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PubMed2004

A simulation method for calculating the absolute entropy and free energy of fluids: application to liquid argon and water.

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy and free energy by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by adding its atoms gradually to the initially empty volume, i.e., by placing them in their positions at i using transition probabilities (TPs). At each step of the process, the volume is divided into two parts, the already visited part (the "past") and the "future" part, where obtaining the TP requires calculating partition functions over the future part in the presence of the frozen past. In recent publications, the TPs were calculated approximately by taking into account only partial future. Here we present a "complete HSMC" procedure, where the TPs are calculated from MC simulations carried out over the complete future. The complete HSMC method is applied to systems of liquid argon and the TIP3P model of water, and very good results for the free energy are obtained, as compared with results obtained by thermodynamic integration.

Argon↗

PubMed2004

Simulation method for calculating the entropy and free energy of peptides and proteins.

A method called complete hypothetical scanning Monte Carlo has been introduced for calculating the absolute entropy, S, and free energy, F, of fluids. Here, the method is extended to peptide chains in vacuum. Thus, S is calculated from a given sample by reconstructing each conformation step-by-step by using transition probabilities (TPs); at each step, part of the chain coordinates have already been determined (the "frozen past"), and the TP is obtained from a Monte Carlo simulation of the (future) part of the chain whose TPs as yet have not been calculated. Very accurate results for S and F are obtained for the helix, extended, and hairpin microstates of a simplified model of decaglycine (Gly)(10) and (Gly)(16). These results agree well with results obtained by the quasiharmonic approximation and the local states method. The complete HSMC method can be applied to a macromolecule with any degree of flexibility, ranging from local fluctuations to a random coil. Also, the difference in stability, Delta F(mn) = F(m) - F(n) between significantly different microstates m and n can be obtained from two simulations only without the need to resort to thermodynamic integration. Our long-term goal is to extend this method to any peptide and apply it to a peptide immersed in a box with explicit water.

Biophysics↗

PubMed2004

The ribosome as an entropy trap.

To determine the effectiveness of the ribosome as a catalyst, we compared the rate of uncatalyzed peptide bond formation, by the reaction of the ethylene glycol ester of N-formylglycine with Tris(hydroxymethyl)aminomethane, with the rate of peptidyl transfer by the ribosome. Activation parameters were also determined for both reactions, from the temperature dependence of their second-order rate constants. In contrast with most protein enzymes, the enthalpy of activation is slightly less favorable on the ribosome than in solution. The 2 x 10(7)-fold rate enhancement produced by the ribosome is achieved entirely by lowering the entropy of activation. These results are consistent with the view that the ribosome enhances the rate of peptide bond formation mainly by positioning the substrates and/or water exclusion within the active site, rather than by conventional chemical catalysis.

Binding Sites↗

PubMed2006

Entropy-driven spatial organization of highly confined polymers: lessons for the bacterial chromosome.

Despite recent progress in visualization experiments, the mechanism underlying chromosome segregation in bacteria still remains elusive. Here we address a basic physical issue associated with bacterial chromosome segregation, namely the spatial organization of highly confined, self-avoiding polymers (of nontrivial topology) in a rod-shaped cell-like geometry. Through computer simulations, we present evidence that, under strong confinement conditions, topologically distinct domains of a polymer complex effectively repel each other to maximize their conformational entropy, suggesting that duplicated circular chromosomes could partition spontaneously. This mechanism not only is able to account for the spatial separation per se but also captures the major features of the spatiotemporal organization of the duplicating chromosomes observed in Escherichia coli and Caulobacter crescentus.

Caulobacter crescentus↗

PubMed2002

The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: application to liquid para-hydrogen.

We present a method based on augmenting an exact relation between a frequency-dependent diffusion constant and the imaginary time velocity autocorrelation function, combined with the maximum entropy numerical analytic continuation approach to study transport properties in quantum liquids. The method is applied to the case of liquid para-hydrogen at two thermodynamic state points: a liquid near the triple point and a high-temperature liquid. Good agreement for the self-diffusion constant and for the real-time velocity autocorrelation function is obtained in comparison to experimental measurements and other theoretical predictions. Improvement of the methodology and future applications are discussed.

Diffusion↗

PubMed1996

A small engineered protein lacks structural uniqueness by increasing the side-chain conformational entropy.

A small globular protein, the third repeat of the c-Myb DNA-binding domain, which is composed of 54 amino acid residues, was engineered so as to understand the structural uniqueness of native proteins. This small protein has three alpha-helices that form a helix-turn-helix structure, which is maintained by the hydrophobic core with three Ile residues. One of the mutant proteins, with two of the buried Ile (Ile-155 and Ile-181) substituted with Leu residues, showed multiple conformations, as monitored by heteronuclear magnetic resonance spectroscopy for 13C- and 15N-labeled proteins. The increase in the side-chain conformational entropy, caused by changing the Ile to a Leu residue on an alpha-helix, could engender the lack of structural uniqueness. In native proteins, the conformations of not only the beta-branched side chains, but also those of the neighboring bulky side chains, can be greatly restricted, depending upon the local backbone structure.

Amino Acid Sequence↗

PubMed2004

Mammographic image restoration using maximum entropy deconvolution.

An image restoration approach based on a Bayesian maximum entropy method (MEM) has been applied to a radiological image deconvolution problem, that of reduction of geometric blurring in magnification mammography. The aim of the work is to demonstrate an improvement in image spatial resolution in realistic noisy radiological images with no associated penalty in terms of reduction in the signal-to-noise ratio perceived by the observer. Images of the TORMAM mammographic image quality phantom were recorded using the standard magnification settings of 1.8 magnification/fine focus and also at 1.8 magnification/broad focus and 3.0 magnification/fine focus; the latter two arrangements would normally give rise to unacceptable geometric blurring. Measured point-spread functions were used in conjunction with the MEM image processing to de-blur these images. The results are presented as comparative images of phantom test features and as observer scores for the raw and processed images. Visualization of high resolution features and the total image scores for the test phantom were improved by the application of the MEM processing. It is argued that this successful demonstration of image de-blurring in noisy radiological images offers the possibility of weakening the link between focal spot size and geometric blurring in radiology, thus opening up new approaches to system optimization.

Algorithms↗

PubMed2006

Investigation of a 2D two-point maximum entropy regularization method for signal-to-noise ratio enhancement: application to CT polymer gel dosimetry.

This study presents a new method of image signal-to-noise ratio (SNR) enhancement by utilizing a newly developed 2D two-point maximum entropy regularization method (TPMEM). When utilized as an image filter, it is shown that 2D TPMEM offers unsurpassed flexibility in its ability to balance the complementary requirements of image smoothness and fidelity. The technique is evaluated for use in the enhancement of x-ray computed tomography (CT) images of irradiated polymer gels used in radiation dosimetry. We utilize a range of statistical parameters (e.g. root-mean square error, correlation coefficient, error histograms, Fourier data) to characterize the performance of TPMEM applied to a series of synthetic images of varying initial SNR. These images are designed to mimic a range of dose intensity patterns that would occur in x-ray CT polymer gel radiation dosimetry. Analysis is extended to a CT image of a polymer gel dosimeter irradiated with a stereotactic radiation therapy dose distribution. Results indicate that TPMEM performs strikingly well on radiation dosimetry data, significantly enhancing the SNR of noise-corrupted images (SNR enhancement factors >15 are possible) while minimally distorting the original image detail (as shown by the error histograms and Fourier data). It is also noted that application of this new TPMEM filter is not restricted exclusively to x-ray CT polymer gel dosimetry image data but can in future be extended to a wide range of radiation dosimetry data.

Algorithms↗

PubMed2002

A maximum entropy method to compute the 13NH3 pulmonary transit time from right to left ventricle in cardiac PET studies.

The distribution function of pulmonary transit times (fPTTs) contains information on the transit time of blood through the lungs and the dispersion in transit times. Most of the previous studies have used specific functional forms with adjustable parameters to characterize the fPTT. It is the purpose here to investigate the possibility of estimating the fPTT in a model-free way. The method employs the maximum entropy principle and is used, in particular, on cardiac positron emission tomographic (PET) studies but is believed to be more generally applicable. Using this principle in a test case, we were able to accurately identify a two-peaked transfer function, which may theoretically be seen in patients with pulmonary disease confined to one lung. Transit time values for [13N]-ammonia were produced by applying the algorithm to PET studies from normal volunteers.

Algorithms↗

PubMed2006

Analysis of electroencephalograms in Alzheimer's disease patients with multiscale entropy.

The aim of this study was to analyse the electroencephalogram (EEG) background activity of Alzheimer's disease (AD) patients using multiscale entropy (MSE). MSE is a recently developed method that quantifies the regularity of a signal on different time scales. These time scales are inspected by means of several coarse-grained sequences formed from the analysed signals. We recorded the EEGs from 19 scalp electrodes in 11 AD patients and 11 age-matched controls and estimated the MSE profile for each epoch of the EEG recordings. The shape of the MSE profiles reveals the EEG complexity, and it suggests that the EEG contains information in deeper scales than the smallest one. Moreover, the results showed that the EEG background activity is less complex in AD patients than control subjects. We found significant differences between both subject groups at electrodes F3, F7, Fp1, Fp2, T5, T6, P3, P4, O1 and O2 (p-value < 0.01, Student's t-test). These findings indicate that the EEG complexity analysis performed on deeper time scales by MSE may be a useful tool in order to increase our knowledge of AD.

Aged↗

PubMed2004

Protein secondary structure: entropy, correlations and prediction.

MOTIVATION: Is protein secondary structure primarily determined by local interactions between residues closely spaced along the amino acid backbone or by non-local tertiary interactions? To answer this question, we measure the entropy densities of primary and secondary structure sequences, and the local inter-sequence mutual information density. RESULTS: We find that the important inter-sequence interactions are short ranged, that correlations between neighboring amino acids are essentially uninformative and that only one-fourth of the total information needed to determine the secondary structure is available from local inter-sequence correlations. These observations support the view that the majority of most proteins fold via a cooperative process where secondary and tertiary structure form concurrently. Moreover, existing single-sequence secondary structure prediction algorithms are almost optimal, and we should not expect a dramatic improvement in prediction accuracy. AVAILABILITY: Both the data sets and analysis code are freely available from our Web site at http://compbio.berkeley.edu/

Algorithms↗

PubMed1999

Comparison of bispectral index, 95% spectral edge frequency and approximate entropy of the EEG, with changes in heart rate variability during induction of general anaesthesia.

We have compared bispectral index (BIS), 95% spectral edge frequency (SEF) and approximate entropy (ApEn) in 37 patients during induction and recovery from a short general anaesthetic. Heart rate variability (HRV) was also compared during induction only. These indices were noted at the start of induction, when a syringe held between the thumb and fingertips was dropped, at insertion of a laryngeal mask or tracheal tube (tube insertion), at incision, at the end of surgery, on return of the gag reflex and when the patient could follow a verbal command. When indices at the start of induction were compared with those at tube insertion, all four decreased significantly. BIS decreased from a mean of 95.38 (SEM 1.02) to 44.22 (1.05), mean SEF from 20.91 (1.19) to 14.14 (0.70) Hz, mean HRV from 37.1 (7.75) to 17.9 (3.6) bpm2 and ApEn from 0.90 (0.06) to 0.65 (0.04). Using logistic regression, the indices were compared both individually and in combination as to the power of distinguishing awake (at pre-induction) from asleep (at tube insertion) states. BIS had the best predictive power, with a sensitivity of 97.3%, specificity 94.4%, positive predictive value 94.7% and negative predictive value 97.1%. A combination of the indices conferred no additional predictive advantage.

Adolescent↗

PubMed2005

Relationship between Bispectral Index, electroencephalographic state entropy and effect-site EC50 for propofol at different clinical endpoints.

BACKGROUND: State entropy (SE) is a newly available monitor for depth of anaesthesia. We investigated whether the relationship between predicted effect-site propofol concentration and Bispectral Index (BIS) and SE values is useful for predicting loss of verbal contact and loss of consciousness during steady-state conditions. METHODS: Twenty unpremedicated patients undergoing elective major abdominal surgery were recruited. A target-controlled infusion of propofol was administered using Schneider's pharmacokinetic model. The propofol infusion was set at an initial site effect concentration of 1.0 microg ml(-1) and increased by 1.0 microg ml(-1) steps every 4 min up to 6.0 microg ml(-1). A 4-min interval was chosen to ensure that steady-state effect-site concentrations were obtained. Propofol site effect concentrations and BIS and SE values were recorded at loss of verbal contact (LVC) and loss of consciousness (LOC). Population values for predicted effect-site concentrations at the clinical endpoints were estimated and correlated with BIS and SE values. RESULTS: For LVC, the effect-site concentration for 90% of patients was 1.1 (1.1-3.2) microg ml(-1) and for LOC it was 2.8 (2.8-5.65) microg ml(-1). LVC occurred in 90% of patients at a BIS value of 70.2 (70.2-90.2) and an SE value of 60.3 (60.3-75.5), and LOC occurred at a BIS value of 38.2 (38.2-70.4) and an SE value of 42.2 (42.2-60.4). CONCLUSIONS: LVC and LOC occurred within a defined range of predicted effect-site concentrations. SE had a smaller range than BIS and greater correlation with effect-site concentration and may be more useful than BIS in predicting both LVC and LOC.

Abdomen↗

PubMed2005

Relationship between bispectral index, electroencephalographic state entropy and effect-site EC50 for propofol at different clinical endpoints.

BACKGROUND: State entropy (SE) is a newly available monitor for depth of anaesthesia. We investigated whether the relationship between predicted effect-site propofol concentration and both bispectral index (BIS) and SE values is useful for predicting loss of verbal contact and loss of consciousness during steady-state conditions. METHODS: Twenty unpremedicated patients undergoing elective major abdominal surgery were recruited. A target-controlled infusion of propofol was administered using Schneider's pharmacokinetic model. The propofol infusion was set at an initial site-effect concentration of 1.0 microg ml(-1), and increased by 1.0 microg ml(-1) steps every 4 min, up to 6.0 microg ml(-1). A 4-min interval was chosen to ensure that steady-state site-effect concentrations were obtained. Propofol site-effect concentrations and BIS and SE values were recorded at loss of verbal contact (LVC) and loss of consciousness (LOC). Population values for predicted effect-site concentrations at the clinical endpoints were estimated and correlated with BIS and SE values. RESULTS: For LVC, the effect-site concentration for 90% of patients was 1.1 (1.1-3.2) microg ml(-1) and for LOC 2.8 (2.8-5.65) microg ml(-1). LVC occurred in 90% of patients at a BIS value of 70.2 (70.2-90.2) and an SE value of 60.3 (60.3-75.5) and LOC occurred at a BIS value of 38.2 (38.2-70.4) and an SE value of 42.2 (42.2-60.4). CONCLUSIONS: LVC and LOC occurred within a defined range of predicted effect-site concentrations. SE had a smaller range than BIS and higher correlation with effect-site concentration and may be more useful than BIS in predicting both LVC and LOC.

Abdomen↗

PubMed2006

Correlation and agreement between bispectral index and state entropy of the electroencephalogram during propofol anaesthesia.

BACKGROUND: Bispectral index (BIS) and state entropy (SE) monitor hypnosis. We evaluated the correlation and the agreement between those parameters during propofol anaesthesia and laryngoscopy with and without muscle relaxation. METHODS: A total of 25 patients were anaesthetized with propofol. At steady state (SS: BIS 40-50), they randomly received rocuronium (R) or saline (S); 3 min thereafter, a 20 s laryngoscopy was performed. Correlation (regression analysis) and agreement (Bland-Altman analysis) were evaluated before induction (baseline), at loss of eyelash reflex (LER), at SS and during the first 3 min after laryngoscopy (L). RESULTS: The correlation coefficient r (95% CI), the mean difference (MD) (95% CI), and the limits of agreement [lower-upper limits of 95% CI of MD (sd 1.96)] between BIS and SE were as follows. Overall recordings: 0.87 (0.83 to 0.90), 2.5 (1.2 to 3.0), and [-19.5 to 24.6]; Baseline: 0.45 (0.06 to 0.72), 7.6 (6.0 to 9.2), and [-2.7 to 17.9]; LER: 0.74 (0.47 to 0.88), 8.3 (3.5 to 13.2), and [-22.6 to 39.3]; SS, all patients: 0.41 (0.14 to 0.63), 2.0 (-0.5 to 4.6), and [-19.0 to 23.3]; SS, Group S: 0.36 (-0.07 to 0.68), 1.9 (-2.5 to 6.3), and [-25.0 to 28.8]; SS, Group R: 0.63 (0.32 to 0.82), 0.2 (-2.0 to 2.3), and [-14.0 to 14.4]; L, all patients: 0.49 (0.32 to 0.63), 0.7 (-1.6 to 3.0), and [-25.6 to 27.1]; L, Group S: 0.41 (0.13 to 0.63), 2.3 (-2.4 to 7.1), and [-36.7 to 41.3]; L, Group R: 0.72 (0.56 to 0.83), -0.6 (-2.2 to 1.0), and [-14.3 to 13.1]. The correlation was good except for SS in Group S. The MD was significantly different from 0 for overall recordings, during baseline and LER, but not for the other conditions. The agreement was poor except for baseline, and SS and L in Group R. CONCLUSIONS: BIS and SE are globally well correlated. In contrast, agreement is poor as differences of more than 20 units are frequently observed, except for awake and paralysed patients.

Adult↗

PubMed2001

Receptor dissociation constants and the information entropy of membranes coding ligand concentration.

The binding of ligands to receptor proteins embedded in cell membranes drives cellular responses that involve either second messenger cascades or directly gated ion channels. It is known that a single class of receptor proteins expresses approximately 98% of its graded response to ligand concentrations over four orders of magnitude, where the response is measured by the equilibrium proportion of bound ligand-receptor complexes. This four-decadic concentration range is centered on a logarithmic scale around logK, where K is the dissociation constant defined by the ratio of ligand-receptor unbinding (k-) to binding (k+) rates. Remarkably, this four-decadic concentration range is intrinsic to all homogeneous ligand-receptor (or, equivalently, enzyme-substrate) systems. Thus, adapting the sensitivity of cell membranes to narrower or wider ranges of ligand concentrations, respectively, requires multivalent receptors or heterogeneous populations of receptors. Here we use a normalized Shannon-Weaver measure of information entropy to represent the efficiency of coding over given concentrations for membranes containing a population of univalent receptors with a specified distribution of dissociation constants, or a homogeneous population of strongly cooperative multivalent receptors. Assuming a specified level of resolution in the response of cellular or neural systems downstream from the membrane that 'read' the ligand concentration 'code', we calculate the range of concentrations over which the coding efficiency of the membrane itself is maximized. Our results can be used to hypothesize the number of receptor types associated with the membranes of particular cells. For example, from data in the literature, we conclude that the response of most general olfactory sensory neurons can be explained in terms of a homogeneous population of receptor proteins, while the response of pheromone sensory neurons is satisfactorily explained by the presence of two types of membrane receptor protein with pheromone-binding dissociation constants that have values at least one to two orders of magnitude apart.

Animals↗

PubMed2004

Bipartite pattern discovery by entropy minimization-based multiple local alignment.

Many multimeric transcription factors recognize DNA sequence patterns by cooperatively binding to bipartite elements composed of half sites separated by a flexible spacer. We developed a novel bipartite algorithm, bipartite pattern discovery (Bipad), which produces a mathematical model based on information maximization or Shannon's entropy minimization principle, for discovery of bipartite sequence patterns. Bipad is a C++ program that applies greedy methods to search the bipartite alignment space and examines the upstream or downstream regions of co-regulated genes, looking for cis-regulatory bipartite patterns. An input sequence file with zero or one site per locus is required, and the left and right motif widths and a range of possible gap lengths must be specified. Bipad can run in either single-block or bipartite pattern search modes, and it is capable of comprehensively searching all four orientations of half-site patterns. Simulation studies showed that the accuracy of this motif discovery algorithm depends on sample size and motif conservation level, but results were independent of background composition. Bipad performed equivalent with or better than other pattern search algorithms in correctly identifying Escherichia coli cyclic AMP receptor protein and Bacillus subtilis sigma factor binding site sequences based on experimentally defined benchmarks. Finally, a new bipartite information weight matrix for vitamin D3 receptor/retinoid X receptor alpha (VDR/RXRalpha) binding sites was derived that comprehensively models the natural variability inherent in these sequence elements.

Algorithms↗

PubMed1997

Improving pKa calculations with consideration of hydration entropy.

Continuum dielectric modelling of electrostatics interactions in macromolecules provides a valuable tool in the study of structure-function relationships, but falls short of providing consistently accurate calculated pKas. It is suggested that the model can be significantly improved with the inclusion of a term that estimates the entropy associated with first hydration shell solvent ordering, with reference to computed results for cysteines in DsbA and thioredoxin, and aspartic and glutamic acids in a number of proteins. The modification is based on the geometry of charge burial and an hydration number, which is adjustable (by fit to experiment), and is uniform within each class of ionizable group studied. The potential for further development is clear within this framework, since experiment and simulation can furnish non-adjustable, ionizable group-specific, hydration numbers.

Amino Acids↗