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PubMed1997

The sensitivity of new color systems in blood-flow diagnosis. The maximum entropy method and angio-color-comparative in vitro flow measurements to determine sensitivity.

BACKGROUND: Two new blood-flow-diagnosis techniques have recently been developed as supplements to the established color techniques: the MEM (maximum entropy method) technique and color flow amplitude (power Doppler). These are capable of representing blood flow in distinctly more slowly flowing areas than is possible with the conventional Doppler technique. METHODS: Both methods make use of the Doppler technique in part, yet analyze the reflected signal in a different manner, in so doing optimizing the relation between the noise and the signal. Measurements were obtained on two anatomic flow models to test the sensitivity of both techniques under slow flow conditions. RESULTS: The slowest flow the MEM technique was capable of recording was 0.5 mm/s, albeit utilizing a 5-MHz transducer for the MEM technique and a 10-MHz transducer for the angio technique. One may thus assume that the MEM technique would be still more sensitive when utilizing a 10-MHz transducer. The advantage of the MEM technique is its real-time flow representation: The angio technique requires a few seconds of acquisition time. This could have serious consequences during clinical utilization. Doppler sonography was merely capable of detecting a minimum flow velocity of 15 mm/s. The angio technique is less dependent on the angle during flow representation than the MEM technique. CONCLUSIONS: The distinctly higher sensitivity of these two new color techniques offers new possibilities in the clinical sector as far as the perfusion diagnosis of organs and tumors is concerned.

Angiography↗

PubMed2006

A novel approach to measure variability in the anterior cruciate ligament deficient knee during walking: the use of the approximate entropy in orthopaedics.

OBJECTIVE: The evaluation of variability of biological rhythmic activities through measures such as Approximate Entropy (ApEn) has provided important information regarding pathology in disciplines such as cardiology and neurology. This research lead to the "loss of complexity hypothesis" where decreased variability is associated with loss of healthy flexibility rendering the system more rigid and unable to adapt to stresses. ApEn as a measure of variability and complexity, correlates well with pathology while, in some cases, it is predictive of subsequent clinical changes. The study of human gait could benefit from the application of ApEn since it is also a rhythmical oscillation. Our aim was to assess the variability of the ACL deficient knee, since ACL rupture is a common musculoskeletal injury and is accompanied by altered gait patterns and future pathology in the joint. We hypothesized that the ACL deficient knee will exhibit more regular and less variable walking patterns than the contralateral intact knee. METHODS: Ten subjects with unilateral deficiency walked on a treadmill at their self-selected speed, 20% faster, and 20% slower, while kinematics were collected (50 Hz) from 80 consecutive strides for each condition. The ApEn of the resulted knee joint flexion-extension time series was calculated. RESULTS: Significantly smaller ApEn values were found in the ACL deficient knee when compared with the contralateral intact (F = 5.57, p = 0.022), for all speeds. ApEn values significantly increased (F = 5.79, p = 0.005) with increases in walking speed. CONCLUSIONS: The altered properties of the ACL deficient knee, which exhibits more regular and less variable patterns than the contralateral intact knee, may decrease the adaptability of the system rendering it less able to adjust to perturbations. This could explain the increased future pathology found in the deficient knee. ApEn can be an important tool in assessing pathology and therapeutic interventions in orthopaedics.

Adult↗

PubMed2006

Commentary on: "Photosynthesis and negative entropy production" by Jennings and coworkers.

This commentary argues against the view that photochemical energy conversion violates the second law of thermodynamics, as expressed in a recent paper [R.C. Jennings, E. Engelmann, F. Garlaschi, A.P. Casazza, G. Zucchelli. Photosynthesis and negative entropy production. Biochim. Biophys. Acta 1709 (2005) 251-255]. The basic principles of free energy conversion by a photo-electrochemical cell are outlined, emphasizing the fact that the potential depends on the relative population of the excited state and thus on the illumination intensity.

Energy Transfer↗

PubMed2004

Cluster and information entropy patterns in immunoglobulin complementarity determining regions.

Previous studies of antibody binding domains have established many crucial features that include important structural positions, canonical formations, and the geometric correlations with the binding site nature and topography. In this work, position-specific frequency and hierarchical clustering analysis are used to explore the statistical pattern of the residues in the complementarity determining regions of human antibodies. In addition, Shannon's information entropy is computed for the entire heavy and light chains and compared with germline patterns to seek variability due to antibody clonal selection. Results are compared with reported analyses based on structural data and ligand-protein contact point computations based on Protein Data Bank records. Observations derived from the present sequence analysis are consistent with previous structural based methods. In the absence of structural data, methods used in this work can be effective and efficient computational tools used for identifying residues that are important for antigen targeting and predicting the probable amino acid distribution expected at these positions. The results in turn can be applied to help design or plan mutagenesis experiments to improve the binding properties of antibodies.

Amino Acid Sequence↗

PubMed2004

Hidden assumptions in a maximum-entropy method stacking analyses.

Two models have been used to describe indefinite self-association (stacking). In the more popular isodesmic model addition of molecules to the growing stack occurs with the same equilibrium constant, while in the attenuated model successive equilibrium constants decrease in value. In an attempt to choose between the two models application was made of the maximum-entropy method. This paper points out that the conclusions drawn from this method are not proven as the application assumed specific limiting values for experimental values of a molecule in the interior of a stack, and these values are not identical in the two models for the two systems considered.

Entropy↗

PubMed2005

Shannon information, LMC complexity and Rényi entropies: a straightforward approach.

The LMC complexity, an indicator of complexity based on a probabilistic description, is revisited. A straightforward approach allows us to establish the time evolution of this indicator in a near-equilibrium situation and gives us a new insight for interpreting the LMC complexity for a general non equilibrium system. Its relationship with the Rényi entropies is also explained. One of the advantages of this indicator is that its calculation does not require a considerable computational effort in many cases of physical and biological interest.

Entropy↗

PubMed2005

Analysis of regularity in the EEG background activity of Alzheimer's disease patients with Approximate Entropy.

OBJECTIVE: The aim of this study was to analyse the regularity of the EEG background activity of Alzheimer's disease (AD) patients to test the hypothesis that the irregularity of the AD patients' EEG is lower than that of age-matched controls. METHODS: We recorded the EEG from 19 scalp electrodes in 10 AD patients and 8 age-matched controls and estimated the Approximate Entropy (ApEn). ApEn is a non-linear statistic that can be used to quantify the irregularity of a time series. Larger values correspond to more complexity or irregularity. A spectral analysis was also performed. RESULTS: ApEn was significantly lower in the AD patients at electrodes P3 and P4 (P < 0.01), indicating a decrease of irregularity. We obtained 70% sensitivity and 100% specificity at P3, and 80% sensitivity and 75% specificity at P4. Results seemed to be complementary to spectral analysis. CONCLUSIONS: The decreased irregularity found in the EEG of AD patients in the parietal region leads us to think that EEG analysis with ApEn could be a useful tool to increase our insight into brain dysfunction in AD. However, caution should be applied due to the small sample size. SIGNIFICANCE: This article represents a first step in demonstrating the feasibility of ApEn for recognition of EEG changes in AD.

Aged↗

PubMed2004

Prediction of peptide conformation using a scale-transformed entropy sampling algorithm.

An algorithm for predicting the lowest energy structure of a peptide has been developed. High-energy barriers on an energy surface can be easily overcome by logarithmically transforming the energy space. For efficient optimizations, the energy space is searched using a scale-transformed entropy sampling method, and conformations specific to a primary structure of the peptide are sampled with large weights. The efficiency of the present method is demonstrated by calculations on cholecystokinin octapeptide (CCK-8).

Algorithms↗

PubMed2005

Unified drug-target interaction thermodynamic Markov model using stochastic entropies to predict multiple drugs side effects.

Most of present molecular descriptors consider just the molecular structure. In the present article we pretend extending the use of Markov chain (MC) models to define novel molecular descriptors, which consider in addition other parameters like target site or toxic effect. Specifically, this molecular descriptor takes into consideration not only the molecular structure but the specific system the drug affects too. Herein, it is developed a general Markov model that describes 21 different drugs side effects grouped in 10 affected biological systems for 193 drugs, being 311 cases finally. The data were processed by linear discriminant analysis (LDA) classifying drugs according to their specific side effects, forward stepwise was fixed as strategy for variables selection. The average percentage of good classification and number of compounds used in the training/predicting sets were 92.6/91.7% for cardiovascular manifestation (25 out of 27)/(18 out of 20); 89.3/83.9% for dermal manifestations (25 out of 18)/(18 out of 21); 88.9/88.9% for endocrine manifestations (16 out of 18)/(12 out of 14); 88.9/88.2% for psychiatric manifestations (32 out of 36)/(24 out of 27); 88.5/85.6% for systemic phenomena (23 out of 26)/(17 out of 20); 85.7/91.7% for gastrointestinal manifestations (36 out of 42)/(29 out of 32); 83.3/79.2% for metabolic manifestations (15 out of 18)/(11 out of 14); 81.8/78.0% for neurological manifestations (27 out of 33)/(20 out of 25); 75.0/74.0% for hematological manifestations (36 out of 48)/(27 out of 36) and 74.3/72.8% for breathing manifestations (26 out of 35)/(19 out of 26). Finally, application of back-projection analysis (BPA) provides physic interpretation in structural terms through molecular graphics of the toxic effects predicted with these QSTR models. This article develops a mathematical model that encompasses a large number of drugs side effects grouped in specifics systems using stochastic entropies of interaction (Thetak (j)) by the first time.

Drug Interactions↗

PubMed2004

Binding sub-site dissection of a carbohydrate-binding module reveals the contribution of entropy to oligosaccharide recognition at "non-primary" binding subsites.

The optimal ligands for many carbohydrate-binding proteins are often oligosaccharides comprising two, three, or more monosaccharide units. The binding affinity for these sugars is increased incrementally by contributions from binding subsites on the protein that accommodate the individual monosaccharide residues of the oligosaccharide. Here, we use CsCBM6-1, a xylan-specific type B carbohydrate-binding module (CBM) from Clostridium stercorarium falling into amino acid sequence family CBM6, as a model system to investigate the structural and thermodynamic contributions of binding subsites in this protein to carbohydrate recognition. The three-dimensional structures of uncomplexed CsCBM6-1 (at 1.8 A resolution) and bound to the oligosaccharides xylobiose, xylotriose, and xylotetraose (at 1.70 A, 1.89 A, and 1.69 A resolution, respectively) revealed the sequential occupation of four subsites within the binding site in the order of subsites 2, 3, 4 then 1. Overall, binding to all of the xylooligosaccharides tested was enthalpically favourable and entropically unfavourable, like most protein-carbohydrate interactions, with the primary subsites 2 and 3 providing the bulk of the free energy and enthalpy of binding. In contrast, the contributions to the changes in entropy of the non-primary subsites 1 and 4 to xylotriose and xylotetraose binding, respectively, were positive. This observation is remarkable, in that it shows that the 10-20-fold improvement in association constants for oligosaccharides longer than a disaccharide is facilitated by favourable entropic contributions from the non-primary binding subsites.

Absorption↗

PubMed2006

One protein, two enzymes revisited: a structural entropy switch interconverts the two isoforms of acireductone dioxygenase.

Acireductone dioxygenase (ARD) catalyzes different reactions between O2 and 1,2-dihydroxy-3-oxo-5-(methylthio)pent-1-ene (acireductone) depending upon the metal bound in the active site. Ni2+ -ARD cleaves acireductone to formate, CO and methylthiopropionate. If Fe2+ is bound (ARD'), the same substrates yield methylthioketobutyrate and formate. The two forms differ in structure, and are chromatographically separable. Paramagnetism of Fe2+ renders the active site of ARD' inaccessible to standard NMR methods. The structure of ARD' has been determined using Fe2+ binding parameters determined by X-ray absorption spectroscopy and NMR restraints from H98S ARD, a metal-free diamagnetic protein that is isostructural with ARD'. ARD' retains the beta-sandwich fold of ARD, but a structural entropy switch increases order at one end of a two-helix system that bisects the beta-sandwich and decreases order at the other upon interconversion of ARD and ARD', causing loss of the C-terminal helix in ARD' and rearrangements of residues involved in substrate orientation in the active site.

Binding Sites↗

PubMed2006

High flow-resolution for mobility estimation in 2D-ENMR of proteins using maximum entropy method (MEM-ENMR).

Multidimensional electrophoretic NMR (nD-ENMR) is a potentially powerful tool for structural characterization of co-existing proteins and protein conformations. By applying a DC electric field pulse, the electrophoretic migration rates of different proteins were detected experimentally in a new dimension of electrophoretic flow. The electrophoretic mobilities were employed to differentiate protein signals. In U-shaped ENMR sample chambers, individual protein components in a solution mixture followed a cosinusoidal electrophoretic interferogram as a function of its unique electrophoretic migration rate. After Fourier transformation in the electrophoretic flow dimension, the protein signals were resolved at different resonant frequencies proportional to their electrophoretic mobilities. Currently, the mobility resolution of the proteins in the electrophoretic flow dimension is limited by severe truncations of the electrophoretic interferograms due to the finite electric field strength available before the onset of heat-induced convection. In this article, we present a successful signal processing method, the Burg's maximum entropy method (MEM), to analyze the truncated ENMR signals (MEM-ENMR). Significant enhancement in flow resolution was demonstrated using two-dimensional ENMR of two protein samples: a lysozyme solution and a solution mixture of bovine serum albumin (BSA) and ubiquitin. The electrophoretic mobilities of lysozyme, BSA and ubiquitin were measured from the MEM analysis as 7.5x10(-5), 1.9x10(-4) and 8.7x10(-5) cm2 V-1 s-1, respectively. Results from computer simulations confirmed a complete removal of truncation artifacts in the MEM-ENMR spectra with 3- to 6-fold resolution enhancement.

Computer Simulation↗

PubMed2006

Comparison of maximum entropy and filtered back-projection methods to reconstruct rapid-scan EPR images.

Reconstruction of two-dimensional images by filtered back-projection (FBP) and by the maximum entropy method (MEM) was compared for spectral-spatial EPR images with differing signal-to-noise ratios. Experimental projections were recorded using direct-detected rapid scans in the presence of a series of magnetic field gradients. The slow-scan absorption lineshapes were calculated by Fourier deconvolution. A Hamming filter was used in conjunction with FBP, but not for MEM. Imperfections in real experimental data, as well as random noise, contribute to discrepancies between the reconstructed image and experimental projections, which may make it impossible to achieve the customary MEM criterion for convergence. The Cambridge MEM algorithm, with allowance for imperfections in experimental data, produced images with more linear intensity scales and more accurate linewidths for weak signals than was obtained with another MEM method. The more effective elimination of noise in baseline regions by MEM made it possible to detect weak trityl (13)C trityl hyperfine lines that could not be distinguished from noise in images reconstructed by FBP. Another advantage of MEM is that projections do not need to be equally spaced. FBP has the advantages that computational time is less, the amplitude scale is linear, and there is less noise superimposed on peaks in images. It is useful to reconstruct images by both methods and compare results. Our observations indicate that FBP works well when the number of projections is large enough that the star effect is negligible. When there is a smaller number of projections, projections are unequally spaced, and/or signal-to-noise is lower MEM is advantageous.

Algorithms↗

PubMed2004

Bacteriorhodopsin photocycle kinetics analyzed by the maximum entropy method.

A maximum entropy method (MEM) was developed for the study of the bacteriorhodopsin photocycle kinetics. The method can be applied directly to experimental kinetic absorption data without any assumption for the number of the intermediate states taking part in the photocycle. Though this method does not give a specific kinetics, its result is very useful for selection between possible photocycle kinetics. Using simulated data, it is shown that MEM gives correct results for the number of the intermediate states and the amplitude distributions around the characteristic lifetimes. Analyzing experimental absorption data at five different wavelengths, MEM gives seven or eight characteristic lifetimes, which means that at least so many distinct intermediate states exist during the photocycle. Many possible photocycle kinetic models were studied and compared with the MEM result. The best agreement was found with a branching photocycle model of eight intermediate states (K, L, M(1), M(2), M(3), M(4), N, O). The branching occurs at the L intermediate state (M(1) and M(2) being in one branch and M(3) and M(4) in the other branch), but at high pH it occurs already at the K state.

Absorption↗

PubMed2005

Profiling cytogenetic diversity with entropy-based karyotypic analysis.

Regardless the high degree of variation observed in solid tumor karyotypes, the use of diversity as a measurable phenomenon remains unexplored. Here we present a systematic cytogenetic analysis using Shannon's entropy as a measure for karyotypic diversity. Karyotypes from 14 epithelial tumor types (n = 1232) have the aneuploidy status scored, resulting in highly asymmetrical sample distribution, for which we determine the index of diversity (Shannon H') of structural and numerical chromosomal aberrations. Since karyotypic diversity is tissue-specific, this approach may give rise to new insights into the processes that may account for aneuploidy progression and solid tumor outcomes.

Chromosome Aberrations↗

PubMed2006

Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model.

We consider a nonlinear system describing a juvenile-adult population undergoing small mutations. We analyze two aspects: from a mathematical point of view, we use an entropy method to prove that the population neither goes extinct nor blows-up; from an adaptive evolution point of view, we consider small mutations on a long time scale and study how a monomorphic or a dimorphic initial population evolves towards an Evolutionarily Stable State. Our method relies on an asymptotic analysis based on a constrained Hamilton-Jacobi equation. It allows to recover earlier predictions in Calsina and Cuadrado [A. Calsina, S. Cuadrado, Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics, J. Math. Biol. 48 (2004) 135; A. Calsina, S. Cuadrado, Stationary solutions of a selection mutation model: the pure mutation case, Math. Mod. Meth. Appl. Sci. 15(7) (2005) 1091.] that we also assert by direct numerical simulation. One of the interests here is to show that the Hamilton-Jacobi approach initiated in Diekmann et al. [O. Diekmann, P.-E. Jabin, S. Mischler, B. Perthame, The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach, Theor. Popul. Biol. 67(4) (2005) 257.] extends to populations described by systems.

Animals↗

PubMed2001

Entropy and heat capacity of DNA melting from temperature dependence of single molecule stretching.

When a single molecule of double-stranded DNA is stretched beyond its B-form contour length, the measured force shows a highly cooperative overstretching transition. We have measured the force at which this transition occurs as a function of temperature. To do this, single molecules of DNA were captured between two polystyrene beads in an optical tweezers apparatus. As the temperature of the solution surrounding a captured molecule was increased from 11 degrees C to 52 degrees C in 500 mM NaCl, the overstretching transition force decreased from 69 pN to 50 pN. This reduction is attributed to a decrease in the stability of the DNA double helix with increasing temperature. These results quantitatively agree with a model that asserts that DNA melting occurs during the overstretching transition. With this model, the data may be analyzed to obtain the change in the melting entropy DeltaS of DNA with temperature. The observed nonlinear temperature dependence of DeltaS is a result of the positive change in heat capacity of DNA upon melting, which we determine from our stretching measurements to be DeltaC(p) = 60 +/- 10 cal/mol K bp, in agreement with calorimetric measurements.

Calorimetry↗

PubMed2002

Analysis of kinetics using a hybrid maximum-entropy/nonlinear-least-squares method: application to protein folding.

A hybrid analysis that combines the maximum entropy method (MEM) with nonlinear least squares (NLS) fitting has been developed to interpret a general time-dependent signal. Data that include processes of opposite sign and a slow baseline drift can be inverted to obtain both a continuous distribution of lifetimes and a sum of discrete exponentials. Fits by discrete exponentials are performed with initial parameters determined from the distribution of lifetimes obtained with the MEM. The regularization of the parameter space achieved by the MEM stabilizes the introduction of each successive exponential in the NLS fits. This hybrid approach is particularly useful when fitting by a large number of exponentials. Revision of the MEM "prior" based on features in the data can improve the lifetime distribution obtained. Standard errors in the mean are estimated automatically for raw data. The results presented for simulated data and for fluorescence measurements of protein folding illustrate the utility and accuracy of the hybrid algorithm. Analysis of the folding of dihydrofolate reductase reveals six kinetic processes, one more than previously reported.

Algorithms↗