation are introduced and several generalizations are discussed. The capability to describe the structure of information carriers as DNA, proteins, texts and musical strings is investigated. The relation between order and the predictability of informational strings is discussed. As examples we study the mutual information function of virus DNA and several long proteins. Further we show some (rather formal) analogies to the structure of texts, and strings generated by musical melodies. It is shown that several information carriers show long-range correlations.

DNA↗

PubMed1998

Entropy maps characterize drug effects on brain dynamics in Alzheimer's disease.

Non-linear quantifiers of brain electrical dynamics (entropy maps computed from the degradation of temporal forecasting of EEG signals) were studied in relation to drug treatment of Alzheimer's disease. A placebo condition was compared to three drug doses (50, 100 and 200 mg). A significant general effect of the drug was found when compared to placebo and specific contrasts between placebo and each of the three drug doses only reveal a significant entropy increase for the highest dose. These effects were localized bilaterally in fronto-temporal areas and support changes in the dynamics of the cerebral structures involved in memory processes.

Acoustic Stimulation↗

PubMed1997

Negative entropy of halothane binding to protein: 19F-NMR with a novel cell.

An obvious difficulty of the study of binding of volatile anesthetics to proteins is to prevent loss of the ligand during the procedure. A novel NMR tube was designed that consists of concentric double cylinders which slide each other under sealed condition. A gas space is left in the tube to measure the free anesthetic concentration in the gas phase, which is in equilibrium with the solution. The enthalpy change of anesthetic transfer from water to BSA, deltaH(w-->r) was -40 kJ x mol(-1). The Gibbs free energy deltaG(w-->r) was -14.0 kJ x mol(-1) at 283 K (K(D) = 2.6 mM) and increased to -11.6 kJ x mol(-1) at 310 K (K(D) = 10.9 mM). The maximum binding site (Bmax) was 19.3 at 10 degrees C and increased to 34.5 at 37 degrees C. The entropy change, deltaS(w-->r) was -92 J x mol(-1) x K(-1) and was almost constant in the temperature range 10 approximately 37 degrees C. Contrary to the general consensus that hydrophobic interaction is entropy-driven, the binding of halothane to BSA was enthalpy-driven, compensating the opposing effect of deltaS with negative deltaH at the biologically meaningful temperature range. Possible cause of the negative deltaS relating to the conformational change of BSA is discussed.

Entropy↗

PubMed2005

An entropy-based measure of founder informativeness.

Optimizing quantitative trait locus (QTL) mapping experiments requires a generalized measure of marker informativeness because variable information is obtained from different marker systems, marker distribution and pedigree types. Such a measure can be derived from the concept of Shannon entropy, a central concept in information theory. Here we introduce entropy-based founder informativeness (EFI), a new measure of information content generalized across pedigrees, maps, marker systems and mating configurations. We derived equations for inbred- and outbred-derived mapping populations. Mathematical properties of EFI include enhanced sensitivity to mapping population type and extension to any number of founders. To illustrate the use of EFI, we compared experimental designs for QTL mapping for three examples: (i) different marker systems for an F2 pedigree, (ii) different marker densities and sampling sizes for a BC1 pedigree and (iii) a comparison of haplotypic versus zygotic analyses of an outbred pedigree. As an a priori generalized measure of information content, EFI does not require phenotypic data for optimizing experimental designs for QTL mapping.

Alleles↗