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PubMed2004

Pharmacodynamic interaction between propofol and remifentanil regarding hypnosis, tolerance of laryngoscopy, bispectral index, and electroencephalographic approximate entropy.

BACKGROUND: The purpose of this investigation was to describe the pharmacodynamic interaction between propofol and remifentanil for probability of no response to shaking and shouting, probability of no response to laryngoscopy, Bispectral Index (BIS), and electroencephalographic approximate entropy (AE). METHODS: Twenty healthy volunteers received either propofol or remifentanil alone and then concurrently with a fixed concentration of remifentanil or propofol, respectively, via a target-controlled infusion. Responses to shaking and shouting and to laryngoscopy were assessed multiple times after allowing for plasma effect site equilibration. The raw electroencephalogram and BIS were recorded throughout the study, and AE was calculated off-line. Response surfaces were fit to the clinical response data using logistic regression or hierarchical response models. Response surfaces were also estimated for BIS and AE. Surfaces were visualized using three-dimensional rotations. Model parameters were estimated with NONMEM. RESULTS: Remifentanil alone had no appreciable effect on response to shaking and shouting or response to laryngoscopy. Propofol could ablate both responses. Modest remifentanil concentrations dramatically reduced the concentrations of propofol required to ablate both responses. The hierarchical response surface described the data better than empirical logistic regression. BIS and AE are more sensitive to propofol than to remifentanil. CONCLUSIONS: Remifentanil alone is ineffective at ablating response to stimuli but demonstrates potent synergy with propofol. BIS and AE values corresponding to 95% probability of ablating response are influenced by the combination of propofol and remifentanil to achieve this endpoint, with higher propofol concentrations producing lower values for BIS and AE.

Adult↗

PubMed1999

MAXED, a computer code for maximum entropy deconvolution of multisphere neutron spectrometer data.

Reliable neutron dosimetry requires knowledge of the neutron spectrum. We discuss the problem of analyzing data from a multisphere neutron spectrometer to infer the energy spectrum of the incident neutrons and describe the code MAXED, a computer program developed to apply the maximum entropy principle to this problem. The code and documentation are available from the authors upon request.

Documentation↗

PubMed2006

Complex analysis of intracranial hypertension using approximate entropy.

OBJECTIVE: To determine whether decomplexification of intracranial pressure dynamics occurs during periods of severe intracranial hypertension (intracranial pressure >25 mm Hg for >5 mins in the absence of external noxious stimuli) in pediatric patients with intracranial hypertension. DESIGN: Retrospective analysis of clinical case series over a 30-month period from April 2000 through January 2003. SETTING: Multidisciplinary 16-bed pediatric intensive care unit. PATIENTS: Eleven episodes of intracranial hypertension from seven patients requiring ventriculostomy catheter for intracranial pressure monitoring and/or cerebral spinal fluid drainage. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: We measured changes in the intracranial pressure complexity, estimated by the approximate entropy (ApEn), as patients progressed from a state of normal intracranial pressure (<25 mm Hg) to intracranial hypertension. We found the ApEn mean to be lower during the intracranial hypertension period than during the stable and recovering periods in all the 11 episodes (0.5158 +/- 0.0089, 0.3887 +/- 0.077, and 0.5096 +/- 0.0158, respectively, p < .01). Both the mean reduction in ApEn from the state of normal intracranial pressure (stable region) to intracranial hypertension (-0.1271) and the increase in ApEn from the ICH region to the recovering region (0.1209) were determined to be statistically significant (p < .01). CONCLUSIONS: Our results indicate that decreased complexity of intracranial pressure coincides with periods of intracranial hypertension in brain injury. This suggests that the complex regulatory mechanisms that govern intracranial pressure may be disrupted during acute periods of intracranial hypertension. This phenomenon of decomplexification of physiologic dynamics may have important clinical implications for intracranial pressure management.

Acute Disease↗

PubMed2003

Network rigidity at finite temperature: relationships between thermodynamic stability, the nonadditivity of entropy, and cooperativity in molecular systems.

A statistical mechanical distance constraint model (DCM) is presented that explicitly accounts for network rigidity among constraints present within a system. Constraints are characterized by local microscopic free-energy functions. Topological rearrangements of thermally fluctuating constraints are permitted. The partition function is obtained by combining microscopic free energies of individual constraints using network rigidity as an underlying long-range mechanical interaction, giving a quantitative explanation for the nonadditivity in component entropies exhibited in molecular systems. Two exactly solved two-dimensional toy models representing flexible molecules that can undergo conformational change are presented to elucidate concepts, and to outline a DCM calculation scheme applicable to many types of physical systems. It is proposed that network rigidity plays a central role in balancing the energetic and entropic contributions to the free energy of biopolymers, such as proteins. As a demonstration, the distance constraint model is solved exactly for the alpha-helix to coil transition in homogeneous peptides. Temperature and size independent model parameters are fitted to Monte Carlo simulation data, which includes peptides of length 10 for gas phase, and lengths 10, 15, 20, and 30 in water. The DCM is compared to the Lifson-Roig model. It is found that network rigidity provides a mechanism for cooperativity in molecular structures including their ability to spontaneously self-organize. In particular, the formation of a characteristic topological arrangement of constraints is associated with the most probable microstates changing under different thermodynamic conditions.

Entropy↗

PubMed2003

Universality and Shannon entropy of codon usage.

The distribution functions of codon usage probabilities, computed over all the available GenBank data for 40 eukaryotic biological species and five chloroplasts, are best fitted by the sum of a constant, an exponential, and a linear function in the rank of usage. For mitochondria the analysis is not conclusive. These functions are characterized by parameters that strongly depend on the total guanine and cytosine (GC) content of the coding regions of biological species. It is predicted that the codon usage is the same in all exonic genes with the same GC content. The Shannon entropy for codons, also strongly dependent on the exonic GC content, is computed.

Amino Acids↗

PubMed2003

Reparametrizing the loop entropy weights: effect on DNA melting curves.

Recent advances in the understanding of the melting behavior of double-stranded DNA with statistical mechanics methods lead to improved estimates of the weight factors for the dissociation events of the chains, in particular for interior loop melting. So far, in the modeling of DNA melting, the entropy of denaturated loops has been estimated from the number of configurations of a closed self-avoiding walk. It is well understood now that a loop embedded in a chain is characterized by a loop closure exponent c which is higher than that of an isolated loop. Here we report an analysis of DNA melting curves for sequences of a broad range of lengths (from 10 to 10(6) base pairs) calculated with a program based on the algorithms underlying MELTSIM. Using the embedded loop exponent we find that the cooperativity parameter is one order of magnitude bigger than current estimates. We argue that in the melting region the double helix persistence length is greatly reduced compared to its room temperature value, so that the use of the embedded loop closure exponent for real DNA sequences is justified.

Algorithms↗

PubMed2005

Natural entropy fluctuations discriminate similar-looking electric signals emitted from systems of different dynamics.

Complexity measures are introduced that quantify the change of the natural entropy fluctuations at different length scales in time series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death (SD) by analyzing 15 min electrocardiograms, and comparing to those of truly healthy humans (H). These measures seem to be complementary to the ones suggested recently [Phys. Rev. E 70, 011106 (2004)]] and altogether enable the classification of individuals into three categories: H, heart disease patients, and SD. All the SD individuals, who exhibit critical dynamics, result in a common behavior.

Algorithms↗

PubMed2005

Entropy reduction effect imposed by hydrogen bond formation on protein folding cooperativity: evidence from a hydrophobic minimalist model.

Conformational restrictions imposed by hydrogen bond formation during protein folding are investigated by Monte Carlo simulations of a non-native-centric, two-dimensional, hydrophobic model in which the formation of favorable contacts is coupled to an effective reduction in lattice coordination. This scheme is intended to mimic the requirement that polar backbone groups of real proteins must form hydrogen bonds concomitantly to their burial inside the apolar protein core. In addition to the square lattice, with z=3 conformations per monomer, we use extensions in which diagonal step vectors are allowed, resulting in z=5 and z=7. Thermodynamics are governed by the hydrophobic energy function, according to which hydrophobic monomers tend to make contacts unspecifically while the reverse is true for hydrophilic monomers, with the additional restriction that only contacts between monomers adopting one of zh<z local conformations contribute to the energy, where zh is the number of local conformations assumed to be compatible with hydrogen bond formation. The folding transition abruptness and van't Hoff-to-calorimetric-enthalpy ratio are found to increase dramatically by this simple and physically motivated mechanism. The observed increase in folding cooperativity is correlated to an increase in the convexity of the underlying microcanonical conformational entropy as a function of energy. Preliminary simulations in three dimensions, even though using a smaller relative reduction in lattice effective coordination zh/z=4/5, display a slight increase in cooperativity for a hydrophobic model of 40 monomers and a more pronounced increase in cooperativity for a native-centric Go-model with the same native conformation, suggesting that this purely entropic effect is not an artifact of dimensionality and is likely to be of fundamental importance in the theoretical understanding of folding cooperativity.

Amino Acid Sequence↗

PubMed2006

Dynamical complexity detection in short-term physiological series using base-scale entropy.

Physiological systems generate complex fluctuations in their output signals that reflect the underlying dynamics. The base-scale entropy method was proposed as a complexity measure to investigate the complexity of time series. The advantages of this method are simplicity and extremely fast calculation for very short data sets. This method enables analyzing very short, nonstationary, and noisy data sets. We employed this method for short-term physiological time series for analysis of heart-rate variability signals. The results show that the simple and easily calculated measure can effectively detect the complexity dissimilarity of physiological time series in different physiological or pathological states, which is convenient for clinical applications.

Algorithms↗

PubMed2006

Correlation entropy of synaptic input-output dynamics.

The responses of synapses in the neocortex show highly stochastic and nonlinear behavior. The microscopic dynamics underlying this behavior, and its computational consequences during natural patterns of synaptic input, are not explained by conventional macroscopic models of deterministic ensemble mean dynamics. Here, we introduce the correlation entropy of the synaptic input-output map as a measure of synaptic reliability which explicitly includes the microscopic dynamics. Applying this to experimental data, we find that cortical synapses show a low-dimensional chaos driven by the natural input pattern.

Action Potentials↗

PubMed2001

Temporal correlations and neural spike train entropy.

Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of ensembles of neural spike trains, which performs reliably for limited samples of data. This approach also yields insight to the role of correlations between spikes in temporal coding mechanisms. The method, when applied to recordings from complex cells of the monkey primary visual cortex, results in lower rms error information estimates in comparison to a "brute force" approach.

Action Potentials↗

PubMed2002

Multiscale entropy analysis of complex physiologic time series.

There has been considerable interest in quantifying the complexity of physiologic time series, such as heart rate. However, traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long-range correlations. This paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics. We introduce a method to calculate multiscale entropy (MSE) for complex time series. We find that MSE robustly separates healthy and pathologic groups and consistently yields higher values for simulated long-range correlated noise compared to uncorrelated noise.

Algorithms↗

PubMed2006

Entropy-driven formation of a chiral liquid-crystalline phase of helical filaments.

We study the liquid-crystalline phase behavior of a concentrated suspension of helical flagella isolated from Salmonella typhimurium. Flagella are prepared with different polymorphic states, some of which have a pronounced helical character while others assume a rodlike shape. We show that the static phase behavior and dynamics of chiral helices are very different when compared to simpler achiral hard rods. With increasing concentration, helical flagella undergo an entropy-driven first order phase transition to a liquid-crystalline state having a novel chiral symmetry.

Entropy↗

PubMed2005

Entropy and surface engineering in protein crystallization.

Protein crystallization remains a key limiting step in the characterization of the atomic structures of proteins and their complexes by X-ray diffraction methods. Current data indicate that standard screening procedures applied to soluble well folded prokaryotic proteins yield X-ray diffraction crystals with an approximately 20% success rate and for eukaryotic proteins this figure may be significantly lower. Protein crystallization is predominantly dependent on entropic effects and the driving force appears to be the release of ordered water from the sites of crystal contacts. This is countered by the entropic cost of ordering of protein molecules and by the loss of conformational freedom of side chains involved in the crystal contacts. Mutational surface engineering designed to create patches with low conformational entropy and thereby conducive to formation of crystal contacts promises to be an effective tool allowing direct enhancement of the success rate of macromolecular crystallization.

Crystallization↗

PubMed1999

Estimating unobserved reflection intensities in Laue diffraction by the maximum-entropy method.

In protein crystallography, the use of low-resolution reflections is important in defining the molecular mask and polypeptide backbone. However, in Laue data collection, the loss of low-resolution reflection data (>2dmin) can be as high as 40-50%, even after the deconvolution of multiples. To estimate the reflection intensities that are not recorded in data collection, a new method is presented based on maximizing the entropy of the Patterson function subject to the constraints imposed by the intensities of the observed reflections. The method has been tested with Laue diffraction data from hen egg-white lysozyme. All unobserved reflections within 5 A resolution were estimated, and their inclusion in the electron-density-map calculation significantly improved the connectivity. This method could also be applied to improve the completeness of monochromatic data.

Animals↗

PubMed2000

Fast maximum entropy approximation in SPECT using the RBI-MAP algorithm.

In this work, we present a method for approximating constrained maximum entropy (ME) reconstructions of SPECT data with modifications to a block-iterative maximum a posteriori (MAP) algorithm. Maximum likelihood (ML)-based reconstruction algorithms require some form of noise smoothing. Constrained ME provides a more formal method of noise smoothing without requiring the user to select parameters. In the context of SPECT, constrained ME seeks the minimum-information image estimate among those whose projections are a given distance from the noisy measured data, with that distance determined by the magnitude of the Poisson noise. Images that meet the distance criterion are referred to as feasible images. We find that modeling of all principal degrading factors (attenuation, detector response, and scatter) in the reconstruction is critical because feasibility is not meaningful unless the projection model is as accurate as possible. Because the constrained ME solution is the same as a MAP solution for a particular value of the MAP weighting parameter, beta, the constrained ME solution can be found with a MAP algorithm if the correct value of beta is found. We show that the RBI-MAP algorithm, if used with a dynamic scheme for estimating beta, can approximate constrained ME solutions in 20 or fewer iterations. We compare results for various methods of achieving feasible images on a simulation of Tl-201 cardiac SPECT data. Results show that the RBI-MAP ME approximation provides images and quantitative estimates close to those from a slower algorithm that gives the true ME solution. Also, we find that the ME results have higher spatial resolution and greater high-frequency noise content than a feasibility-based stopping rule, feasibility-based low-pass filtering, and a quadratic Gibbs prior with beta selected according to the feasibility criterion. We conclude that fast ME approximation is possible using either RBI-MAP with the dynamic procedure or a feasibility-based stopping rule, and that such reconstructions may be particularly useful in applications where resolution is critical.

Algorithms↗

PubMed2004

Entropy-based generation of supervised neural networks for classification of structured patterns.

Sperduti and Starita proposed a new type of neural network which consists of generalized recursive neurons for classification of structures. In this paper, we propose an entropy-based approach for constructing such neural networks for classification of acyclic structured patterns. Given a classification problem, the architecture, i.e., the number of hidden layers and the number of neurons in each hidden layer, and all the values of the link weights associated with the corresponding neural network are automatically determined. Experimental results have shown that the networks constructed by our method can have a better performance, with respect to network size, learning speed, or recognition accuracy, than the networks obtained by other methods.

Entropy↗

PubMed2006

Batch map extensions of the kernel-based maximum entropy learning rule.

In this letter, two batch-map extensions are described for the kernel-based maximum entropy learning rule (kMER). In the first, the weights are iteratively set to weighted component-wise medians, while in the second the generalized median is used, enabling kMER to process symbolic data. Simulations are performed to illustrate the extensions.

Algorithms↗