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PubMed2001

A "loop entropy reduction" phage-display selection for folded amino acid sequences.

As a step toward selecting folded proteins from libraries of randomized sequences, we have designed a 'loop entropy reduction'-based phage-display method. The basic premise is that insertion of a long disordered sequence into a loop of a host protein will substantially destabilize the host because of the entropic cost of closing a loop in a disordered chain. If the inserted sequence spontaneously folds into a stable structure with the N and C termini close in space, however, this entropic cost is diminished. The host protein function can, therefore, be used to select folded inserted sequences without relying on specific properties of the inserted sequence. This principle is tested using the IgG binding domain of protein L and the lck SH2 domain as host proteins. The results indicate that the loop entropy reduction screen is capable of discriminating folded from unfolded sequences when the proper host protein and insertion point are chosen.

Amino Acid Sequence↗

PubMed2006

Learning Tetris using the noisy cross-entropy method.

The cross-entropy method is an efficient and general optimization algorithm. However, its applicability in reinforcement learning (RL) seems to be limited because it often converges to suboptimal policies. We apply noise for preventing early convergence of the cross-entropy method, using Tetris, a computer game, for demonstration. The resulting policy outperforms previous RL algorithms by almost two orders of magnitude.

Algorithms↗

PubMed2001

The use of statistical entropy to evaluate the utilisation of incinerator ashes for the production of cement.

The paper discusses the utilisation of MSW incinerator residues for the production of cement with regard to materials management. Two objectives of waste management are the protection of men and the environment and resource conservation. Thus metals have to be recycled or transferred into appropriate final sinks. For both options a concentrating step is indispensable. MSW incinerators are such concentrating processes, as they accumulate metals in their residues. The mixing of high-concentrated residues with low-concentrated clinker in order to produce cement results in dilution of metals. This contradicts the above objectives. Concentrating and dilution processes can be described by materials balances. To evaluate different uses of MSW residues in the cement production the statistical entropy of the resulting distributions of selected metals (Cd, Pb, Cu) is assessed. The result is that in order to avoid an increase in the entropy, neither fly ashes nor bottom ashes of MSW incinerators should be utilised at large scale without pre-treatment. The method can be used to determine the quality of the residues so that they can be used in accordance with the objectives of waste management.

Conservation of Natural Resources↗

PubMed2005

Approximate entropy in the electroencephalogram during wake and sleep.

Entropy measurement can discriminate among complex systems, including deterministic, stochastic and composite systems. We evaluated the changes of approximate entropy (ApEn) in signals of the electroencephalogram (EEG) during sleep. EEG signals were recorded from eight healthy volunteers during nightly sleep. We estimated the values of ApEn in EEG signals in each sleep stage. The ApEn values for EEG signals (mean +/- SD) were 0.896 +/- 0.264 during eyes-closed waking state, 0.738 +/- 0.089 during Stage I, 0.615 +/- 0.107 during Stage II, 0.487 +/- 0.101 during Stage II, 0.397 +/- 0.078 during Stage IV and 0.789 +/- 0.182 during REM sleep. The ApEn values were found to differ with statistical significance among the six different stages of consciousness (ANOVA, p<0.001). ApEn of EEG was statistically significantly lower during Stage IV and higher during wake and REM sleep. We conclude that ApEn measurement can be useful to estimate sleep stages and the complexity in brain activity.

Adult↗

PubMed2006

Sample sizes for identifying the key types of container occupied by dengue-vector pupae: the use of entropy in analyses of compositional data.

A method has been developed for estimating the sample sizes needed to identify categories that comprise a large proportion of a compositional data-set. The method is to be used in the design of surveys of mosquito pupae, for identifying the key container types from which the majority of adult dengue vectors emerge. Although a finite-population correction was devised for estimating the mean of a negative binomial distribution, other complications of parametric approaches make them unlikely to yield methods simple enough to be practically applicable. The Shannon-Wiener index was therefore investigated as a more useful alternative, at the cost of theoretical generalizability, in an approach based on re-sampling methods in conjunction with the use of entropy. This index can be used to summarize the degree to which pupae are either concentrated in a few container types, or dispersed among many. An empirical relationship between the index and the repeatability of surveys of differing sample sizes was observed. A step-wise rule, based on the entropy of the cumulative data, was devised for determining the sample size, in terms of the number of houses positive for pupae, at which a pupal survey might reasonably be stopped.

Aedes↗

PubMed2005

An entropy-based gene selection method for cancer classification using microarray data.

BACKGROUND: Accurate diagnosis of cancer subtypes remains a challenging problem. Building classifiers based on gene expression data is a promising approach; yet the selection of non-redundant but relevant genes is difficult. The selected gene set should be small enough to allow diagnosis even in regular clinical laboratories and ideally identify genes involved in cancer-specific regulatory pathways. Here an entropy-based method is proposed that selects genes related to the different cancer classes while at the same time reducing the redundancy among the genes. RESULTS: The present study identifies a subset of features by maximizing the relevance and minimizing the redundancy of the selected genes. A merit called normalized mutual information is employed to measure the relevance and the redundancy of the genes. In order to find a more representative subset of features, an iterative procedure is adopted that incorporates an initial clustering followed by data partitioning and the application of the algorithm to each of the partitions. A leave-one-out approach then selects the most commonly selected genes across all the different runs and the gene selection algorithm is applied again to pare down the list of selected genes until a minimal subset is obtained that gives a satisfactory accuracy of classification. The algorithm was applied to three different data sets and the results obtained were compared to work done by others using the same data sets. CONCLUSION: This study presents an entropy-based iterative algorithm for selecting genes from microarray data that are able to classify various cancer sub-types with high accuracy. In addition, the feature set obtained is very compact, that is, the redundancy between genes is reduced to a large extent. This implies that classifiers can be built with a smaller subset of genes.

Algorithms↗

PubMed2006

Aging of the brain, entropy, and Alzheimer disease.

Sporadic Alzheimer disease (AD) is related to advancing age far more than to any other risk factor and ultimately affects almost half of the population over age 85. Despite its remarkable prevalence among the elderly, it has been regarded as a specific disease, distinct from "normal aging." This view is supported in large part by clinical and pathologic similarities to early-onset, dominantly inherited familial AD, where genetic mutations related to beta-amyloid have been identified. There is much evidence that sporadic AD overlaps with normal aging in many clinical and pathologic features. Some of the many molecular age-related changes (ARCs) affecting the brain, both intrinsic (programmed) and extrinsic (stochastic), are reviewed, with discussion of the effects they have singly and collectively on neuronal viability and vulnerability. The effect of ARCs on the brain is seen as the biologic manifestation of increasing entropy, an approach that helps to explain the progressive decline of neural and cognitive function over time; the ability of multiple, varied ARCs to summate as individuals age; the transitional relationship between normal aging, mild cognitive impairment, and AD; and the apparent differences between normal aging and AD. Increasing entropy, manifest through a complex network of interacting ARCs, is seen as the fundamental driving cause of neural and cognitive decline in the elderly, as well as the overriding etiologic principle in further transition to sporadic AD. Research on sporadic AD has largely focused on finding a single causal metabolic disorder or genetic mutation. Multiple ARCs contribute to declining function and increased frailty in the aging brain, however, and to the catastrophic disintegration of sporadic AD. Effective prevention or treatment will depend on recognizing the contributions of a multiplicity of ARCs to AD and reducing the burden of as many as possible. The role of amyloid is seen as one element in the larger network of senescent changes involving the aging brain.

Aging↗

PubMed2005

Characterization of depolarizing optical media by means of the entropy factor: application to biological tissues.

Polarized light imaging is a potential tool to obtain an adequate description of the properties of depolarizing media such as biological tissues. In many biomedical applications, for instance, dermatology, ophthalmology, or urology, imaging polarimetry provides a noninvasive diagnosis of a wide range of disease states, and, likewise, it could be applied to the study of internal tissues though the use of endoscopes that use optical fibers. We introduce an algebraic method, based on the Mueller-coherence matrix, for a clearer analysis of the polarization characteristics of depolarizing media via the entropy factor. First-order errors introduced by the measurement system are corrected. Entropy defines three kinds of media according to their depolarizing behavior, and several examples corresponding to each region are shown. The calculation of this factor provides clearer information than that provided by the traditional Mueller matrix in the analysis of biological tissue properties by polarization measurement techniques.

Entropy↗

PubMed2001

Multicriterion cross-entropy minimization approach to positron emission tomographic imaging.

A multicriterion cross-entropy minimization approach to positron emission tomographic (PET) imaging is described. An unexplored multicriterion cross-entropy optimization algorithm based on weighted-sum scalarization is used to solve this problem. The efficacy of the algorithm is compared with that of the single-criterion optimization algorithm and the convolution backprojection method for image reconstruction from computer-generated projection data and Siemens PET scanner data. The algorithms described have been implemented on a PIII/686 microcomputer.

Algorithms↗

PubMed2003

Band-target entropy minimization (BTEM) applied to hyperspectral Raman image data.

Band-target entropy minimization (BTEM) has been applied to extraction of component spectra from hyperspectral Raman images. In this method singular value decomposition is used to calculate the eigenvectors of the spectroscopic image data set. Bands in non-noise eigenvectors that would normally be used for recovery of spectra are examined for localized spectral features. For a targeted (identified) band, information entropy minimization or a closely related algorithm is used to recover the spectrum containing this feature from the non-noise eigenvectors, plus the next 5-30 eigenvectors, in which noise predominates. Tests for which eigenvectors to include are described. The method is demonstrated on one synthesized Raman image data set and two bone tissue specimens. By inclusion of small amounts of signal that would be unused in other methods, BTEM enables the extraction of a larger number of component spectra than are otherwise obtainable. An improvement in signal/noise ratio of the recovered spectra is also obtained.

Aged↗

PubMed2005

Entropy and oligomerization in GPCRs.

Evolutionary trace (ET) and entropy are two related methods for analyzing a multiple sequence alignment to determine functionally important residues in proteins. In this article, these methods have been enhanced with a view to reinvestigate the issue ofGPCR dimerization and oligomerization. In particular, cluster analysis has replaced the subjective visual analysis element of the original ET method. Previous applications of the ET method predicted two dimerization interfaces on the external transmembrane lipid-facing region of GPCRs; these were discussed in terms of dimerization and linear oligomers. Removing the subjective element of the ET method gives rise to the prediction of functionally important residues on the external face of each transmembrane helix for a large number of class A GPCRs. These results are consistent with a growing body of experimental information that, taken over many receptor subtypes, has implicated each transmembrane helix in dimeric interactions. In this application, entropy gave superior results to those obtained from the ET method in that its use gives rise to higher z-scores and fewer instances of z-scores below 3.

Animals↗

PubMed2004

Distributions in protein conformation space: implications for structure prediction and entropy.

By considering how polymer structures are distributed in conformation space, we show that it is possible to quantify the difficulty of structural prediction and to provide a measure of progress for prediction calculations. The critical issue is the probability that a conformation is found within a specified distance of another conformer. We address this question by constructing a cumulative distribution function (CDF) for the average probability from observations about its limiting behavior at small displacements and numerical simulations of polyalanine chains. We can use the CDF to estimate the likelihood that a structure prediction is better than random chance. For example, the chance of randomly predicting the native backbone structure of a 150-amino-acid protein to low resolution, say within 6 A, is 10(-14). A high-resolution structural prediction, say to 2 A, is immensely more difficult (10(-57)). With additional assumptions, the CDF yields the conformational entropy of protein folding from native-state coordinate variance. Or, using values of the conformational entropy change on folding, we can estimate the native state's conformational span. For example, for a 150-mer protein, equilibrium alpha-carbon displacements in the native ensemble would be 0.3-0.5 A based on T Delta S of 1.42 kcal/(mol residue).

Algorithms↗

PubMed2005

Translational-entropy gain of solvent upon protein folding.

We show that even in the complete absence of potential energies among the atoms in a protein-aqueous solution system, there is a physical factor that favors the folded state of the protein. It is a gain in the translational entropy (TE) of water originating from the translational movement of water molecules. An elaborate statistical-mechanical theory is employed to analyze the TE of water in which a protein or peptide with a prescribed conformation is immersed. It is shown that if the number of residues is sufficiently large, the TE gain is powerful enough to compete with the conformational-entropy loss upon folding. For protein G we have tested over 100 compact conformations generated by a computer simulation with the all-atom potentials as well as the native structure. A significant finding is that the largest TE is attained in the native structure. The translational movement of water molecules is quite effective in achieving the tight packing in the interior of a natural protein. These results are true only when the solvent is water whose molecular size is the smallest among the ordinary liquids in nature.

Computer Simulation↗

PubMed2005

Dissecting homo-heptamer thermodynamics by isothermal titration calorimetry: entropy-driven assembly of co-chaperonin protein 10.

Normally, isothermal titration calorimetry (ITC) is used to study binding reactions between two different biomolecules. Self-association processes leading to homo-oligomeric complexes have usually not been studied by ITC; instead, methods such as spectroscopy and analytical ultracentrifugation, which only provide affinity and Gibbs-free energy (i.e., K(D) and DeltaG), are employed. We here demonstrate that complete thermodynamic descriptions (i.e., K(D), DeltaG, DeltaH, and DeltaS) for self-associating systems can be obtained by ITC-dilution experiments upon proper analysis. We use this approach to probe the dissociation (and thus association) equilibrium for the heptameric co-chaperonin proteins 10 (cpn10) from Aquifex aeolicus (Aacpn10-del25) and human mitochondria (hmcpn10). We find that the midpoints for the heptamer-monomer equilibrium occur at 0.51 +/- 0.03 microM and 3.5 +/- 0.1 microM total monomer concentration (25 degrees C), for Aacpn10-del25 and hmcpn10, respectively. For both proteins, association involves endothermic enthalpy and positive entropy changes; thus, the reactions are driven by the entropy increase. This is in accord with the release of ordered water molecules and, for the thermophilic variant, a relaxation of monomer-tertiary structure when the heptamers form.

Bacteria↗

PubMed2006

Entropy-driven genome organization.

DNA and RNA polymerases active on bacterial and human genomes in the crowded environment of a cell are modeled as beads spaced along a string. Aggregation of the large polymerizing complexes increases the entropy of the system through an increase in entropy of the many small crowding molecules; this occurs despite the entropic costs of looping the intervening DNA. Results of a quantitative cost/benefit analysis are consistent with observations that active polymerases cluster into replication and transcription "factories" in both pro- and eukaryotes. We conclude that the second law of thermodynamics acts through nonspecific entropic forces between engaged polymerases to drive the self-organization of genomes into loops containing several thousands (and sometimes millions) of basepairs.

Computer Simulation↗

PubMed2006

Technology in the high entropy world.

Modern growing society is mainly driven by oils and may be designated "petroleum civilisation". However, the basic energy used to drive the global ecosystem is solar radiation. The amount of fossil energy consumption is minimal in the whole global energy balance. Economic growth is mainly controlled by the fossil (commercial) energy consumption rate in urban areas. Water and sanitation systems are bridging economical activities and global ecosystems. Therefore, vast amounts of high entropy solar energy should always be taken into account in the water industry. Only in urban/industrial areas where most of the GDP is earned, are commercial energy driven systems inevitably introduced with maximum effort for energy saving. A water district concept to ensure appropriate quality use with the least deterioration of the environment is proposed. In other areas, decentralised water and sanitation systems driven on soft energy paths would be recommended. A process and system designed on a high entropy energy system would be the foundation for a future urban metabolic system revolution for when oil-based energy become scarce.

Animals↗

PubMed2005

Maximizing the entropy of histogram bar heights to explore neural activity: a simulation study on auditory and tactile fibers.

Neurophysiologists often use histograms to explore patterns of activity in neural spike trains. The bin size selected to construct a histogram is crucial: too large bin widths result in coarse histograms, too small bin widths expand unimportant detail. Peri-stimulus time (PST) histograms of simulated nerve fibers were studied in the current article. This class of histograms gives information about neural activity in the temporal domain and is a density estimate for the spike rate. Scott's rule based on modem statistical theory suggests that the optimal bin size is inversely proportional to the cube root of sample size. However, this estimate requires a priori knowledge about the density function. Moreover, there are no good algorithms for adaptive-mesh histograms, which have variable bin sizes to minimize estimation errors. Therefore, an unconventional technique is proposed here to help experimenters in practice. This novel method maximizes the entropy of histogram-bar heights to find the unique bin size, which generates the highest disorder in a histogram (i.e., the most complex histogram), and is useful as a starting point for neural data mining. Although the proposed method is ad hoc from a density-estimation point of view, it is simple, efficient and more helpful in the experimental setting where no prior statistical information on neural activity is available. The results of simulations based on the entropy method are also discussed in relation to Ellaway's cumulative-sum technique, which can detect subtle changes in neural activity in certain conditions.

Algorithms↗

PubMed2001

[Detection of spikes in epileptic EEG based on Multiresolution Tsallis' entropy].

In this paper, the detection of the spikes in the epileptic EEG signal was studied based on Multiresolution Tsallis' entropy (MRET). First, EEG signals were decomposed into wavelet series, and then, at every scale, the abnormal spikes were distinguished from normal background EEG activities by using MRET. The analysis of 6 patients' EEG data showed that the abnormal epileptiform spikes in EEG can be accurately detected with this method, which opens up the perspectives of building up automatic detection devices for spikes in EEG. Compared with the Shannon entropy, the MRET provides one with more detailed information.

Electroencephalography↗